Higgs production in bottom quark annihilation: Transverse momentum distribution at NNLO+NNLL

TL;DR

This work delivers a precise prediction for the Higgs transverse momentum distribution in bottom-quark annihilation within the five-flavor scheme by performing soft and collinear resummation to NNLL and matching to the NNLO fixed-order result. A key contribution is the determination of the hard coefficient H_b^{H,(2)} both numerically and analytically, enabling full NNLO+NNLL accuracy for the b bbar H process. The authors demonstrate a significant reduction in theoretical uncertainties, especially from scale variations, and validate the approach with comprehensive checks and cross-method comparisons. These results are particularly relevant for scenarios with enhanced bottom Yukawa couplings, such as certain 2HDM/MSSM realizations, and provide a robust framework for precision Higgs phenomenology and bottom-density studies.

Abstract

We present the inclusive transverse momentum distribution for Higgs bosons produced in bottom quark annihilation at the LHC. The results are obtained in the five-flavor scheme. The soft and collinear terms at small $p_T$ are resummed through NNLL accuracy and matched to the NNLO transverse momentum distribution at large $p_T$. We find that the theoretical uncertainty, derived from a variation of the unphysical scales entering the calculation, is significantly reduced with respect to lower orders.

Figures (22)

• Figure 1: Transverse momentum spectrum at .9 NLO (blue, dashed line) and at .9 NLO.9 +.9 NLL (red, solid line) for (a) $Q=M/2$ and (b) $Q=M/4$. (Here and in the following plots, $m_H=M$ is the Higgs mass.)
• Figure 2: (a) Transverse momentum spectrum at .9 NNLO (blue, dashed line) and at .9 NNLO.9 +.9 NNLL (red, solid line) for the central scales; (b) only the $b\bar{b}$ channel for that quantity.
• Figure 3: Resummed-matched $p_T$ distribution at .9 NLO.9 +.9 NLL (blue, dashed line) and .9 NNLO.9 +.9 NNLL (red, solid line); lines: central scale choices; bands: uncertainty due to $\mu_{\rm F}{},\mu_{\rm R}{}$-variation.
• Figure 4: Resummed-matched $p_T$ distribution at .9 NLO.9 +.9 NLL (blue, dashed line) and .9 NNLO.9 +.9 NNLL (red, solid line); lines: central scale choices; bands: uncertainty due to $Q{}$-variation.
• Figure 5: Resummed-matched $p_T$ distribution at .9 NLO.9 +.9 NLL (blue, dashed line) and .9 NNLO.9 +.9 NNLL (red, solid line); lines: central scale choices; bands: uncertainty due to variation of all scales.