Charmless three-body decays ofBmesons

Abstract

An exploratory study of charmless 3-body decays of B mesons is presented using a simple model based on the framework of the factorization approach. The nonresonant contributions arising from B ! P 1 P 2 transitions are evaluated using heavy meson chiral perturbation theory (HMChPT). The momentum dependence of nonresonant amplitudes is assumed to be in the exponential form e ÿ NR p B p i p j so that the HMChPT results are recovered in the soft meson limit p i ; p j ! 0. In addition, we have identified another large source of the nonresonant signal in the matrix elements of scalar densities, e.g. hK Kj ssj0i, which can be constrained from the decayThe intermediate vector-meson contributions to 3-body decays are identified through the vector current, while the scalar meson resonances are mainly associated with the scalar density. Their effects are described in terms of the Breit-Wigner formalism. Our main results are: (i) All KKK modes are dominated by the nonresonant background. The predicted branching ratios of K K ÿ K SL , K K ÿ K ÿ and K ÿ K S K S modes are consistent with the data within errors. (ii) Although the penguin-dominated B 0 ! K K ÿ K S decay is subject to a potentially significant tree pollution, its effective sin2 is very similar to that of the K S K S K S mode. However, direct CP asymmetry of the former, being of order ÿ4%, is more prominent than the latter. (iii) For B ! K decays, we found sizable nonresonant contributions in K ÿ ÿ and K 0 ÿ modes, in agreement with the Belle measurements but larger than the BABAR result. (iv) Time-dependent CP asymmetries in K S 0 0 , a purely CP-even state, and K S ÿ , an admixture of CP-even and CP-odd components, are studied. (v) The ÿ 0 mode is found to have a rate larger than ÿ ÿ even though the former involves a 0 in the final state. They are both dominated by resonant contributions. (vi) We have computed the resonant contributions to 3-body decays and determined the rates for the quasi-two-body decays B ! VP and B ! SP. The predicted , f 0 980K and f 0 980 rates are in agreement with the data, while the calculated K, K , K and K 0 1430 are in general too small compared to experiment. (vii) Sizable direct CP asymmetry is found in K K ÿ K ÿ and K K ÿ ÿ modes.

Charmless three-body decays ofBsmesons

“…As stressed in [4,6], the matrix element of scalar densities M 1 M 2 |q 1 q 2 |0 must have a large nonresonant component in order to explain the large nonresonant signals observed in penguin-dominated three-body B decays. In other words, nonresonant contributions to penguin-dominated three-body B decays are also penguin dominated.…”

“…If the soft meson result is assumed to be the same in the whole Dalitz plot, the decay rate will be greatly overestimated. To overcome this issue, we have proposed in [6] to parameterize the momentum dependence of nonresonant amplitudes induced by b → u transition in an exponential form 4) so that the HMChPT results are recovered in the soft pseudoscalar meson limit. The parameter α NR = 0.081 +0.015 −0.009 GeV −2 [4] is fixed by the measured nonresonant rate in the tree-dominated decay B − → π + π − π − , where the nonresonant background due to the penguin diagram is suppressed by the smallness of penguin Wilson coefficients.…”

Quasi-two-body decays B(s)→Pρ→Pππ in the perturbative QCD approach

“…In Refs. [40,41], the authors studied the nonresonant contributions using heavy meson chiral perturbation theory (HMChPT) [42][43][44] with some modifications and analyzed the resonant contributions with the isobar model in terms of the usual Breit-Wigner formalism [45]. The perturbative QCD (PQCD) approach based on the k T factorization theorem [46,47] has also been adopted in Refs.…”

“…Different frameworks have been developed for the study of the three-body hadronic B meson decays, based on the symmetry principles [16][17][18][19][20][21][22][23][24] or factorization theorems [25][26][27][28][29][30][31][32][33][34]. The QCD-improved factorization (QCDF) [31][32][33][34] has been widely used in the study of the three-body charmless hadronic B meson decays [35][36][37][38][39][40][41]. In Refs.…”

Measurement of CP-Violating Asymmetries In Neutral B Meson Decays Into Three Kaons

“…For 25) where in the last step we have used the fact that most of the CKM matrix elements are real in the Wolfenstein parameterization (Eq. 2.2).…”