Parity Symmetry at High-Energy: How High?

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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. The leading-order solution • The solution Parity symmetry at high-energy

16. CP phases Parity symmetry at high-energy

17. 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

18. mK

19. 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

20. 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

21. 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

22. 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 > 2.5 TeV! Parity symmetry at high-energy

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

24. 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

25. K-decay parameter 

26. : 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

27. 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

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

29. Neutron EDM dn

30. 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

31. 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

32. Bound on MWR from EDM Parity symmetry at high-energy

33. S(BJ/KS)

34. 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 Parity symmetry at high-energy

35. CKM fit Parity symmetry at high-energy

36. New contribution Parity symmetry at high-energy

37. Constraint from S(BJ/KS) • M>2.5 TeV Parity symmetry at high-energy

38. 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

39. 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