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

TL;DR

This paper compares Standard Model predictions for the rare $B\to K^*\nu\bar\nu$ decay using two different form factor models, highlighting potential for future experimental discrimination and the robustness of the polarization fraction as a New Physics probe.

Contribution

It provides a detailed comparison of $B\to K^*$ form factors from holographic light-front QCD and Sum Rules, predicting differential branching ratios and polarization fractions.

Findings

Predicted total branching ratios differ between models.

Differential branching ratios show significant differences at low momentum transfer.

Longitudinal polarization fraction $F_L$ is insensitive to form factor models.

Abstract

We compare the Standard Model (SM) predictions for the differential branching ratio of the rare $B\to K^*\nu\bar\nu$ decays using $B \to K^*$ form factors obtained from holographic light-front QCD (hLFQCD) and Sum Rules (SR) Distribution Amplitudes. For the total branching ratio, we predict $\mathcal{BR}(\process)_{\rm hLFQCD}=(6.36^{+0.59}_{-0.74})\times 10^{-6}$ and $\mathcal{BR}(\process)_{\rm SR}=(8.14^{+0.16}_{- 0.17})\times 10^{-6}$. 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 $K^*$ 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 $F_L=0.40^{+0.02}_{-0.01}(0.41\pm 0.01)$ using hLFQCD (SR).