Massive on-shell supersymmetric scattering amplitudes. (English) Zbl 1427.81168
Summary: We introduce a manifestly little group covariant on-shell superspace for massive particles in four dimensions using the massive spinor helicity formalism. This enables us to construct massive on-shell superfields and fully utilize on-shell symmetry considerations to derive all possible \(\mathcal{N} = 1\) three-particle amplitudes for particles of spin as high as one, as well as some simple amplitudes for particles of any spin. Throughout, the conceptual and computational simplicity of this approach is exhibited.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
References:
| [1] | Cohen, T.; Elvang, H.; Kiermaier, M., On-shell constructibility of tree amplitudes in general field theories, JHEP, 04, 053 (2011) · Zbl 1250.81072 · doi:10.1007/JHEP04(2011)053 |
| [2] | Conde, E.; Marzolla, A., Lorentz Constraints on Massive Three-Point Amplitudes, JHEP, 09, 041 (2016) · Zbl 1390.81626 · doi:10.1007/JHEP09(2016)041 |
| [3] | Schwinn, C.; Weinzierl, S., SUSY ward identities for multi-gluon helicity amplitudes with massive quarks, JHEP, 03, 030 (2006) · Zbl 1226.81142 · doi:10.1088/1126-6708/2006/03/030 |
| [4] | Kleiss, R.; Stirling, WJ, Spinor Techniques for Calculating pp → w^±/Z^0+Jets, Nucl. Phys., B 262, 235 (1985) · doi:10.1016/0550-3213(85)90285-8 |
| [5] | Dittmaier, S., Weyl-van der Waerden formalism/or helicity amplitudes of massive particles, Phys. Rev., D 59, 016007 (1998) |
| [6] | N. Arkani-Hamed, T.-C. Huang and Y.-t. Huang, Scattering Amplitudes For All Masses and Spins,arXiv: 1709.04891 [INSPIRE]. · Zbl 1521.81418 |
| [7] | Shadmi, Y.; Weiss, Y., Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons, JHEP, 02, 165 (2019) · doi:10.1007/JHEP02(2019)165 |
| [8] | H. Elvang and Y. t. Huang, Scattering Amplitudes, to be published by Cambridge University Press, Cambridge U.S.A. (2015), arXiv:1308 . 1697 [INSPIRE]. · Zbl 1332.81010 |
| [9] | Boels, RH; Schwinn, C., On-shell supersymmetry for massive multiplets, Phys. Rev., D 84, 065006 (2011) |
| [10] | M. Srednicki, Quantum field theory, Cambridge University Press, Cambridge U.S.A. (2007). · Zbl 1113.81002 · doi:10.1017/CBO9780511813917 |
| [11] | J. Wess and J. Bagger, Supersymmetry and supergravity, Princeton University Press, Princeton U.S.A. (1992). · Zbl 0516.53060 |
| [12] | Ferrara, S.; Savoy, CA; Zumino, B., General Massive Multiplets in Extended Supersymmetry, Phys. Lett., B 100, 393 (1981) · doi:10.1016/0370-2693(81)90144-1 |
| [13] | Fayet, P., Spontaneous Generation of Massive Multiplets and Central Charges in Extended Supersymmetric Theories, Nucl. Phys., B 149, 137 (1979) · doi:10.1016/0550-3213(79)90162-7 |
| [14] | A. Herderschee, S. Koren and T. Trott, Constructing \(\mathcal{N} = 4\) Coulomb branch superamplitudes, JHEP08 (2019) 107 [arXiv: 1902 . 07205] [ inSPIRE]. · Zbl 1421.81149 |
| [15] | Caron-Huot, S.; Zahraee, Z., Integrability of Black Hole Orbits in Ma ximal Supergravity, JHEP, 07, 179 (2019) · Zbl 1418.83068 · doi:10.1007/JHEP07(2019)179 |
| [16] | Elvang, H.; Huang, Y-t; Peng, C., On-shell superamplitudes in N < 4 SYM, JHEP, 09, 031 (2011) · Zbl 1301.81120 · doi:10.1007/JHEP09(2011)031 |
| [17] | Nair, VP, A Current Algebra for Some Gauge Theory Amplitudes, Phys. Lett., B 214, 215 (1988) · doi:10.1016/0370-2693(88)91471-2 |
| [18] | Witten, E., Perturbativ e gauge theory as a string theory in twistor space, Commun. Math. Phys., 252, 189 (2004) · Zbl 1105.81061 · doi:10.1007/s00220-004-1187-3 |
| [19] | N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory ?, JHEP09 (2010) 016 [arXiv:0808.1446] [ inSPIRE]. · Zbl 1291.81356 |
| [20] | Drummond, JM; Henn, J.; Korchemsky, GP; Sokatchev, E., Dual superconformal symmetry of scatt ering amplitudes in \(\mathcal{N} = 4\) super- Yang-Mills theory, Nucl. Phys., B 828, 317 (2010) · Zbl 1203.81112 · doi:10.1016/j.nuclphysb.2009.11.022 |
| [21] | A. Brandhuber, P. Heslop and G. Travaglini, A Note on dual superconformal symmetry of the \(\mathcal{N} = 4\) super Yang-Mills S-matrix, Phys. Rev.D 78 (2008) 125005 [arXiv:0807 . 4097] [INSPIRE]. · Zbl 1273.81201 |
| [22] | J.M. Drummond and J.M. Henn, All tree-level amplitudes in \(\mathcal{N} = 4\) SYM, JHEP04 (2009) 018 [arXiv:0808.2475] [ inSPIRE]. |
| [23] | S. He and T. McLoughlin, On All-loop Integrands of Scattering Amplitudes in Planar \(\mathcal{N} = 4\) SYM, JHEP 02 (2011) 116 [arXiv:1010.6256] [ inSPIRE]. · Zbl 1294.81111 |
| [24] | Arkani-Hamed, N.; Bourjaily, JL; Cachazo, F.; Caron-Huot, S.; Trnka, J., The All-Loop Integrand For Scattering Amplitudes in Planar \(\mathcal{N} = 4\) SYM, JHEP, 01, 041 (2011) · Zbl 1214.81141 · doi:10.1007/JHEP01(2011)041 |
| [25] | Cachazo, F.; Guevara, A.; Heydeman, M.; Mizera, S.; Schwarz, JH; Wen, C., The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps, JHEP, 09, 125 (2018) · Zbl 1398.81255 · doi:10.1007/JHEP09(2018)125 |
| [26] | Elvang, H.; Freedman, DZ; Kiermaier, M., Solution to the Ward Identities forSuperamplitudes, JHEP, 10, 103 (2010) · Zbl 1291.81243 · doi:10.1007/JHEP10(2010)103 |
| [27] | H.K. Dreiner, H.E. Haber and S.P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept. 494 (2010) 1 [arXiv: 0812 .1594] [inSPIRE]. |
| [28] | S. Weinberg, The quantum theory of fields. Volume 3: Supersymmetry, Cambridge University Press, Cambridge U.S.A. (2013). · Zbl 1264.81010 |
| [29] | J.M. Cornwall, D.N. Levin and G. Tiktopoulos, Derivation of Gauge Invariance from High-Energy Unitarity Bounds on the S Matrix, Phys. Rev. D 10 (1974) 1145 [ Erratum ibid. D 11 (1975) 972] [inSPIRE]. |
| [30] | S.L. Adler, Collinearity constraints for on-shell massless particle three-point functions and implications for allowed-forbidden n + 1-point functions, Phys. Rev. D 93 (2016) 065028 [arXiv: 1602 .05060] [inSPIRE]. |
| [31] | McGady, DA; Rodina, L., Higher-spin massless S-matrices in four-dimensions, Phys. Rev., D 90, 084048 (2014) |
| [32] | Ferrara, S.; Remiddi, E., Absence of the Anomalous Magnetic Moment in a Supersymmetric Abelian Gauge Theory, Phys. Lett., B 53, 347 (1974) · doi:10.1016/0370-2693(74)90399-2 |
| [33] | Schuster, PC; Toro, N., Constructing the Tree-Level Yang-Mills S-matrix Using Complex Factorization, JHEP, 06, 079 (2009) · doi:10.1088/1126-6708/2009/06/079 |
| [34] | L. Andrianopoli, S. Ferrara and M.A. Lled6, Axion gauge symmetries and generalized Chern-Simons terms in \(\mathcal{N} = 1\) supersymmetric theories, JHEP 04 (2004) 005 [hep-th/0402142] [inSPIRE]. |
| [35] | Anastasopoulos, P.; Bianchi, M.; Dudas, E.; Kiritsis, E., Anomalies, anomalous U(1)’s and generalized Chern-Simons terms, JHEP, 11, 057 (2006) · doi:10.1088/1126-6708/2006/11/057 |
| [36] | Anastasopoulos, P.; Fucito, F.; Lionetto, A.; Pradisi, G.; Racioppi, A.; Stanev, YS, Minimal Anomalous U(1)’ Extension of the MSSM, Phys. Rev., D 78, 085014 (2008) |
| [37] | Ferrara, S.; Porrati, M.; Telegdi, VL, g = 2 as the natural value of the tree-level gyromagnetic ratio of elementary particles, Phys. Rev., D 46, 3529 (1992) |
| [38] | Guevara, A., Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering, JHEP, 04, 033 (2019) · Zbl 1415.81107 · doi:10.1007/JHEP04(2019)033 |
| [39] | K. Hagiwara, R.D. Peccei, D. Zeppenfeld and K. Hikasa, Probing the Weak Boson Sector in e^+e^- → w^+w^-, Nucl. Phys. B 282 (1987) 253 [INSPIRE]. |
| [40] | P. Benincasa and F. Cachazo, Consistency Conditions on the S-matrix of Massless Particles,arXiv:0705.4305 [inSPIRE]. |
| [41] | H. Elvang, M. Hadjiantonis, C.R.T. Jones and S. Paranjape, Soft Bootstrap and Supersymmetry, JHEP01 (2019) 195 [arXiv: 1806 .06079] [INSPIRE]. · Zbl 1409.81146 |
| [42] | Chung, M-Z; Huang, Y-t; Kim, J-W; Lee, S., The simplest massive S-matrix: from minimal coupling to Black Holes, JHEP, 04, 156 (2019) · Zbl 1415.83014 · doi:10.1007/JHEP04(2019)156 |
| [43] | A. Guevara, A. Ochirov and J. Vines, Scattering of Spinning Black Holes from Exponentiated Soft Factors,arXiv: 1812.06895 [INSPIRE]. · Zbl 1423.83030 |
| [44] | Plefka, J.; Schuster, T.; Verschinin, V., From Six to Four and More: Massless and Massive Maximal Super Yang-Mills Amplitudes in 6d and 4d and their Hidden Symmetries, JHEP, 01, 098 (2015) · doi:10.1007/JHEP01(2015)098 |
| [45] | Georgi, H., Lie algebras in particle physics, Front. Phys., 54, 1 (1999) |
| [46] | Mangano, ML; Parke, SJ, Multiparton amplitudes in gauge theories, Phys. Rept., 200, 301 (1991) · doi:10.1016/0370-1573(91)90091-Y |
| [47] | Schwinn, C.; Weinzierl, S., On-shell recursion relations for all Born QCD amplitudes, JHEP, 04, 072 (2007) · doi:10.1088/1126-6708/2007/04/072 |
| [48] | Ochirov, A., Helicity amplitudes for QCD with massive quarks, JHEP, 04, 089 (2018) · doi:10.1007/JHEP04(2018)089 |
| [49] | Badger, SD; Glover, EWN; Khoze, VV; Svrcek, P., Recursion relations for gauge theory amplitudes with massive particles, JHEP, 07, 025 (2005) · doi:10.1088/1126-6708/2005/07/025 |
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