出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We estimate the long-distance contribution to the width difference of the Bs–¯Bs system, based mainly on two-body D() s ¯D() s modes and three-body D() s ¯D() ¯K () modes (and their CP conjugates). Some higher c ¯ s resonances are also considered. The contribution to DGs=Gs by two-body modes is (10:23:0)%, slightly smaller than the short-distance result of (13:33:2)%. The contribution to DGs=Gs by Ds0(2317), Ds1(2460), and Ds1(2536) resonances is negligible. For the three-body D() s ¯D() ¯K () modes, we adopt the factorization formalism and model the form factors with off-shell D() s poles, the DsJ(2700) resonance, and nonresonant contributions. These threebody modes can arise through current-produced or transition diagrams, but only SU(3)-related D() u;d ¯D () ¯K modes from the current diagram have been measured so far. The pole model results for Du;d ¯D() ¯K agree well with the data, while Du;d ¯D() ¯K rates agree with the data only within a factor of 2 to 3. All measured D() u;d ¯D () ¯K rates can be reproduced by including nonresonant contributions. The total DGs=Gs obtained is (16:78:5)%, which agrees with the short-distance result within uncertainties. For illustration, we also demonstrate the effect of DsJ(2700) in modes with D()K. In all scenarios, the total DGs=Gs 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 Bs !D() s ¯D() s decays to saturate DGs has a large correction, (c) the effect of three-body modes cannot be neglected, and (d) in addition to the Ds and Ds poles, the DsJ(2700) resonance also plays an important role in three-body modes. Future experiments are necessary to improve the estimation of DGs from the long-distance point of view.
