Precision phenomenology with MCFM

TL;DR

The paper introduces a major overhaul of the public code MCFM to push fixed‑order QCD predictions to per mille precision at hadron colliders. It achieves this through a highly parallelized Vegas integration, automatic tau_cut extrapolation with differential fitting, boosted jettiness definitions, and leading power corrections, enabling robust NNLO studies with multiple PDF sets and correlated sampling. Key contributions include automated differential tau_cut assessments, correlated multi‑PDF set uncertainties, and a full performance study benchmarking integration strategies and uncertainty estimation methods. The results demonstrate per mille‑level control across a broad set of color‑singlet processes, paving the way for reliable NNLO predictions with jet activity at Born level and facilitating precise PDF comparisons and new physics sensitivity studies.

Abstract

Without proper control of numerical and methodological errors in theoretical predictions at the per mille level it is not possible to study the effect of input parameters in current hadron-collider measurements at the required precision. We present a new version of the parton-level code MCFM that achieves this requirement through its highly-parallelized nature, significant performance improvements and new features. An automatic differential cutoff extrapolation is introduced to assess the cutoff dependence of all results, thus ensuring their reliability and potentially improving fixed-cutoff results by an order of magnitude. The efficient differential study of PDF uncertainties and PDF set differences at NNLO, for multiple PDF sets simultaneously, is achieved by exploiting correlations. We use these improvements to study uncertainties and PDF sensitivity at NNLO, using 371 PDF set members. The work described here permits NNLO studies that were previously prohibitively expensive, and lays the groundwork necessary for a future implementation of NNLO calculations with a jet at Born level in MCFM.

Figures (33)

• Figure 1: .9 NNLO $e^+$ rapidity distributions for $W^+$ production in the forward region, computed with uncertainties from a variety of .9 PDF sets, normalized to the central .9 PDF4LHC prediction.
• Figure 2: The transverse momentum distribution of the hardest photon in diphoton production, computed at .9 NNLO. Results are shown for $\tau_\text{cut}=10^{-3}$ GeV (blue) and $\tau_\text{cut}=10^{-4}$ GeV (red), as well as the results obtained using automatic fitting (darker blue and red). All results are normalized to the fit from $\tau_\text{cut}=10^{-4}$ GeV.
• Figure 3: The dependence of the integral for the .9 NNLO Higgs production double real emission contribution (for $\alpha=1$ and $\tau_\text{cut}=0.002$ GeV) on the accumulated number of calls. The red data corresponds to using the Sobol sequence and blue to a .9 MT19937 sequence. Each point represents a new estimate from a new iteration.
• Figure 4: The dependence of the estimated uncertainty of the .9 NNLO Higgs production double real emission contribution (for $\alpha=1$ and $\tau_\text{cut}=0.002$ GeV) on the accumulated number of calls. The red data corresponds to using the Sobol sequence and blue to the .9 MT19937 sequence. Each point represents a new estimate from a new iteration. The dashed line represents the uncertainty from the Vegas routine, while the points and solid line represent the "true" error, assuming that the average from the last reported numbers of sequences is the most precise with an uncertainty of $\pm2.5$.
• Figure 5: The dependence of the integral for the .9 NNLO Higgs production double real emission contribution (for $\alpha=1$ and $\tau_\text{cut}=0.002$ GeV) on the accumulated number of calls. The black points correspond to our default setup, while the others (labelled by "'lim") are obtained by limiting the calls per iteration to $10^6$.