DOE OSTI2011
We estimate the long-distance contribution to the width difference of the B{sub s}-B{sub s} system, based mainly on two-body D{sub s}{sup (*)}D{sub s}{sup (*)} modes and three-body D{sub s}{sup (*)}D{sup (*)}K{sup (*)} modes (and their CP conjugates). Some higher cs resonances are also considered. The contribution to {Delta}{Gamma}{sub s}/{Gamma}{sub 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}{sub s}/{Gamma}{sub s} by D{sub s0}*(2317), D{sub s1}(2460), and D{sub s1}(2536) resonances is negligible. For the three-body D{sub s}{sup (*)}D{sup (*)}K{sup (*)} modes, we adopt the factorization formalism and model the form factors with off-shell D{sub s}{sup (*)} poles, the D{sub sJ}(2700) resonance, and nonresonant contributions. These three-body modes can arise through current-produced or transition diagrams, but only SU(3)-related D{sub u,d}{sup (*)}D{sup (*)}K modes from the current diagram have been measured so far. The pole model results for D{sub u,d}*D{sup (*)}K agree well with the data, while D{sub u,d}D{sup (*)}K rates agree with the data only within a factor of 2 to 3. All measured D{sub u,d}{sup (*)}D{sup (*)}K rates can be reproduced by including nonresonant contributions. The total {Delta}{Gamma}{sub s}/{Gamma}{sub 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{sub sJ}(2700) in modes with D{sup (*)}K{sup *}. In all scenarios, the total {Delta}{Gamma}{sub s}/{Gamma}{sub 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{sub s}{yields}D{sub s}{sup (*)}D{sub s}{sup (*)} decays to saturate {Delta}{Gamma}{sub s} has a large correction, (c) the effect of three-body modes cannot be neglected, and (d) in addition to the D{sub s} and D{sub s}* poles, the D{sub sJ}(2700) resonance also plays an important role in three-body modes. Future experiments are necessary to improve the estimation of {Delta}{Gamma}{sub s} from the long-distance point of view.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗