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## Parity Symmetry at High-Energy: How High?

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### Parity Symmetry at High-Energy: How High?

Xiangdong Ji

U of Maryland

In collaboration with

Zhang Yue

An Haipeng

R.N. Mohapatra

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

Parity symmetry at high-energy

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?

Parity symmetry at high-energy

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?

Parity symmetry at high-energy

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

Parity symmetry at high-energy

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

Parity symmetry at high-energy

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 > 800 GeV): MWR = gvR
- They mix
- The mixing angle depends on the vevs

W1 = WLcos + WRsin

tan = '/vR2 = MWL2/MWR2 , = ’/

Parity symmetry at high-energy

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

Parity symmetry at high-energy

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.

Parity symmetry at high-energy

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.

Parity symmetry at high-energy

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.

Parity symmetry at high-energy

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.

Parity symmetry at high-energy

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

Parity symmetry at high-energy

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 <1

Parity symmetry at high-energy

CP phases

Parity symmetry at high-energy

Main features

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

Parity symmetry at high-energy

KL-KS mixing

- The mass difference between KL-KS due to weak interaction.
- mK = 3.5 X 10–12 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.

Parity symmetry at high-energy

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/ms+md)2 ms ~ 100 MeV

Parity symmetry at high-energy

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

Parity symmetry at high-energy

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 2Mexp
- Using this criteria, one finds,

MWR > 2.5 TeV!

Parity symmetry at high-energy

Comparison with previous bounds

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

Parity symmetry at high-energy

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!

Parity symmetry at high-energy

: Indirect CP violating in K-decay

- KL (predominantly CP-odd state) can decay into state (CP-even)
- The decay rate is proportional to =3x10–3
- In SM, arises from the box diagram with top-quark intermediate states.
- In LRSM, WLWR box diagram provides the additional contribution.

Parity symmetry at high-energy

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

Parity symmetry at high-energy

Neutron EDM

- Current best exp. bound

dn < 3.0 x 10–26 ecm

- A new EDM exp. at LANL

dn < 6.0 x 10–29 ecm, improvement by 500

- Standard Model prediction
- Second-order weak effect (hadron level 10–7)
- CP phase in s->d channel (10–4 )
- dn ~ 10–32 ecm

Parity symmetry at high-energy

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

Parity symmetry at high-energy

Bound on MWR from EDM

Parity symmetry at high-energy

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(BJ/KS) is so accurate that it does not allow significant contribution from new physics.
- SM phase

Parity symmetry at high-energy

CKM fit

Parity symmetry at high-energy

New contribution

Parity symmetry at high-energy

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?

Parity symmetry at high-energy

LHC & ILC

- At LHC, RH-W can be searched through 2 lepton+2 jet signals.

A year running -> bound 3.5 TeV

- At ILC, impossible in direct production

Asymmetries through virtual production

Parity symmetry at high-energy

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