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Parity Symmetry at High-Energy: How High?
Xiangdong JiU of Maryland
In collaboration withZhang YueAn HaipengR.N. Mohapatra
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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
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3/20/07 Parity symmetry at high-energy
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?
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3/20/07 Parity symmetry at high-energy
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?
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
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 , = ’/
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
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.
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3/20/07 Parity symmetry at high-energy
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.
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3/20/07 Parity symmetry at high-energy
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.
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3/20/07 Parity symmetry at high-energy
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.
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
The leading-order solution The solution
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3/20/07 Parity symmetry at high-energy
CP phases
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3/20/07 Parity symmetry at high-energy
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.
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mK
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3/20/07 Parity symmetry at high-energy
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.
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
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!
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3/20/07 Parity symmetry at high-energy
Comparison with previous bounds Smaller strange quark mass QCD running effects In the most general CP-violation scenario.
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3/20/07 Parity symmetry at high-energy
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!
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K-decay parameter
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3/20/07 Parity symmetry at high-energy
: 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.
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
Fixing SCPV phase
We have ignored large angle solutions
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Neutron EDM dn
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
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
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3/20/07 Parity symmetry at high-energy
Bound on MWR from EDM
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S(BJ/KS)
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3/20/07 Parity symmetry at high-energy
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
*
*
*
*
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3/20/07 Parity symmetry at high-energy
CKM fit
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3/20/07 Parity symmetry at high-energy
New contribution
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3/20/07 Parity symmetry at high-energy
Constraint from S(BJ/KS) M>2.5 TeV
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3/20/07 Parity symmetry at high-energy
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?
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3/20/07 Parity symmetry at high-energy
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