QED factorization of two-body non-leptonic and semi-leptonic $B$ to charm decays

TL;DR

This paper investigates the impact of QED corrections on theoretically clean two-body B meson decays, finding sub-percent amplitude effects and up to a few percent rate corrections, crucial for precise experimental comparisons.

Contribution

It extends the QCD factorization framework to include QED effects in B decays, providing a detailed analysis of their size and phenomenological importance.

Findings

QED effects at the amplitude level are at the sub-percent level.

Rate corrections due to ultrasoft photons can reach a few percent.

QED effects are comparable to QCD uncertainties in these decays.

Abstract

The QCD$\times$QED factorization is studied for two-body non-leptonic and semi-leptonic $B$ decays with heavy-light final states. These non-leptonic decays, like $\bar{B}^0_{(s)}\to D^+_{(s)} \pi^-$ and $\bar{B}_d^0 \to D^+ K^-$, are among the theoretically cleanest non-leptonic decays as penguin loops do not contribute and colour-suppressed tree amplitudes are suppressed in the heavy-quark limit or even completely absent. Advancing the theoretical calculations of such decays requires therefore also a careful analysis of QED effects. Including QED effects does not alter the general structure of factorization which is analogous for both semi-leptonic and non-leptonic decays. For the latter, we express our result as a correction of the tree amplitude coefficient $a_1$. At the amplitude level, we find QED effects at the sub-percent level, which is of the same order as the QCD uncertainty. We discuss the phenomenological implications of adding QED effects in light of discrepancies observed between theory and experimental data, for ratios of non-leptonic over semi-leptonic decay rates. At the level of the rate, ultrasoft photon effects can produce a correction up to a few percent, requiring a careful treatment of such effects in the experimental analyses.