Study of the Scalar Meson in B Decays

1. Study of the Scalar Meson in B Decays Ying Li (李营) Yonsei & YTU

3. Although QCD theory can describe strong interaction successfully, there are many divergencesonthe scalar meson. It can not conclude whether they are two quake states, or four quark states or molecule states. • At present, most research on the scalar meson are focus on the low energy physics within the effective theory. People can explore their properties though their decays. So, we will analysis this issue from another view, we will research the scalar mesons through their production in weak interaction.

4. Motivation • Comparing with results of pseudo scalar meson, we try to looking for the signals of new physics. • For , it is a penguin dominator process, and we can calculate ， we will check if the result consistent with it from . • In the experimental side, there are much data about the scalar meson in two B factories. The richer data will put the research of scalar meson forward.

5. Experimental Data X 10-6

6. Properties of the Scalar Meson • It is known that the underlying structure of scalar mesons is not well established theoretically. • It is suggested that the light scalars below or near 1 Gev, namely and form a SU(3) nonet(nonet=octet+singlet). • While the scalars above 1 Gev, • and form another SU(3) nonet.

7. There are two different scenarios to describe these two nonets. • A consistent pictureprovided by the data suggests that the scalarmeson states above 1 GeV can be identified as a conventionalnonet with some possible glueball content. • For the first nonet, there are some different suggestion: • The four-quark scenario: This is supported by the lattice calculation.

8. The four-quark scenario seems plausible when the light scalar meson is produced in the low energy reactions. • When the energetic f0(980) produced in B decays is dominated by the four-quark configuration, it requires to pick up two energetic quark-antiquark pairs to form a fast moving light four-quark scalar meson, so this process should be suppressed (OZI Rule). • The two-quark scenario:

9. Classification of the multiplets and exotic states are not physical state • The existence of glueballs Lattice results: the mass of the scalar glueball lies in (1500-1800)MeV

10. In the last slide, f0(980) and σ are the ideal mixing , so the f0(980) is heavier than the σ. In this picture, f0(980) is a pure ssbar component, and this is supported by the data : and However, there also exist some experimental evidences indicating that f0(980) is not purely a ss state. • More words aboutf0(980)

11. Therefore, iso-scalars f0(980) and σ(600) must have a mixing : The f0(980) - σ(600) mixing angle be can determined by the following experimental data:

12. f0(980) • f0(980) is the first scalar meson observed in B decays with the decay mode B → f0(980)K. In the three-body decays B± → K±pi∓pi± , Belle found a large branching ratio for B→K−f0(980) → K−(pi+pi−), which was confirmed by BaBar later. • In 2003, C.H. Chen preformed this decay in two quark model within PQCD approach, and got a small branching ratio which can not agree with data. • C.H. Chen, Phys. Rev. D 67, 014012(2003); 67,094011(2003) • In 2005, H.Y.Cheng et.al calculated the latest decay constants and distribution amplitudes in QCD Sum Rules. Then, they got a large ratio in the QCDF approach, and can explain the data with large uncertainties. • Cheng et al Phys. Rev. D 71,054020(2005); 73, 014017(2006) • In 2006, Giri had calculated this process in the naïve factorization approach considering the new physics contribution.

13. For B → f0(1500)K, there is a puzzle in experiments: both Belle and BaBar have found a resonance in the K+K− mass spectrum of B → (K+K−)K decays, whose mass and width are consistent with f0(1500). Due to the large ratio Γ (f0(1500) → pipi)/ Γ (f0(1500) → K K ) = 4.06, we expect the similar peak in the corresponding channel. But there is no signal in the decays of B → K(pi+pi−) . In order to make it clear, more experimental data are required. Belle collaboration, PRD71,092003(2005). BaBar collaboration, PRD72,072003(2005) On the other side we should also know the theoretical predictions on B → f0(1500)K. However, the theoretical calculation becomes not clean because there exists the glueball contribution. f0(1370), f0(1500) and f0(1710)are assumed to be mixing of quark-antiquark and glueball states • f0(1500)

14. Cheng et al Close and Zhao Because we have little information about the glueball, so we here ignore the contribution from the glueball and recognize it as mixing result of nnbar and ssbar.

15. Experimental data: In past years, there are many puzzles in transition, such as , which are regarded as signals of new physics. • K0*(1430) BaBar, PRL98, 051801, 2007 Belle, PRL101, 161801, 2008

16. In 2007, Chen and Geng calculated this process in the generalized factorization approach through introducing an effective color number .And they found the branching ratio is much sensitive to this parameter. C.-H. Chen and C.-Q Geng, PRD 75, 054010 (2007) In 2008, Cheng et.al predicted central value of this mode is somewhat larger (smaller) than experimental data in the different senarios, though it can explain data within large theoretical errors. However, the results in the QCDF suffer large uncertainties from the annihilation diagrams, which can not calculated effectively because of endpoint singularity. H.-Y Cheng, et.al, PRD77, 014034, 2008 • Theoretical Calculation :

17. Basis of our calculation • Scenario1： f0(980)is two quark state, and it is the low lying states • f0(1500)is the first excited states。 • Scenario2：f0(980)is four quark state, but f0(1500) is the low lying states • f0(980)is four quark state, but its distribution amplitudes are still absent, we will not discuss this part.

18. Properties of the Scalar Meson Definition of the decay constant 0 Definition of the distribution amplitude Normalization: C.D. Lu, et.al arXiv:hep-ph/0612210

19. A ~ ∫d4k1 d4k2 d4k3 Tr [ C(t)B(k1) 1(k2) 2(k3)H(k1,k2,k3,t) ] exp{–S(t)} (k)is wave function in the light cone, which is universal. C(t): Wilson coefficients of corresponding four quark operators exp{-S(t)} are Sudukov form factor (double log resummation)， which relate the long distance contribution and short one. And the long distance effects have been suppressed. H(k1,k2,k3,t) is six quark interaction, and it can be calculated perturbatively, and it is process depended.

20. Hard kernel diagrams • Only the twist-3 wave function contribute to the factorizable emission diagram, if the emitted meson is a scalar. (S-P S+P density current) • There is enhancement rather than cancellation between the two nonfactorizable diagrams.

21. W. Wang, Y.L.Shen, Y. Li and C.D. Lu, Phys. Rev. D 74,114010 • For : the larger decay constant leads to larger amplitudes. • For : The nonfactorizable emission diagrams and annihilation diagrams give the dominant contribution , which comes from the Gegenbauer moments of the twist 2 LCDA.

23. SI SII

24. Discussion Forf0(980), if it is a two quark states, our results agree with data within a large mixing angle. And no new physics effects are needed. For f0(980), although the twist-2 distribution amplitude is normalized to 0, it plays an important role because it is anti-symmetric. For f0(1500), if we ignore the glueball contribution, our results support that it is a low lying state of two quark model We can calculation the f0(1370), f0(1710)，however the experimental dataare still absence.

25. Numerical Results for K*0(1430)phi

27. Discussion The factorizable emission diagrams play the major role, and the penguin operators in the annihilation diagrams can change the ratio remarkably. The form factor F1=0.42 arrived from PQCD approach is larger than the 0.26, which is calculated in the covariant light-front model and adopted in QCD factorization. So, the center value of our results are larger than that from QCD factorization. the CP asymmetry in the charged channel is not sensitive to CKM angle gamma.

28. Compared with experimental data from BaBar, in the S1, the result of neutral channel is agree with experimental data well, but the result of the charged one is smaller than the data, though it is consistent within theoretical uncertainties. In the S2, both results are much larger than the data. We favored that K0*(1430) is the first excited state. Moreover, in our framework, we can not explain the large SU(3) asymmetry revealed from experimental data. This large asymmetry is regarded as a "puzzle" in these decay mode both in PQCD approach and QCD factorization approach. More accurate experimental data are needed!

29. Uncertainty Higher twist distribution amplitude of the scalar meson are not clear now. NLO corrections of PQCD with scalar meson have not explored, though PP and PV modes have been calculated by Mishima.et.al. Final states interaction may play more important contribution. Glueball contribution has not been considerd now Some uncertainties from the light pseudo-scalar/vector meson and the sub-leading component of B meson distribution amplitude

30. Consider JP=0+ scalar mesons  L=1 if they are made of qq • Two nonets have been observed: • light nonet (< 1 GeV) I=0: (500), f0(980), I=1/2:  (800), I=1: a0(980), • heavy nonet (> 1 GeV) • I=0: f0(1370), f0(1500), f0(1710), I=1/2: K*0(1430) , I=1: a0(1450) Lattice ⇒ some states in heavy nonet are low-lying qq classified as 2S+1LJ = 3P0 ⇒ states in light nonet are S-wave four-quark states ? 30 30 30

31. Within PQCD approach, decays are consistent with the experiment in two quark picture. Also consistent with QCDF. If we regard as , it being a ground state is more favored. We need more precise non-perturbative parameters, such as the twist-3 distribution amplitudes etc. The glueball contribution should be included for completeness, especially in the form factor of Bf0. Summary

32. Thank you for your kind attention!