Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N$^3$LL

TL;DR

This paper delivers a high-precision prediction for Higgs production via bottom-quark annihilation at the LHC by combining fixed-order $N^3$LO results with threshold resummation at $N^3$LL. The authors compute the process-dependent constant $g_{b,0}^{(3)}$ using the three-loop bottom quark form factor and the third-order soft distribution, enabling a consistent $N^3$LO$+$N$^3$LL prediction when matched to the full $N^3$LO results of Duhr et al. The work analyzes the phenomenological impact of resummed threshold contributions across energies (7–14 TeV) and examines renormalization and factorization scale dependencies, PDF uncertainties, and matching to fixed-order predictions. The outcome is the most precise inclusive cross-section for $H$ production from $b\bar b$ annihilation to date, with improved perturbative stability and quantified theoretical uncertainties.

Abstract

We present an accurate theoretical prediction for the production of Higgs boson through bottom quark annihilation at the LHC up to next-to-next-to-next-to leading order (N$^3$LO) plus next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. We determine the third order perturbative Quantum Chromodynamics (QCD) correction to the process dependent constant in the resummed expression using the three loop bottom quark form factor and third order quark soft distribution function. Thanks to the recent computation of N$^3$LO corrections to this production cross-section from all the partonic channels, an accurate matching can be obtained for a consistent predictions at N$^3$LO+N$^3$LL accuracy in QCD. We have studied in detail the impact of resummed threshold contributions to inclusive cross-sections at various centre-of-mass energies and also discussed their sensitivity to renormalization and factorization scales at next-to-next-to leading order (NNLO) matched with next-to-next-to leading logarithm (NNLL). At N$^3$LO+N$^3$LL, we predict the cross-section for different centre-of-mass energies using the recently available results in \cite{Duhr:2019kwi} as well as study the renormalization scale dependence at the same order.

Figures (4)

• Figure 1: Left: Resummed cross-section plotted against the hadronic center-of-mass energy ($E_{CM}$). The band corresponds to the scale variation around the central scale choice $(\mu_r^{(c)},\mu_f^{(c)}) = (1,1/4) m_h$ along with the prediction for the central scale. In the lower inset the resummed K-factor has been shown along with scale uncertainties (see text). Right: Same plot as the left but for the comparison of fixed order and resummed contribution at NNLO level.
• Figure 2: Fixed order and resummed cross-sections are plotted successively at each order up to NNLO level with unphysical factorization ($\mu_f$) scale varied in the range $(1/10,10) m_h$ keeping renormalization scale ($\mu_r$) fixed at central value $m_h$. Similar variation for $\mu_r$ is done in the second panel keeping $\mu_f=m_h/4$. In the last panel, the $\mu_r$ is set to $\mu_f$ and is varied in the same range.
• Figure 3: The perturbative convergence is shown for fixed order and resummed order for $13$ TeV LHC. The central scale is fixed at $(1,1/4)m_h$ and the asymmetric error bars are obtained by varying the $\mu_r,\mu_f$ scales by $(1/2,2)$ around their central scale.
• Figure 4: Fixed order and resummed cross-sections are plotted at N$^3$LO level against unphysical renormalization ($\mu_r$) scale varied in the range $(1/2,2) m_h$ keeping factorization scale ($\mu_f$) fixed at central value $m_h/4$. All the parameters are chosen same as in Duhr:2019kwi.