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Supersymmetry, Higgs Physics and CP-Violation Carlos E.M. Wagner Argonne National Laboratory EFI, University of Chicago SUSY04 Conference, Tsukuba, Japan, June 23, 2004

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Supersymmetry and Higgs Physics Low energy supersymmetry provides a well defined and predictive framework, in which scalars and, in particular, Higgs boson fields are naturally incorporated. In spite of the multiplicity of scalar fields, the Higgs is naturally the one acquiring v.e.v. due to negative corrections induced by loop corrections induced by the large top Yukawa coupling. The relevance of a well defined and predictive framework cannot be underestimated, and, in minimal SUSY extensions, the properties of the Higgs sector provide crucial test of low energy SUSY. Low energy supersymmetry has other attractive properties beyond radiative electroweak symmetry breaking, unification and a source of dark matter: Electroweak Baryogenesis, which demands non-vanishing CP-violating phases in the SUSY breaking parameters.

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Minimal Supersymmetric Extensions In the minimal SUSY extension, there are one charged and three neutral Higgs boson degrees of freedom. If CP is conserved, thre are two CP-even and one CP-odd neutral Higgs bosons. At tree-level, all CP-violating phases, if present, may be absorved into a redefinition of the fields. CP-violation in the Higgs sector appears at the loop-level, but can still have important consequences for Higgs physics

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Tree-level Higgs spectrum and properties The real part of the neutral component of the two Higgs doublets, H1 and H2 mix, with a mixing angle, leading to the two CP-even Higgs bosons. The charged and the complex part of the neutral component of two Higgs doublets lead to the Goldstone as well as the CP-odd A and charged Higgs bosons Ratio of Higgs vacuum expectation values,, determines the mixing angle between Goldstone modes and physical Higgs states.

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For moderate or large values of the CP-odd Higgs boson mass, the mass of lightest CP-even state is given by while all the other Higgs boson masses are of order mA. Couplings of Higgs boson to weak gauge bosons determined by the projection of the lightest Higgs on the one that acquires v.e.v.,

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Loop Corrections to Higgs boson masses Most important corrections come from the stop sector, where the off-diagonal term depends on the stop-Higgs trilinear couplings, For large CP-odd Higgs boson masses, and with dominant one-loop corrections are given by, where After two-loop corrections: Okada, Yamaguchi, Yanagida; Ellis et al, Haber et al. ’90 Carena, Espinosa, Quiros, C.W.’95; Haber and Hempling ’96; Heinemeyer, Hollik, Weiglein’98

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Two-loop effects At one loop, Higgs masses up to 150 GeV may be obtained for stop masses of order 1 TeV. Apart from lowering the Higgs mass by about 10--15 percent of its tree – level value by log. corrections, an asymmetry in the Higgs mass under change of sign of Xt appears. Such an asymmetry is induced by one-loop corrections to the relation between the top-quark mass and the top Yukawa coupling, which depend on the product of Xt and the gluino mass. Carena, Haber, Hollik, Heinemeyer, Weiglein, C.W. ’00

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Allowing 2 -- 3 TeV stop masses, the Revised top-quark mass value and playing with all other parameters, upper bound on the lightest Higgs mass can be pushed up to about 145 GeV. P. Slavich, this conference. Carena, Haber, Hollik, Heinemeyer, Weiglein, C.W. ’00 Heinemeyer, Hollik, Weiglein’02 Degrassi, Slavich, Zwirner ‘02 m h (GeV) X t (GeV)

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Espinosa,Gunion; Carena,Mrenna,C.W.

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Hall, Rattazzi, Sarid ; Carena, Olechowski, Pokorski, C.W.’93

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Elements of CP-even Higgs mass Matrix Off-diagonal elements are proportional to When off-diagonal elements vanish, either vanish and therefore there is a strong suppression of the coupling of the SM-like Higgs boson to the bottom-quarks or tau-leptons. Particularly strong effects for. These effects are absent in the case of minimal or maximal mixing. Carena, Mrenna, C.W. ‘98

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Carena, Mrenna, Wagner ’98/99; Haber et al ‘99 Large corrections have important consequences for the Higgs sector: Destroy the relationship between the tau and bottom couplings and the corresponding masses Carena, Garcia, Nierste, C.W.’99/00; Gambino et al. ‘00

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MSSM Higgs Boson Searches at Hadron Colliders Due to dependence on parameters, full scan is too involved Benchmark scenarios, that summarize most important Higgs properties, likely to have an impact on collider physics Production and decay channels analized : Tevatron : W H and ZH, with H decaying to bottom quarks. Associated production with bottom quarks, decaying to tau’s or b’s. LHC: Weak boson fusion, with decays to taus, gammas or W’s. Associated production with top-quarks, decaying to b’s or gammas Gluon fusion production, with decays to gammas.

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Carena, Mrenna,C.W.’99; Carena,Heinemeyer,Weiglein,C.W.’01

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Vector Boson Fusion (tau’s final state) Asociated production with top quarks (b’s final state) Gamma-gamma final state

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Carena,Mrenna,Wagner; Carena,Heinemeyer,Weiglein,C.W. Clear separation between regions with suppressed coupling to taus and bottoms

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CP-Violation in Supersymmetric Models In low energy supersymmetry, there are extra CP-violating phases beyond the CKM ones, associated with complex supersymmetry breaking parameters. These phases may have an impact on low energy observables, and induce new contributions to the e.d.m. of the electron and the neutron, and hence are cautiosly set to zero in most models. However, effects on observables are small in large regions of parameter space, where either first or second generation scalars are heavy, cancellations occur or simply the relevant CP-violating phase for such a given observable vanishes. Effect on Higgs physics associated with third generation scalars and/or gaugino-Higgsino sector, and it is worth studying.

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Motivation for CP-Violation in SUSY Models One of the most important consequences of CP-violation is its possible impact on the explanation of the matter-antimatter asymmetry. Electroweak baryogenesis may be realized even in the simplest supersymmetric extensions of the Standard Model, but demands new sources of CP-violation associated with the third generation sector and/or the gaugino-Higgsino sector. In the minimal supersymmetric model, it also demand a light and a heavy top-squark, in order to induce a strongly first order phase transition. In the nMSSM, there are no constraints on the third generation sector. A. Menon, D. Morrissey, C.W. ‘04

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MSSM: Limits on the Stop and Higgs Masses to preserve the baryon asymmetry Higgs masses smaller than 120 GeV and a stop masses below the top quark mass required. M. Carena, M. Quiros, C.W.’98

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Tevatron stop searches and dark matter constraints Carena, Balazs and C.W. ‘04 Searches for light stops difficult in stop-neutralino coannihilarion region. LHC will have equal difficulties. Searches become easier at a linear collider !

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CP-Violation in the Higgs sector CP-violating effects absent at tree-level At loop-level, important CP-violating effects may be induced Many possible phases, but in minimal flavor violating models, due to symmetries of conformal invariant sector, only relevant phases where is the bilinear mass parameter in the Higgs potential. Pilaftis’98, Pilaftsis,C.W.’99; Demir’99; Drees,Choi,Lee’00; Carena,Ellis,Pilaftsis,C.W.’00 Talks by Akeroyd, Hidaka, Lee and Schumacher at this conference.

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Loop-Induced CP-Violation Main Effect of CP-Violation is the mixing of the three neutral Higgs boson states. Mixing between would-be CP-odd and CP-even sates are predominantly governed by stop-induced loop effects and proportional to Gluino phase relevant at two-loop level. Small gaugino effects may be enhanced at large values of tan (Nath et al, 2002).

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Comments on Higgs Boson Mixing Elements of matrix O are similar to in the CP- conserving case. But third row and column are zero in the non-diagonal elements in such a case. Couplings of the Higgs bosons to vector bosons still depend on projection of Higgs that acquires v.e.v. to the different Higgs bosons. Three neutral Higgs bosons can now couple to the vector bosons in a way similar to the SM Higgs. Similar to the decoupling limit in the CP-conserving case, for large values of the charged Higgs mass, light Higgs boson with Standard Model properties.

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Large CP-Violating couplings CP-Violating phases affect masses and couplings in relevant ways. CP-violation manifest in Higgs boson couplings. Effects depend both on the dominant stop sector phases, as well as on the subdominant gaugino phases, affecting the vertex corrections. Cases with gluino mass phase zero (solid lines) and 90 degrees (dashed lines) shown in figures.

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Coupling dependence on gluino phases Region of paramaeters consistent with electroweak baryogenesis. Large suppression of the bottom Yukawa coupling may be obtained, with Standard Model like couplings to vector gauge bosons, for gluino mass parameter phases of order 90 degrees (dashed lines). Carena, Ellis, Pilaftsis, C.W. ‘00

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Carena, Ellis, Pilaftsis, C.W.’00 110 GeV

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In certain regions of parameter space the heavier Higgs bosons may decay into lighter ones. If lighter one has reduced couplings to the Z, Higgs detection at LEP challenged.

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Carena, Ellis, Mrenna, Pilaftsis, C.W.’02

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Light Higgs Boson H 1 border of discovery region at low tanb mostly determined by availability of inputs (VBF >110 GeV, ttH and > 70 GeV) border at low M H+- due to decoupling of H 1 from W,Z and t 30 fb -1 300 fb -1 ATLAS preliminary for VBF channels: assume same efficiencies for contribution of CP even and CP odd states (needs to be checked) for ttH: efficiencies for CP even and odd bosons are the same M. Schumacher, this conference.

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Looking for Standard signatures not sufficient to probe the presence of Higgs bosons decaying into lighter Higgs states. Lighter states have weak couplings to the weak gauge bosons, but large couplings to third generation down quarks and leptons. Possibility of looking for two taus and two bottoms (jets) signatures at LHC in the weak boson fusion production channel of two heavier Higgs bosons. J. Gunion, at this conference, argued that with luminosity about 300 inverse fb, the LHC will be able to detect such states. A detailed experimental simulation should be performed to test this possibility.

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CPsuperH Code to compute Higgs spectrum, couplings and decay modes in the presence of CP-violation Lee, Pilaftsis, Carena, Choi, Drees,Ellis, Lee,C.W.’03 CP-conserving case: Set phases to zero. Similar to HDECAY, but with the advantage that charged and neutral sector treated with same rate of accuracy. Combines calculation of masses and mixings by Carena, Ellis, Pilaftsis,C.W. with analysis of decays by Choi, Drees, Hagiwara, Lee and Song. Available at http://theory.ph.man.ac.uk/~jslee/CPsuperH.html

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Conclusions Low energy supersymmetry has an important impact on Higgs physics. It leads to definite predictions to the Higgs boson couplings to fermions and gauge bosons. Such couplings, however, are affected by radiative corrections induced by supersymmetric particle loops. CP-violation in low energy SUSY: Electroweak Baryogenesis. CP-violation in the Higgs sector is well motivated and should be studied in detail. It affects the searches for Higgs bosons at hadron and lepton colliders in an important way. At a minimum, it stresses the relevance of studying non-standard Higgs boson production and decay channels at lepton and hadron colliders.

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Generation Process Interaction with Higgs background creates a net chargino excess through CP-violating interactions Chargino interaction with plasma creates an excess of left-handed anti-baryons (right-handed baryons). Left-handed baryon asymmetry partially converted to lepton asymmetry via anomalous processes Remaining baryon asymmetry diffuses into broken phase Diffusion equations describing these processes derived

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Relevant masses and Phases The chargino mass matrix contains new CP violating phases Some of the phases may be absorved in field redefinition. For real Higgs v.e.v.’s, the phase is physical Sources depend on the Higgs profile. They vanish for large values of

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Gaugino and Higgsino masses of the order of the weak scale highly preferred M.Carena, M.Quiros, M. Seco and C.W. ‘02 Baryon Asymmetry Dependence on the Chargino Mass Parameters Baryon Asymmetry Enhanced for Even for large values of the CP-odd Higgs mass, acceptable values obtained for phases of order one. Results for maximal CP violation

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