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About June Workshop

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China-US workshop on parity conservation at high-energy, IHEP, June 11-12 ... that there is a hierarchy between different vevs, ' barring a fine tuning. ... – PowerPoint PPT presentation

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Title: About June Workshop


1
About 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

2
Parity Symmetry at High-Energy How High?
In collaboration with Zhang Yue An Haipeng R.N.
Mohapatra
  • Xiangdong Ji
  • UMD/PKU/ITP,CAS

3
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

4
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?

5
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?

6
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 violation

7
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

8
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 gt 800
    GeV) MWR gvR
  • They mix
  • The mixing angle depends on the vevs

W1 WLcos? WRsin?
tan ? ??'/vR2 MWL2/MWR2 ?, ? ?/?
9
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

10
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.

11
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.

12
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.

13
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.

14
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

15
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? lt1

16
The leading-order solution
  • The solution

17
CP phases
18
Main 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
20
KL-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.

21
LRSM 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

22
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

23
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 2?Mexp
  • Using this criteria, one finds,
  • MWR gt 3.6 TeV!

24
Comparison with previous bounds
  • Smaller strange quark mass
  • QCD running effects

25
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!

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.

28
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?

29
Fixing SCPV phase ?
We have ignored large angle solutions
30
Neutron EDM dn
31
Neutron 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

32
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

33
Bound on MWR from EDM
34
Uncertainty from hadronic physics
35
S(B?J/?KS)
36
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(B?J/?KS)
    is so accurate that it does not allow significant
    contribution from new physics.
  • SM phase

37
CKM fit
38
New contribution
39
Constraint from S(B?J/?KS)
40
Possible ways out
  • Add supersymmetry
  • Different Higgs structure?
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