Polarization Study in B u,d,s,c Decays to Vector Final States

Transcription

1 Polarization Study in B u,d,s,c Decays to Vector Final States Cai-Dian LÜ( 吕才典 )(IHEP,Beijng) Collaborators:A. Ali, Y.Li, X. Liu, Z.T. Zou, arxiv: C.D. Lu 1

2 Outline Polarization problem in decays B( B s ) VV Numerical analysis in PQCD approach based on k T factorization/comparison with other solutions Summary C.D. Lu 2

3 Polarization of Bà VV decays C.D. Lu 3

4 Polarization of Bà VV decays 0.52±0.10±0.04 C.D. Lu 4

5 Polarization of Bà VV decays PRD83 (2011) ±0.12± ±0.10±0.04 C.D. Lu 5

6 Definitions of observables flavor-tagged definitions 2 A0,, fl,, B = A A + A 2, 2 f B Ā 0,, L,, = Ā 2 Ā Ā 2, flavor-averaged quantities and asymmetries φb, =arga, A 0, φ B, =arg Ā, Ā 0, f h = 1 2 ( f B h + f B h φ h φ B h φ h (mod 2π) ), A h CP = f B h f B h f B h + f B h φ B h + φ h (mod 2π), π 2 φ h < π 2 h = L,, In absence of CP violation, A h CP =0and δφ h =0. C.D. Lu 6

7 Counting Rules for Bà VV Polarization n The measured longitudinal fractions R L for Bà ρρ are close to 1. n R L ~ 0.5 in φ K * dramatically differs from the counting rules. n Are the φ K* polarizations understandable? Starting point: left-handed current in weak interaction C.D. Lu 7

8 Helicity flip suppression of the transverse polarization amplitude H 00 : H : H ++ O(1) : O(1/m b ) : O(1/m 2 b ) 00,, ++ stand for longitudinal, negative, positive helicity H /H 00 = O(m φ /m b ):thehelicityflipfor s in the φ meson is required C.D. Lu 8

9 Theoretical attempts to solve these puzzles n New physics (Grossman;Yang;Giri; Das et al.) n Annihilation effect in QCDF (Kagan) n Charming penguin in SCET (Bauer et al) n FSI effect (Colangelo; Ladisa; Cheng, et al) n Exotic bà sg (Hou,Nagashima) n Most can not fully explain all the measurements, especially relative phases except Annihilation/ charming penguin : Beneke, Yang, Rohrer(2006), Cheng, Chua(2009) C.D. Lu 9

10 Polarization anomaly in B φk * [Cheng, Chua, Soni] Confirmed for B ρρ with f L 0.97 but for B φk * f L 0.50, f 0.25, f 0.25 n Get large transverse polarization from B D s* D * and then convey it to φk * via FSI B * * D s D s * D (*) D s φ K * B D (*) D s φ K * f L (D s* D * ) 0.51 f 0.41, f 0.08 contributes to f only C.D. Lu 10

11 B Large cancellation occurs in B {D s* D,D s D*} φk* processes. This can be understood as CP & SU(3) symmetry D φ * s D s * D (*) D s K * very small perpendicular polarization, f 2%, in sharp contrast to f 15% obtained by Colangelo, De FArzio, Pham B D (*) D s + 0! While f T 0.50 is achieved, why is f not so small? Cancellation in B {VP,PV} φk* can be circumvented in B {SA,AS} φk*. For S,A=D**,D s ** f 0.22 It is very easy to explain why f L 0.50 by FSI, but it takes some efforts to understand why f f C.D. Lu 11 φ K *

12 There are still problems for some of the explanations The perpendicular polarization is given by: Final state interaction can not explain R N =R T and some others are difficult to explain the relative phase C.D. Lu 12

13 A Large Annihilation Can Help Annihilation-Type diagrams W W annihilation A. Kagan W W exchange W Time-like penguin W Space-like penguin C.D. Lu 13

14 The annihilation diagram Fierz Transformation The (S+P)(S-P) current can break the counting rule, The annihilation diagram contributes equally to the three polarization amplitudes C.D. Lu 14

15 Example: annihilation graphs due to QCD penguin operator Q 6 < ( db) S P ( sd) S+P > (part of P ) d s s (d b) S-P (s d) S+P b s d φk ( sd) S+P 0 A 0, A = O ( 1 m 2 ln2 m Λ h ), A + = O( 1 m 4 ) annihilation topology = overall 1/m helicity-flips = rest of 1/m factors, or twists C.D. Lu 15

16 For (V-A)(V-A), left-handed current p 2 B p 1 spin (this configuration is not allowed) fermion flow momentum Like Bà e ν e pseudo-scalar B requires spins in opposite directions, namely, helicity conservation Annihilation suppression ~ 1/m B ~ 10% C.D. Lu 16

17 No suppression for O 6 n Space-like penguin n Become (s-p)(s+p) operator after Fiertz transformation Chirally enhanced n No suppression, contribution big (20-30%) d b d (s) u d π π + (K + ) C.D. Lu 17

18 Endpoint singularity in collinear factorization In QCDF, the annihilation diagram can only be parameterized, data fitting C.D. Lu 18

19 f L can be accomodated with O(1) QCD annihilation amplitude - formally O(ln 2 /m 2 ) ρ = O(1) large S =1B φk, K π rates can be accounted for with O(1) QCD annihilation amplitudes ρ = O(1). A CP (K + π ) can be accounted for with ρ = O(1) +large strong phase in QCD annihilation In principle all of the above could also be accounted for with charming penguins : Leading power? Bauer et al, Subleading power? Ciuchini et al, FSI models Cheng et al, Colangelo et al Can annihilation dynamics be probed directly: can we test for O(1) power corrections, or ρ 1 in BBNS parametrization? C.D. Lu 19

20 Compare Annihilation and e + e - à M 1 M 2 d s s (d b) S-P (s d) S+P b s d M 1 M 2 sd 0 M 1 M 2 q γ µ q 0 C.D. Lu 20

21 V q 1/s 2 ln 2 ( s/λ) Vector-current annihilation form factors VP q γ µ q 0 = 2iV q m P + m V ϵ µνρσ ϵ ν p σ V p ρ P P 1 P 2 q γ m uq 0 = F q (p 1 p 2 ) µ V 1 V 2 q γ µ q 0 contains three form factors F q :finite1/s contribution Brodsky, Lepage + 1/s 2 ln 2 ( s/λ) correction Use continuum CLEO-c (20.46 pb 1 )+ BES VP data at s 3.7 GeV, near ψ(2s), to extract V q.comparewithbbnsparametrization,pqcd extrapolate to larger s m B,comparewithreachofluminosityatm B from initial state radiation (ISR) C.D. Lu 21

22 e + e VP in BBNS parametrization considered three values of α s =1,.5, α s ( p sλh );threevaluesofstrongphase φ A =0, ±π/2, π. Measurements ρ A 1 or (m/ s) Log s/λ 1 K 0 K 0 φ a =0 π 2 π ρπ 0 π 2 π V s V u s =3.67 GeV s =3.67 GeV ρ A ρ A ωπ 0 π 2 π ωπ 0 π 2 π V u V u s =3.67 GeV s = mj/psi ρ A ρ A C.D. Lu 22

23 e + e K 0 K 0 in PQCD V s in PQCD Vs V s vs. b max, s =3.67 GeV b max GeV 1 CDL,Wang 2, PRD 75, (2007) PQCD annihilation in right ballpark, but C.D. Lu 23

24 e + e VV K K q γ µ q 0 = V q 1 (ϵ µ η p 1 ηµ ϵ p 2 )+V q 2 (ϵ η )q µ + V q ϵ p 2 η p 1 3 Q 2 q µ Polarizations: V q 1 LT, Amp 1/Q3 Log 2 Q/Λ h Q s V q 3 TT, Amp 1/Q4 Log 2 Q/Λ h, V q 2 LL, Amp m q/q 4 Log 2 Q/Λ h V s (K K ) s =3.67 gev α s (0.7) = 1 σ (K + K ) [pb] α s (1.0) = 0.5 α s ( sλ h )=.3 ρ A s =3.67 GeV, φ =0, left : V s 1 (K + K ) vs. ρ; right: σ LT (K + K ) [pb] vs. ρ for V1 u = V 1 d =0(lower), SU(3) limit V s 1 = V d,u 1 (upper). ρ A C.D. Lu 24

25 Strategies in penguin-dominated decays QCDF loses predictive power in penguin annihilations with transverse polarization; Use information from experiments as much as we can; Strategy 1: fit only the penguin annihilation from B φk measurements; Strategy 2: fit the whole penguin amplitude from B φk ; Trust the predictions for other topological amplitudes using QCDF; Constrained X A : ϱ A =0.5 ± 0.2 exp. ϕ A =( 43 ± 19 exp. ), ˆα c 4 = αc 4 + β 3 from data: with α c 3 Ā = A K φλ (s) c P K φ, P K φ = ( ± 0.008(exp) (th)) from QCDF ˆα c 4 +i (0.021 ± 0.015(exp) (th)), =( 0.08 ± 0.02) + i (0.03 ± 0.02). C.D. Lu 25

26 In Perturbative QCD approach, we do not neglect the quark transverse momentum Then there is no endpoint singularity large double logarithm are produced after radiative corrections, they should be resummed to generate the Sudakov form factor to improve the perturbation theory. C.D. Lu 26

27 PQCD approach n A ~ d 4 k 1 d 4 k 2 d 4 k 3 Tr [ C(t) Φ B (k 1 ) Φ π (k 2 ) Φ π (k 3 ) H(k 1,k 2,k 3,t) ] exp{-s(t)} n Φ π (k 3 ) are the light-cone wave functions for mesons: non-perturbative, but universal n C(t) is Wilson coefficient of 4-quark operator n exp{-s(t)} is Sudakov factor,to relate the shortand long-distance interaction n H(k 1,k 2,k 3,t) is perturbative calculation of six quark interaction C.D. Lu 27

28 PQCD approach n A ~ d 4 k 1 d 4 k 2 d 4 k 3 Tr [ C(t) Φ B (k 1 ) Φ π (k 2 ) Φ π (k 3 ) H(k 1,k 2,k 3,t) ] exp{-s(t)} n Φ π (k 3 ) are the light-cone wave functions for mesons: non-perturbative, but universal n C(t) is Wilson coefficient of channel 4-quark dependent operator n exp{-s(t)} is Sudakov factor,to relate the shortand long-distance interaction n H(k 1,k 2,k 3,t) is channel perturbative dependent calculation of six quark interaction C.D. Lu 28

29 Perturbative Calculation of H(t) in PQCD Approach Form factor factoriz able Nonfactori zable C.D. Lu 29

30 Perturbative Calculation of H(t) in PQCD Approach Nonfactorizable annihilation diagram D (*) D (*) Factorizable annihilation diagram C.D. Lu 30

31 n All diagrams using the same wave functions n All channels use same wave functions n Number of parameters reduced C.D. Lu 31

32 New calcula)on with updated vector meson wave func)ons Longitudinal wave functions are different from transverse wave functions Twist-3 Twist-2 C.D. Lu 32

33 New calcula)on with updated vector meson wave func)ons Longitudinal wave functions are different from transverse wave functions Twist-3 Twist-2 C.D. Lu 33

34 The twist-2 distribution amplitudes The twist-2 distribution amplitudes are not far away from the asymptotic form C.D. Lu 34

35 The twist-2 distribution amplitudes Comparing with previous input C.D. Lu 35

36 New calcula)on with updated vector meson wave func)ons ) ( ) ( ) ( t f t f t f t f V a V V v V T V s V T V t V = + = = = φ φ φ φ There are not enough information to constrain the twist-3 distribution amplitudes. We just use the asymptotic form for simplicity. C.D. Lu 36

37 B ρρ(ω) decays Branching ra)o(10-6 ) f_l QCDF PQCD Expt QCDF PQCD Expt B + ρ + ρ ± ±0.016 B 0 ρ + ρ ± ±0.026 B 0 ρ 0 ρ ± ± ± 0.30 ± ± B + ρ + ω ± ±0.06 H. Y. Cheng and C. K. Chua, Phys. Rev. D 80, (2009) C.D. Lu 37

38 Two operators contribute to B 0 ρ 0 ρ 0 decay u b d d b d d B 0 ρ 0 B 0 ρ 0 O1 = ( uu) ( bd ) color enhanced 0 ρ u O2 = ( ud ) ( bu) color suppressed C 1 ~ 0.2 ~ C 2 (1/3 ) C 2 /N c ~ 1/3 u 0 ρ u C.D. Lu 38

39 Two operators contribute to B 0 ρ 0 ρ 0 decay: u b d d b d d B 0 ρ 0 B 0 ρ 0 O1 = ( uu) ( bd ) color enhanced 0 ρ u O2 = ( ud ) ( bu) color suppressed 0 ρ C 1 ~ 0.2 ~ C 2 (1/3 +s ) C 2 /N eff 8 c ~ 1/3 + u u C.D. Lu 39

40 Branching ra)o(10-6 ) f_l QCDF PQCD Expt QCDF PQCD Expt B 0 ρ 0 ω < B 0 ωω < B 0 ρ 0 Ф < B + ρ + Ф < B 0 ωф B 0 ФФ C.D. Lu 40 7

41 B K * ρ(ω) decays Branching ra)o(10-6 ) f_l QCDF PQCD Expt QCDF PQCD Expt B + K *0 ρ ± ±0.08 B + K *+ ρ ± ±0.12 B + K *+ ω < ±0.19 B 0 K *0 ρ ± ±0.10 B 0 K *+ ρ <12.0 (10.3) ±0.13 ±0.03 (BaBar) B 0 K *0 ω ± ±0.13 C.D. Lu 41

42 B K * K * decays Branching ra)o(10-6 ) f_l QCDF PQCD Expt QCDF PQCD Expt B + K *+ K * ± ±0.25 B 0 K *+ K * <2.0 ~1.0 ~1.0 B 0 K *0 K * ± ±0.13 C.D. Lu 42

43 Bs à VV decays Bs ρρ(ω) decays Branching ra)o(10-6 ) f_l QCDF PQCD Expt QCDF PQCD Expt Bs ρ + ρ Bs ρ 0 ρ Bs ρ 0 ω Bs ωω C.D. Lu 43

44 Bs K * ρ(ω) decays Branching ra)o(10-6 ) f_l QCDF PQCD Expt QCDF PQCD Expt Bs K *- ρ Bs K *0 ρ Bs K *0 ω C.D. Lu 44

45 Branching ra)o(10-6 ) f_l QCDF PQCD Expt QCDF PQCD Expt Bs K *+ K * Bs K *0 K * ±4.6± ±0.13 Bs ρ 0 Ф Bs ωф Bs ФФ ± ±0.022 Bs K *0 Ф ± ±0.17 C.D. Lu 45

46 More obsevables C.D. Lu 46

47 More obsevables C.D. Lu 47

48 Summary n The polarization in Bà VV decays can be explained by PQCD Important role of Annihilation type diagram New physics seems still not show up C.D. Lu 48

49 Thank you! C.D. Lu 49