Title: About June Workshop
1About June Workshop
- China-US workshop on parity conservation at
high-energy, IHEP, June 11-12 - International Committee
- G.Altarelli, A.Arima, K.T.Chao, H.S.Chen,
F.Gilman, X.Ji, Y.P.Kuang, Y.K.Kim, T.D. Lee,
R.Mohapatra, H. W.Panofsky, Y.L.Wu, M.H.Ye - Speakers from overseas
- Speakers from China?
- Website under construction
2Parity Symmetry at High-Energy How High?
In collaboration with Zhang Yue An Haipeng R.N.
Mohapatra
- Xiangdong Ji
- UMD/PKU/ITP,CAS
3Outline
- 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
4Parity 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?
5Parity 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?
6Left-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 violation
7A 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
8Charged 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 gt 800
GeV) MWR gvR - They mix
- The mixing angle depends on the vevs
W1 WLcos? WRsin?
tan ? ??'/vR2 MWL2/MWR2 ?, ? ?/?
9Quark 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
10Quark 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.
11Special 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.
12Manifest 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.
13Pseudo-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.
14A 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
15Equation 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? lt1
16The leading-order solution
17CP phases
18Main features
- The hierarchical structure of the mixing is
similar to that of CKM. - Every element has a significant CP phase (first
two families, order ? third family order 1),
all related to the SCPV phase ? - 32 discrete solutions are manifest.
- From the above solution, one can construct the
unknown h-tilde and solve Mu more accurately.
19?mK
20KL-KS mixing
- The mass difference between KL-KS due to weak
interaction. - ?mK 3.5 X 1012 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.
21LRSM contribution
- Large!
- QCD correction, running from WR scale to 2 GeV,
yielding a factor of 2.8 - Large logarithms ln(mWR2/mc2)
- Large QCD matrix elements
- (mK/msmd)2 ms 100 MeV
22The 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
23Constraint 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 2?Mexp - Using this criteria, one finds,
- MWR gt 3.6 TeV!
24Comparison with previous bounds
- Smaller strange quark mass
- QCD running effects
25Is 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!
26 K-decay parameter ?
27? Indirect CP violating in K-decay
- KL (predominantly CP-odd state) can decay into ??
state (CP-even) - The decay rate is proportional to ?3x103
- In SM, ? arises from the box diagram with
top-quark intermediate states. - In LRSM, WLWR box diagram provides the additional
contribution.
28Box 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?
29Fixing SCPV phase ?
We have ignored large angle solutions
30Neutron EDM dn
31Neutron EDM
- Current best exp. bound
- dn lt 3.0 x 1026 ecm
- A new EDM exp. at LANL
- dn lt 6.0 x 1029 ecm, improvement by 500
- Standard Model prediction
- Second-order weak effect (hadron level 107)
- CP phase in s-gtd channel (104 )
- dn 1032 ecm
32EMD 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
33 Bound on MWR from EDM
34Uncertainty from hadronic physics
35S(B?J/?KS)
36B-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(B?J/?KS)
is so accurate that it does not allow significant
contribution from new physics. - SM phase
37CKM fit
38New contribution
39Constraint from S(B?J/?KS)
40Possible ways out
- Add supersymmetry
- Different Higgs structure?