Minkowski space structure of the Higgs potential in the twoHiggsdoublet 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 chargebreaking and neutral vacua never coexist in 2HDM and establish conditions when the most general explicitly CPconserving Higgs potential has spontaneously CPviolating 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 highorder algebraic equations.
 Authors:
 Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, I87036 Arcavacata di Rende, Cosenza (Italy)
 (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, B4000 Liege. Minkowski space structure of the Higgs potential in the twoHiggsdoublet 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, B4000 Liege. Minkowski space structure of the Higgs potential in the twoHiggsdoublet 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, B4000 Liege. Thu .
"Minkowski space structure of the Higgs potential in the twoHiggsdoublet model". United States.
doi:10.1103/PHYSREVD.75.035001.
@article{osti_21011004,
title = {Minkowski space structure of the Higgs potential in the twoHiggsdoublet model},
author = {Ivanov, I. P. and Physique theorique fondamentale, Departement de Physique, Universite de Liege, Allee du 6 Aout 17, batiment B5a, B4000 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 chargebreaking and neutral vacua never coexist in 2HDM and establish conditions when the most general explicitly CPconserving Higgs potential has spontaneously CPviolating 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 highorder 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}
}

Minkowski space structure of the Higgs potential in the twoHiggsdoublet model. II. Minima, symmetries, and topology
We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the twoHiggsdoublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3quadrics in the 3+1dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twicedegenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3quadrics, we give concise criteria for existence of noncontractible paths in the Higgs orbit space.more » 
Higgs boson masses of the general twoHiggsdoublet model in the Minkowskispace formalism
We study the masses of the Higgs bosons in the most general twoHiggsdoublet model in a basisindependent approach. We adapt the recently developed Minkowskispace formalism to this problem and calculate traces of any power of the mass matrix in a compact and reparametrizationinvariant form. Our results can be used to gain insight into the dynamics of the scalar sector of the general twoHiggsdoublet model. 
Constraining the twoHiggsdoubletmodel parameter space
We confront the twoHiggsdoublet 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, neutralHiggs boson ismore » 
Generalized CP symmetries and special regions of parameter space in the twoHiggsdoublet model
We consider the impact of imposing generalized CP symmetries on the Higgs sector of the twoHiggsdoublet 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 basisinvariant 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 »