Long-distance contribution to Delta Gamma(s) of the B-s-(B)over-bar(s) system

作者：Chua Chun Khiang^*; Hou Wei Shu; Shen Chia Hsien

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2011, 84(7): 074037.

DOI：10.1103/PhysRevD.84.074037

We estimate the long-distance contribution to the width difference of the B-s-(B) over bar (s) system, based mainly on two-body D-s(*)(D) over bar (s)(*) modes and three-body D-s(*)(D) over bar(*)(K) over bar(*) modes (and their CP conjugates). Some higher c (s) over bar resonances are also considered. The contribution to Delta Gamma(s)/Gamma(s) by two-body modes is (10.2 +/- 3.0)%, slightly smaller than the short-distance result of (13.3 +/- 3.2)%. The contribution to Delta Gamma(s)/Gamma(s) by D-s0*(2317), D-s1(2460), and D-s1(2536) resonances is negligible. For the three-body D-s(*)(D) over bar(*)(K) over bar(*) modes, we adopt the factorization formalism and model the form factors with off-shell D-s(*) poles, the D-sJ(2700) resonance, and nonresonant contributions. These three-body modes can arise through current-produced or transition diagrams, but only SU(3)-related D-s(*)(D) over bar(*)(K) over bar(*) modes from the current diagram have been measured so far. The pole model results for D-u,D-d*(D) over bar*(K) over bar agree well with the data, while D-u,D-d(D) over bar(*)(K) over bar rates agree with the data only within a factor of 2 to 3. All measured D-u,D-d*(D) over bar*(K) over bar rates can be reproduced by including nonresonant contributions. The total Delta Gamma(s)/Gamma(s) obtained is (16.7 +/- 8.5)%, which agrees with the short-distance result within uncertainties. For illustration, we also demonstrate the effect of D-sJ(2700) in modes with D(*)K*. In all scenarios, the total Delta Gamma(s)/Gamma(s) remain consistent with the short-distance result. Our results indicate that (a) the operator product expansion in the short-distance picture is a valid assumption, (b) approximating the B-s -> D-s(*)(D) over bar (s)(*) decays to saturate Delta Gamma(s) has a large correction, (c) the effect of three-body modes cannot be neglected, and (d) in addition to the D-s and D-s* poles, the D-sJ(2700) resonance also plays an important role in three-body modes. Future experiments are necessary to improve the estimation of Delta Gamma(s) from the long-distance point of view.

• 出版日期2011-10-31