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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