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TMD phenomenology motivated by nonperturbative structures
Ted Rogers, Fatma Aslan, Mariaelena Boglione, J. Osvaldo Gonzalez-Hernandez, Tommaso Rainaldi, Andrea Simonelli
Aug 15 2024 hep-ph hep-th nucl-th arXiv:2408.07170v1

@misc{2408.07170, author = {Ted Rogers and Fatma Aslan and Mariaelena Boglione and J.~Osvaldo Gonzalez-Hernandez and Tommaso Rainaldi and Andrea Simonelli}, title = {{TMD} phenomenology motivated by nonperturbative structures}, year = {2024}, eprint = {2408.07170}, note = {arXiv:2408.07170v1} }
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This talk summarized work done recently to organize the steps for implementing TMD phenomenology in a way optimized for contexts where the extraction and interpretation of hadronic structures and nonperturbative effects is the primary driving motivation.
Python4Physics: A physics outreach program
Raúl Briceño, Ted Rogers
Jun 13 2024 physics.ed-ph hep-lat hep-ph physics.soc-ph arXiv:2406.07668v1

@misc{2406.07668, author = {Raúl Briceño and Ted Rogers}, title = {{P}ython4{P}hysics: {A} physics outreach program}, year = {2024}, eprint = {2406.07668}, note = {arXiv:2406.07668v1} }
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We describe a summer outreach program developed to cultivate interest in physics in particular and physical sciences more broadly among high school and early college students using small projects in the Python programming language. We discuss the lessons we learned in the hopes that they will be valuable to other physicists in planning their own outreach efforts. We also provide links to resources and materials from the Python4Physics program, which we hope might be useful in other outreach programs.
Avenues for a number density interpretation of dihadron fragmentation functions
T. Rogers, A. Courtoy
Apr 04 2024 hep-ph nucl-ex nucl-th arXiv:2404.02281v1

@misc{2404.02281, author = {T.~Rogers and A.~Courtoy}, title = {{A}venues for a number density interpretation of dihadron fragmentation functions}, year = {2024}, eprint = {2404.02281}, note = {arXiv:2404.02281v1} }
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In this comment, we reassess the underlying physics of the number sum rule for dihadron fragmentation functions. We will argue that, currently, there are no settled constraints on what constitutes a valid number density interpretation for multihadron fragmentation functions. Imposing overly restrictive criteria might lead to misinterpretating the data. Most importantly, and on the basis of phenomenological analyses, the slightly varying definitions used in previous work are not excluded from possessing legitimate number density interpretations (up to the usual issues with ultraviolet divergences and renormalization), so long as they are paired with appropriate factorization theorems. We advocate for further theoretical analyses to be challenged with experimental data, available at JLab or at the future EIC.
Phenomenology of TMD parton distributions in Drell-Yan and $Z^0$ boson production in a hadron structure oriented approach
F. Aslan, M. Boglione, J. O. Gonzalez-Hernandez, T. Rainaldi, T. C. Rogers, A. Simonelli
Jan 26 2024 hep-ph nucl-th arXiv:2401.14266v2

@misc{2401.14266, author = {F.~Aslan and M.~Boglione and J.~O.~Gonzalez-Hernandez and T.~Rainaldi and T.~C.~Rogers and A.~Simonelli}, title = {{P}henomenology of {TMD} parton distributions in {D}rell-{Y}an and ${Z}^0$ boson production in a hadron structure oriented approach}, year = {2024}, eprint = {2401.14266}, note = {arXiv:2401.14266v2} }
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We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to TMD phenomenology applied to Drell-Yan like processes, including lepton pair production at moderate $Q^2$ and $Z^0$ boson production. We compare and contrast general features of our methodology with other common practices and emphasize the improvements derived from our approach that we view as essential for applications where extracting details of nonperturbative transverse hadron structure is a major goal. These include the HSO's preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution, explicit preservation of the integral relationship between TMD and collinear pdfs, and the ability to meaningfully compare different theoretical models of nonperturbative TMD parton distributions. In our examples, we show that there is significant sensitivity at moderate $Q^2$ to both the form of the nonperturbative transverse momentum dependence and the parametrization of collinear parton densities. However, we also find that evolving to $Q^2 = M_Z^2$, without fitting, results in a satisfactory postdiction of existing data for $Z^0$ production, nearly independently of the modeling of nonperturbative transverse momentum behavior. We argue that this demonstrates that moderate $Q$ measurements should be given greater weight than high $Q$ measurements in extractions of nonperturbative transverse momentum dependence. We also obtain new extractions of the nonperturbative Collins-Soper kernel within the HSO approach. We discuss its features and compare with some earlier extractions.
On the definition of fragmentation functions and the violation of sum rules
John Collins, Ted Rogers
Sep 08 2023 hep-ph hep-th nucl-th arXiv:2309.03346v3

@misc{2309.03346, author = {John Collins and Ted Rogers}, title = {{O}n the definition of fragmentation functions and the violation of sum rules}, year = {2023}, eprint = {2309.03346}, note = {arXiv:2309.03346v3} }
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We point out a problem with the formulation and derivations of sum rules for quark fragmentation functions that impacts their validity in QCD, but which potentially points toward an improved understanding of final states in inclusive hard processes. Fragmentation functions give the distribution of final-state hadrons arising from a parton exiting a hard scattering, and the sum rules for momentum, electric charge, etc express conservation of these quantities. The problem arises from a mismatch between the quark quantum numbers of the initial quark and the fact that all observed final-state hadrons are confined bound states with color zero. We point that, in a confining theory like QCD, the Wilson line in the operator definition of a fragmentation function entails that the final state in a fragmentation function includes a bound state in the external field generated by the Wilson line. We justify this with the aid of general features of string hadronization. The anomalous bound states are restricted to fractional momentum $z=0$. They tend to invalidate sum rules like the one for charge conservation when applied to the fragmentation functions inferred from experimental data, but not the momentum sum rule. We propose to exploit our ideas in future studies as a way to relate the ffs extracted from inclusive cross sections to more detailed non-perturbative descriptions of final state hadronization. We also describe scenarios wherein the traditional sum rules might remain approximately valid with a reasonably high degree of accuracy.
Strong Interaction Physics at the Luminosity Frontier with 22 GeV Electrons at Jefferson Lab
A. Accardi, P. Achenbach, D. Adhikari, A. Afanasev, C.S. Akondi, N. Akopov, M. Albaladejo, H. Albataineh, M. Albrecht, B. Almeida-Zamora, M. Amaryan, D. Androić, W. Armstrong, D.S. Armstrong, M. Arratia, J. Arrington, A. Asaturyan, A. Austregesilo, H. Avagyan, T. Averett, et al (424)
Jun 19 2023 nucl-ex hep-ex hep-ph nucl-th arXiv:2306.09360v2

@misc{2306.09360, author = {A.~Accardi and P.~Achenbach and D.~Adhikari and A.~Afanasev and C.S.~Akondi and N.~Akopov and M.~Albaladejo and H.~Albataineh and M.~Albrecht and B.~Almeida-Zamora and M.~Amaryan and D.~Androić and W.~Armstrong and D.S.~Armstrong and M.~Arratia and J.~Arrington and A.~Asaturyan and A.~Austregesilo and H.~Avagyan and T.~Averett and C.~Ayerbe Gayoso and A.~Bacchetta and A.B.~Balantekin and N.~Baltzell and L.~Barion and P.~C.~Barry and A.~Bashir and M.~Battaglieri and V.~Bellini and I.~Belov and O.~Benhar and B.~Benkel and F Benmokhtar and W.~Bentz and V.~Bertone and H.~Bhatt and A.~Bianconi and L.~Bibrzycki and R.~Bijker and D.~Binosi and D.~Biswas and M.~Boër and W.~Boeglin and S.A.~Bogacz and M.~Boglione and M.~Bondí and E.E.~Boos and P.~Bosted and G.~Bozzi and E.J.~Brash and R.~A.~Briceño and P.D.~Brindza and W.J.~Briscoe and S.J Brodsky and W.K.~Brooks and V.D.~Burkert and A.~Camsonne and T.~Cao and L.S.~Cardman and D.S.~Carman and M Carpinelli and G.D.~Cates and J.~Caylor and A.~Celentano and F.G.~Celiberto and M.~Cerutti and Lei Chang and P.~Chatagnon and C.~Chen and J-P Chen and T.~Chetry and A.~Christopher and E.~Christy and E.~Chudakov and E.~Cisbani and I.~C.~Cloët and J.J.~Cobos-Martinez and E.~O.~Cohen and P.~Colangelo and P.L.~Cole and M.~Constantinou and M.~Contalbrigo and G.~Costantini and W.~Cosyn and C.~Cotton and A.~Courtoy and S.~Covrig Dusa and V.~Crede and Z.-F.~Cui and A.~D'Angelo and M.~Döring and M.~M.~Dalton and I.~Danilkin and M.~Davydov and D.~Day and F.~De Fazio and M.~De Napoli and R.~De Vita and D.J.~Dean and M.~Defurne and A.~Deur and B.~Devkota and S.~Dhital and P.~Di Nezza and M.~Diefenthaler and S.~Diehl and C.~Dilks and M.~Ding and C.~Djalali and S.~Dobbs and R.~Dupré and D.~Dutta and R.G.~Edwards and H.~Egiyan and L.~Ehinger and G.~Eichmann and M.~Elaasar and L.~Elouadrhiri and A.~El Alaoui and L.~El Fassi and A.~Emmert and M.~Engelhardt and R.~Ent and D.J Ernst and P.~Eugenio and G.~Evans and C.~Fanelli and S.~Fegan and C.~Fernández-Ramírez and L.A.~Fernandez and I.~P.~Fernando and A.~Filippi and C.S.~Fischer and C.~Fogler and N.~Fomin and L.~Frankfurt and T.~Frederico and A.~Freese and Y.~Fu and L.~Gamberg and L.~Gan and F.~Gao and H.~Garcia-Tecocoatzi and D.~Gaskell and A.~Gasparian and K Gates and G.~Gavalian and P.K.~Ghoshal and A.~Giachino and F.~Giacosa and F.~Giannuzzi and G.-P.~Gilfoyle and F-X Girod and D.~I.~Glazier and C.~Gleason and S.~Godfrey and J.L.~Goity and A.A.~Golubenko and S.~Gonzàlez-Solís and R.W.~Gothe and Y.~Gotra and K.~Griffioen and O.~Grocholski and B.~Grube and P.~Guèye and F.-K.~Guo and Y.~Guo and L.~Guo and T.~J.~Hague and N.~Hammoud and J.-O.~Hansen and M.~Hattawy and F.~Hauenstein and T.~Hayward and D.~Heddle and N.~Heinrich and O.~Hen and D.W.~Higinbotham and I.M.~Higuera-Angulo and A.~N.~Hiller Blin and A.~Hobart and T.~Hobbs and D.E Holmberg and T.~Horn and P.~Hoyer and G.M.~Huber and P.~Hurck and P.~T.~P.~Hutauruk and Y.~Ilieva and I.~Illari and D.G Ireland and E.L.~Isupov and A.~Italiano and I.~Jaegle and N.S.~Jarvis and DJ Jenkins and S.~Jeschonnek and C-R.~Ji and H.S.~Jo and M.~Jones and R.T.~Jones and D.C.~Jones and K.~Joo and M.~Junaid and T.~Kageya and N.~Kalantarians and A.~Karki and G.~Karyan and A.T.~Katramatou and S.J.D Kay and R.~Kazimi and C.D.~Keith and C.~Keppel and A.~Kerbizi and V.~Khachatryan and A.~Khanal and M.~Khandaker and A.~Kim and E.R.~Kinney and M.~Kohl and A.~Kotzinian and B.~T.~Kriesten and V.~Kubarovsky and B.~Kubis and S.E.~Kuhn and V.~Kumar and T.~Kutz and M.~Leali and R.F.~Lebed and P.~Lenisa and L.~Leskovec and S.~Li and X.~Li and J.~Liao and H.-W.~Lin and L.~Liu and S.~Liuti and N.~Liyanage and Y.~Lu and I.J.D.~MacGregor and D.~J.~Mack and L Maiani and K.~A.~Mamo and G.~Mandaglio and C.~Mariani and P.~Markowitz and H.~Marukyan and V.~Mascagna and V.~Mathieu and J.~Maxwell and M.~Mazouz and M.~McCaughan and R.D.~McKeown and B.~McKinnon and D.~Meekins and W.~Melnitchouk and A.~Metz and C.~A.~Meyer and Z.-E.~Meziani and C.~Mezrag and R.~Michaels and G.A.~Miller and T.~Mineeva and A.S.~Miramontes and M.~Mirazita and K.~Mizutani and H.~Mkrtchyan and A.~Mkrtchyan and B.~Moffit and P.~Mohanmurthy and V.I.~Mokeev and P.~Monaghan and G.~Montaña and R.~Montgomery and A.~Moretti and J.M.~Morgado Chàvez and U.~Mosel and A.~Movsisyan and P.~Musico and S.A Nadeeshani and P.~M.~Nadolsky and S.X.~Nakamura and J.~Nazeer and A.V.~Nefediev and K.~Neupane and D.~Nguyen and S.~Niccolai and I.~Niculescu and G.~Niculescu and E.R.~Nocera and M.~Nycz and F.I.~Olness and P.~G.~Ortega and M.~Osipenko and E.~Pace and B Pandey and P.~Pandey and Z.~Papandreou and J.~Papavassiliou and L.L.~Pappalardo and G.~Paredes-Torres and R.~Paremuzyan and S.~Park and B.~Parsamyan and K.D.~Paschke and B.~Pasquini and E.~Passemar and E.~Pasyuk and T.~Patel and C.~Paudel and S.J.~Paul and J-C.~Peng and L.~Pentchev and R.~Perrino and R.J.~Perry and K.~Peters and G.~G.~Petratos and W.~Phelps and E.~Piasetzky and A.~Pilloni and B.~Pire and D.~Pitonyak and M.L.~Pitt and A.D.~Polosa and M.~Pospelov and A.C.~Postuma and J.~Poudel and L.~Preet and S.~Prelovsek and J.W.~Price and A.~Prokudin and A.~J.~R.~Puckett and J.R.~Pybus and S.-X.~Qin and J.-W.~Qiu and M.~Radici and H.~Rashidi and A.D Rathnayake and B.A.~Raue and T.~Reed and P.~E.~Reimer and J.~Reinhold and J.-M.~Richard and M.~Rinaldi and F.~Ringer and M.~Ripani and J.~Ritman and J.~Rittenhouse West and A.~Rivero-Acosta and C.D.~Roberts and A.~Rodas and S.~Rodini and J.~Rodríguez-Quintero and T.C.~Rogers and J.~Rojo and P.~Rossi and G.C.~Rossi and G.~Salmè and S.~N.~Santiesteban and E.~Santopinto and M.~Sargsian and N.~Sato and S.~Schadmand and A.~Schmidt and S.M Schmidt and G.~Schnell and R.~A.~Schumacher and P.~Schweitzer and I.~Scimemi and K.C Scott and D.A Seay and J.~Segovia and K.~Semenov-Tian-Shansky and A.~Seryi and A.S Sharda and M.~R.~Shepherd and E.V.~Shirokov and S.~Shrestha and U.~Shrestha and V.I.~Shvedunov and A.~Signori and K.~J.~Slifer and W.~A.~Smith and A.~Somov and P.~Souder and N.~Sparveris and F.~Spizzo and M.~Spreafico and S.~Stepanyan and J.~R.~Stevens and I.I.~Strakovsky and S.~Strauch and M.~Strikman and S.~Su and B.C.L.~Sumner and E.~Sun and M.~Suresh and C.~Sutera and E.S.~Swanson and A.P Szczepaniak and P.~Sznajder and H.~Szumila-Vance and L.~Szymanowski and A.-S.~Tadepalli and V.~Tadevosyan and B.~Tamang and V.V.~Tarasov and A.~Thiel and X.-B.~Tong and R.~Tyson and M.~Ungaro and G.M.~Urciuoli and A.~Usman and A.~Valcarce and S.~Vallarino and C.A.~Vaquera-Araujo and L.~Venturelli and F.~Vera and A.~Vladimirov and A.~Vossen and J.~Wagner and X.~Wei and L.B.~Weinstein and C.~Weiss and R.~Williams and D.~Winney and B.~Wojtsekhowski and M.~H.~Wood and T.~Xiao and S.-S.~Xu and Z.~Ye and C.~Yero and C.-P.~Yuan and M.~Yurov and N.~Zachariou and Z.~Zhang and Z.W.~Zhao and Y.~Zhao and X.~Zheng and X.~Zhou and V.~Ziegler and B.~Zihlmann and W de Paula and G.~F.~de Téramond}, title = {{S}trong {I}nteraction {P}hysics at the {L}uminosity {F}rontier with 22 {G}e{V} {E}lectrons at {J}efferson {L}ab}, year = {2023}, eprint = {2306.09360}, note = {arXiv:2306.09360v2} }
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This document presents the initial scientific case for upgrading the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) to 22 GeV. It is the result of a community effort, incorporating insights from a series of workshops conducted between March 2022 and April 2023. With a track record of over 25 years in delivering the world's most intense and precise multi-GeV electron beams, CEBAF's potential for a higher energy upgrade presents a unique opportunity for an innovative nuclear physics program, which seamlessly integrates a rich historical background with a promising future. The proposed physics program encompass a diverse range of investigations centered around the nonperturbative dynamics inherent in hadron structure and the exploration of strongly interacting systems. It builds upon the exceptional capabilities of CEBAF in high-luminosity operations, the availability of existing or planned Hall equipment, and recent advancements in accelerator technology. The proposed program cover various scientific topics, including Hadron Spectroscopy, Partonic Structure and Spin, Hadronization and Transverse Momentum, Spatial Structure, Mechanical Properties, Form Factors and Emergent Hadron Mass, Hadron-Quark Transition, and Nuclear Dynamics at Extreme Conditions, as well as QCD Confinement and Fundamental Symmetries. Each topic highlights the key measurements achievable at a 22 GeV CEBAF accelerator. Furthermore, this document outlines the significant physics outcomes and unique aspects of these programs that distinguish them from other existing or planned facilities. In summary, this document provides an exciting rationale for the energy upgrade of CEBAF to 22 GeV, outlining the transformative scientific potential that lies within reach, and the remarkable opportunities it offers for advancing our understanding of hadron physics and related fundamental phenomena.
The resolution to the problem of consistent large transverse momentum in TMDs
J. O. Gonzalez-Hernandez, T. Rainaldi, T. C. Rogers
Mar 10 2023 hep-ph hep-ex nucl-ex nucl-th arXiv:2303.04921v1

@misc{2303.04921, author = {J.~O.~Gonzalez-Hernandez and T.~Rainaldi and T.~C.~Rogers}, title = {{T}he resolution to the problem of consistent large transverse momentum in {TMD}s}, year = {2023}, eprint = {2303.04921}, note = {arXiv:2303.04921v1} }
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Parametrizing TMD parton densities and fragmentation functions in ways that consistently match their large transverse momentum behavior in standard collinear factorization has remained notoriously difficult. We show how the problem is solved in a recently introduced set of steps for combining perturbative and nonperturbative transverse momentum in TMD factorization. Called a ``bottom-up'' approach in a previous article, here we call it a ``hadron structure oriented'' (HSO) approach to emphasize its focus on preserving a connection to the TMD parton model interpretation. We show that the associated consistency constraints improve considerably the agreement between parametrizations of TMD functions and their large-$k_T$ behavior, as calculated in collinear factorization. The procedure discussed herein will be important for guiding future extractions of TMD parton densities and fragmentation functions and for testing TMD factorization and universality. We illustrate the procedure with an application to semi-inclusive deep inelastic scattering (SIDIS) structure functions at an input scale $Q_0$, and we show that there is improved consistency between different methods of calculating at moderate transverse momentum. We end with a discussion of plans for future phenomenological applications.
Basics of factorization in a scalar Yukawa field theory
F. Aslan, L. Gamberg, J. O. Gonzalez-Hernandez, T. Rainaldi, T. C. Rogers
Dec 02 2022 hep-ph hep-ex hep-th nucl-th arXiv:2212.00757v2

@misc{2212.00757, author = {F.~Aslan and L.~Gamberg and J.~O.~Gonzalez-Hernandez and T.~Rainaldi and T.~C.~Rogers}, title = {{B}asics of factorization in a scalar {Y}ukawa field theory}, year = {2022}, eprint = {2212.00757}, note = {arXiv:2212.00757v2} }
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The factorization theorems of quantum chromodynamics (QCD) apply equally well to most simple quantum field theories that require renormalization but where direct calculations are much more straightforward. Working with these simpler theories is convenient for stress-testing the limits of the factorization program and for examining general properties of the parton density functions (pdfs) or other correlation functions that might be necessary for a factorized description of a process. With this view in mind, we review the steps of factorization in a real scalar Yukawa field theory for both deep inelastic scattering (DIS) and semi-inclusive deep inelastic scattering (SIDIS) cross sections. In the case of SIDIS, we illustrate how to separate the small transverse momentum region, where transverse momentum dependent (TMD) pdfs are needed, from a purely collinear large transverse momentum region, and we examine the influence of subleading power corrections. We also review the steps for formulating TMD factorization in transverse coordinate space, and we study the effect of transforming to the well-known $b_*$-scheme. Within the Yukawa theory, we investigate the consequences of switching to a generalized parton model (GPM) approach, and compare with a fully factorized approach. Our results highlight the need to address similar or analogous issues in QCD.
Combining nonperturbative transverse momentum dependence with TMD evolution
J. O. Gonzalez-Hernandez, T. C. Rogers, N. Sato
May 13 2022 hep-ph hep-ex nucl-ex nucl-th arXiv:2205.05750v1

@misc{2205.05750, author = {J.~O.~Gonzalez-Hernandez and T.~C.~Rogers and N.~Sato}, title = {{C}ombining nonperturbative transverse momentum dependence with {TMD} evolution}, year = {2022}, eprint = {2205.05750}, note = {arXiv:2205.05750v1} }
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Central to understanding the nonpertubative, intrinsic partonic nature of hadron structure are the concepts of transverse momentum dependent (TMD) parton distribution and fragmentation functions. A TMD factorization approach to the phenomenology of semi-inclusive processes that includes evolution, higher orders, and matching to larger transverse momentum, is ultimately necessary for reliably connecting with phenomenologically extracted nonperturbative structures, especially when widely different scales are involved. In this paper, we will address some of the difficulties that arise when phenomenological techniques that were originally designed for very high energy applications are extended to studies of hadron structures, and we will solidify the connection between standard high energy TMD implementations and the more intuitive, parton model based approaches to phenomenology that emphasize nonperturbative hadron structure. In the process, we will elaborate on differences between forward and backward TMD evolution, which in the context of this paper we call "bottom-up" and "top-down" approaches, and we will explain the advantages of a bottom-up strategy. We will also emphasize and clarify the role of the integral relations that connect TMD and collinear correlation functions. We will show explicitly how they constrain the nonperturbative "$g$-functions" of standard Collins-Soper-Sterman (CSS) implementations of TMD factorization. This paper is especially targeted toward phenomenologists and model builders who are interested in merging specific nonperturbative models and calculations (including lattice QCD) with TMD factorization at large $Q$. Our main result is a recipe for incorporating nonperturbative models into TMD factorization, and for constraining their parameters in a way that matches to perturbative QCD and evolution.
Positivity and renormalization of parton densities
John Collins, Ted C. Rogers, Nobuo Sato
Nov 03 2021 hep-ph hep-ex nucl-th arXiv:2111.01170v2

@misc{2111.01170, author = {John Collins and Ted C.~Rogers and Nobuo Sato}, title = {{P}ositivity and renormalization of parton densities}, year = {2021}, eprint = {2111.01170}, doi = {10.1103/PhysRevD.105.076010}, note = {arXiv:2111.01170v2} }
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There have been recent debates about whether $\overline{\text{MS}}$ parton densities exactly obey positivity bounds (including the Soffer bound), and whether the bounds should be applied as a constraint on global fits to parton densities and on nonperturbative calculations. A recent paper (JHEP ${\bf \text{11}}$ (2020) 129) appears to provide a proof of positivity in contradiction with earlier work by other authors. We examine their derivation and find that its primary failure is in the apparently uncontroversial statement that bare pdfs are always positive. We show that under the conditions used in the derivation, that statement fails. We provide some elementary calculations in a model QFT that show how this situation can generically arise in reality. In addition, we observe that the methods used in the derivation are in common with much, but not all, other work where factorization is derived. Our examination pinpoints considerable difficulties with these methods that render them either wrong or highly problematic. The issue of positivity highlights that these methods can lead to wrong results of phenomenological importance. From our analysis we identify the restricted situations in which positivity can be violated.
QCD Factorization and Quantum Mechanics
C. A. Aidala, T. C. Rogers
Aug 30 2021 quant-ph hep-ph nucl-th arXiv:2108.12319v1

@misc{2108.12319, author = {C.~A.~Aidala and T.~C.~Rogers}, title = {{QCD} {F}actorization and {Q}uantum {M}echanics}, year = {2021}, eprint = {2108.12319}, doi = {10.1098/rsta.2021.0058}, note = {arXiv:2108.12319v1} }
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It is unusual to find QCD factorization explained in the language of quantum information science. However, we will discuss how the issue of factorization and its breaking in high-energy QCD processes relates to phenomena like decoherence and entanglement. We will elaborate with several examples and explain them in terms familiar from basic quantum mechanics and quantum information science.
Simultaneous Monte Carlo analysis of parton densities and fragmentation functions
E. Moffat, W. Melnitchouk, T. C. Rogers, N. Sato
Jan 13 2021 hep-ph hep-ex nucl-th arXiv:2101.04664v2

@misc{2101.04664, author = {E.~Moffat and W.~Melnitchouk and T.~C.~Rogers and N.~Sato}, title = {{S}imultaneous {M}onte {C}arlo analysis of parton densities and fragmentation functions}, year = {2021}, eprint = {2101.04664}, howpublished = {Phys. Rev. D 104, 016015 (2021)}, doi = {10.1103/PhysRevD.104.016015}, note = {arXiv:2101.04664v2} }
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We perform a comprehensive new Monte Carlo analysis of high-energy lepton-lepton, lepton-hadron and hadron-hadron scattering data to simultaneously determine parton distribution functions (PDFs) in the proton and parton to hadron fragmentation functions (FFs). The analysis includes all available semi-inclusive deep-inelastic scattering and single-inclusive $e^+ e^-$ annihilation data for pions, kaons and unidentified charged hadrons, which allows the flavor dependence of the fragmentation functions to be constrained. Employing a new multi-step fitting strategy and more flexible parametrizations for both PDFs and FFs, we assess the impact of different data sets on sea quark densities, and confirm the previously observed suppression of the strange quark distribution. The new fit, which we refer to as "JAM20-SIDIS", will allow for improved studies of universality of parton correlation functions, including transverse momentum dependent (TMD) distributions, across a wide variety of process, and the matching of collinear to TMD factorization descriptions.
Transverse moments of TMD parton densities and ultraviolet divergences
Ted Rogers
Aug 13 2020 hep-ph hep-ex nucl-th arXiv:2008.05351v2

@misc{2008.05351, author = {Ted Rogers}, title = {{T}ransverse moments of {TMD} parton densities and ultraviolet divergences}, year = {2020}, eprint = {2008.05351}, note = {arXiv:2008.05351v2} }
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I review some open questions relating to the large transverse momentum divergences in transverse moments of transverse momentum dependent (TMD) parton correlation func- tions. I also explain, in an abbreviated and summarized form, recent work that shows that the resulting violations of a commonly used integral relation are not perturbatively suppressed. I argue that this implies a need for more precise definitions for the correlation functions used to describe transverse moments.
Parton distributions and lattice QCD calculations: toward 3D structure
Martha Constantinou, Aurore Courtoy, Markus A. Ebert, Michael Engelhardt, Tommaso Giani, Tim Hobbs, Tie-Jiun Hou, Aleksander Kusina, Krzysztof Kutak, Jian Liang, Huey-Wen Lin, Keh-Fei Liu, Simonetta Liuti, Cédric Mezrag, Pavel Nadolsky, Emanuele R. Nocera, Fred Olness, Jian-Wei Qiu, Marco Radici, Anatoly Radyushkin, et al (7)
Jun 17 2020 hep-ph hep-lat arXiv:2006.08636v2

@misc{2006.08636, author = {Martha Constantinou and Aurore Courtoy and Markus A.~Ebert and Michael Engelhardt and Tommaso Giani and Tim Hobbs and Tie-Jiun Hou and Aleksander Kusina and Krzysztof Kutak and Jian Liang and Huey-Wen Lin and Keh-Fei Liu and Simonetta Liuti and Cédric Mezrag and Pavel Nadolsky and Emanuele R.~Nocera and Fred Olness and Jian-Wei Qiu and Marco Radici and Anatoly Radyushkin and Abha Rajan and Ted Rogers and Juan Rojo and Gerrit Schierholz and C.-P.~Yuan and Jian-Hui Zhang and Rui Zhang}, title = {{P}arton distributions and lattice {QCD} calculations: toward 3{D} structure}, year = {2020}, eprint = {2006.08636}, note = {arXiv:2006.08636v2} }
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The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs.
Intrinsic Transverse Momentum and Evolution in Weighted Spin Asymmetries
Jian-Wei Qiu, Ted C. Rogers, Bowen Wang
Apr 29 2020 hep-ph nucl-th arXiv:2004.13193v2

@misc{2004.13193, author = {Jian-Wei Qiu and Ted C.~Rogers and Bowen Wang}, title = {{I}ntrinsic {T}ransverse {M}omentum and {E}volution in {W}eighted {S}pin {A}symmetries}, year = {2020}, eprint = {2004.13193}, howpublished = {Phys. Rev. D 101, 116017 (2020)}, doi = {10.1103/PhysRevD.101.116017}, note = {arXiv:2004.13193v2} }
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The transverse momentum dependent (TMD) and collinear higher twist theoretical factorization frameworks are the most frequently used approaches to describing spin dependent hard cross sections weighted by and integrated over transverse momentum. Of particular interest is the contribution from small transverse momentum associated with the target bound state. In phenomenological applications, this contribution is often investigated using transverse momentum weighted integrals that sharply regulate the large transverse momentum contribution, for example with Gaussian parametrizations. Since the result is a kind of hybrid of TMD and collinear (inclusive) treatments, it is important to establish if and how the formalisms are related in applications to weighted integral observables. The suppression of a large transverse momentum tail, for example, can potentially affect the type of evolution that is applicable. We find that a naive version of a widely used identity relating the $k_T^2$-weighted and integrated Sivers TMD function to a renormalized twist-3 function has strongly ambiguous ultraviolet contributions, and that corrections to it are not necessarily perturbatively suppressed. We discuss the implications for applications, arguing in particular that the relevant evolution for transverse momentum weighted and integrated cross sections with sharp effective large transverse momentum cutoffs is of the TMD form rather than the standard renormalization group evolution of collinear correlation functions.
Origin of single transverse-spin asymmetries in high-energy collisions
Justin Cammarota, Leonard Gamberg, Zhong-Bo Kang, Joshua A. Miller, Daniel Pitonyak, Alexei Prokudin, Ted C. Rogers, Nobuo Sato
Feb 21 2020 hep-ph hep-ex hep-lat nucl-ex nucl-th arXiv:2002.08384v2

@misc{2002.08384, author = {Justin Cammarota and Leonard Gamberg and Zhong-Bo Kang and Joshua A.~Miller and Daniel Pitonyak and Alexei Prokudin and Ted C.~Rogers and Nobuo Sato}, title = {{O}rigin of single transverse-spin asymmetries in high-energy collisions}, year = {2020}, eprint = {2002.08384}, note = {arXiv:2002.08384v2} }
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In this paper we perform the first simultaneous QCD global analysis of data from semi-inclusive deep inelastic scattering, Drell-Yan, $e^+e^-$ annihilation into hadron pairs, and proton-proton collisions. Consequently, we are able to extract a universal set of non-perturbative functions that describes the observed asymmetries in these reactions. The outcome of our analysis indicates single transverse-spin asymmetries in high-energy collisions have a common origin. Furthermore, we achieve the first phenomenological agreement with lattice QCD on the up and down quark tensor charges.
Collinear Factorization in Wide-Angle Hadron Pair Production in $e^+e^-$ Annihilation
E. Moffat, T. C. Rogers, N. Sato, A. Signori
Sep 09 2019 hep-ph nucl-th arXiv:1909.02951v2

@misc{1909.02951, author = {E.~Moffat and T.~C.~Rogers and N.~Sato and A.~Signori}, title = {{C}ollinear {F}actorization in {W}ide-{A}ngle {H}adron {P}air {P}roduction in $e^+e^-$ {A}nnihilation}, year = {2019}, eprint = {1909.02951}, note = {arXiv:1909.02951v2} }
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We compute the inclusive unpolarized dihadron production cross section in the far from back-to-back region of $e^+ e^-$ annihilation in leading order pQCD using existing fragmentation function fits and standard collinear factorization, focusing on the large transverse momentum region where transverse momentum is comparable to the hard scale (the center-of-mass energy). We compare with standard transverse-momentum-dependent (TMD) fragmentation function-based predictions intended for the small transverse momentum region with the aim of testing the expectation that the two types of calculation roughly coincide at intermediate transverse momentum. We find significant tension, within the intermediate transverse momentum region, between calculations done with existing non-perturbative TMD fragmentation functions and collinear factorization calculations if the center-of-mass energy is not extremely large. We argue that $e^+ e^-$ measurements are ideal for resolving this tension and exploring the large-to-small transverse momentum transition, given the typically larger hard scales ($\gtrsim 10$ GeV) of the process as compared with similar scenarios that arise in semi-inclusive deep inelastic scattering and fixed-target Drell-Yan measurements.
Mapping the Kinematical Regimes of Semi-Inclusive Deep Inelastic Scattering
M. Boglione, A. Dotson, L. Gamberg, S. Gordon, J. O. Gonzalez-Hernandez, A. Prokudin, T. C. Rogers, N. Sato
May 01 2019 hep-ph nucl-ex nucl-th arXiv:1904.12882v1

@misc{1904.12882, author = {M.~Boglione and A.~Dotson and L.~Gamberg and S.~Gordon and J.~O.~Gonzalez-Hernandez and A.~Prokudin and T.~C.~Rogers and N.~Sato}, title = {{M}apping the {K}inematical {R}egimes of {S}emi-{I}nclusive {D}eep {I}nelastic {S}cattering}, year = {2019}, eprint = {1904.12882}, note = {arXiv:1904.12882v1} }
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We construct a language for identifying kinematical regions of transversely differential semi-inclusive deep inelastic scattering cross sections with particular underlying partonic pictures, especially in regions of moderate to low $Q$ where sensitivity to kinematical effects outside the usual very high energy limit becomes non-trivial. The partonic pictures map to power law expansions whose leading contributions ultimately lead to well-known QCD factorization theorems. We propose methods for estimating the consistency of any particular region of overall hadronic kinematics with the kinematics of a given underlying partonic picture. The basic setup of kinematics of semi-inclusive deep inelastic scattering is also reviewed in some detail.
Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering Beyond Lowest Order
B. Wang, J. O. Gonzalez-Hernandez, T. C. Rogers, N. Sato
Mar 06 2019 hep-ph nucl-th arXiv:1903.01529v1

@misc{1903.01529, author = {B.~Wang and J.~O.~Gonzalez-Hernandez and T.~C.~Rogers and N.~Sato}, title = {{L}arge {T}ransverse {M}omentum in {S}emi-{I}nclusive {D}eeply {I}nelastic {S}cattering {B}eyond {L}owest {O}rder}, year = {2019}, eprint = {1903.01529}, note = {arXiv:1903.01529v1} }
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Motivated by recently observed tension between $O\left(\alpha_s^2\right)$ calculations of very large transverse momentum dependence in both semi-inclusive deep inelastic scattering and Drell-Yan scattering, we repeat the details of the calculation through $O\left(\alpha_s^2\right)$ transversely differential cross section. The results confirm earlier calculations, and provide further support to the observation that tension exists with current parton distribution and fragmentation functions.
What does kinematical target mass sensitivity in DIS reveal about hadron structure?
E. Moffat, T. C. Rogers, W. Melnitchouk, N. Sato, F. Steffens
Jan 28 2019 hep-ph nucl-th arXiv:1901.09016v1

@misc{1901.09016, author = {E.~Moffat and T.~C.~Rogers and W.~Melnitchouk and N.~Sato and F.~Steffens}, title = {{W}hat does kinematical target mass sensitivity in {DIS} reveal about hadron structure?}, year = {2019}, eprint = {1901.09016}, note = {arXiv:1901.09016v1} }
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We study the role of purely external kinematical approximations in inclusive deep-inelastic lepton--hadron scattering within QCD factorization, and consider factorization with an exact treatment of the target hadron mass. We discuss how an observed phenomenological improvement obtained by accounting for target mass kinematics could be interpreted in terms of general properties of target structure, and argue that such an improvement implies a hierarchy of nonperturbative scales within the hadron.
Challenges with Large Transverse Momentum in Semi-Inclusive Deeply Inelastic Scattering
J. O. Gonzalez-Hernandez, T. C. Rogers, N. Sato, B. Wang
Aug 15 2018 hep-ph hep-ex arXiv:1808.04396v2

@misc{1808.04396, author = {J.~O.~Gonzalez-Hernandez and T.~C.~Rogers and N.~Sato and B.~Wang}, title = {{C}hallenges with {L}arge {T}ransverse {M}omentum in {S}emi-{I}nclusive {D}eeply {I}nelastic {S}cattering}, year = {2018}, eprint = {1808.04396}, note = {arXiv:1808.04396v2} }
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We survey the current phenomenological status of semi-inclusive deep inelastic scattering at moderate hard scales and in the limit of very large transverse momentum. As the transverse momentum becomes comparable to or larger than the overall hard scale, the differential cross sections should be calculable with fixed order pQCD methods, while small transverse momentum (TMD factorization) approximations should eventually break down. We find large disagreement between HERMES and COMPASS data and fixed order calculations done with modern parton densities, even in regions of kinematics where such calculations should be expected to be very accurate. Possible interpretations are suggested.
Graphical Structure of Hadronization and Factorization in Hard Collisions
John Collins, Ted C. Rogers
Jan 10 2018 hep-ph hep-th arXiv:1801.02704v2

@misc{1801.02704, author = {John Collins and Ted C.~Rogers}, title = {{G}raphical {S}tructure of {H}adronization and {F}actorization in {H}ard {C}ollisions}, year = {2018}, eprint = {1801.02704}, note = {arXiv:1801.02704v2} }
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Models of hadronization of hard jets in QCD are often presented in terms of Feynman-graph structures that can be thought of as effective field theory approximations to dynamical non-perturbative physics in QCD. Such models can be formulated as a kind of multiperipheral model. We obtain general constraints on such models in order for them to be self-consistent, and we relate the constraints to the space-time structure of hadronization. We show that appropriate models can be considered as implementing string-like hadronization. When the models are put in a multiperipheral form, the effective vertices and/or lines must be momentum non-conserving: they take 4-momentum from the external string-like field.
Connecting Different TMD Factorization Formalisms in QCD
John Collins, Ted C. Rogers
May 23 2017 hep-ph arXiv:1705.07167v3

@misc{1705.07167, author = {John Collins and Ted C.~Rogers}, title = {{C}onnecting {D}ifferent {TMD} {F}actorization {F}ormalisms in {QCD}}, year = {2017}, eprint = {1705.07167}, note = {arXiv:1705.07167v3} }
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In the original Collins-Soper-Sterman (CSS) presentation of the results of transverse-momentum-dependent (TMD) factorization for the Drell-Yan process, results for perturbative coefficients can be obtained from calculations for collinear factorization. Here we show how to use these results, plus known results for the quark form factor, to obtain coefficients for TMD factorization in more recent formulations, e.g., that due to Collins, and apply them to known results at order $\alpha_s^2$ and $\alpha_s^3$. We also show that the "non-perturbative" functions as obtained from fits to data are equal in the two schemes. We compile the higher-order perturbative inputs needed for the updated CSS scheme by appealing to results obtained in a variety of different formalisms. In addition, we derive the connection between both versions of the CSS formalism and several formalisms based in soft-collinear effective theory (SCET). Our work uses some important new results for factorization for the quark form factor, which we derive.
What are the low-$Q$ and large-$x$ boundaries of collinear QCD factorization theorems?
E. Moffat, W. Melnitchouk, T. C. Rogers, N. Sato
Feb 15 2017 hep-ph hep-ex nucl-th arXiv:1702.03955v2

@misc{1702.03955, author = {E.~Moffat and W.~Melnitchouk and T.~C.~Rogers and N.~Sato}, title = {{W}hat are the low-${Q}$ and large-$x$ boundaries of collinear {QCD} factorization theorems?}, year = {2017}, eprint = {1702.03955}, howpublished = {Phys. Rev. D 95, 096008 (2017)}, doi = {10.1103/PhysRevD.95.096008}, note = {arXiv:1702.03955v2} }
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Familiar factorized descriptions of classic QCD processes such as deeply-inelastic scattering (DIS) apply in the limit of very large hard scales, much larger than nonperturbative mass scales and other nonperturbative physical properties like intrinsic transverse momentum. Since many interesting DIS studies occur at kinematic regions where the hard scale, $Q \sim$ 1-2 GeV, is not very much greater than the hadron masses involved, and the Bjorken scaling variable $x_{bj}$ is large, $x_{bj} \gtrsim 0.5$, it is important to examine the boundaries of the most basic factorization assumptions and assess whether improved starting points are needed. Using an idealized field-theoretic model that contains most of the essential elements that a factorization derivation must confront, we retrace the steps of factorization approximations and compare with calculations that keep all kinematics exact. We examine the relative importance of such quantities as the target mass, light quark masses, and intrinsic parton transverse momentum, and argue that a careful accounting of parton virtuality is essential for treating power corrections to collinear factorization. We use our observations to motivate searches for new or enhanced factorization theorems specifically designed to deal with moderately low-$Q$ and large-$x_{bj}$ physics.
Combining TMD factorization and collinear factorization
J. Collins, L. Gamberg, A. Prokudin, T.C. Rogers, N.Sato, B.Wang
Feb 02 2017 hep-ph arXiv:1702.00387v1

@misc{1702.00387, author = {J.~Collins and L.~Gamberg and A.~Prokudin and T.C.~Rogers and N.Sato and B.Wang}, title = {{C}ombining {TMD} factorization and collinear factorization}, year = {2017}, eprint = {1702.00387}, note = {arXiv:1702.00387v1} }
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We examine some of the complications involved when combining (matching) TMD factorization with collinear factorization to allow accurate predictions over the whole range of measured transverse momentum in a process like Drell-Yan. Then we propose some improved methods for combining the two types of factorization. (This talk is based on work reported in arXiv:1605.00671.)
Kinematics of Current Region Fragmentation in Semi-Inclusive Deeply Inelastic Scattering
M. Boglione, J. Collins, L. Gamberg, J. O. Gonzalez-Hernandez, T. C. Rogers, N. Sato
Dec 01 2016 hep-ph nucl-th arXiv:1611.10329v2

@misc{1611.10329, author = {M.~Boglione and J.~Collins and L.~Gamberg and J.~O.~Gonzalez-Hernandez and T.~C.~Rogers and N.~Sato}, title = {{K}inematics of {C}urrent {R}egion {F}ragmentation in {S}emi-{I}nclusive {D}eeply {I}nelastic {S}cattering}, year = {2016}, eprint = {1611.10329}, doi = {10.1016/j.physletb.2017.01.021}, note = {arXiv:1611.10329v2} }
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Different kinematical regimes of semi-inclusive deeply inelastic scattering (SIDIS) processes correspond to different underlying partonic pictures, and it is important to understand the transition between them. This is particularly the case when there is sensitivity to intrinsic transverse momentum, in which case kinematical details can become especially important. We address the question of how to identify the current fragmentation region --- the kinematical regime where a factorization picture with fragmentation functions is appropriate. We distinguish this from soft and target fragmentation regimes. Our criteria are based on the kinematic regions used in derivations of factorization theorems. We argue that, when hard scales are of order a few GeVs, there is likely significant overlap between different rapidity regions that are normally understood to be distinct. We thus comment on the need to take this into account with more unified descriptions of SIDIS, which should span all rapidities for the produced hadron. Finally, we propose general criteria for estimating the proximity to the current region at large Q.
Relating Transverse Momentum Dependent and Collinear Factorization Theorems in a Generalized Formalism
J. Collins, L. Gamberg, A. Prokudin, T. C. Rogers, N. Sato, B. Wang
May 04 2016 hep-ph arXiv:1605.00671v2

@misc{1605.00671, author = {J.~Collins and L.~Gamberg and A.~Prokudin and T.~C.~Rogers and N.~Sato and B.~Wang}, title = {{R}elating {T}ransverse {M}omentum {D}ependent and {C}ollinear {F}actorization {T}heorems in a {G}eneralized {F}ormalism}, year = {2016}, eprint = {1605.00671}, note = {arXiv:1605.00671v2} }
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We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard $W+Y$ prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and $Q$-dependence of the cross sections at lower $Q$ are largely governed by the matching to the $Y$-term.
TMD Evolution at Moderate Hard Scales
Ted C. Rogers, John Collins
Jan 12 2016 hep-ph arXiv:1601.02571v1

@misc{1601.02571, author = {Ted C.~Rogers and John Collins}, title = {{TMD} {E}volution at {M}oderate {H}ard {S}cales}, year = {2016}, eprint = {1601.02571}, note = {arXiv:1601.02571v1} }
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We summarize some of our recent work on non-perturbative transverse momentum dependent (TMD) evolution, emphasizing aspects that are necessary for dealing with moderately low scale processes like semi-inclusive deep inelastic scattering.
An Overview of Transverse Momentum Dependent Factorization and Evolution
Ted C. Rogers
Sep 17 2015 hep-ph arXiv:1509.04766v1

@misc{1509.04766, author = {Ted C.~Rogers}, title = {{A}n {O}verview of {T}ransverse {M}omentum {D}ependent {F}actorization and {E}volution}, year = {2015}, eprint = {1509.04766}, note = {arXiv:1509.04766v1} }
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I review TMD factorization and evolution theorems, with an emphasis on the treatment by Collins and originating in the Collins-Soper-Sterman (CSS) formalism. I summarize basic results while attempting to trace their development over that past several decades.
TMD factorization and evolution at large $b_T$
John Collins, Ted C. Rogers
Jul 21 2015 hep-ph arXiv:1507.05542v1

@misc{1507.05542, author = {John Collins and Ted C.~Rogers}, title = {{TMD} factorization and evolution at large $b_{T}$}, year = {2015}, eprint = {1507.05542}, note = {arXiv:1507.05542v1} }
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In using transverse-momentum-dependent (TMD) parton densities and fragmentation functions, important non-perturbative information is at large transverse position $b_T$. This concerns both the TMD functions and their evolution. Fits to high energy data tend to predict too rapid evolution when extrapolated to low energies where larger values of $b_T$ dominate. I summarize a new analysis of the issues. It results in a proposal for much weaker $b_T$ dependence at large $b_T$ for the evolution kernel, while preserving the accuracy of the existing fits. The results are particularly important for using transverse-spin-dependent functions like the Sivers function.
Understanding the large-distance behavior of transverse-momentum-dependent parton densities and the Collins-Soper evolution kernel
John Collins, Ted Rogers
Dec 15 2014 hep-ph arXiv:1412.3820v3

@misc{1412.3820, author = {John Collins and Ted Rogers}, title = {{U}nderstanding the large-distance behavior of transverse-momentum-dependent parton densities and the {C}ollins-{S}oper evolution kernel}, year = {2014}, eprint = {1412.3820}, howpublished = {Phys. Rev. D 91, 074020 (2015)}, doi = {10.1103/PhysRevD.91.074020}, note = {arXiv:1412.3820v3} }
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There is considerable controversy about the size and importance of nonperturbative contributions to the evolution of transverse-momentum-dependent (TMD) parton distribution functions. Standard fits to relatively high-energy Drell-Yan data give evolution that when taken to lower Q is too rapid to be consistent with recent data in semi-inclusive deeply inelastic scattering. Some authors provide very different forms for TMD evolution, even arguing that nonperturbative contributions at large transverse distance b_T are not needed or are irrelevant. Here, we systematically analyze the issues, both perturbative and nonperturbative. We make a motivated proposal for the parameterization of the nonperturbative part of the TMD evolution kernel that could give consistency: with the variety of apparently conflicting data, with theoretical perturbative calculations where they are applicable, and with general theoretical nonperturbative constraints on correlation functions at large distances. We propose and use a scheme- and scale-independent function A(b_T) that gives a tool to compare and diagnose different proposals for TMD evolution. We also advocate for phenomenological studies of A(b_T) as a probe of TMD evolution. The results are important generally for applications of TMD factorization. In particular, they are important to making predictions for proposed polarized Drell-Yan experiments to measure the Sivers function.
TMDlib and TMDplotter: library and plotting tools for transverse-momentum-dependent parton distributions
F. Hautmann, H. Jung, M. Krämer, P. J. Mulders, E. R. Nocera, T. C. Rogers, A. Signori
Aug 14 2014 hep-ph arXiv:1408.3015v2

@misc{1408.3015, author = {F.~Hautmann and H.~Jung and M.~Krämer and P.~J.~Mulders and E.~R.~Nocera and T.~C.~Rogers and A.~Signori}, title = {{TMD}lib and {TMD}plotter: library and plotting tools for transverse-momentum-dependent parton distributions}, year = {2014}, eprint = {1408.3015}, note = {arXiv:1408.3015v2} }
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Transverse-momentum-dependent distributions (TMDs) are central in high-energy physics from both theoretical and phenomenological points of view. In this manual we introduce the library, TMDlib, of fits and parameterisations for transverse-momentum-dependent parton distribution functions (TMD PDFs) and fragmentation functions (TMD FFs) together with an online plotting tool, TMDplotter. We provide a description of the program components and of the different physical frameworks the user can access via the available parameterisations.
Limits on TMD Evolution From Semi-Inclusive Deep Inelastic Scattering at Moderate $Q$
C. A. Aidala, B. Field, L. P. Gamberg, T. C. Rogers
Jan 14 2014 hep-ph nucl-th arXiv:1401.2654v4

@misc{1401.2654, author = {C.~A.~Aidala and B.~Field and L.~P.~Gamberg and T.~C.~Rogers}, title = {{L}imits on {TMD} {E}volution {F}rom {S}emi-{I}nclusive {D}eep {I}nelastic {S}cattering at {M}oderate ${Q}$}, year = {2014}, eprint = {1401.2654}, howpublished = {Phys. Rev. D 89, 094002 (2014)}, doi = {10.1103/PhysRevD.89.094002}, note = {arXiv:1401.2654v4} }
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In the QCD evolution of transverse momentum dependent parton distribution and fragmentation functions, the Collins-Soper evolution kernel includes both a perturbative short-distance contribution as well as a large-distance non-perturbative, but strongly universal, contribution. In the past, global fits, based mainly on larger $Q$ Drell-Yan-like processes, have found substantial contributions from non-perturbative regions in the Collins-Soper evolution kernel. In this article, we investigate semi-inclusive deep inelastic scattering measurements in the region of relatively small $Q$, of the order of a few GeV, where sensitivity to non-perturbative transverse momentum dependence may become more important or even dominate the evolution. Using recently available deep inelastic scattering data from the COMPASS experiment, we provide estimates of the regions of coordinate space that dominate in TMD processes when the hard scale is of the order of only a few GeV. We find that distance scales that are much larger than those commonly probed in large $Q$ measurements become important, suggesting that the details of non-perturbative effects in TMD evolution are especially significant in the region of intermediate $Q$. We highlight the strongly universal nature of the non-perturbative component of evolution, and its potential to be tightly constrained by fits from a wide variety of observables that include both large and moderate $Q$. On this basis, we recommend detailed treatments of the non-perturbative component of the Collins-Soper evolution kernel for future TMD studies.
Summary of the Workshop on Multi-Parton Interactions (MPI@LHC 2012)
H. Abramowicz, P. Bartalini, M. Baehr, N. Cartiglia, R. Ciesielski, E. Dobson, F. Ferro, K. Goulianos, B. Guiot, X. Janssen, H. Jung, Iu. Karpenko, J. Kaspar, J. Katzy, F. Krauss, P. Laycock, E. Levin, M. Mangano, Ch. Mesropian, A. Moraes, et al (17)
Jun 25 2013 hep-ph arXiv:1306.5413v2

@misc{1306.5413, author = {H.~Abramowicz and P.~Bartalini and M.~Baehr and N.~Cartiglia and R.~Ciesielski and E.~Dobson and F.~Ferro and K.~Goulianos and B.~Guiot and X.~Janssen and H.~Jung and Iu.~Karpenko and J.~Kaspar and J.~Katzy and F.~Krauss and P.~Laycock and E.~Levin and M.~Mangano and Ch.~Mesropian and A.~Moraes and M.~Myska and D.~Moran and R.~Muresan and Z.~Nagy and T.~Pierog and A.~Pilkington and M.~Poghosyan and T.~Rogers and S.~Sen and M.H.~Seymour and A.~Siodmok and M.~Strikman and P.~Skands and D.~Treleani and D.~Volyanskyy and K.~Werner and P.~Wijeratne}, title = {{S}ummary of the {W}orkshop on {M}ulti-{P}arton {I}nteractions ({MPI}@{LHC} 2012)}, year = {2013}, eprint = {1306.5413}, note = {arXiv:1306.5413v2} }
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With short resumes and highlights the discussions in the different working groups of the workshop MPI@LHC 2012 is documented.
Extra Spin Asymmetries From the Breakdown of TMD-Factorization in Hadron-Hadron Collisions
Ted C. Rogers
Apr 16 2013 hep-ph hep-ex nucl-ex arXiv:1304.4251v1

@misc{1304.4251, author = {Ted C.~Rogers}, title = {{E}xtra {S}pin {A}symmetries {F}rom the {B}reakdown of {TMD}-{F}actorization in {H}adron-{H}adron {C}ollisions}, year = {2013}, eprint = {1304.4251}, doi = {10.1103/PhysRevD.88.014002}, note = {arXiv:1304.4251v1} }
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We demonstrate that partonic correlations that would traditionally be identified as subleading on the basis of a generalized TMD-factorization conjecture can become leading-power because of TMD-factorization breaking that arises in hadron-hadron collisions with large transverse momentum back-to-back hadrons produced in the final state. General forms of TMD-factorization fail for such processes because of a previously noted incompatibility between the requirements for TMD-factorization and the Ward identities of non-Abelian gauge theories. We first review the basic steps for factorizing the gluon distribution and then show that a conflict between TMD-factorization and the non-Abelian Ward identity arises already at the level of a single extra soft or collinear gluon when the partonic subprocess involves a TMD gluon distribution. Next we show that the resulting TMD-factorization violating effects produce leading-power final state spin asymmetries that would be classified as subleading in a generalized TMD-factorization framework. We argue that similar extra TMD-factorization breaking effects may be necessary to explain a range of open phenomenological QCD puzzles. The potential to observe extra transverse spin or azimuthal asymmetries in future experiments is highlighted as their discovery may indicate an influence from novel and unexpected large distance parton correlations.
Equality of Two Definitions for Transverse Momentum Dependent Parton Distribution Functions
John C. Collins, Ted C. Rogers
Oct 09 2012 hep-ph hep-ex arXiv:1210.2100v2

@misc{1210.2100, author = {John C.~Collins and Ted C.~Rogers}, title = {{E}quality of {T}wo {D}efinitions for {T}ransverse {M}omentum {D}ependent {P}arton {D}istribution {F}unctions}, year = {2012}, eprint = {1210.2100}, doi = {10.1103/PhysRevD.87.034018}, note = {arXiv:1210.2100v2} }
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We compare recent, seemingly different, approaches to TMD-factorization (due to Echevarria, Idilbi, and Scimemi and to Collins), and show that they are the same, apart from an apparent difference in their definition of the \MSbar renormalization scheme.
Calculation of TMD Evolution for Transverse Single Spin Asymmetry Measurements
S. Mert Aybat, Alexei Prokudin, Ted C. Rogers
Dec 20 2011 hep-ph arXiv:1112.4423v3

@misc{1112.4423, author = {S.~Mert Aybat and Alexei Prokudin and Ted C.~Rogers}, title = {{C}alculation of {TMD} {E}volution for {T}ransverse {S}ingle {S}pin {A}symmetry {M}easurements}, year = {2011}, eprint = {1112.4423}, doi = {10.1103/PhysRevLett.108.242003}, note = {arXiv:1112.4423v3} }
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The Sivers transverse single spin asymmetry (TSSA) is calculated and compared at different scales using the TMD evolution equations applied to previously existing extractions. We apply the Collins-Soper-Sterman (CSS) formalism, using the version recently developed by Collins. Our calculations rely on the universality properties of TMD-functions that follow from the TMD-factorization theorem. Accordingly, the non-perturbative input is fixed by earlier experimental measurements, including both polarized semi-inclusive deep inelastic scattering (SIDIS) and unpolarized Drell-Yan (DY) scattering. It is shown that recent COMPASS measurements are consistent with the suppression prescribed by TMD evolution.
The QCD Evolution of the Sivers Function
S. Mert Aybat, John C. Collins, Jian-Wei Qiu, Ted C. Rogers
Oct 31 2011 hep-ph arXiv:1110.6428v3

@misc{1110.6428, author = {S.~Mert Aybat and John C.~Collins and Jian-Wei Qiu and Ted C.~Rogers}, title = {{T}he {QCD} {E}volution of the {S}ivers {F}unction}, year = {2011}, eprint = {1110.6428}, doi = {10.1103/PhysRevD.85.034043}, note = {arXiv:1110.6428v3} }
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We extend the Collins-Soper-Sterman (CSS) formalism to apply it to the spin-dependence governed by the Sivers function. We use it to give a correct numerical QCD evolution of existing fixed-scale fits of the Sivers function. With the aid of approximations useful for the non-perturbative region, we present the results as parametrizations of a Gaussian form in transverse momentum space, rather than in the Fourier conjugate transverse coordinate space normally used in the CSS formalism. They are specifically valid at small transverse momentum. Since evolution has been applied, our results can be used to make predictions for Drell-Yan and semi-inclusive deep inelastic scattering at energies different from those where the original fits were made. Our evolved functions are of a form that they can be used in the same parton model factorization formulas as used in the original fits, but now with a predicted scale dependence in the fit parameters. We also present a method by which our evolved functions can be corrected to allow for twist-3 contributions at large parton transverse momentum.
Universality and Evolution of TMDs
S. Mert Aybat, Ted C. Rogers
Oct 28 2011 hep-ph arXiv:1110.6099v1

@misc{1110.6099, author = {S.~Mert Aybat and Ted C.~Rogers}, title = {{U}niversality and {E}volution of {TMD}s}, year = {2011}, eprint = {1110.6099}, note = {arXiv:1110.6099v1} }
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In this talk, we summarize how QCD evolution can be exploited to improve the treatment of transverse momentum dependent (TMD) parton distribution and fragmentation functions. The methods allow existing non-perturbative fits to be turned into fully evolved TMDs that are consistent with a complete TMD-factorization formalism over the full range of kT. We argue that evolution is essential to the predictive power of calculations that utilize TMD parton distribution and fragmentation functions, especially TMD observables that are sensitive to transverse spin.
Gluons and the quark sea at high energies: distributions, polarization, tomography
D. Boer, M. Diehl, R. Milner, R. Venugopalan, W. Vogelsang, A. Accardi, E. Aschenauer, M. Burkardt, R. Ent, V. Guzey, D. Hasch, K. Kumar, M. A. C. Lamont, Y. Li, W. J. Marciano, C. Marquet, F. Sabatie, M. Stratmann, F. Yuan, S. Abeyratne, et al (169)
Aug 08 2011 nucl-th hep-ph nucl-ex arXiv:1108.1713v2

@misc{1108.1713, author = {D.~Boer and M.~Diehl and R.~Milner and R.~Venugopalan and W.~Vogelsang and A.~Accardi and E.~Aschenauer and M.~Burkardt and R.~Ent and V.~Guzey and D.~Hasch and K.~Kumar and M.~A.~C.~Lamont and Y.~Li and W.~J.~Marciano and C.~Marquet and F.~Sabatie and M.~Stratmann and F.~Yuan and S.~Abeyratne and S.~Ahmed and C.~Aidala and S.~Alekhin and M.~Anselmino and H.~Avakian and A.~Bacchetta and J.~Bartels and H.~BC and J.~Beebe-Wang and S.~Belomestnykh and I.~Ben-Zvi and G.~Beuf and J.~Blumlein and M .~Blaskiewicz and A.~Bogacz and S.~J.~Brodsky and T.~Burton and R.~Calaga and X.~Chang and I.~O.~Cherednikov and P.~Chevtsov and G.~A.~Chirilli and C.~Ciofi degli Atti and I.~C.~Cloet and A.~Cooper-Sarkar and R.~Debbe and Ya.~Derbenev and A.~Deshpande and F.~Dominguez and A.~Dumitru and R.~Dupre and B.~Erdelyi and C.~Faroughy and S.~Fazio and A.~Fedotov and J.~R.~Forshaw and R.~Geraud and K.~Gallmeister and L.~Gamberg and J.-H.~Gao and D.~Gassner and F.~Gelis and G.~P.~Gilfoyle and G.~Goldstein and K.~Golec-Biernat and V.~P.~Goncalves and M.~Gonderinger and M.~Guzzi and P.~Hagler and H.~Hahn and L.~Hammons and Y.~Hao and P.~He and T.~Horn and W.~A.~Horowitz and M.~Huang and A.~Hutton and B.~Jager and W.~Jackson and A.~Jain and E.~C.~Johnson and Z.-B.~Kang and L.~P.~Kaptari and D.~Kayran and J.~Kewisch and Y.~Koike and A.~Kondratenko and B.~Z.~Kopeliovich and Y.~V.~Kovchegov and G.~Krafft and P.~Kroll and S.~Kumano and K.~Kumericki and T.~Lappi and T.~Lautenschlager and R.~Li and Z.-T.~Liang and V.~N.~Litvinenko and S.~Liuti and Y.~Luo and D.~Muller and G.~Mahler and A.~Majumder and S.~Manikonda and F.~Marhauser and G.~McIntyre and M.~Meskauskas and W.~Meng and A.~Metz and C.~B.~Mezzetti and G.~A.~Miller and M.~Minty and S.-O.~Moch and V.~Morozov and U.~Mosel and L.~Motyka and H.~Moutarde and P.~J.~Mulders and B.~Musch and P.~Nadel-Turonski and P.~Nadolsky and F.~Olness and P.~N.~Ostrumov and B.~Parker and B.~Pasquini and K.~Passek-Kumericki and A.~Pikin and F.~Pilat and B.~Pire and H.~Pirner and C.~Pisano and E.~Pozdeyev and A.~Prokudin and V.~Ptitsyn and X.~Qian and J.-W.~Qiu and M.~Radici and A.~Radyushkin and T.~Rao and R.~Rimmer and F.~Ringer and S.~Riordan and T.~Rogers and J.~Rojo and T.~Roser and R.~Sandapen and R.~Sassot and T.~Satogata and H.~Sayed and A.~Schafer and G.~Schnell and P.~Schweitzer and B.~Sheehy and J.~Skaritka and G.~Soyez and M.~Spata and H.~Spiesberger and A.~M.~Stasto and N.~G.~Stefanis and M.~Strikman and M.~Sullivan and L.~Szymanowski and K.~Tanaka and S.~Taneja and S.~Tepikian and B.~Terzic and Y.~Than and T.~Toll and D.~Trbojevic and E.~Tsentalovich and N.~Tsoupas and K.~Tuchin and J.~Tuozzolo and T.~Ullrich and A.~Vossen and S.~Wallon and G.~Wang and H.~Wang and X.-N.~Wang and S.~Webb and C.~Weiss and Q.~Wu and B.-W.~Xiao and W.~Xu and B.~Yunn and A.~Zelenski and Y.~Zhang and J.~Zhou and P.~Zurita}, title = {{G}luons and the quark sea at high energies: distributions, polarization, tomography}, year = {2011}, eprint = {1108.1713}, note = {arXiv:1108.1713v2} }
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This report is based on a ten-week program on "Gluons and the quark sea at high-energies", which took place at the Institute for Nuclear Theory in Seattle in Fall 2010. The principal aim of the program was to develop and sharpen the science case for an Electron-Ion Collider (EIC), a facility that will be able to collide electrons and positrons with polarized protons and with light to heavy nuclei at high energies, offering unprecedented possibilities for in-depth studies of quantum chromodynamics. This report is organized around four major themes: i) the spin and flavor structure of the proton, ii) three-dimensional structure of nucleons and nuclei in momentum and configuration space, iii) QCD matter in nuclei, and iv) Electroweak physics and the search for physics beyond the Standard Model. Beginning with an executive summary, the report contains tables of key measurements, chapter overviews for each of the major scientific themes, and detailed individual contributions on various aspects of the scientific opportunities presented by an EIC.
TMD-factorization, Factorization Breaking and Evolution
S.M. Aybat, T.C. Rogers
Jul 21 2011 hep-ph arXiv:1107.3973v1

@misc{1107.3973, author = {S.M.~Aybat and T.C.~Rogers}, title = {{TMD}-factorization, {F}actorization {B}reaking and {E}volution}, year = {2011}, eprint = {1107.3973}, note = {arXiv:1107.3973v1} }
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We give an overview of the current status of perturbative QCD factorization theorems in processes that involve transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FF). We enumerate those cases where TMD-factorization is well-established, and mention cases where it is likely to fail. We discuss recent progress in the implementation of specific TMD-factorization calculations, including the implementation of evolution. We also give examples of hard part calculations. We end by discussing future strategies for the implementation of TMD-factorization in phenomenological applications.
Gauge links, TMD-factorization, and TMD-factorization breaking
P.J. Mulders, T.C. Rogers
Feb 23 2011 hep-ph arXiv:1102.4569v1

@misc{1102.4569, author = {P.J.~Mulders and T.C.~Rogers}, title = {{G}auge links, {TMD}-factorization, and {TMD}-factorization breaking}, year = {2011}, eprint = {1102.4569}, note = {arXiv:1102.4569v1} }
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In this section, we discuss some basic features of transverse momentum dependent, or unintegrated, parton distribution functions. In particular, when these correlation functions are combined in a factorization formulae with hard processes beyond the simplest cases, there are basic problems with universality and factorization. We discuss some of these problems as well as the opportunities that they offer.
TMD Parton Distribution and Fragmentation Functions with QCD Evolution
S. Mert Aybat, Ted C. Rogers
Jan 27 2011 hep-ph arXiv:1101.5057v2

@misc{1101.5057, author = {S.~Mert Aybat and Ted C.~Rogers}, title = {{TMD} {P}arton {D}istribution and {F}ragmentation {F}unctions with {QCD} {E}volution}, year = {2011}, eprint = {1101.5057}, howpublished = {Phys.Rev.D83:114042,2011}, doi = {10.1103/PhysRevD.83.114042}, note = {arXiv:1101.5057v2} }
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We assess the current phenomenological status of transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs) and study the effect of consistently including perturbative QCD (pQCD) evolution. Our goal is to initiate the process of establishing reliable, QCD-evolved parametrizations for the TMD PDFs and TMD FFs that can be used both to test TMD-factorization and to search for evidence of the breakdown of TMD-factorization that is expected for certain processes. In this article, we focus on spin-independent processes because they provide the simplest illustration of the basic steps and can already be used in direct tests of TMD-factorization. Our calculations are based on the Collins-Soper-Sterman (CSS) formalism, supplemented by recent theoretical developments which have clarified the precise definitions of the TMD PDFs and TMD FFs needed for a valid TMD-factorization theorem. Starting with these definitions, we numerically generate evolved TMD PDFs and TMD FFs using as input existing parametrizations for the collinear PDFs, collinear FFs, non-perturbative factors in the CSS factorization formalism, and recent fixed-scale fits. We confirm that evolution has important consequences, both qualitatively and quantitatively, and argue that it should be included in future phenomenological studies of TMD functions. Our analysis is also suggestive of extensions to processes that involve spin-dependent functions such as the Boer-Mulders, Sivers, or Collins functions, which we intend to pursue in future publications. At our website we have made available the tables and calculations needed to obtain the TMD parametrizations presented herein.
No Generalized TMD-Factorization in the Hadro-Production of High Transverse Momentum Hadrons
Ted C. Rogers, Piet J. Mulders
Jan 19 2010 hep-ph arXiv:1001.2977v2

@misc{1001.2977, author = {Ted C.~Rogers and Piet J.~Mulders}, title = {{N}o {G}eneralized {TMD}-{F}actorization in the {H}adro-{P}roduction of {H}igh {T}ransverse {M}omentum {H}adrons}, year = {2010}, eprint = {1001.2977}, howpublished = {Phys.Rev.D81:094006,2010}, doi = {10.1103/PhysRevD.81.094006}, note = {arXiv:1001.2977v2} }
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It has by now been established that standard QCD factorization using transverse momentum dependent parton distribution functions fails in hadro-production of nearly back-to-back hadrons with high transverse momentum. The essential problem is that gauge invariant transverse momentum dependent parton distribution functions cannot be defined with process-independent Wilson line operators, thus implying a breakdown of universality. This has led naturally to proposals that a correct approach is to instead use a type of "generalized" transverse momentum dependent factorization in which the basic factorized structure is assumed to remain valid, but with transverse momentum dependent parton distribution functions that contain non-standard, process dependent Wilson line structures. In other words, to recover a factorization formula, it has become common to assume that it is sufficient to simply modify the Wilson lines in the parton correlation functions for each separate hadron. In this paper, we will illustrate by direct counter-example that this is not possible in a non-Abelian gauge theory. Since a proof of generalized transverse momentum dependent factorization should apply generally to any hard hadro-production process, a single counter-example suffices to show that a general proof does not exist. Therefore, to make the counter-argument clear and explicit, we illustrate with a specific calculation for a double spin asymmetry in a spectator model with a non-Abelian gauge field. The observed breakdown of generalized transverse momentum dependent factorization challenges the notion that the role of parton transverse momentum in such processes can be described using separate correlation functions for each external hadron.
Multiple Hard Partonic Collisions with Correlations in Proton-Proton Scattering
T.C. Rogers, M. Strikman
Aug 04 2009 hep-ph arXiv:0908.0251v2

@misc{0908.0251, author = {T.C.~Rogers and M.~Strikman}, title = {{M}ultiple {H}ard {P}artonic {C}ollisions with {C}orrelations in {P}roton-{P}roton {S}cattering}, year = {2009}, eprint = {0908.0251}, howpublished = {Phys.Rev.D81:016013,2010}, doi = {10.1103/PhysRevD.81.016013}, note = {arXiv:0908.0251v2} }
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We propose a simple method for incorporating correlations into the impact parameter space description of multiple (semi-)hard partonic collisions in high energy hadron-hadron scattering. The perturbative QCD input is the standard factorization theorem for inclusive dijet production with a lower cutoff on transverse momentum. The width of the transverse distribution of hard partons is fixed by parameterizations of the two-gluon form factor. We then reconstruct the hard contribution to the total inelastic profile function and obtain corrections due to correlations to the more commonly used eikonal description. Estimates of the size of double correlation corrections are based on the rate of double collisions measured at the Tevatron. We find that, if typical values for the lower transverse momentum cutoff are used in the calculation of the inclusive hard dijet cross section, then the correlation corrections are necessary for maintaining consistency with expectations for the total inelastic proton-proton cross section at LHC energies.
Proceedings of the workshop: HERA and the LHC workshop series on the implications of HERA for LHC physics
H. Jung, A. De Roeck, Z. J. Ajaltouni, S. Albino, G. Altarelli, F. Ambroglini, J. Anderson, G. Antchev, M. Arneodo, P. Aspell, V. Avati, M. Bahr, A. Bacchetta, M. G. Bagliesi, R. D. Ball, A. Banfi, S. Baranov, P. Bartalini, J. Bartels, F. Bechtel, et al (249)
Mar 24 2009 hep-ph arXiv:0903.3861v2

@misc{0903.3861, author = {H.~Jung and A.~De Roeck and Z.~J.~Ajaltouni and S.~Albino and G.~Altarelli and F.~Ambroglini and J.~Anderson and G.~Antchev and M.~Arneodo and P.~Aspell and V.~Avati and M.~Bahr and A.~Bacchetta and M.~G.~Bagliesi and R.~D.~Ball and A.~Banfi and S.~Baranov and P.~Bartalini and J.~Bartels and F.~Bechtel and V.~Berardi and M.~Berretti and G.~Beuf and M.~Biasini and I.~Bierenbaum and J.~Blumlein and R.~E.~Blair and C.~Bombonati and M.~Boonekamp and U.~Bottigli and S.~Boutle and M.~Bozzo and E.~Brucken and J.~Bracinik and A.~Bruni and G.~E.~Bruno and A.~Buckley and A.~Bunyatyan and H.~Burkhardt and P.~Bussey and A.~Buzzo and M.~Cacciari and F.~Cafagna and M.~Calicchio and F.~Caola and M.~G.~Catanesi and P.~L.~Catastini and R.~Cecchi and F.~A.~Ceccopieri and S.~Cerci and S.~Chekanov and R.~Chierici and M.~Ciafaloni and M.~A.~Ciocci and V.~Coco and D.~Colferai and A.~Cooper-Sarkar and G.~Corcella and M.~Czakon and A.~Dainese and M.~Dasgupta and M.~Deak and M.~Deile and P.~A.~Delsart and L.~Del Debbio and A.~de Roeck and C.~Diaconu and M.~Diehl and E.~Dimovasili and M.~Dittmar and I.~M.~Dremin and K.~Eggert and R.~Engel and V.~Eremin and S.~Erhan and C.~Ewerz and L.~Fano and J.~Feltesse and G.~Ferrera and F.~Ferro and R.~Field and S.~Forte and F.~Garcia and A.~Geiser and F.~Gelis and S.~Giani and S.~Gieseke and M.~A.~Gigg and A.~Glazov and K.~Golec-Biernat and K.~Goulianos and J.~Grebenyuk and V.~Greco and D.~Grellscheid and G.~Grindhammer and M.~Grothe and A.~Guffanti and C.~Gwenlan and V.~Halyo and K.~Hamilton and F.~Hautmann and J.~Heino and G.~Heinrich and T.~Hilden and K.~Hiller and J.~Hollar and X.~Janssen and S.~Joseph and A.~W.~Jung and H.~Jung and V.~Juranek and J.~Kaspar and O.~Kepka and V.~A.~Khoze and Ch.~Kiesling and M.~Klasen and S.~Klein and B.~A.~Kniehl and A.~Knutsson and J.~Kopal and G.~Kramer and F.~Krauss and V.~Kundrat and K.~Kurvinen and K.~Kutak and L.~Lonnblad and S.~Lami and G.~Latino and J.~I.~Latorre and O.~Latunde-Dada and R.~Lauhakangas and V.~Lendermann and P.~Lenzi and G.~Li and A.~Likhoded and A.~Lipatov and E.~Lippmaa and M.~Lokajicek and M.~Lo Vetere and F.~Lucas Rodriguez and G.~Luisoni and E.~Lytken and K.~Muller and M.~Macri and G.~Magazzu and A.~Majhi and S.~Majhi and P.~Marage and L.~Marti and A.~D.~Martin and M.~Meucci and D.~A.~Milstead and S.~Minutoli and A.~Nischke and A.~Moares and S.~Moch and L.~Motyka and T.~Namsoo and P.~Newman and H.~Niewiadomski and C.~Nockles and E.~Noschis and G.~Notarnicola and J.~Nystrand and E.~Oliveri and F.~Oljemark and K.~Osterberg and R.~Orava and M.~Oriunno and S.~Osman and S.~Ostapchenko and P.~Palazzi and E.~Pedreschi and A.~V.~Pereira and H.~Perrey and J.~Petajajarvi and T.~Petersen and A.~Piccione and T.~Pierog and J.~L.~Pinfold and O.~I.~Piskounova and S.~Platzer and M.~Quinto and Z.~Rurikova and E.~Radermacher and V.~Radescu and E.~Radicioni and F.~Ravotti and G.~Rella and P.~Richardson and E.~Robutti and G.~Rodrigo and E.~Rodrigues and M.~Rogal and T.~C.~Rogers and J.~Rojo and P.~Roloff and L.~Ropelewski and C.~Rosemann and Ch.~Royon and G.~Ruggiero and A.~Rummel and M.~Ruspa and M.~G.~Ryskin and D.~Salek and W.~Slominski and H.~Saarikko and A.~Sabio Vera and T.~Sako and G.~P.~Salam and V.~A.~Saleev and C.~Sander and G.~Sanguinetti and A.~Santroni and Th.~Schorner-Sadenius and R.~Schicker and I.~Schienbein and W.~B.~Schmidke and F.~Schwennsen and A.~Scribano and G.~Sette and M.~H.~Seymour and A.~Sherstnev and T.~Sjostrand and W.~Snoeys and G.~Somogyi and L.~Sonnenschein and G.~Soyez and H.~Spiesberger and F.~Spinella and P.~Squillacioti and A.~M.~Stasto and A.~Starodumov and H.~Stenzel and Ph.~Stephens and A.~Ster and D.~Stocco and M.~Strikman and C.~Taylor and T.~Teubner and R.~S.~Thorne and Z.~Trocsanyi and M.~Treccani and D.~Treleani and L.~Trentadue and A.~Trummal and J.~Tully and W.~K.~Tung and M.~Turcato and N.~Turini and M.~Ubiali and A.~Valkarova and A.~van Hameren and P.~Van Mechelen and J.~A.~M.~Vermaseren and A.~Vogt and B.~F.~L.~Ward and G.~Watt and B.~R.~Webber and Ch.~Weiss and Ch.~White and J.~Whitmore and R.~Wolf and J.~Wu and A.~Yagues-Molina and S.~A.~Yost and G.~Zanderighi and N.~Zotov and M.~zur Nedden}, title = {{P}roceedings of the workshop: {HERA} and the {LHC} workshop series on the implications of {HERA} for {LHC} physics}, year = {2009}, eprint = {0903.3861}, note = {arXiv:0903.3861v2} }
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2nd workshop on the implications of HERA for LHC physics. Working groups: Parton Density Functions Multi-jet final states and energy flows Heavy quarks (charm and beauty) Diffraction Cosmic Rays Monte Carlos and Tools
Next-to-Leading Order Hard Scattering Using Fully Unintegrated Parton Distribution Functions
Ted C. Rogers
Jul 16 2008 hep-ph arXiv:0807.2430v2

@misc{0807.2430, author = {Ted C.~Rogers}, title = {{N}ext-to-{L}eading {O}rder {H}ard {S}cattering {U}sing {F}ully {U}nintegrated {P}arton {D}istribution {F}unctions}, year = {2008}, eprint = {0807.2430}, howpublished = {Phys.Rev.D78:074018,2008}, doi = {10.1103/PhysRevD.78.074018}, note = {arXiv:0807.2430v2} }
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We calculate the next-to-leading order fully unintegrated hard scattering coefficient for unpolarized gluon-induced deep inelastic scattering using the logical framework of parton correlation functions developed in previous work. In our approach, exact four-momentum conservation is maintained throughout the calculation. Hence, all non-perturbative functions, like parton distribution functions, depend on all components of parton four-momentum. In contrast to the usual collinear factorization approach where the hard scattering coefficient involves generalized functions (such as Dirac $\delta$-functions), the fully unintegrated hard scattering coefficient is an ordinary function. Gluon-induced deep inelastic scattering provides a simple illustration of the application of the fully unintegrated factorization formalism with a non-trivial hard scattering coefficient, applied to a phenomenologically interesting case. Furthermore, the gluon-induced process allows for a parameterization of the fully unintegrated gluon distribution function.
The Gluon Distribution Function and Factorization in Feynman Gauge
J. C. Collins, T. C. Rogers
May 14 2008 hep-ph arXiv:0805.1752v2

@misc{0805.1752, author = {J.~C.~Collins and T.~C.~Rogers}, title = {{T}he {G}luon {D}istribution {F}unction and {F}actorization in {F}eynman {G}auge}, year = {2008}, eprint = {0805.1752}, howpublished = {Phys.Rev.D78:054012,2008}, doi = {10.1103/PhysRevD.78.054012}, note = {arXiv:0805.1752v2} }
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A complication in proving factorization theorems in Feynman gauge is that individual graphs give a super-leading power of the hard scale when all the gluons inducing the hard scattering are longitudinally polarized. With the aid of an example in gluon-mediated deep inelastic scattering, we show that, although the super-leading terms cancel after a sum over graphs, there is a residual non-zero leading term from longitudinally polarized gluons. This is due to the non-zero transverse momenta of the gluons in the target. The non-cancellation, due to the non-Abelian property of the gauge group, is necessary to obtain the correct form of the gluon distribution function as a gauge-invariant matrix element.
Unitarity Constraints on Semi-hard Jet Production in Impact Parameter Space
T.C. Rogers, A.M. Stasto, M. I. Strikman
Jan 02 2008 hep-ph arXiv:0801.0303v1

@misc{0801.0303, author = {T.C.~Rogers and A.M.~Stasto and M.~I.~Strikman}, title = {{U}nitarity {C}onstraints on {S}emi-hard {J}et {P}roduction in {I}mpact {P}arameter {S}pace}, year = {2008}, eprint = {0801.0303}, howpublished = {Phys.Rev.D77:114009,2008}, doi = {10.1103/PhysRevD.77.114009}, note = {arXiv:0801.0303v1} }
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The perturbative QCD formula for minijet production consitutes an important ingredient in models describing the total cross section and multiparticle production in hadron-hadron scattering at high energies. Using arguments based on s-channel unitarity we set bounds on the minimum value of p_T for which the leading twist minijet formula can be used. For large impact parameters where correlations between partons appear to be small we find that the minimum value of p_T should be greater than 2.5 GeV for LHC energies and greater than 3.5 GeV for cosmic ray energies of about 50 TeV. We also argue that for collisions with values of impact parameters typical for heavy particle production the values of minimum p_T are likely to be considerably larger. We also analyze and quantify the potential role of saturation effects in the gluon density. We find that although saturation effects alone are not sufficient to restore unitarity, they are likely to play an important role at LHC energies.
Parton correlation functions and factorization in deep inelastic scattering
T. C. Rogers
Dec 10 2007 hep-ph arXiv:0712.1195v1

@misc{0712.1195, author = {T.~C.~Rogers}, title = {{P}arton correlation functions and factorization in deep inelastic scattering}, year = {2007}, eprint = {0712.1195}, howpublished = {PoSRADCOR2007:031,2007}, note = {arXiv:0712.1195v1} }
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We outline the basic properties of a pertubative QCD factorization formalism that maintains exact over-all kinematics in both the initial and final states. Such a treatment requires the use of non-perturbative factors that depend on all components of parton four-momentum. These objects are referred to as parton correlation functions. We describe the complications faced in defining parton correlation functions and discuss recent progress. Emphasis is placed on the need for precise operator definitions in a complete derivation of factorization.
Fully Unintegrated Parton Correlation Functions and Factorization in Lowest Order Hard Scattering
J.C. Collins, T.C. Rogers, A.M. Staśto
Aug 22 2007 hep-ph arXiv:0708.2833v2

@misc{0708.2833, author = {J.C.~Collins and T.C.~Rogers and A.M.~Staśto}, title = {{F}ully {U}nintegrated {P}arton {C}orrelation {F}unctions and {F}actorization in {L}owest {O}rder {H}ard {S}cattering}, year = {2007}, eprint = {0708.2833}, howpublished = {Phys.Rev.D77:085009,2008}, doi = {10.1103/PhysRevD.77.085009}, note = {arXiv:0708.2833v2} }
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Motivated by the need to correct the potentially large kinematic errors in approximations used in the standard formulation of perturbative QCD, we reformulate deeply inelastic lepton-proton scattering in terms of gauge invariant, universal parton correlation functions which depend on all components of parton four-momentum. Currently, different hard QCD processes are described by very different perturbative formalisms, each relying on its own set of kinematical approximations. In this paper we show how to set up formalism that avoids approximations on final-state momenta, and thus has a very general domain of applicability. The use of exact kinematics introduces a number of significant conceptual shifts already at leading order, and tightly constrains the formalism. We show how to define parton correlation functions that generalize the concepts of parton density, fragmentation function, and soft factor. After setting up a general subtraction formalism, we obtain a factorization theorem. To avoid complications with Ward identities the full derivation is restricted to abelian gauge theories; even so the resulting structure is highly suggestive of a similar treatment for non-abelian gauge theories.
Coherent Vector Meson Photo-Production from Deuterium at Intermediate Energies
T.C. Rogers, M.M. Sargsian, M.I. Strikman
Sep 13 2005 hep-ph arXiv:hep-ph/0509101v4

@misc{hep-ph/0509101, author = {T.C.~Rogers and M.M.~Sargsian and M.I.~Strikman}, title = {{C}oherent {V}ector {M}eson {P}hoto-{P}roduction from {D}euterium at {I}ntermediate {E}nergies}, year = {2005}, eprint = {hep-ph/0509101}, howpublished = {Phys.Rev.C73:045202,2006}, doi = {10.1103/PhysRevC.73.045202}, note = {arXiv:hep-ph/0509101v4} }
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We analyze the cross section for vector meson photo-production off a deuteron for the intermediate range of photon energies starting at a few GeVs above the threshold and higher. We reproduce the steps in the derivation of the conventional non-relativistic Glauber expression based on an effective diagrammatic method while making corrections for Fermi motion and intermediate energy kinematic effects. We show that, for intermediate energy vector meson production, the usual Glauber factorization breaks down and we derive corrections to the usual Glauber method to linear order in longitudinal nucleon momentum. The purpose of our analysis is to establish methods for probing interesting physics in the production mechanism for phi-mesons and heavier vector mesons. We demonstrate how neglecting the breakdown of Glauber factorization can lead to errors in measurements of basic cross sections extracted from nuclear data.
The Black Body Limit in Deep Inelastic Scattering
T.C. Rogers, M.I. Strikman
Oct 06 2004 hep-ph arXiv:hep-ph/0410070v2

@misc{hep-ph/0410070, author = {T.C.~Rogers and M.I.~Strikman}, title = {{T}he {B}lack {B}ody {L}imit in {D}eep {I}nelastic {S}cattering}, year = {2004}, eprint = {hep-ph/0410070}, note = {arXiv:hep-ph/0410070v2} }
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We use information from DIS and the two gluon nucleon form factor to estimate the impact parameter amplitude of hadronic configurations in the dipole model of DIS. We demonstrate that only a small fraction of the total $\gamma^{\ast}N$ cross section at $x\sim 10^{-4}$ is due to scattering that occurs near the black body limit. We also make comparisons with other models and we point out that a quark mass of $\lesssim 100$ MeV leads to a strong variation of the the $t$-dependence with $Q^{2}$.
Determining the Proximity of \Gamma^∗ N Scattering to the Black Body Limit Using DIS and J/ \psi Production
T. Rogers, V. Guzey, M. Strikman, X. Zu
Sep 10 2003 hep-ph arXiv:hep-ph/0309099v3

@misc{hep-ph/0309099, author = {T.~Rogers and V.~Guzey and M.~Strikman and X.~Zu}, title = {{D}etermining the {P}roximity of \{G}amma^∗ {N} {S}cattering to the {B}lack {B}ody {L}imit {U}sing {DIS} and {J}/ \psi {P}roduction}, year = {2003}, eprint = {hep-ph/0309099}, howpublished = {Phys.Rev. D69 (2004) 074011}, doi = {10.1103/PhysRevD.69.074011}, note = {arXiv:hep-ph/0309099v3} }
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We use information about DIS and $J/ \psi$ production on hydrogen to model the $t$-dependence of the $\gamma^{\ast} N$ scattering amplitude. We investigate the profile function for elastic scattering of hadronic components of the virtual photon off both a nucleon and heavy nuclear target, and we estimate the value of the impact parameter where the black body limit is reached. We also estimate the fraction of the cross section that is due to hadronic configurations in the virtual photon wave function that approach the unitarity limit. We extract, from these considerations, approximate lower limits on the values of $x$ where the leading twist approximation in DIS is violated. We observe that the black body limit may be approached within HERA kinematics with $Q^{2}$ equal to a few GeV$^2$ and $x \sim 10^{-4}$. Comparisons are made with earlier predictions by Munier \it et al., and the longitudinal structure function is compared with preliminary HERA data. The principle advantage of our method is that we do not rely solely on the $t$-dependence of $\rho$-meson production data. This allows us to extend our analysis down to very small impact parameters and dipole sizes. Finally, we perform a similar calculation with a $^{208}$Pb target, and we demonstrate that the black body limit is already approached at $Q^{2} \sim 20$ GeV$^{2}$ and $x \sim 10^{-4}$.