1. Parity Symmetry at High- Energy: How High? Xiangdong Ji U of Maryland In collaboration with Zhang Yue An Haipeng R.N. Mohapatra

2. 3/20/07Parity symmetry at high-energy Outline Introduction A minimal left-right symmetric model Solving for the right-handed quark mixing K L -K S mixing K-decay  and neutron EDM CP-violating in B-decay Outlook

3. 3/20/07Parity 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?

4. 3/20/07Parity 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?

5. 3/20/07Parity symmetry at high-energy Left-right symmetric model (LRSM) Based on gauge group SU L (2)XSU R (2)XU B-L (1) with parity symmetry at high-energy New gauge bosons: W R & Z' Explain the SM hypercharge Q = I 3L + I 3R + (B – L)/2 Right-handed neutrino R (massive neutrinos!) Manifest and spontaneous CP violations

6. 3/20/07Parity 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,v R ) v R is at least TeV scale One Higgs bi-doublet, , generating standard electroweak symmetry breaking  is a CP violating phase  and  ' are electroweak scale vevs

7. 3/20/07Parity symmetry at high-energy Charged gauge bosons The mass of the W L is close to the SM gauge boson (80 GeV) The mass of the W R is unknown (exp bound > 800 GeV): M W R = gv R They mix The mixing angle depends on the vevs W 1 = W L cos  + W R sin  tan  =  '/v R 2 = M W L 2 /M W R 2 ,  =  ’/ 

8. 3/20/07Parity 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. 2 5 = 32 discrete sectors

9. 3/20/07Parity 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. M u and M d 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.

10. 3/20/07Parity 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.

11. 3/20/07Parity 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.

12. 3/20/07Parity 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.

13. 3/20/07Parity symmetry at high-energy A solution in general case Observation: Because m t is much large m b, it is quite possible that there is a hierarchy between different vevs,  ' barring a fine tuning. If so M u is nearly hermitian, and one can neglect the small  h-tilde term. Now the equation diagonlizing M d is

14. 3/20/07Parity symmetry at high-energy Equation for V R 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 V R Let  = r m b /m t, the solution exists only for rsin  <1

15. 3/20/07Parity symmetry at high-energy The leading-order solution The solution

16. 3/20/07Parity symmetry at high-energy CP phases

17. 3/20/07Parity symmetry at high-energy 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 M u more accurately.

18. mKmK

19. 3/20/07Parity symmetry at high-energy K L -K S mixing The mass difference between K L -K S due to weak interaction.  m K = 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.

20. 3/20/07Parity symmetry at high-energy LRSM contribution Large! QCD correction, running from W R scale to 2 GeV, yielding a factor of ~ 1.4 Large logarithms ln(m W R 2 /m c 2 ) Large QCD matrix elements ~ (m K /m s +m d ) 2 m s ~ 100 MeV

21. 3/20/07Parity symmetry at high-energy The B-factor It was calculated by Wilson fermion formulation by UK QCD collaboration ( Allton et al. PLB453,30 ) B 4 = 1.03 Recently it has also been calculated in domain- wall fermion formulation by Babich et al B 4 = 0.8 (hep-lat/0605016) and CP-PACS (hep-lat/0610075) B 4 = 0.70

22. 3/20/07Parity symmetry at high-energy Constraint on M W R Because of the large hadronic matrix element, the bound on M W R 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  M exp Using this criteria, one finds, M W R > 2.5 TeV!

23. 3/20/07Parity symmetry at high-energy Comparison with previous bounds Smaller strange quark mass QCD running effects In the most general CP-violation scenario.

24. 3/20/07Parity 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!

25. K-decay parameter 

26. 3/20/07Parity symmetry at high-energy  : Indirect CP violating in K-decay K L (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, W L W R box diagram provides the additional contribution.

27. 3/20/07Parity 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 

28. 3/20/07Parity symmetry at high-energy Fixing SCPV phase  We have ignored large angle solutions

29. Neutron EDM d n

30. 3/20/07Parity symmetry at high-energy Neutron EDM Current best exp. bound d n < 3.0 x 10 –26 ecm A new EDM exp. at LANL d n < 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 ) d n ~ 10 –32 ecm

31. 3/20/07Parity symmetry at high-energy EMD in LRSM First-order effect from W L & W R mixing: W 1 = W L sin  + W R cos  Flavor-conserving, CP-odd weak current Hadronic uncertainty Single quark EDM Hadron loop calculation

32. 3/20/07Parity symmetry at high-energy Bound on M W R from EDM

33. S(B  J/  K S )

34. 3/20/07Parity 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(B  J/  K S ) is so accurate that it does not allow significant contribution from new physics. SM phase

35. 3/20/07Parity symmetry at high-energy CKM fit

36. 3/20/07Parity symmetry at high-energy New contribution

37. 3/20/07Parity symmetry at high-energy Constraint from S(B  J/  K S ) M>2.5 TeV

38. 3/20/07Parity symmetry at high-energy Outlook and conclusion With the standard Higgs choice, the bound on M W R on is about 2.5 TeV. Possible lower bound? Add supersymmetry Different Higgs structure Two Higgs doublet Hard to generate fermion mass LHC? ILC?

39. 3/20/07Parity 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