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Learning ( 0 ) from B decays. Chuan-Hung Chen. Department of Physics, National Cheng-Kung University, Tainan, Taiwan. Introduction & Our question. - 0 mixing. B ! K (*) ( 0 ) decays. Discussion. b. d. t. t. b. d. Introduction: what questions can we ask in B Physics?.
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Learning (0) from B decays Chuan-Hung Chen Department of Physics, National Cheng-Kung University, Tainan, Taiwan • Introduction & Our question • -0 mixing • B! K(*)(0)decays • Discussion
b d t t b d • Introduction: what questions can we ask in B Physics? • Determine the CP violating phases: A3Rbe-i3 A3Rte-i1 Precision measurement • Find new CP violating sources
Test standard model & search for the new effects: • Extra dimensions • Noncommutative spaces … • Supersymmetric models … • Grand unified theories (GUTs) … • Clarify and find new states or new decay modes, such as • DsJ(2317) , DsJ(2457), B! X(3872) K,… • Why PL» PT in B! K* decays? • Test QCD approach Belle Collaboration • QCD factorization approach, perturbative QCD approach… • Do final state interactions play important role in B decays?
How to understand? Our question: C.W. Chiang etal., hep-ph/0404037 (in units of 10-6 ) Theoretical estimation Br(B!0 K0 )» 35 £ 10-6
1 0 8 • However, UA(1) is broken by anomaly, 1 cannot be a Goldstone boson, m0=958 MeV; m=547 MeV -0 mixing: According to quark model with SU(3) flavor symmetry, the mesonic states could be obtained by • If UA(1) is a good symmetry and quarks are massless, there are nine Goldstone bosons • Since ms>>mu,d, 8 and 1 will mix.
The decay constants, defined as will have the relation With a parton Fock state decomposition, One-angle scheme:
RJ/=5.0 ± 0.8 Combining P!, J/! P decays and P transition form factors, it has been shown that one-angle parametrization cannot match with the results of ’Pt and experiments
Therefore, two-angle scheme is introduced. Leutwyler, NPPS64, 223(‘98)
Another quark-flavor scheme is introduced, T. Feldmann, P. Kroll, B. Stech, PRD58,114006(98); PLB449,339 (99)
Why do we need another scheme? In B decays, we need to deal with the matrix elements, for instance, If we know the matrix element for axial current, It seems can be obtained in terms of equation of motion But, ms! 0, f and M’ 0 For displaying the SU(3) limit explicitly, it is better to use bases qq and ss We can have mass matrix
The mass matrix can be diagonalized via 8 and 1 are not independent Free parameters:
Vtb W Vts Tree u u s b penguin t W b g s Vub Vus q q Effective operators Tree g u u b s Penguin s b penguin Hence, u V-A s u b g C3-6 C1,2 b s q q q q V-A V± A V-A Bd! K0(0)decays Effective interactions for b! s qq
(0) (0) s s K s s s d b s V± A b s b B K d V-A V± A B V-A K B (0) V-A V± A (b) (0) (d) (a) d,u d,u V± A b s d d B V-A K K (0) d d (c) Penguin annihilation s d V± A V± A B B s d V-A V-A b b (0) K (f) (e) s s Topologies for Bd! K0(0) Since VubVus<<VtbVts, penguin dominates. Penguin emission Usually, (e), (f) < (a), (b), (c), (d) Tree’s contributions are similar to (c) except the CKM matrix elements
K s d b d (0) V-A V-A B (a) K s d b d (0) V-A V+A B (a) (0) (0) s s s s b b s s B B V-A V-A V-A V+A K K (b) (b) Hadronic matrix elements: Only show the factorizable effects (V-A)(V+A)=-2(S-P)(S+P)
(cont’ed) (0) d,u d,u V-A b s B V-A K (c) (0) d,u d,u V+A b s B V-A K (c) (0) s s V-A b s B V-A K (d) (0) s s V+A b s B V-A K (d)
Numerical analyses: • In order to calculate hadronic matrix elements, such as • we need to know the wave functions of B, K, q and s • The wave functions of B and K meson have been studied in the literature. • We have to assume that q and s have the same asymptotic behavior • as those of -meson.
(cont’ed) If one takes recourse to the first order of flavor symmetry breaking, one expects T. Feldmann, P. Kroll, B. Stech, PRD58,114006(98); PLB449,339 (99) Another way to understand above assumptions, we can use the mass matrix of octet-singlet, in which we know M288=(4m2K-m2)/3, Gell-Mann-Okubo relation By basis rotations, we obtain M288=(2m2ss+m2qq )/3, if we set mqq=m, we get m2ss=2m2K-m2. T. Feldmann and P. Kroll, hep-ph/0201044 Angle
(cont’ed) In the framework of perturbative QCD However, F0B! K(0)=0.35± 0.05 ) Taking the conventional values of fq(s) and m0q(s) cannot enhance Bd!0 K0
(cont’ed) • By M288=(2m2ss+m2qq )/3, why not m2ss=2(m2K-m2 ) and m2qq=3m2 ? • Or M288=(4m2K-m2)/3 (1+), why not m2qq > m2 ? T. Feldmann and P. Kroll, hep-ph/0201044 • And also Anomaly Maybe we should take fq>f and mqq>m
Besides, we also calculate Bd!(0) K*0 (cont’ed) Taking mqq» 1.65 m GeV, fq=1.07f, F+B! K=0.38
Other contributions: Intrinsic charm-quark T. Feldmann, P. Kroll, B. Stech, PRD58,114006(98) Two-gluon content
M. Beneke and M. Neubert, Nucl.Phys. B651 (2003) 225-248 F+B!(0) » 0.21 (0.32) F+B!0(0)» 0.32 (0.27) C.S. Kim et al., hep-ph/0305032
The considering effects could be distinguished from BN’s two-gluon mechanism, in which With our consideration, Discussion: • If taking mqq > m, the branching ratio of the decay Bd!0 K0 could be enhanced efficiently. • The possible exotic mechanisms can be also tested by B!(0)ℓ ℓ decays, in which the original BR is order of 10-8. With BN’s two-gluon content the BR could reach to 10-7 that is the same order of magnitude as the decays B! K ℓ ℓ , measured by Belle and Babar. B!(0) decays could be the candidates
1.48 1.19 • One phenomenon is worth noticing (mild), i.e. why is the branching ratio of B+!0 K+ so high? We expect B(B+!0 K+)/B(B0!0 K0)»(B+}/(B0) =1.08 • The more serious one: Babar Collaboration, hep-ex/0403046 Final state interactions ? or “New” effects ? BThero.<< 10-6
Two-angle scheme
With a parton Fock state decomposition, For simplicity, we can redefine the wave functions as Hence, As a result, the decay constants, defined as
b d t t b d
