parity symmetry at high- energy: how high? xiangdong ji u of maryland in collaboration with zhang...

Parity Symmetry at High-Energy: How High?

Xiangdong JiU of Maryland

In collaboration withZhang YueAn HaipengR.N. Mohapatra

3/20/07 Parity symmetry at high-energy

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 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 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?


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


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


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 = MWL

2/MWR2 , = ’/


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


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.


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.


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.


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.


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


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


The leading-order solution The solution


CP phases


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 Mu more accurately.


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.


LRSM contribution

Large! QCD correction, running from WR scale to 2 GeV,

yielding a factor of ~ 1.4 Large logarithms ln(mWR

2/mc2)

Large QCD matrix elements ~ (mK/ms+md)2 ms ~ 100 MeV


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


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 2Mexp

Using this criteria, one finds, MWR

> 2.5 TeV!


Comparison with previous bounds Smaller strange quark mass QCD running effects In the most general CP-violation scenario.


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!

K-decay parameter


: 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.


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


Fixing SCPV phase

We have ignored large angle solutions

Neutron EDM dn


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


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


Bound on MWR from EDM

S(BJ/KS)


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(BJ/KS) is so accurate that it does not allow significant contribution from new physics.

SM phase

cscb

cscb

tdtb

tdtb

VVVV

VVVV

*

*

*

*


CKM fit


New contribution


Constraint from S(BJ/KS) M>2.5 TeV


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?


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 productionAsymmetries through virtual production

parity symmetry at high- energy: how high? xiangdong ji u of maryland in collaboration with zhang...

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