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Nonperturbative corrections to the Drell-Yan transverse momentum distribution

Sofiane Tafat

TL;DR

The paper develops a nonperturbative framework for corrections to the Drell-Yan transverse momentum distribution by recasting soft-gluon effects as a vacuum Wilson loop (the Sudakov factor) and separating perturbative resummation from nonperturbative boundary conditions.It shows how perturbative Sudakov resummation emerges from the Wilson loop through cusp anomalous dimensions, while IR renormalons signal power corrections that are absorbed into a nonperturbative boundary $W_0(b^2,Q^2)$.Nonperturbative contributions are computed via a gauge-invariant nonlocal field-strength correlator, allowing a lattice-informed modeling that yields small-$b^2$ and large-$b^2$ asymptotics and a concrete ansatz for the correlator.Comparisons with phenomenology indicate qualitative agreement with large-$q_T$ behavior and deviations at small $q_T$, supporting the view that nonperturbative QCD vacuum structure plays a role in shaping the full $q_T$ spectrum.

Abstract

We study nonperturbative corrections to the transverse momentum distribution of vector bosons in the Drell-Yan process. Factorizing out the Sudakov effects due to soft gluons we express their contribution to the distribution in the form of the vacuum averaged Wilson loop operator. We calculate the nonperturbative contribution to the Sudakov form factor using the expansion of the Wilson loop over vacuum fields supplemented with the expression for nonlocal gauge invariant field strength correlator. Although the Wilson loop is defined in an essentially Minkowski kinematics, the part of the nonperturbative contribution depending on the invariant mass of the produced vector bosons is governed by asymptotics of the correlator at large space-like (Euclidean) separations and therefore can be calculated using conventional nonperturbative methods. Applying the results of lattice calculations we found that the obtained expression for the nonperturbative power corrections is in qualitative agreement with known phenomenological expressions at large transverse momenta and deviate from them at small transverse momenta.

Nonperturbative corrections to the Drell-Yan transverse momentum distribution

TL;DR

The paper develops a nonperturbative framework for corrections to the Drell-Yan transverse momentum distribution by recasting soft-gluon effects as a vacuum Wilson loop (the Sudakov factor) and separating perturbative resummation from nonperturbative boundary conditions.It shows how perturbative Sudakov resummation emerges from the Wilson loop through cusp anomalous dimensions, while IR renormalons signal power corrections that are absorbed into a nonperturbative boundary $W_0(b^2,Q^2)$.Nonperturbative contributions are computed via a gauge-invariant nonlocal field-strength correlator, allowing a lattice-informed modeling that yields small-$b^2$ and large-$b^2$ asymptotics and a concrete ansatz for the correlator.Comparisons with phenomenology indicate qualitative agreement with large-$q_T$ behavior and deviations at small $q_T$, supporting the view that nonperturbative QCD vacuum structure plays a role in shaping the full $q_T$ spectrum.

Abstract

We study nonperturbative corrections to the transverse momentum distribution of vector bosons in the Drell-Yan process. Factorizing out the Sudakov effects due to soft gluons we express their contribution to the distribution in the form of the vacuum averaged Wilson loop operator. We calculate the nonperturbative contribution to the Sudakov form factor using the expansion of the Wilson loop over vacuum fields supplemented with the expression for nonlocal gauge invariant field strength correlator. Although the Wilson loop is defined in an essentially Minkowski kinematics, the part of the nonperturbative contribution depending on the invariant mass of the produced vector bosons is governed by asymptotics of the correlator at large space-like (Euclidean) separations and therefore can be calculated using conventional nonperturbative methods. Applying the results of lattice calculations we found that the obtained expression for the nonperturbative power corrections is in qualitative agreement with known phenomenological expressions at large transverse momenta and deviate from them at small transverse momenta.

Paper Structure

This paper contains 10 sections, 78 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Factorization of soft gluons
  3. Perturbative contribution
  4. IR renormalons in Wilson loops
  5. Wilson loop in vacuum fields
  6. Asymptotic behavior of Wilson loop
  7. Small $b^2$ behavior
  8. Large $b^2$ behavior
  9. Ansatz for the nonlocal correlator
  10. Conclusion

Figures (3)

  • Figure 1: The integration path $C_{\rm DY}$ defining the eikonal phase (\ref{['6']}). Straightforward lines correspond to classical trajectories of quark and antiquark with momenta $p_1$ and $p_2$, respectively.
  • Figure 2: The profile function $w(b/\lambda)$ governing the $b-$dependence of nonperturbative contribution to the Sudakov form factor (\ref{['prof']}). The dash-dotted line describes the asymptotic behaviour (\ref{['sol-2']}).
  • Figure 3: The nonperturbative primordial distribution $f_{\rm nonPT}(k^2,Q^2)$ at $Q=91 \ {\rm GeV}$ and $Q_0=1.6 \ {\rm GeV}$. The dash-dotted line describes the Gaussian distribution corresponding to (\ref{['sol-1']}).