Four-body contributions to B -> Xs gamma at NLO

TL;DR

This paper calculates four-body NLO contributions to the B -> Xs gamma decay, reducing theoretical uncertainties and confirming that these contributions are small, less than 1%, thus supporting existing error estimates.

Contribution

It provides the first complete NLO calculation of four-body contributions to B -> Xs gamma decay, improving the precision of theoretical predictions.

Findings

Four-body contributions are positive and less than 1% of the total decay rate.

The calculation confirms previous estimates of perturbative uncertainties.

The results support the current theoretical accuracy of B -> Xs gamma decay predictions.

Abstract

Ongoing efforts to reduce the perturbative uncertainty in the B -> Xs gamma decay rate have resulted in a theory estimate to NNLO in QCD. However, a few contributions from multi-parton final states which are formally NLO are still unknown. These are parametrically small and included in the estimated error from higher order corrections, but must be computed if one is to claim complete knowledge of the B -> Xs gamma rate to NLO. A major part of these unknown pieces are four-body contributions corresponding to the partonic process b -> s qbar q gamma. We compute these NLO four-body contributions to B -> Xs gamma, and confirm the corresponding tree-level leading-order results. While the NLO contributions arise from tree-level and one-loop Feynman diagrams, the four-body phase-space integrations make the computation non-trivial. The decay rate contains collinear logarithms arising from the mass regularization of collinear divergences. We perform an exhaustive numerical analysis, and find that these contributions are positive and amount to no more than 1% of the total rate in the Standard Model, thus confirming previous estimates of the perturbative uncertainty.