Testing the Structure of Scalar Mesons in B
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, PLB 737(2014)70; M. Bayar, W. H. Liang, E. Oset, PRD 90(2014)114004; W. H. Liang, J. J. Xie, E. Oset, ar. Xiv: 1501. 00088[hep-ph]. 1
Outline • Introduction and motivation • ü Formalism ü Results and discussions • • Summary 2
u Introduction and motivation • The nature of the light scalar mesons is a topic of longstanding debate. In the Quark Model: meson Comparing with the Quark Model’s predictions, there exist much more light scalar mesons. Scalar mesons below 1 Ge. V: Possible structures: 3 3
u Introduction and motivation • In the Chiral Unitary Approach: [Oller and Oset, NPA 620(1997)438] 4
u Introduction and motivation • The weak decay of B mesons is a good place for testing the structure of the light scalar mesons. Experimental results: LHCb: PLB 698(2011)115; PRD 86(2012)052006; PRD 87(2013)052001; PRD 89(2014)092006; PRD 90(2014)012003; Belle, PRL 106(2011)121802; D 0, PRD 85(2012)011103. CDF, PRD 84(2011)052012; 5
u Introduction and motivation [ Belle, PRD 76(2007)012006 ] Belle: [ LHCb, PRL 109(2012)131801 ] 6
u 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
u • Formalism are the matrix elements of the CKM matrix, related to the Cabbibo angle: 8
u The pair is allowed to hadronize into a pair of pseudoscalar mesons. 9 9
u 10
u 11
(direct mechanism) (rescattering mechanism) 12 12
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divergent 3 -momentum cut off renormalization scheme following the Bethe-Salpeter Equation in coupled channels: 14
u 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, NPA 620(1997)438] [Gamermann, Oset, PRD 76(2007)074016] 15
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u • Results and discussions [Data from LHCb, 2014] Clean case: 18
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u 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. 20
u • Formalism The Cabibbo favored dominant mechanism: a vector meson or a pair of PS mesons Assume: 21
Ø a pair of PS mesons Let these PS mesons interact. 22
[Oller and Oset, NPA 620(1997)438] [F. K. Guo et al. , NPA 773(2006)78] 23
Ø ( L=1, P-wave ) The amplitudes: 24
The decay width: Convert the total date for vector production into a mass distibution: 25
• Results and discussions Ø [ Belle, PRD 76(2007)012006 ] 26
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Ø [ Belle, PRD 76(2007)012006 ] A good agreement within errors. 29
u Summary Ø 30
Ø Ø Thank you for your attention! 31
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