We consider the Two-Higgs-Doublet Model and determine the range of parameters
for which CP violation and Flavor Changing Neutral Current effects are
naturally small. It corresponds to small values of the mass parameter m_{12}^2,
describing soft (\phi_1,\phi_2) mixing in the potential. We discuss how, in
this approach, some Higgs bosons can be heavy, with mass of the order of 1 TeV.
  The possibility that at the Tevatron, LHC and an e^+e^- Linear Collider, only
one Higgs boson will be found, with properties indistinguishable from those in
the Standard Model (SM), we define as the SM-like scenario. While this scenario
can be obtained with large \mu^2 \sim \Re m_{12}^2 parameter, in which case
there is decoupling, we here discuss the opposite case of small \mu^2, without
decoupling.Comment: 5 pages, LaTeX, including figures. Presented at SUSY02, DESY, June
  2002 and LCWS02, Jeju, Korea, August 2002. To appear in the proceedings.
  Version 2: minor changes, additional reference

Ginzburg, Ilya F.

Krawczyk, Maria

Osland, Per

English

arXiv

We consider the Two-Higgs-Doublet Model (2HDM) and determine the range of parameters for which CP violation and Flavor Changing Neutral Current effects are naturally small. It corresponds to small values of the mass parameter m_{12}^2, describing soft (\phi_1,\phi_2) mixing in the potential. We discuss how, in this approach, some Higgs bosons can be heavy, with mass of the order of 1 TeV. The possibility that at the Tevatron, LHC and an e^+e^- Linear Collider, only one Higgs boson will be found, with properties indistinguishable from those in the Standard Model (SM), we define as the SM-like scenario. While this scenario can be obtained with large \mu^2 \sim \Re m_{12}^2 parameter, in which case there is decoupling, we here discuss the opposite case of small \mu^2, without decoupling.We consider the Two-Higgs-Doublet Model and determine the range of parameters for which CP violation and Flavor Changing Neutral Current effects are naturally small. It corresponds to small values of the mass parameter m_{12}^2, describing soft (\phi_1,\phi_2) mixing in the potential. We discuss how, in this approach, some Higgs bosons can be heavy, with mass of the order of 1 TeV. The possibility that at the Tevatron, LHC and an e^+e^- Linear Collider, only one Higgs boson will be found, with properties indistinguishable from those in the Standard Model (SM), we define as the SM-like scenario. While this scenario can be obtained with large \mu^2 \sim \Re m_{12}^2 parameter, in which case there is decoupling, we here discuss the opposite case of small \mu^2, without decoupling

CERN Document Server

CERN-TH/2002-330IFT - 40/2002hep-ph/0211371November 2002Two-Higgs-Doublet Modelswith CP violation I. F. Ginzburg1, M. Krawczyk2,3 and P. Osland41 Sobolev Institute of Mathematics, SB RAS, 630090 Novosibirsk, Russia2 Theory Division CERN, CH-1211 Geneva 23, Switzerland3 Institute of Theoretical Physics, Warsaw University, Poland4 Department of Physics, University of Bergen, N-5007 Bergen, NorwayAbstractWe consider the Two-Higgs-Doublet Model (2HDM) and determine the range of pa-rameters for which CP violation and Flavor Changing Neutral Current effects are naturallysmall. It corresponds to small values of the mass parameter m212, describing soft (φ1, φ2)mixing in the potential. We discuss how, in this approach, some Higgs bosons can beheavy, with mass of the order of 1 TeV.The possibility that at the Tevatron, LHC and an e+e− Linear Collider, only one Higgsboson will be found, with properties indistinguishable from those in the Standard Model(SM), we define as the SM-like scenario. While this scenario can be obtained with largeµ2  Rem212 parameter, in which case there is decoupling, we here discuss the oppositecase of small µ2, without decoupling.CERN-TH/2002-330IFT - 40/2002hep-ph/0211371November 2002∗Presented at SUSY02, DESY, June 2002 and LCWS02, Jeju, Korea, August 20021 IntroductionWe consider the following Two-Higgs-Doublet Model (2HDM) potential, with quartic and quad-ratic terms separated [1, 2, 3, 4, 5]:V = 121(y11)2 + 122(y22)2 + 3(y11)(y22) + 4(y12)(y21)+ 125(y12)2 + h:c:+6(y11) + 7(y22)(y12) + h:c:}− m211(y11) + m212(y12) + h:c: + m222(y22)}: (1)As is well known, both CP violation in the Higgs sector and flavor-changing neutral currents(FCNC) can be suppressed by imposing a Z2 symmetry [6]. This requires symmetry of thepotential under (1 ! −1; 2 ! 2) (or vice versa), which implies 6 = 7 = m212 = 0. Weshall allow soft violation of this symmetry, i.e., we take 6 = 7 = 0, but allow m212 6= 0 [3, 5, 7].A simple discussion can be given for this case, in which Im m212 6= 0 signals CP violation.2 CP violationWe shall now consider the simpler case of 6 = 7 = 0, and parametrize the minimum of thepotential (or vacuum) as1 =01p2v1; 2 =01p2v2 ei: (2)Naively, the phase  violates CP , but it can be removed by a global phase transformation onthe eld 2, together with the phases of 5, m212 and the fermion elds [3, 8]. It is convenientto dene2 = Re(m212ei)v2v1v2: (3)The phase  can be found from the equationIm(m212 ei) = Im(5 e2i)v1v2: (4)Making use of the rephasing invariance [3, 8], we put  = 0. With this choice, eq. (4) becomesa constraint for the relation of Im(m212) to Im 5.The neutral sector has a mass squared matrix of the formM2 =0B@M211 M212 −12 Im 5v2 sin M212 M222 −12 Im 5v2 cos −12Im 5v2 sin  −12Im 5v2 cos  M2331CA (5)2where M211, M212, M222 and M233 are the same as in the CP-conserving case. When Im 5 = 0,there is no CP violation, the matrix (5) is block diagonal, and the physical states are h, H andA. When Im 5 6= 0, all three neutral Higgs states mix; we denote them by h1, h2 and h3.The mass-squared matrix may be diagonalized via a rotation matrix, dened byRM2 RT = diag(M21 ; M22 ; M23 ): (6)In the limit of weak CP violation, the masses for h1, h2 and h3 will deviate from those of h, Hand A by terms quadratic in Im 5.3 Decoupling or no decoupling?We shall here consider the scenario of weak (or no) CP violation and large masses of Higgsparticles except one, namely Mh1  Mh. Let us discuss how large masses MA (close to Mh3)and MH arise in such a case. The potential (1) (but with 6 = 7 = 0) givesM2A =122 − Re5v2 and M2H = 12 [2 − (4 + Re5)v2]: (7)There are two rather distinct mechanisms for obtaining large mass M2A and M2H : either (i)2 is large (this is extensively discussed by Haber as the decoupling scenario) [2, 5], or (ii) 2is small, whereas jRe5j is \large" [4, 5]. In the latter case, there are obvious upper bounds(from perturbativity and positivity) on how large jRe5j can be. Decoupling properties of theTwo-Higgs-Doublet Model were studied in [9].In this model, one can realize a Standard-Model-Like Scenario: There is a light Higgs boson with couplings to the up (e.g. t) and down (e.g. b) type quarks,and to W and Z, like in the Standard Model,jgij  jgSMi j (i = W; Z; down; up): (8) The other Higgs bosons are heavy, O(1 TeV).Within the Two-Higgs-Doublet Model, this scenario can be realized in two distinct ways.They are [4]:− Solutions A. All basic couplings are approximately the same as in the SM, up to an overallsign.− Solutions B. Like Solutions A, except that the couplings to either up- or down-type quarkshave opposite signs of those in the SM. This case cannot be realized in the decouplingscenario.34 Model II. ObservablesLet us now be more specic, and consider the so-called Model II for Yukawa couplings, wheremasses of down- and up-type quarks originate from couplings to 1 and 2, respectively. Wedenote by hiV , hiu and hid the ratios of the Higgs couplings to W and Z (V ) and to up anddown-type quarks, with respect to those of the Standard Model. In particular, for the Yukawacouplings these ratios can be expressed via elements of the rotational matrix R of eq. (6) ashiu =1sin [Ri2 − iγ5 cos Ri3]; hid =1cos [Ri1 − iγ5 sin Ri3]; (9)where Ri3 is proportional to Im 5. Note that in accordance with eq. (9), the CP violationinduced by Higgs exchange in tt production [10] provides information on Im 5.Furthermore, these relative couplings satisfy a pattern relation [4, 8]:(hiu + hid )hiV = 1 + hiu hid : (10)In the CP-conserving case, even with all basic couplings being the same (up to a sign) asin the SM (8), loop-induced transition rates, like h ! γγ, may dier from the SM prediction.This is due to the dierent behaviors of the trilinear Higgs coupling hH+H− for small and large. In fact, the ratio of this coupling to its SM value can be written ashH  −vghH+H−2M2H=1− M2h2M2HhV +M2h − 22M2H(hu + hd): (11)Thus, if 2  M2H, there is no eect in Γγγ , whereas if 2 < M2H there is a dierence of severalper cent, as illustrated in Fig. 1 (left panel) for the case of Solutions A [4]. Non-decouplingeects in the 2HDM were studied for other processes in [11, 12].These deviations from unity are large enough that the form of the 2HDM potential (largeor small ) can be tested at a γγ Collider [13].Also, the loop-induced couplings to two gluons may dier from those of the SM-value, butthis occurs only for Solutions B. This eect is also illustrated in Fig. 1 (right panel).AcknowledgementsWe are grateful to the CERN, TH Division for kind hospitality and support during work onthis paper. We thank Maria Jose Herrero Solans for informing us about ref. [9]. This work issupported in part by RFBR grants 02-02-17884 and 00-15-96691 and INTAS 00-00679, by thePolish Committee for Scientic Research (grant No. 5 P03B12120 (2002)) and by the EuropeanCommunity’s Human Potential Programme under contract HPRN-CT-2000-00149 Physics atColliders, and by the Research Council of Norway.4150 200 2500.80.911.11.2150 200 25011.11.21.31.4Figure 1: Ratios of the Higgs boson decay widths in the SM-like 2HDM (II) and the SM asfunctions of Mh for mass of charged Higgs boson equal to 800 GeV. Left panel: h ! γγ decaywidths, solutions A, various values of . Right panel: h ! gg, solutions B.References[1] J. L. Diaz-Cruz and A. Mendez, Nucl. Phys. B380 (1992) 39,J. L. Diaz-Cruz and G. Lopez Castro, Phys. Lett. B301 (1993) 405.[2] H. E. Haber, arXiv:hep-ph/9501320.[3] G. C. Branco, L. Lavoura, J. P. Silva, CP Violation (Oxford Univ. Press, 1999)[4] I. F. Ginzburg, M. Krawczyk and P. Osland, Linear Collider Note LC-TH-2001-026, In2nd ECFA/DESY Study 1998–2001, 1705 [arXiv:hep-ph/0101208];I. F. Ginzburg, M. Krawczyk and P. Osland, Nucl. Instrum. Meth. A472 (2001) 149[arXiv:hep-ph/0101229].[5] J. F. Gunion and H. E. Haber, arXiv:hep-ph/0207010.[6] S. L. Glashow and S. Weinberg, Phys. Rev. D15 (1977) 1958.[7] R. Santos, S. M. Oliveira and A. Barroso, arXiv:hep-ph/0112202.[8] I. F. Ginzburg, M. Krawczyk and P. Osland, to be published.[9] P. Ciafaloni and D. Espriu, Phys. Rev. D 56 (1997) 1752 [arXiv:hep-ph/9612383].[10] W. Bernreuther and A. Brandenburg, Phys. Rev. D49 (1994) 4481 [arXiv:hep-ph/9312210].[11] M. Malinsky, arXiv:hep-ph/0207066.5[12] S. Kanemura, S. Kiyoura, Y. Okada, E. Senaha and C. P. Yuan, arXiv:hep-ph/0209326;arXiv:hep-ph/0211308.[13] J. A. Aguilar-Saavedra et al. [ECFA/DESY LC Physics Working Group Collaboration],\TESLA Technical Design Report Part III: Physics at an e+e- Linear Collider," arXiv:hep-ph/0106315.6

Two-Higgs-Doublet Models with CP violation

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Two-Higgs-Doublet Models with CP violation

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