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Baryon washout, electroweak phase transition, and perturbation theory

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Abstract

We analyze the conventional perturbative treatment of sphaleron-induced baryon number washout relevant for electroweak baryogenesis and show that it is not gauge-independent due to the failure of consistently implementing the Nielsen identities order-byorder in perturbation theory. We provide a gauge-independent criterion for baryon number preservation in place of the conventional (gauge-dependent) criterion needed for successful electroweak baryogenesis. We also review the arguments leading to the preservation criterion and analyze several sources of theoretical uncertainties in obtaining a numerical bound. In various beyond the standard model scenarios, a realistic perturbative treatment will likely require knowledge of the complete two-loop finite temperature effective potential and the one-loop sphaleron rate.

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References

  1. E.H. Fradkin and S.H. Shenker, Phase Diagrams of Lattice Gauge Theories with Higgs Fields, Phys. Rev. D 19 (1979) 3682 [SPIRES].

    ADS  Google Scholar 

  2. J. Ambjorn, T. Askgaard, H. Porter and M.E. Shaposhnikov, Lattice simulations of electroweak sphaleron transitions in real time, Phys. Lett. B 244 (1990) 479 [SPIRES].

    ADS  Google Scholar 

  3. K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, A Nonperturbative analysis of the finite T phase transition in SU(2) × U(1) electroweak theory, Nucl. Phys. B 493 (1997) 413 [hep-lat/9612006] [SPIRES].

    Article  ADS  Google Scholar 

  4. K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, Is there a hot electroweak phase transition at m(H) larger or equal to m(W)?, Phys. Rev. Lett. 77 (1996) 2887 [hep-ph/9605288] [SPIRES].

    Article  ADS  Google Scholar 

  5. F. Csikor, Z. Fodor and J. Heitger, Endpoint of the hot electroweak phase transition, Phys. Rev. Lett. 82 (1999) 21 [hep-ph/9809291] [SPIRES].

    Article  ADS  Google Scholar 

  6. Y. Aoki, F. Csikor, Z. Fodor and A. Ukawa, The endpoint of the first-order phase transition of the SU(2) gauge-Higgs model on a 4-dimensional isotropic lattice, Phys. Rev. D 60 (1999) 013001 [hep-lat/9901021] [SPIRES].

    ADS  Google Scholar 

  7. G.D. Moore, Measuring the broken phase sphaleron rate nonperturbatively, Phys. Rev. D 59 (1999) 0144503 [hep-ph/9805264] [SPIRES].

    ADS  Google Scholar 

  8. LEP Working Group for Higgs boson searches collaboration, R. Barate et al., Search for the standard model Higgs boson at LEP, Phys. Lett. B 565 (2003) 61 [hep-ex/0306033] [SPIRES].

    Google Scholar 

  9. M. Quirós, Finite temperature field theory and phase transitions, hep-ph/9901312 [SPIRES].

  10. S.J. Huber, P. John and M.G. Schmidt, Bubble walls, CP-violation and electroweak baryogenesis in the MSSM, Eur. Phys. J. C 20 (2001) 695 [hep-ph/0101249] [SPIRES].

    Article  ADS  Google Scholar 

  11. M. Carena, G. Nardini, M. Quirós and C.E.M. Wagner, The Baryogenesis Window in the MSSM, Nucl. Phys. B 812 (2009) 243 [arXiv:0809.3760] [SPIRES].

    Article  ADS  Google Scholar 

  12. J. Kang, P. Langacker, T.-j. Li and T. Liu, Electroweak baryogenesis in a supersymmetric U(1) -prime model, Phys. Rev. Lett. 94 (2005) 061801 [hep-ph/0402086] [SPIRES].

    Article  ADS  Google Scholar 

  13. D.J.H. Chung and A.J. Long, Electroweak Phase Transition in the munuSSM, Phys. Rev. D 81 (2010) 123531 [arXiv:1004.0942] [SPIRES].

    ADS  Google Scholar 

  14. K. Funakubo and E. Senaha, Electroweak phase transition, critical bubbles and sphaleron decoupling condition in the MSSM, Phys. Rev. D 79 (2009) 115024 [arXiv:0905.2022] [SPIRES].

    ADS  Google Scholar 

  15. C.-W. Chiang and E. Senaha, Electroweak phase transitions in the secluded U(1)-prime-extended MSSM, JHEP 06 (2010) 030 [arXiv:0912.5069] [SPIRES].

    Article  ADS  Google Scholar 

  16. S. Profumo, M.J. Ramsey-Musolf and G. Shaughnessy, Singlet Higgs Phenomenology and the Electroweak Phase Transition, JHEP 08 (2007) 010 [arXiv:0705.2425] [SPIRES].

    Article  ADS  Google Scholar 

  17. S.W. Ham and S.K. Oh, Electroweak phase transition and Higgs self-couplings in the two-Higgs-doublet model, hep-ph/0502116 [SPIRES].

  18. S.W. Ham, S.-A. Shim and S.K. Oh, Electroweak phase transition in an extension of the standard model with scalar color octet, Phys. Rev. D 81 (2010) 055015 [arXiv:1002.0237] [SPIRES].

    ADS  Google Scholar 

  19. M. Laine and K. Rummukainen, The MSSM electroweak phase transition on the lattice, Nucl. Phys. B 535 (1998) 423 [hep-lat/9804019] [SPIRES].

    Article  ADS  Google Scholar 

  20. F. Csikor et al., Electroweak phase transition in the MSSM: 4-dimensional lattice simulations, Phys. Rev. Lett. 85 (2000) 932 [hep-ph/0001087] [SPIRES].

    Article  ADS  Google Scholar 

  21. G.D. Moore and M. Tassler, The Sphaleron Rate in SU(N) Gauge Theory, JHEP 02 (2011) 105 [arXiv:1011.1167] [SPIRES].

    Article  ADS  Google Scholar 

  22. H.A. Kramers, Brownian motion in a field of force and the diffusion model of chemical re actions, Physica 7 (1940) 284 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. L. Carson, X. Li, L.D. McLerran and R.-T. Wang, Exact Computation Of The Small Fluctuation Determinant Around A Sphaleron, Phys. Rev. D 42 (1990) 2127 [SPIRES].

    ADS  Google Scholar 

  24. J. Baacke and S. Junker, Quantum fluctuations around the electroweak sphaleron, Phys. Rev. D 49 (1994) 2055 [hep-ph/9308310] [SPIRES].

    ADS  Google Scholar 

  25. J. Baacke and S. Junker, Quantum fluctuations of the electroweak sphaleron: Erratum and addendum, Phys. Rev. D 50 (1994) 4227 [hep-th/9402078] [SPIRES].

    ADS  Google Scholar 

  26. L. Dolan and R. Jackiw, Symmetry Behavior at Finite Temperature, Phys. Rev. D 9 (1974) 3320 [SPIRES].

    ADS  Google Scholar 

  27. N.K. Nielsen, On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories, Nucl. Phys. B 101 (1975) 173 [SPIRES].

    Article  ADS  Google Scholar 

  28. M.E. Shaposhnikov, Baryon Asymmetry of the Universe in Standard Electroweak Theory, Nucl. Phys. B 287 (1987) 757 [SPIRES].

    Article  ADS  Google Scholar 

  29. M. Dine, P. Huet, R.L. Singleton, Jr and L. Susskind, Creating the baryon asymmetry at the electroweak phase transition, Phys. Lett. B 257 (1991) 351 [SPIRES].

    ADS  Google Scholar 

  30. D.J.H. Chung, B. Garbrecht, M.J. Ramsey-Musolf and S. Tulin, Supergauge interactions and electroweak baryogenesis, JHEP 12 (2009) 067 [arXiv:0908.2187] [SPIRES].

    Article  ADS  Google Scholar 

  31. S. Weinberg, Perturbative Calculations of Symmetry Breaking, Phys. Rev. D 7 (1973) 2887 [SPIRES].

    ADS  Google Scholar 

  32. R. Jackiw, Functional evaluation of the effective potential, Phys. Rev. D 9 (1974) 1686 [SPIRES].

    ADS  Google Scholar 

  33. L. Dolan and R. Jackiw, Gauge invariant signal for gauge symmetry breaking, Phys. Rev. D 9 (1974) 2904 [SPIRES].

    ADS  Google Scholar 

  34. R. Fukuda and T. Kugo, Gauge Invariance in the Effective Action and Potential, Phys. Rev. D 13 (1976) 3469 [SPIRES].

    ADS  Google Scholar 

  35. C. Delaunay, C. Grojean and J.D. Wells, Dynamics of Non-renormalizable Electroweak Symmetry Breaking, JHEP 04 (2008) 029 [arXiv:0711.2511] [SPIRES].

    Article  ADS  Google Scholar 

  36. C.W. Bernard, Feynman Rules for Gauge Theories at Finite Temperature, Phys. Rev. D 9 (1974) 3312 [SPIRES].

    ADS  Google Scholar 

  37. G.W. Anderson and L.J. Hall, The Electroweak phase transition and baryogenesis, Phys. Rev. D 45 (1992) 2685 [SPIRES].

    ADS  Google Scholar 

  38. E. Braaten and R.D. Pisarski, Resummation and Gauge Invariance of the Gluon Damping Rate in Hot QCD, Phys. Rev. Lett. 64 (1990) 1338 [SPIRES].

    Article  ADS  Google Scholar 

  39. G. Thompson and H.-L. Yu, Gauge Covariance Of The Effective Potential, Phys. Rev. D 31 (1985) 2141 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  40. M. Laine, Gauge dependence of the high temperature two loop effective potential for the Higgs field, Phys. Rev. D 51 (1995) 4525 [hep-ph/9411252] [SPIRES].

    ADS  Google Scholar 

  41. A.D. Linde, Phase Transitions in Gauge Theories and Cosmology, Rept. Prog. Phys. 42 (1979) 389 [SPIRES].

    Article  ADS  Google Scholar 

  42. D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and Instantons at Finite Temperature, Rev. Mod. Phys. 53 (1981) 43 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. K. Farakos, K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, 3 − D physics and the electroweak phase transition: Perturbation theory, Nucl. Phys. B 425 (1994) 67 [hep-ph/9404201] [SPIRES].

    Article  ADS  Google Scholar 

  44. A. Jakovac and A. Patkos, Finite temperature reduction of the SU(2) Higgs model with complete static background, Phys. Lett. B 334 (1994) 391 [hep-ph/9405424] [SPIRES].

    ADS  Google Scholar 

  45. Z. Fodor and A. Hebecker, Finite temperature effective potential to order g 4 , λ2 and the electroweak phase transition, Nucl. Phys. B 432 (1994) 127 [hep-ph/9403219] [SPIRES].

    Article  ADS  Google Scholar 

  46. P.B. Arnold and L.D. McLerran, Sphalerons, Small Fluctuations and Baryon Number Violation in Electroweak Theory, Phys. Rev. D 36 (1987) 581 [SPIRES].

    ADS  Google Scholar 

  47. L. Carson and L.D. McLerran, Approximate computation of the small-fluctuation determinant around a sphaleron, Phys. Rev. D 41 (1990) 647 [SPIRES].

    ADS  Google Scholar 

  48. F.R. Klinkhamer and N.S. Manton, A Saddle Point Solution in the Weinberg-Salam Theory, Phys. Rev. D 30 (1984) 2212 [SPIRES].

    ADS  Google Scholar 

  49. A. Strumia and N. Tetradis, A consistent calculation of bubble-nucleation rates, Nucl. Phys. B 542 (1999) 719 [hep-ph/9806453] [SPIRES].

    Article  ADS  Google Scholar 

  50. V. Cirigliano, Y. Li, S. Profumo and M.J. Ramsey-Musolf, MSSM Baryogenesis and Electric Dipole Moments: An Update on the Phenomenology, JHEP 01 (2010) 002 [arXiv:0910.4589] [SPIRES].

    Article  ADS  Google Scholar 

  51. F. Csikor, Z. Fodor and J. Heitger, Where does the hot electroweak phase transition end?, Nucl. Phys. Proc. Suppl. 73 (1999) 659 [hep-ph/9809293] [SPIRES].

    Article  ADS  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, WI, 53706, U.S.A.

    Hiren H. Patel & Michael J. Ramsey-Musolf

  2. Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, CA, 91125, U.S.A.

    Michael J. Ramsey-Musolf

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  1. Hiren H. Patel
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Correspondence to Hiren H. Patel.

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ArXiv ePrint: 1101.4665

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Patel, H.H., Ramsey-Musolf, M.J. Baryon washout, electroweak phase transition, and perturbation theory. J. High Energ. Phys. 2011, 29 (2011). https://doi.org/10.1007/JHEP07(2011)029

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