Skip to main content
SpringerLink
Log in

Real-time fermions for baryogenesis simulations

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study how to numerically simulate quantum fermions out of thermal equilibrium, in the context of electroweak baryogenesis. We find that by combining the lattice implementation of Aarts and Smit [1] with the “low cost” fermions of Borsanyi and Hind-marsh [2], we are able to describe the dynamics of a classical bosonic system coupled to quantum fermions, that correctly reproduces anomalous baryon number violation. To demonstrate the method, we apply it to the 1 + 1 dimensional axial U(1) model, and perform simulations of a fast symmetry breaking transition. Compared to solving all the quantum mode equations as in [1], we find that this statistical approach may lead to a significant gain in computational time, when applied to 3 + 1dimensionalphysics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Aarts and J. Smit, Real-time dynamics with fermions on a lattice, Nucl. Phys. B 555 (1999) 355 [hep-ph/9812413] [SPIRES].

    Article  ADS  Google Scholar 

  2. S. Borsányi and M. Hindmarsh, Low-cost fermions in classical field simulations, Phys. Rev. D 79 (2009) 065010 [arXiv:0809.4711] [SPIRES].

    ADS  Google Scholar 

  3. V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe, Phys. Lett. B 155 (1985) 36 [SPIRES].

    ADS  Google Scholar 

  4. A.G. Cohen, D.B. Kaplan and A.E. Nelson, Progress in electroweak baryogenesis, Ann. Rev. Nucl. Part. Sci. 43 (1993) 27 [hep-ph/9302210] [SPIRES].

    Article  ADS  Google Scholar 

  5. G.D. Moore and K. Rummukainen, Classical sphaleron rate on fine lattices, Phys. Rev. D 61 (2000) 105008 [hep-ph/9906259] [SPIRES].

    ADS  Google Scholar 

  6. M. D’Onofrio, K. Rummukainen and A. Tranberg, T he sphaleron rate at the electroweak crossover, PoS(LATTICE 2010)048 [arXiv:1011.2074] [SPIRES].

  7. K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, Generic rules for high temperature dimensional reduction and their application to the Standard Model, Nucl. Phys. B 458 (1996) 90 [hep-ph/9508379] [SPIRES].

    Article  ADS  Google Scholar 

  8. J.García-Bellido, D.Y. Grigoriev, A. Kusenko and M.E. Shaposhnikov, Non-equilibrium electroweak baryogenesis from preheating after inflation, Phys. Rev. D 60 (1999) 123504 [hep-ph/9902449] [SPIRES].

    ADS  Google Scholar 

  9. L.M. Krauss and M. Trodden, Baryogenesis below the electroweak scale, Phys. Rev. Lett. 83 (1999) 1502 [hep-ph/9902420] [SPIRES].

    Article  ADS  Google Scholar 

  10. A. Rajantie, P.M. Saffin and E.J. Copeland, Electroweak preheating on a lattice, Phys. Rev. D 63 (2001) 123512 [hep-ph/0012097] [SPIRES].

    ADS  Google Scholar 

  11. E.J. Copel and, D. Lyth, A. Rajantie and M. Trodden, Hybrid inflation and baryogenesis at the TeV scale, Phys. Rev. D 64 (2001) 043506 [hep-ph/0103231] [SPIRES].

    ADS  Google Scholar 

  12. A. Tranberg and J. Smit, Baryon asymmetry from electroweak tachyonic preheating, JHEP 11 (2003) 016 [hep-ph/0310342] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. A. Tranberg, A. Hernandez, T. Konstandin and M.G. Schmidt, Cold electroweak baryogenesis with Standard Model CP-violation, Phys. Lett. B 690 (2010) 207 [arXiv:0909.4199] [SPIRES].

    ADS  Google Scholar 

  14. M.E. Shaposhnikov, Baryon asymmetry of the universe in standard electroweak theory, Nucl. Phys. B 287 (1987) 757 [SPIRES].

    Article  ADS  Google Scholar 

  15. V.A. Rubakov and M.E. Shaposhnikov, Electroweak baryon number non-conservation in the early universe and in high-energy collisions, Usp. Fiz. Nauk 166 (1996) 493 [Phys. Usp. 39 (1996) 461] [ hep-ph/9603208] [SPIRES].

    Article  Google Scholar 

  16. J.Smit, Effective CP-violation in the Standard Model, JHEP 09 (2004) 067 [hep-ph/0407161] [SPIRES].

    Article  ADS  Google Scholar 

  17. A. Hernandez, T. Konstandin and M.G. Schmidt, Sizable CP-violation in the bosonized Standard Model, Nucl. Phys. B 812 (2009) 290 [arXiv:0810.4092] [SPIRES].

    Article  ADS  Google Scholar 

  18. C. Garcia-Recio and L.L. Salcedo, CP violation in the effective action of the Standard Model, JHEP 07 (2009) 015 [arXiv:0903.5494] [SPIRES].

    Article  ADS  Google Scholar 

  19. L.L. Salcedo, Leading order one-loop CP and P violating effective action in the Standard Model, Phys. Lett. B 700 (2011) 331 [arXiv:1102.2400] [SPIRES].

    ADS  Google Scholar 

  20. A. Tranberg, Standard Model CP-violation and cold electroweak baryogenesis, arXiv:1009.2358 [SPIRES].

  21. G. Aarts and J. Smit, Particle production and effective thermalization in inhomogeneous mean field theory, Phys. Rev. D 61 (2000) 025002 [hep-ph/9906538] [SPIRES].

    ADS  Google Scholar 

  22. J. Berges, D. Gelfand and J. Pruschke, Quantum theory of fermion preheating, arXiv:1012.4632 [SPIRES].

  23. J. Smit and A. Tranberg, Chern-Simons number asymmetry from CP-violation at electroweak tachyonic preheating, JHEP 12 (2002) 020 [hep-ph/0211243] [SPIRES].

    Article  ADS  Google Scholar 

  24. J. García-Bellido, M. Garcia Perez and A. Gonzalez-Arroyo, Symmetry breaking and false vacuum decay after hybrid inflation, Phys. Rev. D 67 (2003) 103501 [hep-ph/0208228] [SPIRES].

    ADS  Google Scholar 

  25. K. Kajantie, M. Karjalainen, M. Laine, J. Peisa and A. Rajantie, Thermodynamics of gauge-invariant U(1) vortices from lattice Monte Carlo simulations, Phys. Lett. B 428 (1998) 334 [hep-ph/9803367] [SPIRES].

    ADS  Google Scholar 

  26. A. Tranberg, J. Smit and M. Hindmarsh, Simulations of cold electroweak baryogenesis: finite time quenches, JHEP 01 (2007) 034 [hep-ph/0610096] [SPIRES].

    Article  ADS  Google Scholar 

  27. A. Tranberg and J. Smit, Simulations of cold electroweak baryogenesis: dependence on Higgs mass and strength of CP-violation, JHEP 08 (2006) 012 [hep-ph/0604263] [SPIRES].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, U.K.

    Paul M. Saffin

  2. Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2200, Copenhagen, Denmark

    Anders Tranberg

Authors
  1. Paul M. Saffin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anders Tranberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anders Tranberg.

Additional information

ArXiv ePrint: 1105.5546

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saffin, P.M., Tranberg, A. Real-time fermions for baryogenesis simulations. J. High Energ. Phys. 2011, 66 (2011). https://doi.org/10.1007/JHEP07(2011)066

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP07(2011)066

Keywords

Search

Navigation