Probing transition form factors in the rare $B\to K^{\ast }\nu \bar{\nu }$ decay

Abstract

We compare the Standard Model (SM) predictions for the differential branching ratio of the rare $B\to K^{\ast }\nu \bar{\nu }$ decays using $B\to K^{\ast }$ form factors obtained from holographic light-front QCD (hLFQCD) and Sum Rules (SR) Distribution Amplitudes. For the total branching ratio, we predict $\mathcal{B}\mathcal{R}(\text{process}{)}_{\mathrm{hLFQCD}}=(6.36_{-0.74}^{+0.59})\times 10^{-6}$ and $\mathcal{B}\mathcal{R}(\text{process}{)}_{\mathrm{SR}}=(8.14_{-0.17}^{+0.16})\times 10^{-6}$. More interestingly, we find that the two model predictions for the differential branching ratio are sufficiently different at low momentum transfer, so that future measurements at Belle II may be able to discriminate between them. We also confirm numerically that the $K^{\ast }$ longitudinal polarization fraction $F_L$ has little sensitivity to the non-perturbative form factors and is thus an excellent observable to probe New Physics signals. We predict $F_L=0.40_{-0.01}^{+0.02}(0.41\pm 0.01)$ using hLFQCD (SR).

Comments: 13 pages, 5 figures and 4 tables