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Non-perturbative effects in the W and Z transverse momentum distribution

A. Guffanti, G. E. Smye

TL;DR

This work applies the dispersive approach to non-perturbative QCD corrections in the W and Z transverse momentum distribution, formulating power corrections as modifications to the running coupling that translate into -b^2- and -b^2 log Q^2-dependent terms in impact parameter space. By combining single-gluon real emission, all-orders soft/collinear resummation, and a universal low-scale α_s modification, the authors derive a finite, gauge-invariant non-perturbative correction δC(N,b) governed by moments A2 and A2′ of δα_s. They show that the resulting W(τ,b) function, which scales quadratically with b at small b, accounts for a substantial portion of the non-perturbative effects observed in data, and they discuss exponentiation and factorization-scale reinterpretations as ways to gauge theoretical uncertainties. The analysis provides a framework for universality tests and connects to Gaussian fits used in phenomenology, with implications for interpreting vector-boson p_T spectra at current and future colliders. Overall, the paper advances a theoretically grounded route to describe non-perturbative corrections in hadronic vector-boson production.

Abstract

We use the "dispersive method" to investigate non-perturbative effects in the transverse momentum distribution of vector bosons produced in p-pbar collisions. The assumption of a non-perturbative modification to the running coupling at low scales leads to additional contributions in impact parameter space proportional to -b^2 log Q^2 and -b^2. Our results, which we expect to be valid provided tau is not close to 1, are shown to account for a substantial proportion of the total non-perturbative contribution extracted from data.

Non-perturbative effects in the W and Z transverse momentum distribution

TL;DR

This work applies the dispersive approach to non-perturbative QCD corrections in the W and Z transverse momentum distribution, formulating power corrections as modifications to the running coupling that translate into -b^2- and -b^2 log Q^2-dependent terms in impact parameter space. By combining single-gluon real emission, all-orders soft/collinear resummation, and a universal low-scale α_s modification, the authors derive a finite, gauge-invariant non-perturbative correction δC(N,b) governed by moments A2 and A2′ of δα_s. They show that the resulting W(τ,b) function, which scales quadratically with b at small b, accounts for a substantial portion of the non-perturbative effects observed in data, and they discuss exponentiation and factorization-scale reinterpretations as ways to gauge theoretical uncertainties. The analysis provides a framework for universality tests and connects to Gaussian fits used in phenomenology, with implications for interpreting vector-boson p_T spectra at current and future colliders. Overall, the paper advances a theoretically grounded route to describe non-perturbative corrections in hadronic vector-boson production.

Abstract

We use the "dispersive method" to investigate non-perturbative effects in the transverse momentum distribution of vector bosons produced in p-pbar collisions. The assumption of a non-perturbative modification to the running coupling at low scales leads to additional contributions in impact parameter space proportional to -b^2 log Q^2 and -b^2. Our results, which we expect to be valid provided tau is not close to 1, are shown to account for a substantial proportion of the total non-perturbative contribution extracted from data.

Paper Structure

This paper contains 6 sections, 82 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Transverse momentum distribution
  3. Single gluon emission
  4. Multiple gluon emission
  5. Non-perturbative contribution
  6. Results and discussion

Figures (3)

  • Figure 1: Vector boson production with collinear gluon emission.
  • Figure 2: Graph of $W(\tau,b)$ against $\tau$ for $b=1$ GeV$^{-1}$ (solid line), $b=0.1$ GeV$^{-1}$ (dotted) and $b=0.01$ GeV$^{-1}$ (dashed), evaluated at the Z mass with ${\cal A}_2=0.2$ GeV$^2$ and ${\cal A}_2^\prime=0$.
  • Figure 3: Graph of $\hat{W}(\tau,b)$ against $\tau$ for $b=0.5$ GeV$^{-1}$ (solid line), $b=0.1$ GeV$^{-1}$ (dotted) and $b=0.01$ GeV$^{-1}$ (dashed), evaluated at the Z mass with ${\cal A}_2=0.2$ GeV$^2$ and ${\cal A}_2^\prime=0$.