1. Charmless Two-Body B Decays Involving a Tensor Meson Kwei-Chou Yang Chung-Yuan Christian University, Taiwan The 36th International Conference on High Energy Physics (ICHEP2012) in collaboration with Hai-Yang Cheng

2.  Polarization puzzles in ---- SM or New-Physics  B decays involving a tensor meson ----further test: SM or New-Physics  Conclusion Outline

3. 3 Introduction Polarization puzzle in charmless B→VV decays Why is f T sizable ~ 0.5 in B → K * φ decays ? In transversity basis Search of new physics in B→VV decays ?

4. 4 Parametrization Explanation within the SM: Annihilation In SM, the Annihilation effect is important:

5. 5 B → K *  without annihilation)  3 =a 3 +a 5,  4 =a 4 -r   a 6,  3,EW =a 9 +a 7,  3 = penguin ann h=0 h= - h=0 h= - Coefficients are helicity dependent ! constructive (destructive) interference in A - (A 0 ) ⇒ f L ~ 0.58 with  3 =0 NLO corrections alone will bring down f L significantly ! Br ~4.3*10 -6 (without annihilation), too small compared with data PRD,2008, Hai-Yang Cheng, KCY

6. 6 Although f L is reduced to 60% level, polarization puzzle is not resolved as the predicted rate, BR~ 4.3*10 -6, is too small compared to the data, ~ 10*10 -6 for B →K *  penguin annihilation f || ≒ f ⊥ ≒ 0.25

7. 7 constructive destructive constructive ⇒ f L (K *-  0 )=0.96, f L (K *0  0 )=0.47 (=0.91 if a i h are helicity indep) But, the predicted rates for K *-  0 & K *0  0 are too small ! with  3 =0 Without Annihilation

8. 8 Process dependent

9. 9 Tree-dominated VV modes Longitudinal amplitude dominates tree-dominated decays except for  0  Predicted B →  ω  rates agree with the data. H.Y. Cheng & KCY, PRD, 2008 vs. data (2010)

10. 10 Scenario with New Physics

11. Possible New Physics 11 Phys. Rev. D71, 094002 (2005), KCY& Das See also works by Alex Kagan; C.S. Kim, Y.D. Yang;

12. 12

13. 13 Two-body B decays involving a tensor meson

14. 14 Light-cone distribution amplitudes for a tensor meson chiral-even PRD82:054019,2010, H.Y. Cheng,Y. Koike, KCY twist-2:  ∥,   twist-3: g v, g a, h t, h s twist-4: g 3, h 3 Asymptotic form of chiral-even DAs is first studied by Braun & Kivel (‘01) chiral-odd

15. 15 twist-2:  ∥,   twist-3: g  (v),g  (a), h  (t), h ∥ (p) related to twist-2 ones via Wandzura-Wilczek relations (neglecting 3-parton distributions) 3 P 2 tensor meson Due to G-parity,  , h ∥ (t), h ∥ (p),  ∥,g  (v), g  (a) are antisymmetric with the replacement u → 1-u in SU(3) limit C i 3/2 : Gegenbauer polynomial

16. 16 Decay constants Tensor meson cannot be produced from local V-A current owing to   p =0 Can be created from local current involving covariant derivatives with Previous estimates: Aliev & Shifman (’82); Aliev, Azizi, Bashiry (’10) Based on QCD sum rules we obtain (Cheng, Koike, KCY, arXiv:1007.3526) Normalized with

17. 17 VT modes Data from BaBar Naïve factorization, Kim,Lee & Oh, PRD (2003); Munoz,Quintero, J.Phys.G (2009) QCD factorization (without annihilation) too small Within SM, to account for data, penguin annihilation is necessary PRD83:034001,2011, Hai-Yang Cheng, KCY

18. 18 To account for data, penguin annihilation is necessary Process-dependent ? Ann is dominant for

19. 19 Polarization puzzle in B  K 2 *  f L (K 2 *+  ) = 0.56  0.11, f L (K 2 *0  ) = 0.45  0.12, f L (K 2 *+  ) = 0.80  0.10, f L (K 2 *0  ) = 0.901 +0.059 -0.069 f L (K 2 *  ) = 0.88, 0.72, 0.48 for  A TV = -30 o, -45 o, -60 o, f L (K 2 *  )= 0.68, 0.66, 0.64 for  A VT = -30 o, -45 o, -60 o In QCDF, f L is very sensitive to the phase  A TV for B  K 2 * , but not so sensitive to  A VT for B  K 2 *  Why is f T / f L <<1 for B  K 2 *  and f T /f L  1 for B  K 2 *  ? Rates & polarization fractions can be accommodated in QCDF BaBar but no dynamical explanation is offered Why is that f T behaves differently in K 2 *  and K *  ? Fine-tuning!

20. 20 Further test Sizable BR

21. 21 New Physics due to tensor currents Relatively smaller B  K *  B  K 2 *  Larger f L compared with  K*

22. 22 Conclusions New physics solutions: the only candidates are the tensor operators (Pure (S ± P)(S ± P) operators are unlikely) Further information ( b → s s s) can be extracted from and some other modes involving the tensor meson

23. 23 (pseudo-)scalar-type operators tensor-type operators

24. 24 Can only (pseudo-)scalar-type operators explain the data? Answer: NO In the minimal supersymmetric standard model (MSSM), such scalar/pseudoscalar operators can be induced by the penguin diagrams of neutral-Higgs bosons. A combined analysis of the decays shows that the NP effects only due to (pseudo-)scalar-type operators is much smaller in B →K *  modes. and to be consistent with the data for PRD77, 035013 (2008), H. Hatanaka, KCY

25. 25 Penguin-dominated B  TP

26. 26 B -  K 2 *0   vanishes in naïve factorization, while its BR is measured to be ~ 5.6  10 -6  importance of nonfactorizble effects Penguin annihilation is needed in QCDF to account for rates & CP asymmetries   TP =0.83,   TP = -70 o   PT =0.75,   PT = -30 o similar to the parameters for B  PP