Long-distance contribution to ΔΓsof the Bs-B?ssystem
Journal
Physical Review D - Particles, Fields, Gravitation and Cosmology
Journal Volume
84
Journal Issue
7
Date Issued
2011
Author(s)
Abstract
We estimate the long-distance contribution to the width difference of the Bs-B̄s system, based mainly on two-body Ds(*)D̄s(*) modes and three-body Ds(*)D ̄(*)K̄(*) modes (and their CP conjugates). Some higher cs̄ resonances are also considered. The contribution to ΔΓs/Γs by two-body modes is (10.2±3.0)%, slightly smaller than the short-distance result of (13.3±3.2)%. The contribution to ΔΓs/Γs by Ds0*(2317), D s1(2460), and Ds1(2536) resonances is negligible. For the three-body Ds(*)D̄(*)K ̄(*) modes, we adopt the factorization formalism and model the form factors with off-shell Ds(*) poles, the DsJ(2700) resonance, and nonresonant contributions. These three-body modes can arise through current-produced or transition diagrams, but only SU(3)-related Du,d(*)D̄(*)K̄ modes from the current diagram have been measured so far. The pole model results for Du,d*D̄(*)K̄ agree well with the data, while Du,dD̄(*)K̄ rates agree with the data only within a factor of 2 to 3. All measured Du,d(*)D̄(*)K̄ rates can be reproduced by including nonresonant contributions. The total ΔΓs/Γs obtained is (16.7±8.5)%, 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 ΔΓs/Γs 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→Ds(*)D̄s(*) decays to saturate ΔΓs 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 ΔΓs from the long-distance point of view. © 2011 American Physical Society.
Type
journal article