Annihilation contribution and $B\to a_0 \pi, f_0 K$ decays

Abstract

We analyze the decays $B^0 \to a^\pm_0 \pi^\mp$ and $B^{-,0} \to f_0 K^{-,0}$ and show that within the factorization approximation a phenomenological consistent picture can be obtained. We show that in this approach the $O_6$ operator provides the dominant contributions to the suppressed channel $B^0 \to a^+_0 \pi^-$. When the $a_0$ is considered a two quark state, evaluation of the annihilation form factor using Perturbative $QCD$ implies that this contribution is not negligible, and furthermore it can interfere constructively or destructively with other penguin contributions. As a consequence of this ambiguity, the positive identification of $B^0 \to \pi^+ a_0^-$ can not distinguish between the two or four quark assignment of the $a_0$. According to our calculation, a best candidate to distinguish the nature of $a_0$ scalar is $Br(B^-\to \pi^0a_0^-)$ since the predictions for a four quark model is one order of magnitude smaller than for the two quark assignment. When the scalars are seen as two quarks states, simple theoretical assumptions based on SU(2) isospin symmetry provide relations between different B decays involving one scalar and one pseudoscalar meson.