Charmless hadronicBdecays involving scalar mesons: Implications on the nature of light scalar mesons

Abstract

The hadronic charmless B decays into a scalar meson and a pseudoscalar meson are studied within the framework of QCD factorization. Based on the QCD sum rule method, we have derived the leading-twist light-cone distribution amplitudes of scalar mesons and their decay constants. Although the light scalar mesons f 0 980 and a 0 980 are widely perceived as primarily the four-quark bound states, in practice it is difficult to make quantitative predictions based on the four-quark picture for light scalars. Hence, predictions are made in the 2-quark model for the scalar mesons. The short-distance approach suffices to explain the observed large rates of f 0 980K ÿ and f 0 980K 0 that receive major penguin contributions from the b ! ss s process. When f 0 980 is assigned as a four-quark bound state, there exist extra diagrams contributing to B ! f 0 980K. Therefore, a priori the f 0 980K rate is not necessarily suppressed for a four-quark state f 0 980. The predicted B 0 ! a 0 980 and a 0 980K ÿ rates exceed the current experimental limits, favoring a four-quark nature for a 0 980. The penguin-dominated modes a 0 980K and a 0 1450K receive predominant weak annihilation contributions. There exists a twofold experimental ambiguity in extracting the branching ratio of B ÿ ! K 0 0 1430 ÿ , which can be resolved by measuring other K 0 1430 modes in conjunction with the isospin symmetry consideration. Large weak annihilation contributions are needed to explain the K 0 1430 data. The decay B 0 ! K ÿ provides a nice ground for testing the 4-quark and 2-quark nature of the meson. It can proceed through W-exchange and hence is quite suppressed if is made of two quarks, while it receives a tree contribution if is predominately a four-quark state. Hence, an observation of this channel at the level of * 10 ÿ7 may imply a four-quark assignment for the . Mixing-induced CP asymmetries in penguin-dominated modes are studied and their deviations from sin2 are found to be tiny.

Strong and weak interactions in decays

“….46 although recent calculations [ 8,9,10] give a value close to 0.25. Furthermore, the Γ n,s 1 (m ππ ) depend on some poorly determined low energy constants of chiral perturbation theory.…”

“…In summary, uncertainties in F B→(ππ) S 0 (M 2 K ) and in the S-wave scalar form form factors lead to variations of charming penguin parameters, in particular of S u . The scalar form factors that we use give low values for the effective f s f 0 decay constant equal to 94 or 117.5 MeV, to be compared to 370 MeV [ 8] or 245 MeV [ 12]. Despite these uncertainties, our conclusions [ 4] are unchanged.…”

“…[ 13], the a 1 (f 0 K) receives a large contribution from hard spectator interaction which will enhance the M S K (m f 0 ) of Ref. [ 8]. In summary, uncertainties in F B→(ππ) S 0 (M 2 K ) and in the S-wave scalar form form factors lead to variations of charming penguin parameters, in particular of S u .…”

“…[ 8] that the experimental average branching fractions of two-body B ± → f 0 (980)K ± decays, B f 0 , could be reproduced without charming penguin terms. However, we have important differences with Ref.…”

“…Secondly, the fit to experimental data of Ref. [ 8] includes hard spectator scattering terms with the parameters X A (plus annihilation terms with the parameters X H ). As stated in Ref.…”