Minimizing Higgs potentials via numerical polynomial homotopy continuation
- 94 Downloads
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.
KeywordsStationary Point Global Minimum Higgs Doublet Higgs Potential Homotopy Path
- 7.S.P. Martin, (1997) hep-ph/9709356.Google Scholar
- 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
- 17.D. Mehta, PhD Thesis, The University of Adelaide, Australasian Digital Theses Program (2009).Google Scholar
- 18.L. von Smekal, D. Mehta, A. Sternbeck, A.G. Williams, PoS LAT2007, 382 (2007) 0710.2410.Google Scholar
- 19.L. von Smekal, A. Jorkowski, D. Mehta, A. Sternbeck, PoS CONFINEMENT8, 048 (2008) 0812.2992.Google Scholar
- 21.D. Mehta, A. Sternbeck, L. von Smekal, A.G. Williams, PoS QCD-TNT09, 025 (2009) 0912.0450.Google Scholar
- 23.D. Mehta, Adv. High Energy Phys. 2011, 263937 (2011) 1108.1201.Google Scholar
- 26.B. Roth, PhD Thesis, Columbia University (1962).Google Scholar
- 27.E.L. Allgower, K. Georg, Introduction to Numerical Continuation Methods (John Wiley & Sons, New York, 1979).Google Scholar
- 30.D.J. Bates, J.D. Hauenstein, A.J. Sommese, C.W. Wampler, available at www.nd.edu/~sommese/bertini.
- 32.J.D. Hauenstein, F. Sottile, Available at www.math.tamu.edu/~sottile/research/stories/alphaCertified.