Radiative $B$ to axial-vector meson decays at NLO in Soft-Collinear Effective Theory

The rare decay $B\rightarrow A\gamma$, with $A$ representing axial-vector mesons such as $K_1 (1270),\; K_1 (1400),\; b_1(1300),\; a_1(1260)$, is studied at next-to-leading order (NLO) in soft collinear effective theory (SCET). The large outgoing meson energy encourages the study of the decay with an appropriate factorization scheme that separates the factorizable and non-factorizable parts systematically. We have analyzed the leading-power and $\mathcal{O}(\alpha_s)$ diagrams that contribute to matching to SCET$_I$. The new intermediate theory is matched onto SCET$_{II}$ and the running of SCET$_I$ operators is performed to sum large perturbative logarithms. The values of soft-overlap function $\zeta_{\perp}$ for $K_1 (1270,\;1400), a_{1}$ and $b_{1}$ mesons are estimated from the light cone-sum-rules (LCSR), and later using it the corresponding branching fractions for $B \to \left(K_{1}(1270,\; 1400),\; a_{1},\; b_{1}\right)\gamma$ decays are calculated. We find that in case of $B \to K_{1}(1270,\; 1400)\gamma$ decays the results are in good agreement with their experimental measurements. Also the estimated values of the branching ratios of the $B \to (b_{1},\; a_1)\gamma$ decays are potentially large to be measured at the LHCb and future B-factories.