Mixing in Quarks and LeptonsMixing in Quarks and Leptons

Xiao-Gang HeXiao-Gang He

NTU&SJTUNTU&SJTU

1.1.Mixing in Quarks and NeutrinosMixing in Quarks and Neutrinos

2.2.Unitarity Tests of Mixing MatricesUnitarity Tests of Mixing Matrices

3.3.Some Recent Hints of New PhysicsSome Recent Hints of New Physics

4.4.ConclusionsConclusions

1. Mixing in Quarks and Neutrinos1. Mixing in Quarks and Neutrinos

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

The Unitairty Triangle: The Unitairty Triangle:

CPV Jarlskog Parameter J = Area/2CPV Jarlskog Parameter J = Area/2

Test of SM: alpha + beta + gamma = 180 degree. Test of SM: alpha + beta + gamma = 180 degree.

But, does not contain all information of KM matrix! But, does not contain all information of KM matrix!

Only 3 independent parameters, KM has 4 parameters!Only 3 independent parameters, KM has 4 parameters!

Need a better way to represent KM graphically: Need a better way to represent KM graphically:

The Univertarity Boomerang.The Univertarity Boomerang. (Frampton and He)(Frampton and He)

Unitarity Boomerang (Unitarity Boomerang (Frampton and HeFrampton and He))

Combining two unitarity triangle with a common angle form a unitarity Combining two unitarity triangle with a common angle form a unitarity

boomerang which contains all KM information.boomerang which contains all KM information.

Total 9+9 BoomerangsTotal 9+9 Boomerangs

Common Feature: J^2/4 ruleCommon Feature: J^2/4 rule

Neutrino MixingNeutrino Mixing

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

Summary of mixing anglesSummary of mixing angles

Good approximation for neutrino mixing:Good approximation for neutrino mixing:

The tri-bimaximal matrixThe tri-bimaximal matrix

Harrison, Perkins & Scott; Zhi-Zhong Xing; Harrison, Perkins & Scott; Zhi-Zhong Xing; Xiao-Gang He & A. ZeeXiao-Gang He & A. Zee

Good approximation for quark mixing:Good approximation for quark mixing:

The unit matrixThe unit matrix

Very different mixing patterns for quarks and Very different mixing patterns for quarks and neutrinos!neutrinos!

Some interesting featuresSome interesting features

Natural Zero-th order mixing matricesNatural Zero-th order mixing matrices

The natural 0-th order mixing matrix for quarkThe natural 0-th order mixing matrix for quark

The natural 0-th order mixing matrix for neutrino The natural 0-th order mixing matrix for neutrino – tri-bimaximal mixing– tri-bimaximal mixing

Babu and He, He, Keum & VolkasBabu and He, He, Keum & Volkas

Specific models have been constructed with A4 family,Specific models have been constructed with A4 family,Independent of lepton massesIndependent of lepton masses

Good approximation for neutrino mixing:Good approximation for neutrino mixing:

The tri-bimaximal matrixThe tri-bimaximal matrix

Harrison, Perkins & Scott; Zhi-Zhong Xing; Xiao-Gang He & A. ZeeHarrison, Perkins & Scott; Zhi-Zhong Xing; Xiao-Gang He & A. Zee

Good approximation for quark mixing:Good approximation for quark mixing:

The unit matrixThe unit matrix

But:But:

Hint some deeper reason? Q-L ComplementarityHint some deeper reason? Q-L ComplementarityHe, Li & MaHe, Li & Ma

Quark –Lepton ComplementarityQuark –Lepton Complementarity

A better 0th order expansion for quarks?A better 0th order expansion for quarks?

A new proposal: Tri-minimal parameterizationA new proposal: Tri-minimal parameterizationS.-W.Li & Q.-Q. MaS.-W.Li & Q.-Q. Ma

Much faster convergence than Much faster convergence than Wolfenstein parameterization!Wolfenstein parameterization!

He Li & MaHe Li & Ma

Exact Q-L complementarityExact Q-L complementarity

With deviations With deviations

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

2. Unitarity Tests of Mixing Matrices2. Unitarity Tests of Mixing Matrices

The quark sectorThe quark sector

More general W- interaction with quarksMore general W- interaction with quarks

Example: Example:

Left-Right symmetric model with more than Left-Right symmetric model with more than

3 generations can induce right-handed 3 generations can induce right-handed

current to Vcurrent to VCKM CKM and make the 3x3 first 3 and make the 3x3 first 3

generation Vgeneration VCKM CKM non-unitary.non-unitary.

Use unitary gauge if not known the full particle contents.Use unitary gauge if not known the full particle contents.

He, Tandean & Valencia, Xiao et al. ,,,He, Tandean & Valencia, Xiao et al. ,,,

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

Neutrino MixingNeutrino Mixing

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

The lepton sectorThe lepton sector

Summary from Valle.Summary from Valle.

Still has large room for non-unitarity at 10 percent level , something Still has large room for non-unitarity at 10 percent level , something

new may be there to make it happen. Example: Seesaw models.new may be there to make it happen. Example: Seesaw models.

Large light and heavy neutrino mixing in Seesaw modelsLarge light and heavy neutrino mixing in Seesaw models

Can Seesaw Models cause large non-unitary Can Seesaw Models cause large non-unitary deviation in Udeviation in UPMNSPMNS??

Naively, No! … But …Naively, No! … But …

Constraints on elements in UConstraints on elements in U\nu N\nu N

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

Possible to have large elements in UPossible to have large elements in U \nu N\nu N and and

therefore observable non-unitarity in lepton mixing!therefore observable non-unitarity in lepton mixing!

andeanandean

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

4. Some Recent Hints for New Physics4. Some Recent Hints for New Physics

Large CP violation in Bs – anti-Bs system.Large CP violation in Bs – anti-Bs system.

Only change MOnly change M1212 is not enough. Need is not enough. Need 1212 to be large too. Deshpande, He Valencia, PRD to be large too. Deshpande, He Valencia, PRD

Problems with beyond SM models: MProblems with beyond SM models: M1212 easy to change, but easy to change, but 12 12 is not.is not.

Large Large 1212 : Long distance SM physics: need to real show what is : Long distance SM physics: need to real show what is

Happening. No concrete real evaluations.Happening. No concrete real evaluations.

Z’, 4Z’, 4thth Generation, SUSY … easy for large change for M Generation, SUSY … easy for large change for M1212, not , not 12 12

A unparticle possibility: A unparticle possibility:

propagator proportional to (-1)^d , d-dimension of unparticle.propagator proportional to (-1)^d , d-dimension of unparticle.

Unparticle contribution: Unparticle contribution: 1212/M/M12 12 = 2tan( = 2tan( d). Easy to have large d). Easy to have large 1212

(He, Ren and Xie in preparation)(He, Ren and Xie in preparation)

New results from MiniBoon and MINOSNew results from MiniBoon and MINOS

MiniBoon: neutrino oscillation data do not agree with LSND, but anti-MiniBoon: neutrino oscillation data do not agree with LSND, but anti-

neutrino data agree. (Electron neutrino and anti-neutrino)neutrino data agree. (Electron neutrino and anti-neutrino)

MINOS data (muon neutrion and anti-neutrinos)MINOS data (muon neutrion and anti-neutrinos)

Neutrino and anti-neutrinos oscillate differently.Neutrino and anti-neutrinos oscillate differently.

CPT violation? Possible.CPT violation? Possible.

Other possibility also exist: Other possibility also exist:

Min-Boom/LSND: Min-Boom/LSND: non-standard neutrino interaction making Neutrino non-standard neutrino interaction making Neutrino

and anti-neutrino production and detect differently. Need additional sterile and anti-neutrino production and detect differently. Need additional sterile

Neutrions (Akhmedov and Schwetz, arXiv: 1007.4171).Neutrions (Akhmedov and Schwetz, arXiv: 1007.4171).

MINOS: There may be a potential on the earth due to vector like interaction MINOS: There may be a potential on the earth due to vector like interaction

(making neutrino and anti-neutrino interaction change sign).(making neutrino and anti-neutrino interaction change sign).

A lot of activites are going on in trying to explain data.A lot of activites are going on in trying to explain data.

5. Conclusions5. Conclusions

The CKM and PMNS mixing matrices for quark and lepton sectors describe related The CKM and PMNS mixing matrices for quark and lepton sectors describe related phenomena well.phenomena well.

The quark mixing is approximated by a unit matrix and the lepton mixing is by the tri-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 bimaximal matrix. The tri-bimaximal mixing can be understood from theoretical point of view.of view.

There are interesting relations between quark and lepton mixing, the quark-lepton There are interesting relations between quark and lepton mixing, the quark-lepton complementarity. Theoretical understanding these relations are poor.complementarity. Theoretical understanding these relations are poor.

There are rooms of violating the unitarity of the mixing matrices both in quark and There are rooms of violating the unitarity of the mixing matrices both in quark and lepton sector. lepton sector.

Seesaw models can give large mixing between light and heavy neutrinos, and Seesaw models can give large mixing between light and heavy neutrinos, and therefore large violation of unitarity in lepton mixing. Theoretical models can be therefore large violation of unitarity in lepton mixing. Theoretical models can be constructed. There are interesting LHC physics may results. constructed. There are interesting LHC physics may results.

There are hints for new physics beyond SM from Bs mixing and neutrino mixing.There are hints for new physics beyond SM from Bs mixing and neutrino mixing.