Parity Symmetry at High-Energy: How High?

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Parity Symmetry at High-Energy How High?
In collaboration with Zhang Yue An Haipeng R.N.
Mohapatra

• Xiangdong Ji
• U of Maryland

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Outline

• Introduction
• A minimal left-right symmetric model
• Solving for the right-handed quark mixing
• KL-KS mixing
• K-decay ? and neutron EDM
• CP-violating in B-decay
• Outlook

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Parity symmetry and its breaking

• 50 years ago, Lee and Yang discovered that parity
  is not a sacred symmetry of nature, it is broken
  in weak interactions!
• A fundamental discovery revolutionized the modern
  physics.
• However, the origin of this parity asymmetry
  remains obscure till today.
• Why God is left-handed?

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Parity restoration at high-energy?

• Some believe that parity might be a good symmetry
  at a more fundamental theory. It is only broken
  at low-energy due to the structure of the vacuum
  that we live in
• The dynamical equation is symmetric (in parity)
• But the low-energy solution is not!
• What are the signatures?
• To what extent, they are model-independent?

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Left-right symmetric model (LRSM)

• Based on gauge group SUL(2)XSUR(2)XUB-L(1) with
  parity symmetry at high-energy
• New gauge bosons WR Z'
• Explain the SM hypercharge
• Q I3L I3R (B L)/2
• Right-handed neutrino
• ?R (massive neutrinos!)
• Manifest and spontaneous CP violations

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A choice of the Higgs sector

• One left and right-handed triplet, ?L ?R,
  breaking the symmetry to the standard model
• ??R? (0,0,vR) vR is at least TeV scale
• One Higgs bi-doublet, ?, generating standard
  electroweak symmetry breaking
• ? is a CP violating phase
• ? and ?' are electroweak scale vevs

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Charged gauge bosons

• The mass of the WL is close to the SM gauge boson
  (80 GeV)
• The mass of the WR is unknown (exp bound gt 800
  GeV) MWR gvR
• They mix
• The mixing angle depends on the vevs

W1 WLcos? WRsin?
tan ? ??'/vR2 MWL2/MWR2 ?, ? ?/?
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Quark currents

• Both left and right-handed quark currents
  participate in weak interaction.
• The left-handed quark mixing follows the standard
  model CKM matrix.
• The right-handed coupling is a new unitary matrix
  in flavor space (quark mass eigenstates)
• 6 CP violating phases
• 3 rotational angles.
• 25 32 discrete sectors

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Quark mass matrices

• Quarks obtain masses through Yukawa coupling with
  Higgs bi-doublet
• where h and h-tilde are hermitian matrices.
• Mu and Md are general complex matrices and each
  must be diagonalized with two unitary matrices.
  Then right-handed quark mixing is independent of
  that of the left-handed quarks.

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Special limits

• There are two sources of CP violations
• Explicit CP violation in quark Yukawa coupling.
• Spontaneous CP violation (SCPV) in Higgs vev.
• When there is no SCPV, we have the limit of
  manifest left-right symmetry.
• When there is no explicit CPV, we have
  pseudo-manifest left right symmetry.
• In both cases the right-handed quark mixings are
  related to the CKM matrix.

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Manifest left-right symmetry

• When ?0, there is no SCPV, and the quark mass
  matrices are hermitian
• Both can be diagonalized by single unitary
  matrices.
• The right-handed quark mixing is the same as the
  CKM matrix, except for signs.

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Pseudo-manifest LR symmetry

• All CP violation is generated by SCPV.
• The CP phase in the CKM is also generated from
  the phase of the vev.
• Very beautiful idea!
• The quark mass matrices are now complex and
  symmetric, can be diagonalized by single unitary
  matrices
• The right-handed quark mixing elements have the
  same modulus as these of the CKM matrix.

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A solution in general case

• Observation
• Because mt is much large mb, it is quite possible
  that there is a hierarchy between different vevs,
  ???' barring a fine tuning.
• If so Mu is nearly hermitian, and one can neglect
  the small ?h-tilde term.
• Now the equation diagonlizing Md is

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Equation for VR

• Using the hermiticity condition for h-tilde, one
  has,
• Since it is a hermitian matrix eq., it has 9
  independent equations, which are sufficient for
  solving for 9 parameters in VR
• Let ? r mb/mt , the solution exists only for
  rsin? lt1

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The leading-order solution

• The solution

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CP phases
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Main features

1. The hierarchical structure of the mixing is
   similar to that of CKM.
2. Every element has a significant CP phase (first
   two families, order ? third family order 1),
   all related to the SCPV phase ?
3. 32 discrete solutions are manifest.
4. From the above solution, one can construct the
   unknown h-tilde and solve Mu more accurately.

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?mK
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KL-KS mixing

• The mass difference between KL-KS due to weak
  interaction.
• ?mK 3.5 X 1012 MeV
• SM contribution
• Long distance contribution,
• hard to calculate exactly, order 50, right sign
  
• Short distance contribution
• from intermediate charm quark. about 1/3 of the
  contribution, right sign.

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LRSM contribution

• Large!
• QCD correction, running from WR scale to 2 GeV,
  yielding a factor of 1.4
• Large logarithms ln(mWR2/mc2)
• Large QCD matrix elements
• (mK/msmd)2 ms 100 MeV

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The B-factor

• It was calculated by Wilson fermion formulation
  by UK QCD collaboration (Allton et al. PLB453,30)
• B4 1.03
• Recently it has also been calculated in
  domain-wall fermion formulation by Babich et al
• B4 0.8 (hep-lat/0605016)
• and CP-PACS (hep-lat/0610075)
• B4 0.70

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Constraint on MWR

• Because of the large hadronic matrix element, the
  bound on MWR is very strong.
• The new contribution has an opposite sign.
• The standard criteria is that the new
  contribution shall be less than the experimental
  value. This demands the SM contribution is 2?Mexp
• Using this criteria, one finds,
• MWR gt 2.5 TeV!

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Comparison with previous bounds

• Smaller strange quark mass
• QCD running effects
• In the most general CP-violation scenario.

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Is there a way to make the constraint relaxed?

• Cancellation from the top quark contribution?
• Top CKM is too small
• Cancellation from the flavor-changing neutral
  Higgs contribution
• They come with the same sign.
• Smaller right-handed CKM?
• Already fixed by the model, cannot be adjusted!

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K-decay parameter ?
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? Indirect CP violating in K-decay

• KL (predominantly CP-odd state) can decay into ??
  state (CP-even)
• The decay rate is proportional to ?3x103
• In SM, ? arises from the box diagram with
  top-quark intermediate states.
• In LRSM, WLWR box diagram provides the additional
  contribution.

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Box contribution

• Dirac phase contribution
• Large contribution due to enhanced hadronic
  matrix element
• New SCPV phase contribution
• Comes from c-quark intermediate state.
• Two contribution must cancel to generate
  reasonable size this large fixes the parameter
  rsin?

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Fixing SCPV phase ?
We have ignored large angle solutions
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Neutron EDM dn
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Neutron EDM

• Current best exp. bound
• dn lt 3.0 x 1026 ecm
• A new EDM exp. at LANL
• dn lt 6.0 x 1029 ecm, improvement by 500
• Standard Model prediction
• Second-order weak effect (hadron level 107)
• CP phase in s-gtd channel (104 )
• dn 1032 ecm

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EMD in LRSM

• First-order effect from
• WL WR mixing W1 WLsin? WRcos?
• Flavor-conserving, CP-odd weak current
• Hadronic uncertainty
• Single quark EDM
• Hadron loop calculation

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Bound on MWR from EDM
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S(B?J/?KS)
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B-decay constraint

• In general, constraints from B-decay are less
  severe because the hadronic matrix elements
  involved have no chiral enhancement.
• However, CP violation measurement in S(B?J/?KS)
  is so accurate that it does not allow significant
  contribution from new physics.
• SM phase

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CKM fit
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New contribution
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Constraint from S(B?J/?KS)

• Mgt2.5 TeV

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Outlook and conclusion

• With the standard Higgs choice, the bound on MWR
  on is about 2.5 TeV.
• Possible lower bound?
• Add supersymmetry
• Different Higgs structure
• Two Higgs doublet
• Hard to generate fermion mass
• LHC? ILC?

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LHC ILC

• At LHC, RH-W can be searched through 2 lepton2
  jet signals.
• A year running -gt bound 3.5 TeV
• At ILC, impossible in direct production
• Asymmetries through virtual production