Resummation ambiguities in the Higgs transverse-momentum spectrum in the Standard Model and beyond

TL;DR

This work investigates how different matching prescriptions between fixed-order and all-order resummation affect predictions for the Higgs transverse-momentum spectrum in gluon fusion. It compares analytic resummation, MC@NLO, and POWHEG, and evaluates two matching-scale determination strategies (BV and HMW) across SM and 2HDM scenarios with top and bottom loop contributions. The authors quantify ambiguities that arise, showing substantial variations at intermediate and large p_T, and demonstrate that modest modifications to subleading terms can reduce discrepancies between approaches. The results highlight the importance of including matching-scale uncertainties in precision Higgs phenomenology and in BSM scenarios with enhanced bottom Yukawas. The work provides guidance for reliable Higgs p_T predictions and informs future higher-order resummation efforts.

Abstract

We study the prediction for the Higgs transverse momentum distribution in gluon fusion and focus on the problem of matching fixed- and all-order perturbative results. The main sources of matching ambiguities on this distribution are investigated by means of a twofold comparison. On the one hand, we present a detailed qualitative and quantitative comparison of two recently introduced algorithms for determining the matching scale. On the other hand, we apply the results of both methods to three widely used approaches for the resummation of logarithmically enhanced contributions at small transverse momenta: the MC@NLO and POWHEG Monte Carlo approaches, and analytic resummation. While the three sets of results are largely compatible in the low-pT region, they exhibit sizable differences at large pT. We show that these differences can be significantly reduced by suitable modifications of formally subleading terms in the Monte Carlo implementations. We apply our study to the Standard Model Higgs boson and to the neutral Higgs bosons of the Two-Higgs-Doublet Model for representative scenarios of the parameter space, where the top- and bottom-quark diagrams enter the cross section at different strength.

Figures (11)

• Figure 1: A sample of Feynman diagrams for $gg\rightarrow \phi$ contributing to the .9 NLO cross section; (a) .9 LO, (b) virtual and (c-d) real corrections. The graphical notation for the lines is: solid straight $\widehat{=}$ quark; curly $\widehat{=}$ gluon; dashed $\widehat{=}$ Higgs.
• Figure 2: Sample of a shower scale distribution in MadGraph5_aMC@NLO for a $125$ GeV Higgs boson produced in gluon fusion. The distribution is normalized such that it integrates to one.
• Figure 3: On the top (bottom) comparison of the matching scales in the .9 BV and the .9 HMW approach for the scalar (pseudo-scalar). Solid (dashed) curves correspond to the .9 HMW (.9 BV) scales. The scale corresponding to the top (bottom) quark squared matrix element is shown in red (green), while the values to be used for the interference term are in blue.
• Figure 4: Shapes of the transverse-momentum distributions (i.e., normalized such that the integral yields one) for a .9 SM Higgs boson with $m_h=125$ GeV. In the upper plots we show the distributions computed with .9 AR (black, solid), MC@NLO (red, dotted) and POWHEG (blue, dashed overlaid by points), setting the matching scales to the .9 BV values (left) or the .9 HMW values (right). For reference, we also show the fixed-.9 NLO (f.9 NLO) prediction (green, dash-dotted with open boxes). The main frame shows the absolute distributions, the first inset the shape-ratio of the central values to the .9 AR distribution, and the second inset the uncertainty bands, normalized again to the central .9 AR value. In the lower three plots we compare the results within each code, using for the matching scales the .9 BV values (red, dotted) and the .9 HMW values (black, solid), taking the .9 HMW results as reference for the ratios of the insets.
• Figure 5: Same as Figure \ref{['fig:results-sm']}, but with enlarged low-$p_{\bot}$ region.