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Minimizing Higgs potentials via numerical polynomial homotopy continuation

  • M. Maniatis
  • D. Mehta
Regular Article

Abstract

The study of models with extended Higgs sectors requires to minimize the corresponding Higgs potentials, which is in general very difficult. Here, we apply a recently developed method, called numerical polynomial homotopy continuation (NPHC), which guarantees to find all the stationary points of the Higgs potentials with polynomial-like non-linearity. The detection of all stationary points reveals the structure of the potential with maxima, metastable minima, saddle points besides the global minimum. We apply the NPHC method to the most general Higgs potential having two complex Higgs-boson doublets and up to five real Higgs-boson singlets. Moreover the method is applicable to even more involved potentials. Hence the NPHC method allows to go far beyond the limits of the Gröbner basis approach.

Keywords

Stationary Point Global Minimum Higgs Doublet Higgs Potential Homotopy Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    T. Lee, Phys. Rev. D 8, 1226 (1973).ADSCrossRefGoogle Scholar
  2. 2.
    C. Nishi, Phys. Rev. D 77, 055009 (2008) 0712.4260.ADSCrossRefGoogle Scholar
  3. 3.
    I. Ginzburg, I. Ivanov, K. Kanishev, Phys. Rev. D 81, 085031 (2010) 0911.2383.ADSCrossRefGoogle Scholar
  4. 4.
    P. Ferreira, H.E. Haber, M. Maniatis, O. Nachtmann, J.P. Silva, Int. J. Mod. Phys. A 26, 769 (2011) 1010.0935.ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    M. Maniatis, O. Nachtmann, JHEP 11, 151 (2011) 1106.1436.ADSCrossRefGoogle Scholar
  6. 6.
    G. Branco et al., Phys. Rep. 516, 1 (2012) 1106.0034.ADSCrossRefGoogle Scholar
  7. 7.
    S.P. Martin, (1997) hep-ph/9709356.Google Scholar
  8. 8.
    M. Maniatis, Int. J. Mod. Phys. A 25, 3505 (2010) 0906.0777.MathSciNetADSCrossRefzbMATHGoogle Scholar
  9. 9.
    U. Ellwanger, C. Hugonie, A.M. Teixeira, Phys. Rep. 496, 1 (2010) 0910.1785.MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    V. Barger, P. Langacker, H.-S. Lee, G. Shaughnessy, Phys. Rev. D 73, 115010 (2006) hep-ph/0603247.ADSCrossRefGoogle Scholar
  11. 11.
    W. Grimus, L. Lavoura, Phys. Lett. B 572, 189 (2003) hep-ph/0305046.ADSCrossRefGoogle Scholar
  12. 12.
    M. Frigerio, S. Kaneko, E. Ma, M. Tanimoto, Phys. Rev. D 71, 011901 (2005) hep-ph/0409187.ADSCrossRefGoogle Scholar
  13. 13.
    M. Maniatis, A. von Manteuffel, O. Nachtmann, Eur. Phys. J. C 49, 1067 (2007) hep-ph/0608314.ADSCrossRefzbMATHGoogle Scholar
  14. 14.
    A.J. Sommese, C.W. Wampler, The numerical solution of systems of polynomials arising in Engineering and Science (World Scientific Publishing Company, 2005).Google Scholar
  15. 15.
    T.Y. Li, Handb. Num. Anal. XI, 209 (2003).CrossRefGoogle Scholar
  16. 16.
    M. Maniatis, A. von Manteuffel, O. Nachtmann, F. Nagel, Eur. Phys. J. C 48, 805 (2006) hep-ph/0605184.ADSCrossRefGoogle Scholar
  17. 17.
    D. Mehta, PhD Thesis, The University of Adelaide, Australasian Digital Theses Program (2009).Google Scholar
  18. 18.
    L. von Smekal, D. Mehta, A. Sternbeck, A.G. Williams, PoS LAT2007, 382 (2007) 0710.2410.Google Scholar
  19. 19.
    L. von Smekal, A. Jorkowski, D. Mehta, A. Sternbeck, PoS CONFINEMENT8, 048 (2008) 0812.2992.Google Scholar
  20. 20.
    D. Mehta, M. Kastner, Ann. Phys. 326, 1425 (2011) 1010.5335.MathSciNetADSCrossRefzbMATHGoogle Scholar
  21. 21.
    D. Mehta, A. Sternbeck, L. von Smekal, A.G. Williams, PoS QCD-TNT09, 025 (2009) 0912.0450.Google Scholar
  22. 22.
    D. Mehta, Phys. Rev. E 84, 025702 (2011) 1104.5497.ADSCrossRefGoogle Scholar
  23. 23.
    D. Mehta, Adv. High Energy Phys. 2011, 263937 (2011) 1108.1201.Google Scholar
  24. 24.
    M. Kastner, D. Mehta, Phys. Rev. Lett. 107, 160602 (2011).ADSCrossRefGoogle Scholar
  25. 25.
    D. Mehta, J.D. Hauenstein, M. Kastner, Phys. Rev. E 85, 061103 (2012).ADSCrossRefGoogle Scholar
  26. 26.
    B. Roth, PhD Thesis, Columbia University (1962).Google Scholar
  27. 27.
    E.L. Allgower, K. Georg, Introduction to Numerical Continuation Methods (John Wiley & Sons, New York, 1979).Google Scholar
  28. 28.
    J. Verschelde, ACM Trans. Math. Soft. 25, 251 (1999).CrossRefzbMATHGoogle Scholar
  29. 29.
    T.L. Lee, T.Y. Li, C.H. Tsai, Computing 83, 109 (2008).MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    D.J. Bates, J.D. Hauenstein, A.J. Sommese, C.W. Wampler, available at www.nd.edu/~sommese/bertini.
  31. 31.
    J.D. Hauenstein, F. Sottile, ACM Trans. Math. Softw. 38, 4 (2012).MathSciNetCrossRefGoogle Scholar
  32. 32.
    J.D. Hauenstein, F. Sottile, Available at www.math.tamu.edu/~sottile/research/stories/alphaCertified.

Copyright information

© Società Italiana di Fisica and Springer 2012

Authors and Affiliations

  1. 1.Faculty of PhysicsBielefeld UniversityBielefeldGermany
  2. 2.Physics DepartmentSyracuse UniversitySyracuseUSA

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