CP Violation in Hyperon Decays Xiao-Gang He Workshop on form factor, polarization and CP violation in quantum-correlated hyperon-anti-hyperon production Fudan University, Shanghai 7-8, July, 2019

Decay Modes F

Observables (Donoghue and Pakvasa, PRL55(1985)162, Donoghue, He and Pakvasa, PRD 34 (1986)833) B -> F M B initial baryon F baryon in the final state M meson in the final state S p-parity violating P p-parity conserving

CPV observables diS,P –CP violating phase fiS,P – CP conserving phase

Isospin decomposition of Hyperon decay amplitudes

Quantities need to know L -> p N: d1 = 6.0o, d3=-3.8o, d11=-1.1o, d31=-0.7o X -> p L: d2 = -18.7o, d21=-2.7o Amplitudes known from Br S -> p N: d1 = 9.4o, d3=-10.1o, d11=-1.8o, d31=-3.6o Need to know weak phases fS,Pi

SM calculation for Weak phases fS,Pi Tree and penguin contributions A. Buras et al., ReV. Mod. Phys.

Buchalla et al., Rev. Mod. Phys. 68, 1125(1996)

ImC5=Im(-Vtd*Vts/Vud*Vus) Y6

SM for CPV in Hyperon Decays Scaled by ImC5/10-4 ~ 0.8 present value J. Tandean and G. Valencia, Phys. Rev. D 67, 056001 (2003)  [hep-ph/0211165].

J. Tandean, Phys. Rev. D 70, 076005 (2004)  [hep-ph/0406274]. J. Tandean and G. Valencia, Phys. Lett. B 451, 382 (1999)  [hep-ph/9811376] Rate asymmetry 2x10-5

HyperCP Collaboration (Holtmstrom et al, PRL 93(2004)262001) ~ AL + AX Theory SM: |ALX| < 10-4

Beyond SM for CPV in Hyperon Decays Beyond SM, CP violating effects can be larger Examples Left-Right symmetric, Supersymmetric modela A can be as large as ~ a few 10-4

Left-Right symmetric model D. Chang, N. Deshpande, X-G Left-Right symmetric model D. Chang, N. Deshpande, X-G. He PRL74 (1995) 3927 SU(3)C x SU(2)L x SU(2)R x U(1)B-L Besides WL for SU(2)L there is additional WR for SU(2)R They mix with each other Mixing angle x There are VKML and also VKMR More CP violating phases DS = 1 effective Hamiltonian HSM from WL, HR from WR, and HLR from mixing

Using data for CP conserving amplitudes, we have For O+,- contributions, using factorization calculation For the dipole term, using bag model Similar calculation for gluon dipole operator by J. Tandean, Phys. Rev. D 69, 076008 (2004)  [hep-ph/0311036].

Constrained from e’/e = (1.65 +- 0.23)x10-3 (PDG) x < 4 10-3 from data Assuming |VLij| ~ |VRij| New CPV phases take sin(phase) ~1 A(L) can be as large as a few 10-4 A(X) can be as large as 10-4

Supersymmetric Model He, Murayama, Pakvasa, Valencia, PRD61(2000)071701(R) Exchange gluino can induce gluonic color dipole interaction 0.7Bs < Bp < 1.3 Bs

A(L) constrained, but can be as large as a few x10-4 .

Similar things for B-baryon decays M. He, X-G He and G. N Similar things for B-baryon decays M. He, X-G He and G.N. Li PRD92(2015)036010

Interesting U-spin pair relations

CP violation in J/Y -> Hyperon Pairs X-G He, J. P. Ma and B CP violation in J/Y -> Hyperon Pairs X-G He, J. P. Ma and B. McKellar, PRD47(1993)1745(R), PRD49(1994)4548 d term violates CP d term violates CP

CPV observable L -> p p measures spin

With 109 J/Y the sensitivity for hyperon edm Can reach 10-17 ecm Not competative with n and p edm But better than current L edm limit which is 15x 10-16 ecm

Conclusion CP violation effect exist in hyperon decays. Correlated ploarization measurement for the quantity A(B) reaching 10-5 sensitivity will test the the SM to a good precision. With a few 10-4 sensitivity will rule out some theoretical models beyond the SM. J/y decays into L-pair, will also provide important CP violation beyond the SM. BES III can rule out some parameter space in beyond SM models. STCF can reach SM predicted range.