Symmetry-Breaking Effects on Form Factors and Observables in $B\to K_0^{\ast }(1430){\mu }^{+}{\mu }^{-}$ Decay

Abstract

In the heavy-quark and large-energy limits, symmetry relations reduce the number of independent form factors governing heavy-to-light $B$-meson decays. Exploiting these relations, the form factors can be parametrized while systematically incorporating symmetry-breaking corrections from perturbative QCD. Using vertex renormalization together with light-cone distribution amplitudes, we compute the vertex and hard-spectator contributions for the $B\to K_0^{\ast }(1430)$ transition. We then analyze the impact of these form factors on physical observables, including the branching ratio and lepton polarization asymmetries $(P_L,P_N)$, in $B\to K_0^{\ast }(1430){\mu }^{+}{\mu }^{-}$. Our results indicate that perturbative corrections induce modest shifts of $\sim 3\%$ in both the branching ratio and the normal lepton polarization asymmetry. Consequently, any significant deviation observed experimentally from these predictions would provide a clear signal of potential New Physics effects.

Comments: 18 pages, 7 figures