Charmless three-body decays of B mesons

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 -> P1P2 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(NR)(-alpha)p(B)center dot(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. < KK|>ss|0 >, which can be constrained from the decay B-0 -> KSKSKS or B--> K-KSKS. The 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-KS(L), K+K-K- and K-KSKS modes are consistent with the data within errors. (ii) Although the penguin-dominated B-0 -> K+K-KS decay is subject to a potentially significant tree pollution, its effective sin2 beta is very similar to that of the KSKSKS mode. However, direct CP asymmetry of the former, being of order -4%, is more prominent than the latter. (iii) For B -> K pi pi decays, we found sizable nonresonant contributions in K-pi(+)pi(-) and K-0 pi(+)pi(-) modes, in agreement with the Belle measurements but larger than the BABAR result. (iv) Time-dependent CP asymmetries in K-S pi(0)pi(0), a purely CP-even state, and K-S pi(+)pi(-), an admixture of CP-even and CP-odd components, are studied. (v) The pi(+)pi(-)pi(0) mode is found to have a rate larger than pi(+)pi(-)pi(-) even though the former involves a pi(0) in the final state. They are both dominated by resonant rho 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 rho pi, f(0)(980)K and f(0)(980)pi rates are in agreement with the data, while the calculated phi K, K-*pi, rho K and K-0(*)(1430)pi are in general too small compared to experiment. (vii) Sizable direct CP asymmetry is found in K+K-K- and K+K-pi(-) modes.