Charmless hadronic B decays into a tensor meson

Two-body charmless hadronic B decays involving a tensor meson in the final state are studied within the framework of QCD factorization (QCDF). Because of the G-parity of the tensor meson, both the chiral-even and chiral-odd two-parton light-cone distribution amplitudes of the tensor meson are antisymmetric under the interchange of momentum fractions of the quark and antiquark in the SU(3) limit. Our main results are: (i) In the naive factorization approach, the decays such as B- -> (K) over bar*(0)(2)pi(-) and B-0 -> K*(-)(2)pi(+) with a tensor meson emitted are prohibited because a tensor meson cannot be created from the local V - A or tensor current. Nevertheless, the decays receive nonfactorizable contributions in QCDF from vertex, penguin and hard spectator corrections. The experimental observation of B- -> (K) over bar*(0)(2)pi(-) indicates the importance of nonfactorizable effects. (ii) For penguin-dominated B -> TP and TV decays, the predicted rates in naive factorization are usually too small by 1 to 2 orders of magnitude. In QCDF, they are enhanced by power corrections from penguin annihilation and nonfactorizable contributions. (iii) The dominant penguin contributions to B -> (K) over bar*(2)eta((')) arise from the processes: (a) b -> ss (s) over bar -> s eta(s) and (b) b -> sq (q) over bar -> q (K) over bar*(2) with eta(q) (u (u) over bar + d (d) over bar)/root 2 and eta(s) = p and s (s) over bar. The interference, constructive for (K) over bar*(2)eta' and destructive for K*(2)eta, explains why Gamma(B -> K-2*eta') >> Gamma(B -> K-2*eta). (iv) We use the measured rates of B -> (K) over bar*(2)(omega, phi) to extract the penguin- annihilation parameters rho(TV)(A) and rho(VT)(A) A and the observed longitudinal polarization fractions f(L)(K*(2)omega) and f(L)(K*(2)phi) to fix the phases phi(VT)(A) and phi(TV)(A). (v) The experimental observation that f(T)/f(L) << 1 for B -> K-2*(1430)phi, whereas f(T)/f(L) similar to 1 for B -> K*(2)(1430)omega with f(T) being the transverse polarization fraction, can be accommodated in QCDF, but it cannot be dynamically explained at first place. For penguin-dominated B -> TV decays, we find f(L)(K*(2)rho) similar to f(L)(K*(2)omega) similar to 0: 65, whereas f(L)(K* f(2)) similar to 0: 93. It will be of great interest to measure f(L) for these modes to test QCDF. Theoretically, transverse polarization is expected to be small in tree- dominated (B) over bar -> TV decays except for the a(2)(-)rho(0), a(2)(-)rho(+), K*(0)(2)(K) over bar*(-) and K*(0)(2)(K) over bar*(0) modes. (vi) For tree- dominated decays, their rates are usually very small except for the a(2)(0)(pi(-), rho(-)), a(2)(+)(pi(-), rho(-)) and f(2)(pi(-), rho(-)) modes with branching fractions of order 10(-6) or even larger.