$B \to K^* \gamma$: Penguins on the Lattice

TL;DR

This paper computes the $B o K^* \gamma$ decay form factor using lattice QCD, providing a theoretical estimate that aligns with experimental measurements, thus aiding understanding of flavor-changing neutral currents.

Contribution

The study presents the first lattice QCD calculation of the $B o K^* \gamma$ form factor at zero momentum transfer with quenched approximation and improved fermion action.

Findings

Calculated form factor $T_1(q^2=0)=0.15^{+0.05}_{-0.04}$ statistically.

Found $T_1$ is approximately independent of spectator quark mass.

Results are consistent with experimental branching ratios within errors.

Abstract

We calculate the leading-order matrix element for the decay $B \to K^* \gamma$ in the quenched approximation of lattice QCD on a $24^3 \times 48$ lattice at $\beta=6.2$, using an O(a)-improved fermion action. Extrapolating the quark masses to their physical values we obtain an on-shell form factor of $T_1(q^2=0)=0.15+12-14$, where the errors quoted are purely statistical. We find $T_1$ is approximately independent of the spectator quark mass and extract $T_1(q^2=0)=0.15+5-4$ if this independence is assumed. We compare this with the same form factor derived (in the Standard Model) from the CLEO experimental branching ratio of $BR(B \to K^* \gamma) = (4.5 \pm 1.5 \pm 0.9) \times 10^{-5}$ and find the results to be consistent within statistical errors.