×

zbMATH — the first resource for mathematics

Determining the global minimum of Higgs potentials via Groebner bases - applied to the NMSSM. (English) Zbl 1191.81216
Summary: Determining the global minimum of Higgs potentials with several Higgs fields like the next-to-minimal supersymmetric extension of the standard model (NMSSM) is a non-trivial task already at the tree level. The global minimum of a Higgs potential can be found from the set of all its stationary points defined by a multivariate polynomial system of equations. We introduce here the algebraic Groebner basis approach to solve this system of equations. We apply the method to the NMSSM with CP-conserving as well as CP-violating parameters. The results reveal an interesting stationary-point structure of the potential. Requiring the global minimum to give the electroweak symmetry breaking observed in Nature excludes large parts of the parameter space.

MSC:
81V17 Gravitational interaction in quantum theory
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Software:
FGb; NMHDECAY; SINGULAR
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] P. Fayet, Nucl. Phys. B 90, 104 (1975) · doi:10.1016/0550-3213(75)90636-7
[2] M. Drees, Int. J. Mod. Phys. A 4, 3635 (1989) · doi:10.1142/S0217751X89001448
[3] J.R. Ellis, J.F. Gunion, H.E. Haber, L. Roszkowski, F. Zwirner, Phys. Rev. D 39, 844 (1989) and other references quoted therein · doi:10.1103/PhysRevD.39.844
[4] F. Nagel, New aspects of gauge-boson couplings and the Higgs sector, PhD-thesis, Heidelberg University (2004)
[5] M. Maniatis, A. von Manteuffel, O. Nachtmann, F. Nagel, hep-ph/0605184, to be published in Eur. Phys. J. C
[6] B. Buchberger, Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal, PhD-thesis, University Innsbruck (1965) · Zbl 1245.13020
[7] T. Becker, V. Weispfenning, Gröbner Bases (Springer, New York, 1993) · Zbl 0772.13010
[8] N.K. Bose, J.P. Guiver, E.W. Kamen, H.M. Valenzuela, B. Buchberger, D. Reidel, Multidimensional Systems Theory, Progress, Directions and Open Problems in Multidimensional Systems (Publishing Company, 1985)
[9] G.M. Greuel, G. Pfister, H. Schoenemann, SINGULAR – A Computer Algebra System for Polynomial Computations, in: Symbolic Computation and Automated Reasoning, ed. by M. Kerber, M. Kohlhase, The Calculemus-2000 Symposium (2001) 227; SINGULAR is available at http://www.singular.uni-kl.de
[10] U. Ellwanger, J.F. Gunion, C. Hugonie, JHEP 0502, 066 (2005) [hep-ph/0406215] · doi:10.1088/1126-6708/2005/02/066
[11] D.J. Miller, R. Nevzorov, P.M. Zerwas, Nucl. Phys. B 681, 3 (2004) [hep-ph/0304049] · Zbl 02044773 · doi:10.1016/j.nuclphysb.2003.12.021
[12] K. Funakubo, S. Tao, Prog. Theor. Phys. 113, 821 (2005) [hep-ph/0409294] · doi:10.1143/PTP.113.821
[13] J.-C. Faugère, J. Pure. Appl. Algebra 139, 61 (1999) · Zbl 0930.68174 · doi:10.1016/S0022-4049(99)00005-5
[14] J.-C. Faugère, P. Gianni, D. Lazard, T. Mora, J. Symb. Comput. 16, 329 (1993) · Zbl 0805.13007 · doi:10.1006/jsco.1993.1051
[15] H.M. Moeller, Appl. Algebr. Eng. Commun. 4, 217 (1993) · Zbl 0793.13013 · doi:10.1007/BF01200146
[16] D. Hillebrand, Triangulierung nulldimensionaler Ideale – Implementierung und Vergleich zweier Algorithmen, PhD-thesis, University Dortmund (1999)
[17] R. Fletcher, Practical Methods of Optimization, 2nd Ed. (Wiley, Chichester, New York, 1987) · Zbl 0905.65002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.