[Paper Review] Transverse-momentum resummation of colorless final states at the NNLL+NNLO

Marius Wiesemann|arXiv (Cornell University)|Feb 10, 2016

Particle physics theoretical and experimental studies1 references5 citations

TL;DR

This paper presents a general framework for transverse-momentum resummation at NNLL+NNLO accuracy in QCD for colorless final states, implemented in the Matrix code. It enables fully differential predictions for $ZZ$ and $W^{+}W^{-}$ pair production, achieving excellent agreement with CMS data on the $ZZ$ $p_T$ spectrum and demonstrating significant improvements in $p_T$-veto efficiency predictions over lower-order approximations.

ABSTRACT

We present a general framework that allows to compute the resummed transverse-momentum distribution of a system of colorless particles. The implementation is fully differential in the degrees of freedom of the final-state system. As a first application, we consider the transverse-momentum spectrum of ZZ and WW boson pairs produced in hadron collisions, where we resum the logarithmically enhanced contributions due to multiple soft-gluon emission at small transverse momenta to all orders in perturbation theory. We exploit the most advanced perturbative information for the ZZ and WW production processes that is available at present by combining next-to-next-to-leading order QCD corrections with next-to-next-to-leading logarithmic resummation.

Motivation & Objective

• To develop a general, fully differential framework for transverse-momentum resummation of colorless final states in hadron collisions.
• To combine next-to-next-to-leading order (NNLO) QCD corrections with next-to-next-to-leading logarithmic (NNLL) resummation for high-precision predictions.
• To enable accurate modeling of fiducial cuts, off-shell effects, and spin correlations in leptonic decays of vector bosons.
• To provide a benchmark for precision studies of vector-boson pair production, crucial for Higgs and new-physics searches.
• To validate the framework by comparing NNLL+NNLO predictions with experimental $ZZ$ $p_T$ spectrum data from CMS.

Proposed method

• The framework employs the $q_T$-subtraction formalism within the Matrix Monte Carlo program to achieve NNLO accuracy.
• It implements unitary transverse-momentum resummation at NNLL accuracy, ensuring consistency with the known NNLO total cross section upon $p_T$ integration.
• The method is fully differential in the final-state kinematics, including invariant mass, rapidity, and phase-space variables of the colorless system.
• Helicity amplitudes from Refs. [59, 60] are used to include off-shell effects and spin correlations in leptonic decays.
• The resummation is based on the Sudakov form factor with a three-loop soft function $g^{(3)}$, enabling all-order resummation of logarithmically enhanced contributions at small $p_T$.
• Scale uncertainties are estimated via independent variations of factorization, renormalization, and resummation scales ($\mu_F$, $\mu_R$, $Q$).

Experimental results

Research questions

• RQ1 How accurately can NNLL+NNLO resummation describe the transverse-momentum spectrum of $ZZ$ and $W^{+}W^{-}$ pairs in hadron collisions?
• RQ2 To what extent do higher-order corrections and resummation improve the prediction of $p_T$-veto efficiencies compared to lower-order approximations?
• RQ3 How well does the NNLL+NNLO prediction agree with the measured $ZZ$ $p_T$ spectrum from CMS in the fiducial region?
• RQ4 What is the impact of including off-shell effects and spin correlations in the $p_T$ spectrum for leptonic vector-boson decays?
• RQ5 Can the framework be used to improve theoretical modeling for Higgs boson analyses that rely on $p_T$-based categorization?

Key findings

• The NNLL+NNLO prediction for the $ZZ$ $p_T$ spectrum shows excellent agreement with the CMS experimental measurement, particularly in the low-$p_T$ region where resummation effects are most significant.
• The NNLL+NNLO prediction lies consistently closer to the data than the NLO or NLL+NLO results, especially in the $p_T \lesssim 30$ GeV region.
• The $p_T$-veto efficiency for $W^{+}W^{-}$ production is reduced by approximately 5% at $p_T^{\text{veto}} \sim 25-30$ GeV when using NNLL+NNLO instead of the approximate NNLL+NLO result.
• The approximate NNLL+NLO result, used in previous CMS $W^{+}W^{-}$ measurements, overestimates the efficiency by about 5% compared to the full NNLL+NNLO prediction.
• The NNLO and NLL+NLO predictions are in reasonable agreement with data, but the NNLL+NNLO result provides the most accurate description of the $p_T$ shape, particularly in the small-$p_T$ regime.
• The framework successfully recovers the known NNLO total cross section upon integration over $p_T$, confirming consistency of the resummation procedure.