Mixing in Quarks and Leptons Xiao-Gang He NTU&SJTU NTU&SJTU 1. Mixing in Quarks and Neutrinos 2. Unitarity Tests of Mixing Matrices 3. Some Recent Hints of New Physics 4. Conclusions

1. Mixing in Quarks and Neutrinos

Quark mixing A convenient parameterization: The Wolfenstein parameterization A convenient parameterization: The Wolfenstein parameterization

The Unitairty Triangle: CPV Jarlskog Parameter J = Area/2 Test of SM: alpha + beta + gamma = 180 degree. But, does not contain all information of KM matrix! Only 3 independent parameters, KM has 4 parameters! Need a better way to represent KM graphically: The Univertarity Boomerang. (Frampton and He)

Unitarity Boomerang ( Frampton and He ) Combining two unitarity triangle with a common angle form a unitarity boomerang which contains all KM information.

Total 9+9 Boomerangs Common Feature: J^2/4 rule

Neutrino Mixing Three light neutrinos, Z decay, N = 2.983\pm 0.009, 3 neutrino mixing

Summary of mixing angles

Good approximation for neutrino mixing: The tri-bimaximal matrix Harrison, Perkins & Scott; Zhi-Zhong Xing; Xiao-Gang He & A. Zee Good approximation for quark mixing: The unit matrix Very different mixing patterns for quarks and neutrinos! Some interesting features

Natural Zero-th order mixing matrices

The natural 0-th order mixing matrix for quark

The natural 0-th order mixing matrix for neutrino – tri-bimaximal mixing Babu and He, He, Keum & Volkas Specific models have been constructed with A4 family, Independent of lepton masses

Good approximation for neutrino mixing: The tri-bimaximal matrix Harrison, Perkins & Scott; Zhi-Zhong Xing; Xiao-Gang He & A. Zee Good approximation for quark mixing: The unit matrix But: Hint some deeper reason? Q-L Complementarity He, Li & Ma Quark –Lepton Complementarity

A better 0th order expansion for quarks? A new proposal: Tri-minimal parameterization S.-W.Li & Q.-Q. Ma

Much faster convergence than Wolfenstein parameterization! He Li & Ma

Exact Q-L complementarity With deviations A theoretical understanding of Q-L complementarity is still lacking! Exact Q-L complementarity With deviations A theoretical understanding of Q-L complementarity is still lacking!

2. Unitarity Tests of Mixing Matrices The quark sector

More general W- interaction with quarks Example: Left-Right symmetric model with more than 3 generations can induce right-handed current to V CKM and make the 3x3 first 3 generation V CKM non-unitary. Use unitary gauge if not known the full particle contents. He, Tandean & Valencia, Xiao et al.,,,

There are rooms for violation of unitarity. Further tests are needed

Neutrino Mixing Three light neutrinos, Z decay, N = 2.983\pm 0.009, 3 neutrino mixing

The lepton sector Summary from Valle. Still has large room for non-unitarity at 10 percent level, something new may be there to make it happen. Example: Seesaw models.

Large light and heavy neutrino mixing in Seesaw models

Can Seesaw Models cause large non-unitary deviation in U PMNS ? Naively, No! … But … Constraints on elements in U \nu N

Kerstin & Smirnov; Xing et al.; He, Oh, Tandean &Wen

Possible to have large elements in U \nu N and therefore observable non-unitarity in lepton mixing!

andean Interesting application of large U \nu N at the LHC He, Oh, Tandean & Wen; Li & He

4. Some Recent Hints for New Physics Large CP violation in Bs – anti-Bs system.

Only change M 12 is not enough. Need G 12 to be large too. Deshpande, He Valencia, PRD

Problems with beyond SM models: M 12 easy to change, but G 12 is not. Large G 12 : Long distance SM physics: need to real show what is Happening. No concrete real evaluations. Z’, 4 th Generation, SUSY … easy for large change for M 12, not G 12 A unparticle possibility: propagator proportional to (-1)^d, d-dimension of unparticle. Unparticle contribution: G 12 /M 12 = 2tan( p d). Easy to have large G 12 (He, Ren and Xie in preparation)

New results from MiniBoon and MINOS MiniBoon: neutrino oscillation data do not agree with LSND, but anti- neutrino data agree. (Electron neutrino and anti-neutrino) MINOS data (muon neutrion and anti-neutrinos)

Neutrino and anti-neutrinos oscillate differently. CPT violation? Possible. Other possibility also exist: Min-Boom/LSND: non-standard neutrino interaction making Neutrino and anti-neutrino production and detect differently. Need additional sterile Neutrions (Akhmedov and Schwetz, arXiv: ). MINOS: There may be a potential on the earth due to vector like interaction (making neutrino and anti-neutrino interaction change sign). A lot of activites are going on in trying to explain data.

5. Conclusions The CKM and PMNS mixing matrices for quark and lepton sectors describe related phenomena well. The quark mixing is approximated by a unit matrix and the lepton mixing is by the tri- bimaximal matrix. The tri-bimaximal mixing can be understood from theoretical point of view. There are interesting relations between quark and lepton mixing, the quark-lepton complementarity. Theoretical understanding these relations are poor. There are rooms of violating the unitarity of the mixing matrices both in quark and lepton sector. Seesaw models can give large mixing between light and heavy neutrinos, and therefore large violation of unitarity in lepton mixing. Theoretical models can be constructed. There are interesting LHC physics may results. There are hints for new physics beyond SM from Bs mixing and neutrino mixing.