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.
Highlights
The calculation can be divided into: 1. Matching conditions [12,13,14,15,16,17,18,19,20], 2
Ongoing efforts to reduce the perturbative uncertainty in the B → Xsγ decay rate have resulted in a theory estimate to NNLO in QCD
The present article aims at addressing a particular higher-order perturbative contribution, namely the four-body contributions b → sqqγ to Γ(B → Xsγ) at NLO
Summary
The NLO calculation is performed in 4 steps: 1. Evaluation of the cut-diagrams shown in figures 2, 3, 4. Collinear logarithms: having regularized collinear divergences in dimensional regularization, we use the method of splitting functions [50, 55,56,57,58] to transform 1/ coll poles into collinear logarithms of the form log(mq/mb) This requires the computation of the corresponding b → sqq corrections with subsequent photon emission q → q γ (with q = q, s), by evaluation of the diagrams shown, the convolution with the splitting function, and the three-particle phase-space integration. We disregard these mirror contributions in the calculation, but at the end we substitute G(ij1) → G(ij1) + G(j1i) ∗
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