Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Difficulties in the description of Drell-Yan processes at moderate invariant mass and high transverse momentum

Alessandro Bacchetta, Giuseppe Bozzi, Martin Lambertsen, Fulvio Piacenza, Julius Steiglechner, Werner Vogelsang

TL;DR

This paper investigates the Drell–Yan cross section differential in the lepton-pair transverse momentum in fixed-target kinematics, where $Q$ is moderate and $q_T$ approaches $Q$. By comparing fixed-order collinear factorization predictions to data from several experiments, the authors identify a persistent underestimation of the high-$q_T$ tail, prompting the exploration of threshold resummation and intrinsic-$k_T$ smearing as possible remedies. Threshold resummation improves the agreement but does not fully bridge the gap, and Gaussian intrinsic-$k_T$ smearing offers only modest gains, suggesting the need for additional power corrections or a more complete understanding of the matching between TMD and collinear regimes. The results imply that the fixed-target $q_T$ spectrum in the $q_T \sim Q$ region is not yet robustly understood, with implications for interpreting TMDs and the transition to collinear physics. Overall, the study highlights the importance of refining matching procedures and power-suppressed contributions to accurately describe the full Drell–Yan $q_T$ spectrum in fixed-target experiments.

Abstract

We study the Drell-Yan cross section differential with respect to the transverse momentum of the produced lepton pair. We consider data with moderate invariant mass Q of the lepton pair, between 4.5 GeV and 13.5 GeV, and similar (although slightly smaller) values of the transverse momentum q_T. We approach the problem by deriving predictions based on standard collinear factorization, which are expected to be valid toward the high-q_T end of the spectrum and to which any description of the spectrum at lower q_T using transverse-momentum dependent parton distributions ultimately needs to be matched. We find that the collinear framework predicts cross sections that in most cases are significantly below available data at high q_T. We discuss additional perturbative and possible non-perturbative effects that increase the predicted cross section, but not by a sufficient amount.

Difficulties in the description of Drell-Yan processes at moderate invariant mass and high transverse momentum

TL;DR

This paper investigates the Drell–Yan cross section differential in the lepton-pair transverse momentum in fixed-target kinematics, where is moderate and approaches . By comparing fixed-order collinear factorization predictions to data from several experiments, the authors identify a persistent underestimation of the high- tail, prompting the exploration of threshold resummation and intrinsic- smearing as possible remedies. Threshold resummation improves the agreement but does not fully bridge the gap, and Gaussian intrinsic- smearing offers only modest gains, suggesting the need for additional power corrections or a more complete understanding of the matching between TMD and collinear regimes. The results imply that the fixed-target spectrum in the region is not yet robustly understood, with implications for interpreting TMDs and the transition to collinear physics. Overall, the study highlights the importance of refining matching procedures and power-suppressed contributions to accurately describe the full Drell–Yan spectrum in fixed-target experiments.

Abstract

We study the Drell-Yan cross section differential with respect to the transverse momentum of the produced lepton pair. We consider data with moderate invariant mass Q of the lepton pair, between 4.5 GeV and 13.5 GeV, and similar (although slightly smaller) values of the transverse momentum q_T. We approach the problem by deriving predictions based on standard collinear factorization, which are expected to be valid toward the high-q_T end of the spectrum and to which any description of the spectrum at lower q_T using transverse-momentum dependent parton distributions ultimately needs to be matched. We find that the collinear framework predicts cross sections that in most cases are significantly below available data at high q_T. We discuss additional perturbative and possible non-perturbative effects that increase the predicted cross section, but not by a sufficient amount.

Paper Structure

This paper contains 9 sections, 30 equations, 15 figures.

Table of Contents

  1. Introduction
  2. Motivation: from TMDs to the matching regime
  3. Collinear factorization and comparison to fixed-target data
  4. Threshold resummation
  5. Intrinsic-$k_{T}$ smearing and power corrections
  6. Conclusions
  7. LO cross sections
  8. One loop coefficients
  9. LL and NLL functions

Figures (15)

  • Figure 1: Left: the TMD cross section (full line) from the fit in Bacchetta:2017gcc, when extended beyond the fit region, shows markedly different behavior depending on the functional form chosen for $b^*$ in Eq. (\ref{['Wterm']}): the dotted line is obtained with a square-root form, while the dashed line with an exponential form (respectively Eqs. 3.18 and 3.19 of Bacchetta:2015ora). $b_{{\mathrm{max}}}$ is kept fixed at 1.123 GeV$^{-1}$. The asymptotic curve is also plotted (at LO, to be consistent with the fit). Right: matched curve obtained from the same TMD, with the procedure described in Collins:2016hqq. The damping functions are taken as in Sec. IX of the same article. Data are taken from Ito:1980ev.
  • Figure 2: Transverse-momentum distribution of Drell--Yan di-muon pairs at $\sqrt s$ = 38.8 GeV in a selected invariant mass range and Feynman-$x$ range: experimental data from Fermilab E866 (hydrogen target) Webb:2003bj compared to LO QCD and NLO QCD results. Left: NLO QCD $\left(\mathcal{O}\left(\alpha_{s}^{2}\right)\right)$ calculation with central values of the scales $\mu_{R}=\mu_{F}=Q$ = 4.7 GeV, including a 90% confidence interval from the CT14 PDF set Dulat:2015mca. Right: LO QCD and NLO QCD theoretical uncertainty bands obtained by varying the renormalization and factorization scales independently in the range $Q/2<\mu_{R},\mu_{F}<2Q.$
  • Figure 3: E866: comparison between experimental data and NLO QCD predictions for different $x_{F}$ bins. We also show the low-$q_T$ asymptotic part of the cross section. For details, see text.
  • Figure 4: E866: comparison between experimental data and NLO QCD predictions for different invariant mass bins. We also show the low-$q_T$ asymptotic part of the cross section. For details, see text.
  • Figure 5: Left: R209 data Antreasyan:1981eg compared to NLO QCD $\left(\mathcal{O}\left(\alpha_{s}^{2}\right)\right)$. The dashed line shows the asymptotic part. Theoretical results are integrated over the $Q$ range. We have chosen $\mu_{R}=\mu_{F}=Q$. Right: scale variations $\left(Q/2<\mu_{R},\mu_{F}<2Q\right)$ at LO and NLO.
  • ...and 10 more figures