Resummation and Matching of $b$-quark Mass Effects in $b\bar{b}H$ Production

TL;DR

This paper develops a systematic effective field theory approach to accurately compute the $bar{b}H$ production cross section by combining fixed-flavor and variable-flavor schemes, including resummation of collinear logarithms and uncertainty assessment.

Contribution

It introduces a novel method that unifies fixed 4-flavor and 5-flavor schemes for heavy-quark initiated processes, improving accuracy and uncertainty estimation.

Findings

The new approach includes full mass dependence and resummation of collinear logs.

Numerical results at NLO+NLL show reduced uncertainties and larger central values.

Comparison with existing schemes demonstrates improved stability and precision.

Abstract

We use a systematic effective field theory setup to derive the $b\bar{b}H$ production cross section. Our result combines the merits of both fixed 4-flavor and 5-flavor schemes. It contains the full 4-flavor result, including the exact dependence on the $b$-quark mass, and improves it with a resummation of collinear logarithms of $m_b/m_H$. In the massless limit, it corresponds to a reorganized 5-flavor result. While we focus on $b\bar{b}H$ production, our method applies to generic heavy-quark initiated processes at hadron colliders. Our setup resembles the variable flavor number schemes known from heavy-flavor production in deep-inelastic scattering, but also differs in some key aspects. Most importantly, the effective $b$-quark PDF appears as part of the perturbative expansion of the final result where it effectively counts as an $O(\alpha_s)$ object. The transition between the fixed-order (4-flavor) and resummation (5-flavor) regimes is governed by the low matching scale at which the $b$-quark is integrated out. Varying this scale provides a systematic way to assess the perturbative uncertainties associated with the resummation and matching procedure and reduces by going to higher orders. We discuss the practical implementation and present numerical results for the $b\bar{b}H$ production cross section at NLO+NLL. We also provide a comparison to the corresponding predictions in the fixed 4-flavor and 5-flavor results and the Santander matching prescription. Compared to the latter, we find a slightly reduced uncertainty and a larger central value, with its central value lying at the lower edge of our uncertainty band.