Xie Ju Jun, E. Oset, PRD 2014 L.R. Dai PRD 2015
The vector-vector interaction in the local hidden gauge approach Generation of resonances, R B0 and B0
s decay into J/ψ R Ψ(nS) and ϒ(nS) strong and electromagnetic decays into these R
Hidden gauge formalism for vector mesons, pseudoscalars and photons Bando et al. PRL, 112 (85); Phys. Rep. 164, 217 (88)
See practical Feyman rules in Nagahiro, Roca, Hosaka, E.O. Phys. Rev. D 2009
V= +
+
Spin projectors neglecting q/MV, in
L=0
Bethe Salpeter eqn. G is the ρρ propagator
Rho-rho interaction in the hidden gauge approach R.Molina, D. Nicmorus, E. O. PRD (08)
Predicted meson states from V V interaction
(M,Г) MeV
M , Г [MeV]
L.S. Geng , E. O. PRD 2009
By looking at the couplings to the different coupled channels we find f2(1270) and f0(1370) are mostly ρρ f0(1710) and f’2(1525) are moslty K* K*bar K*2(1430) is mostly K* ρ
B0 and B0s -> J/ψ R
u c t d s b
changing
Reviewed in R7 is small because f2(1270) is made mostly of ρρ while f’2(1525) is mostly K* K*bar, and the mesons are contructed from s sbar.
B(B0s-> J/ψ f2(1270)) =(3.0 +1.2
-1.0)10 -6
Sep.13-18, 2015, Hadron2015, JLab
Lian-Rong Dai
(Liaoning Normal University,Dalian, China)
In collaboration with J. J. Xie and E. Oset
Phys. ReV. D91, 094013 (2015)
Motivation Chiral unitary approach Result part 1: Hadronic decay Part 2: Radiative decay Summary
Outline
1
Hadronic decay
Radiative decay
good tool to study the nature of some resonances, in particular those generated dynamically from the interaction of pairs of more elementary hadrons
Motivation
C.P.Shen, et al. [Belle Collaboration], Phys. Rev. D 86, 031102 (2012)
S. Dobbs, A. Tomaradze, T. Xiao and K. K. Seth, [CLEO Collaboration],
Phys. Rev. D 91, 052006 (2015)
New experimental data related to above resonances
hadronic decay radiative decay
2
3
R. Molina, D. Nicmorus and E. Oset, Phys. Rev. D 78, 114018 (2008);
L. S. Geng and E. Oset, Phys. Rev. D 79, 074009 (2009)
Chiral unitary approach
A. Martinez Torres, L.S. Geng, L.R. Dai, B.X. Sun, E. Oset, B.S. Zou, Phys. Lett . B 680 (2009) 310
L.S. Geng, F.K. Guo, C. Hanhart, R. Molina, E. Oset, B.S.Zou, Eur. Phys. J. A 44, 305 (2010)
hadronic decay radiative decay
Successfully test the idea
4
Result part 1: Hadronic decay
A. Martinez Torres, L.S. Geng, L.R. Dai, B.X. Sun, E. Oset, B.S. Zou, Phys. Lett . B 680 (2009) 310;Lian-Rong, Eulogio Oset, Eur. Phys. J. A 49, 230 (2013)
Extend the formalism
5
Transition matrix
The decay widths
A. Martinez Torres, L.S. Geng, L.R. Dai, B.X. Sun, E. Oset, B.S. Zou, Phys. Lett . B 680 (2009) 310
L.S. Geng, E. Oset, Phys. Rev. D 79, 074009 (2009)
The evaluation of the primary weights
6
Three experimental data
C.P.Shen, et al. [Belle Collaboration], Phys. Rev. D 86, 031102 (2012)
we obtain two ratios and find agreement with experiment within errors.
Lian-Rong, Ju-Jun Xie, Eulogio Oset, Phys. Rev. D 91, 094013 (2015)
7
Two experimental data
C.P.Shen, et al. [Belle Collaboration], Phys. Rev. D 86, 031102 (2012)
we obtain one ratio and find agreement with experiment within errors.
Lian-Rong, Ju-Jun Xie, Eulogio Oset, Phys. Rev. D 91, 094013 (2015)
8
Result
Extend the formalism
part 2: Radiative dacay
L.S. Geng, F.K. Guo, C. Hanhart, R. Molina, E. Oset, B.S.Zou, Eur. Phys. J. A 44, 305 (2010); Lian-Rong, Eulogio Oset, Eur. Phys. J. A 49, 230 (2013)
Fig.3(a) dominance over the diagram of Fig.3(b)
the photon was radiated from the state, not from the final VV state. 9
Transition matrix
Phys. Rev. D 79, 074009 (2009)
Eur. Phys. J. A 44, 305 (2010)
The decay widths
10
we find that the agreement of prediction in 2013 with the later experiment (in 2015) is good, except one ratio.
Prediction
Radiative decay
Confirmed
[a] Eur. Phys. J. A 44, 305 (2010)
[b]PRD73,032001;PRD75,072001;PRD83,037101; CLEO Collaboration
EPJA49(2003)130 PRD91(2015)052006
Lian-Rong, Ju-Jun Xie, Eulogio Oset, Phys. Rev. D 91, 094013 (2015)
11
Thank you
Summary
For radiative decays, we find that the agreement of prediction in 2013 with the later experiment (in 2015) is good, except one ratio which calls for a further reanalysis of this datum.
For hadronic decays, we find that the agreement with experimental data available is good within errors.
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