1. Testing the Structure of Scalar Mesons in B Weak Decays
Wei-Hong Liang （梁伟红）
Guangxi Normal University （广西师范大学）
International Workshop on QCD Exotics, 07–12 June 2015, Jinan
Based on:
W.H. Liang, E. Oset, PLB737(2014)70;
M. Bayar, W.H. Liang, E. Oset, PRD90(2014)114004;
W.H. Liang, J.J. Xie, E. Oset, arXiv: [hep-ph].

2. Introduction and motivation
Outline
Introduction and motivation
Formalism
Results and discussions
Summary

3. Introduction and motivation Introduction and motivation
The nature of the light scalar mesons is a topic of long-standing debate.
In the Quark Model: meson
Comparing with the Quark Model’s predictions, there exist
much more light scalar mesons.
Scalar mesons below 1 GeV:
Possible structures: 3

4. Introduction and motivation
In the Chiral Unitary Approach:
[Oller and Oset, NPA620(1997)438]

5. Introduction and motivation
The weak decay of B mesons is a good place for
testing the structure of the light scalar mesons.
Introduction and motivation
Experimental results:
LHCb: PLB698(2011)115; PRD86(2012)052006; PRD87(2013)052001;
PRD89(2014)092006; PRD90(2014)012003;
Belle, PRL106(2011)121802; CDF, PRD84(2011)052012;
D0, PRD85(2012)

6. Introduction and motivation
Belle:
[ Belle, PRD76(2007) ]
[ LHCb, PRL109(2012) ] 6

7. Introduction and motivation
Using these experimental information, we can investigate the production of the light scalar mesons in
Considering the final state interactions between the light pseudoscalar meson pairs in chiral unitary approach,
can be produced dynamically. 7

8. Formalism
are the matrix elements of the CKM matrix, related to the Cabbibo angle: 8

9. The pair is allowed to hadronize into a pair of pseudoscalar mesons.9 9

10. 10

12. (rescattering mechanism)
(direct mechanism)
(rescattering mechanism)
(rescattering mechanism) 12

14. divergent
3-momentum cut off renormalization scheme
following the Bethe-Salpeter Equation in coupled channels:

15. The V matrix elements are taken from
V is the potential which is obtained from the lowest order chiral Lagrangian for PS-PS interaction,
——the pion decay constant
There are 5 coupled channels:
The V matrix elements are taken from
[Oller and Oset, NPA620(1997)438]
[Gamermann, Oset, PRD76(2007)074016]

17. 17

18. Results and discussions
[Data from LHCb, 2014]
Clean case:

20. Exp.
Conclusion:
Our results agree with the experimental results. This gives a strong support to the idea of the low lying scalar mesons as being formed from the interaction of pairs of pseudoscalar mesons.
Exp.

21. Formalism The Cabibbo favored dominant mechanism:
a vector meson or a pair of PS mesons
Assume: 21

22. Let these PS mesons interact.
a pair of PS mesons
Let these PS mesons interact. 22

23. [Oller and Oset, NPA620(1997)438]
[F.K. Guo et al., NPA773(2006)78] 23

24. ( L=1, P-wave )
The amplitudes: 24

25. The decay width:
Convert the total date for vector production into a mass distibution: 25

26. Results and discussions
[ Belle, PRD76(2007) ] 26

27. 27

28. 28

29. A good agreement within errors.
[ Belle, PRD76(2007) ]
A good agreement within errors. 29

30. Summary

31. Thank you for your attention!31