Jet veto resummation for STXS $H+$1-jet bins at aNNLL$'$+NNLO

TL;DR

This work delivers state-of-the-art jet-veto resummation for gluon-fusion Higgs production in exclusive H+1-jet STXS bins, achieving NNLL' resummation matched to NNLO. It refines the jet-veto factorization by refactoring the soft sector into global soft and soft-collinear components and incorporating leading nonglobal logarithms, while accounting for R_J power corrections that are numerically significant. The framework uses theory-nuisance parameters to cover remaining unknown two-loop ingredients, enabling robust uncertainty estimates and improved precision over previous NLL' results. The results provide precise, covariant predictions for STXS bins in the regime p_T^{cut} << p_T^H, with practical implications for Higgs coupling fits and phenomenology at the LHC.

Abstract

Measurements of Higgs boson processes by the ATLAS and CMS experiments at the LHC use Simplified Template Cross Sections (STXS) as a common framework for the combination of measurements in different decay channels and their further interpretation, e.g. to measure Higgs couplings. The different Higgs production processes are measured in predefined kinematic regions -- the STXS bins -- requiring precise theory predictions for each individual bin. In gluon-fusion Higgs production a main division is into 0-jet, 1-jet, and $\geq 2$-jet bins, which are further subdivided in bins of the Higgs transverse momentum $p_T^H$. Requiring a fixed number of jets induces logarithms $\ln p_T^{\mathrm{cut}}/Q$ in the cross section where $p_T^{\mathrm{cut}}$ is the jet-$p_T$ threshold and $Q\sim p_T^H\sim m_H$ the hard-interaction scale. These jet-veto logarithms can be resummed to all orders in perturbation theory to achieve the highest possible perturbative precision. We provide state-of-the art predictions for the $p_T^H$ spectrum in exclusive $H+$1-jet production and the corresponding $H+$1-jet STXS bins in the kinematic regime $p_T^{\mathrm{cut}} \ll p_T^H\sim m_H$. We carry out the resummation at NNLL$'$ accuracy, using theory nuisance parameters to account for the few unknown ingredients at this order, and match to full NNLO. We revisit the jet-veto factorization for this process and find that it requires refactorizing the total soft function into a global and soft-collinear contribution in order to fully account for logarithms of the signal jet radius. The leading nonglobal logarithms are also included, though they are numerically small for the region of phenomenological interest.

Figures (13)

• Figure 1: Depiction of the total soft function $S^T$ (a) present in the $R_J \sim 1$ limit, and of its refactorization into the global soft function $S_\kappa$ (b) and soft-collinear function $\mathcal{S}^R$ (c) in the $R_J\ll1$ limit, the latter two appearing in eq. \ref{['eq:factorization']}.
• Figure 2: The relative correction from nonglobal logarithms up to 2-loop, 3-loop, 4-loop and 5-loop order, using $\alpha_s(M_Z) = 0.118$ as a representative value. For the region of interest the 2-loop thus affects the cross section at the percent level, the 3-loop at the permille level, and beyond it is negligible.
• Figure 3: Full fixed order (red), singular (blue) and nonsingular (green) at NLO, differential in $\ln p_T^\text{2nd}$, for $R_J=0.01, 0.4$ and $0.8$. Wee see that the small $p_T^\text{2nd}$ behaviour of the nonsingular is linear for $R_J=0.01$ and constant for large $R_J$, which implies the presence of $R_J^2 \ln p_T^{\mathrm{cut}}$ power corrections.
• Figure 4: Nonsingular with (blue) and without (red) $R_J^2 \ln p_T^{\mathrm{cut}}$ power corrections for $R_J=0.2$ (left), 0.4 (middle) and (right), using log-log axes (top) and log-linear axes (bottom).
• Figure 5: Decomposition of the full cross section (red) in terms of the singular (blue) and nonsingular (green) as function of $\xi=p_T^{\mathrm{cut}}/p_T^H$. Our transition points are chosen on the basis of this plot. By using $\xi$, this is fairly independent of the hard kinematics, as can be seen by comparing the left ($p_T^H \in [60, 120]$ GeV) and right ($p_T^H \in [120, 200]$ GeV) panel.