B→K1γdecays in the light-cone QCD sum rules

Abstract

We present a detailed study of $B\ensuremath{\rightarrow}{K}_{1}(1270)\ensuremath{\gamma}$ and $B\ensuremath{\rightarrow}{K}_{1}(1400)\ensuremath{\gamma}$ decays. Using the light-cone sum rule technique, we calculate the $B\ensuremath{\rightarrow}{K}_{1A}({1}^{3}{P}_{1})$ and $B\ensuremath{\rightarrow}{K}_{1B}({1}^{1}{P}_{1})$ tensor form factors, ${T}_{1}^{{K}_{1A}}(0)$ and ${T}_{1}^{{K}_{1B}}(0)$, where the contributions are included up to the first order in ${m}_{{K}_{1}}/{m}_{b}$. We resolve the sign ambiguity of the ${K}_{1}(1270)--{K}_{1}(1400)$ mixing angle ${\ensuremath{\theta}}_{{K}_{1}}$ by defining the signs of decay constants, ${f}_{{K}_{1A}}$ and ${f}_{{K}_{1B}}^{\ensuremath{\perp}}$. From the comparison of the theoretical calculation and the data for decays $B\ensuremath{\rightarrow}{K}_{1}\ensuremath{\gamma}$ and ${\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}_{1}^{\ensuremath{-}}(1270){\ensuremath{\nu}}_{\ensuremath{\tau}}$, we find that ${\ensuremath{\theta}}_{{K}_{1}}=\ensuremath{-}(34\ifmmode\pm\else\textpm\fi{}13)\ifmmode^\circ\else\textdegree\fi{}$ is favored. In contrast to $B\ensuremath{\rightarrow}{K}^{*}\ensuremath{\gamma}$, the hard-spectator contribution suppresses the $B\ensuremath{\rightarrow}{K}_{1}(1270)\ensuremath{\gamma}$ and $B\ensuremath{\rightarrow}{K}_{1}(1400)\ensuremath{\gamma}$ branching ratios slightly. The predicted branching ratios are in agreement with the Belle measurement within the errors. We point out that a more precise measurement for the ratio ${R}_{{K}_{1}}=\mathcal{B}(B\ensuremath{\rightarrow}{K}_{1}(1400)\ensuremath{\gamma})/\mathcal{B}(B\ensuremath{\rightarrow}{K}_{1}(1270)\ensuremath{\gamma})$ can offer a better determination for the ${\ensuremath{\theta}}_{{K}_{1}}$, and consequently the theoretical uncertainties can be reduced.