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Title: Minkowski space structure of the Higgs potential in the two-Higgs-doublet model

Abstract

The Higgs potential of 2HDM keeps its generic form under the group of transformation GL(2,C), which is larger than the usually considered reparametrization group SU(2). This reparametrization symmetry induces the Minkowski space structure in the orbit space of 2HDM. Exploiting this property, we present a geometric analysis of the number and properties of stationary points of the most general 2HDM potential. In particular, we prove that charge-breaking and neutral vacua never coexist in 2HDM and establish conditions when the most general explicitly CP-conserving Higgs potential has spontaneously CP-violating minima. We also define the prototypical model of a given 2HDM, which has six free parameters less than the original one but still contains all the essential physics. Our analysis avoids manipulation with high-order algebraic equations.

Authors:
 [1];  [2]
  1. Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy)
  2. (Belgium) and Sobolev Institute of Mathematics, academician Koptyug avenue 4, 630090, Novosibirsk (Russian Federation)
Publication Date:
OSTI Identifier:
21011004
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevD.75.035001; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CP INVARIANCE; HIGGS BOSONS; HIGGS MODEL; MINKOWSKI SPACE; POTENTIALS; QUANTUM FIELD THEORY; SU GROUPS; SYMMETRY; TRANSFORMATIONS

Citation Formats

Ivanov, I. P., and Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B-4000 Liege. Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.035001.
Ivanov, I. P., & Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B-4000 Liege. Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. United States. doi:10.1103/PHYSREVD.75.035001.
Ivanov, I. P., and Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B-4000 Liege. Thu . "Minkowski space structure of the Higgs potential in the two-Higgs-doublet model". United States. doi:10.1103/PHYSREVD.75.035001.
@article{osti_21011004,
title = {Minkowski space structure of the Higgs potential in the two-Higgs-doublet model},
author = {Ivanov, I. P. and Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B-4000 Liege},
abstractNote = {The Higgs potential of 2HDM keeps its generic form under the group of transformation GL(2,C), which is larger than the usually considered reparametrization group SU(2). This reparametrization symmetry induces the Minkowski space structure in the orbit space of 2HDM. Exploiting this property, we present a geometric analysis of the number and properties of stationary points of the most general 2HDM potential. In particular, we prove that charge-breaking and neutral vacua never coexist in 2HDM and establish conditions when the most general explicitly CP-conserving Higgs potential has spontaneously CP-violating minima. We also define the prototypical model of a given 2HDM, which has six free parameters less than the original one but still contains all the essential physics. Our analysis avoids manipulation with high-order algebraic equations.},
doi = {10.1103/PHYSREVD.75.035001},
journal = {Physical Review. D, Particles Fields},
number = 3,
volume = 75,
place = {United States},
year = {Thu Feb 01 00:00:00 EST 2007},
month = {Thu Feb 01 00:00:00 EST 2007}
}
  • We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of noncontractible paths in the Higgs orbit space.more » We also study explicit symmetries of the Higgs potential/Lagrangian and their spontaneous violation from a wider perspective than usual.« less
  • We study the masses of the Higgs bosons in the most general two-Higgs-doublet model in a basis-independent approach. We adapt the recently developed Minkowski-space formalism to this problem and calculate traces of any power of the mass matrix in a compact and reparametrization-invariant form. Our results can be used to gain insight into the dynamics of the scalar sector of the general two-Higgs-doublet model.
  • We confront the two-Higgs-doublet model with a variety of experimental constraints as well as theoretical consistency conditions. The most constraining data are the B{yields}X{sub s}{gamma} decay rate (at low values of M{sub H{sup {+-}}}), and {delta}{rho} (at both low and high M{sub H{sup {+-}}}). We also take into account the BB oscillation rate and R{sub b}, or the width {gamma}(Z{yields}bb) (both of which restrict the model at low values of tan{beta}), and the B{sup -}{yields}{tau}{nu}{sub {tau}} decay rate, which restricts the model at high tan{beta} and low M{sub H{sup {+-}}}. Furthermore, the LEP2 nondiscovery of a light, neutral-Higgs boson ismore » considered, as well as the muon anomalous magnetic moment. Since perturbative unitarity excludes high values of tan{beta}, the model turns out to be very constrained. We outline the remaining allowed regions in the tan{beta}-M{sub H{sup {+-}}} plane for different values of the masses of the two lightest neutral-Higgs bosons, and describe some of their properties.« less
  • We consider the impact of imposing generalized CP symmetries on the Higgs sector of the two-Higgs-doublet model, and identify three classes of symmetries. Two of these classes constrain the scalar potential parameters to an exceptional region of parameter space, which respects either a Z{sub 2} discrete flavor symmetry or a U(1) symmetry. We exhibit a basis-invariant quantity that distinguishes between these two possible symmetries. We also show that the consequences of imposing these two classes of CP symmetry can be achieved by combining Higgs family symmetries, and that this is not possible for the usual CP symmetry. We comment onmore » the vacuum structure and on renormalization in the presence of these symmetries. Finally, we demonstrate that the standard CP symmetry can be used to build all the models we identify, including those based on Higgs family symmetries.« less