Supersymmetry, Higgs Physics and CPViolation

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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, Weiglein98
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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
8

mh(GeV)
Carena, Haber, Hollik, Heinemeyer, Weiglein, C.W.
00 Heinemeyer, Hollik, Weiglein02 Degrassi,
Slavich, Zwirner 02
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.
Xt(GeV)
9
Espinosa,Gunion Carena,Mrenna,C.W.
10
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 taus or bs.
• LHC Weak boson fusion, with decays to taus,
  gammas or Ws.
• Associated production with top-quarks,
  decaying to bs 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 (taus final state)
Asociated production with top quarks (bs 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.

Pilaftis98, Pilaftsis,C.W.99 Demir99
Drees,Choi,Lee00 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 H1
ATLAS preliminary
30 fb-1
300 fb-1

• border of discovery region at low tanb mostly
  determined
• by availability of inputs (VBF gt110 GeV, ttH
  and gg gt 70 GeV)
• border at low MH- due to decoupling of H1 from
  W,Z and t

• 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.htm
  l

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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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Baryon Asymmetry Dependence on the Chargino Mass
Parameters
Results for maximal CP violation
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 Enhanced for
Even for large values of the CP-odd Higgs mass,
acceptable values obtained for phases of order
one.