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Title: Symmetries of two Higgs doublet model and CP violation

Abstract

We use the invariance of a physical picture under a change of Lagrangian, the reparameterization invariance in the space of Lagrangians and its particular case--the rephrasing invariance--for analysis of the two-Higgs-doublet extension of the standard model. We found that some parameters of theory like tan{beta} are reparameterization dependent and therefore cannot be fundamental. We use the Z{sub 2} symmetry of the Lagrangian, which prevents a {phi}{sub 1}{r_reversible}{phi}{sub 2} transition, and the different levels of its violation, soft and hard, to describe the physical content of the model. In general, the broken Z{sub 2} symmetry allows for a CP violation in the physical Higgs sector. We argue that the two-Higgs-doublet model with a soft breaking of Z{sub 2} symmetry is a natural model in the description of electroweak symmetry breaking. To simplify the analysis, we choose among different forms of Lagrangian describing the same physical reality a specific one, in which the vacuum expectation values of both Higgs fields are real. A possible CP violation in the Higgs sector is described by using a two-step procedure with the first step identical to a diagonalization of the mass matrix for CP-even fields in the CP-conserving case. We find a very simple, necessary,more » and sufficient condition for a CP violation in the Higgs sector. We determine the range of parameters for which CP violation and flavor-changing neutral current effects are naturally small--it corresponds to a small dimensionless mass parameter {nu}=Rem{sub 12}{sup 2}/(2v{sub 1}v{sub 2}). We show that for small {nu} some Higgs bosons can be heavy--with mass up to about 0.6 TeV--without violating of the unitarity constraints. If {nu} is large, all Higgs bosons except one can be arbitrarily heavy. We discuss, in particular, main features of this case, which corresponds for {nu}{yields}{infinity} to a decoupling of heavy Higgs bosons. In the model II for Yukawa interactions we obtain the set of relations among the couplings to gauge bosons and to fermions which allows us to analyze different physical situations (including CP violation) in terms of these very couplings, instead of the parameters of Lagrangian.« less

Authors:
 [1];  [2]
  1. Sobolev Institute of Mathematics, SB RAS, 630090 Novosibirsk (Russian Federation)
  2. Institute of Theoretical Physics, Warsaw University (Poland)
Publication Date:
OSTI Identifier:
20774467
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevD.72.115013; (c) 2005 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; DECOUPLING; FERMIONS; FLAVOR MODEL; HIGGS BOSONS; HIGGS MODEL; LAGRANGIAN FIELD THEORY; LAGRANGIAN FUNCTION; MESONS; NEUTRAL CURRENTS; REST MASS; STANDARD MODEL; SYMMETRY BREAKING; TEV RANGE; UNITARITY; UNITARY SYMMETRY

Citation Formats

Ginzburg, Ilya F., and Krawczyk, Maria. Symmetries of two Higgs doublet model and CP violation. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.115013.
Ginzburg, Ilya F., & Krawczyk, Maria. Symmetries of two Higgs doublet model and CP violation. United States. doi:10.1103/PhysRevD.72.115013.
Ginzburg, Ilya F., and Krawczyk, Maria. Thu . "Symmetries of two Higgs doublet model and CP violation". United States. doi:10.1103/PhysRevD.72.115013.
@article{osti_20774467,
title = {Symmetries of two Higgs doublet model and CP violation},
author = {Ginzburg, Ilya F. and Krawczyk, Maria},
abstractNote = {We use the invariance of a physical picture under a change of Lagrangian, the reparameterization invariance in the space of Lagrangians and its particular case--the rephrasing invariance--for analysis of the two-Higgs-doublet extension of the standard model. We found that some parameters of theory like tan{beta} are reparameterization dependent and therefore cannot be fundamental. We use the Z{sub 2} symmetry of the Lagrangian, which prevents a {phi}{sub 1}{r_reversible}{phi}{sub 2} transition, and the different levels of its violation, soft and hard, to describe the physical content of the model. In general, the broken Z{sub 2} symmetry allows for a CP violation in the physical Higgs sector. We argue that the two-Higgs-doublet model with a soft breaking of Z{sub 2} symmetry is a natural model in the description of electroweak symmetry breaking. To simplify the analysis, we choose among different forms of Lagrangian describing the same physical reality a specific one, in which the vacuum expectation values of both Higgs fields are real. A possible CP violation in the Higgs sector is described by using a two-step procedure with the first step identical to a diagonalization of the mass matrix for CP-even fields in the CP-conserving case. We find a very simple, necessary, and sufficient condition for a CP violation in the Higgs sector. We determine the range of parameters for which CP violation and flavor-changing neutral current effects are naturally small--it corresponds to a small dimensionless mass parameter {nu}=Rem{sub 12}{sup 2}/(2v{sub 1}v{sub 2}). We show that for small {nu} some Higgs bosons can be heavy--with mass up to about 0.6 TeV--without violating of the unitarity constraints. If {nu} is large, all Higgs bosons except one can be arbitrarily heavy. We discuss, in particular, main features of this case, which corresponds for {nu}{yields}{infinity} to a decoupling of heavy Higgs bosons. In the model II for Yukawa interactions we obtain the set of relations among the couplings to gauge bosons and to fermions which allows us to analyze different physical situations (including CP violation) in terms of these very couplings, instead of the parameters of Lagrangian.},
doi = {10.1103/PhysRevD.72.115013},
journal = {Physical Review. D, Particles Fields},
number = 11,
volume = 72,
place = {United States},
year = {Thu Dec 01 00:00:00 EST 2005},
month = {Thu Dec 01 00:00:00 EST 2005}
}
  • We carry out a detailed analysis of the general two Higgs doublet model with CP violation. We describe two different parametrizations of this model, and then study the Higgs boson masses and the trilinear Higgs couplings for these two parametrizations. Within a rather general model, we find that the trilinear Higgs couplings have a significant dependence on the details of the model, even when the lightest Higgs boson mass is taken to be a fixed parameter. We include radiative corrections in the one-loop effective potential approximation in our analysis of the Higgs boson masses and the Higgs trilinear couplings. Themore » one-loop corrections to the trilinear couplings of the two Higgs doublet model also depend significantly on the details of the model, and can be rather large. We study quantitatively the trilinear Higgs couplings, and show that these couplings are typically several times larger than the corresponding standard model trilinear Higgs coupling in some regions of the parameter space. We also briefly discuss the decoupling limit of the two Higgs doublet model.« less
  • Spontaneous CP violation motivates the introduction of two Higgs doublets in the electroweak theory, such a simple extension of the standard model has five physical Higgs bosons and rich CP-violating sources. Exploration on more than one Higgs boson is a direct evidence for new physics beyond the standard model. The neutral Higgs production at LHC is investigated in such a general two-Higgs-doublet model with spontaneous CP violation, it is shown that the production cross section and decays of the neutral Higgs boson can significantly be different from the predictions from the standard model.
  • 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
  • In the most general two-Higgs-doublet model with an approximate family symmetry and [ital CP] violation originating solely from the relative phase of two vacuum expectation values, [ital CP] asymmetry in the decay [ital b][r arrow][ital s][gamma] may arise from the [ital CP] violation of the charged Higgs boson interactions with fermions. This asymmetry may be larger than in the standard model and can lie between 10[sup [minus]2] and 10[sup [minus]1]. The decay rate of [ital b][r arrow][ital s][gamma] is allowed to be smaller or larger than in the standard model.
  • In a general two-scalar-doublet model without fermions, there is a unique source of {ital CP} violation, {ital J}{sub 1}, in the gauge interactions of the scalars. It arises in the mixing of the three neutral physical scalars {ital X}{sub 1}, {ital X}{sub 2}, and {ital X}{sub 3}. $CP--- violation may be observed via different decay rates for {ital X}{sub 1}{r_arrow}{ital H}{sup +}{ital W}{sup {minus}} and {ital X}{sub 1}{r_arrow}{ital H}{sup {minus}}{ital W}{sup +} (or, alternatively, for {ital H}{sup +}{r_arrow}{ital X}{sub 1}{ital W}{sup +} and {ital H}{sup {minus}}{r_arrow}{ital X}{sub 1}{ital W}{sup {minus}}, depending on which decays are kinematically allowed). I compute themore » part of those {ital CP}-violating decay-rate differences which is proportional to {ital J}{sub 1}. The {ital CP}-invariant phase is provided by the absorptive parts of the one-loop diagrams. I check the gauge invariance of the whole calculation.« less