Drell-Yan Lepton-Pair-Jet Correlation in pA collisions

TL;DR

The paper investigates forward correlations between a Drell-Yan lepton pair and an associated hadron in proton-nucleus collisions to directly probe the small-$x$ dipole gluon distribution. It employs two parametrizations for the dipole gluon distribution: the GBW model with geometric scaling and BK evolution with both fixed and running couplings, deriving $F_{x_g}(q_\perp)$ and the corresponding cross sections. The results reveal a pronounced away-side suppression and a distinctive double-peak structure in $\Delta\phi$, with the running-coupling BK evolution providing a more realistic large-$q_\perp$ tail and overall behavior, applicable to RHIC and LHC kinematics. These findings offer concrete predictions for upcoming measurements of Drell-Yan pair–hadron correlations and a direct handle on the dipole gluon distribution in dense nuclear matter.

Abstract

In this paper, we numerically study the forward correlations between the lepton-pair and associated hadrons in Drell-Yan process in pA collisions. Using the present knowledge of the dipole gluon distribution from the modified Golec-Biernat-Wüsthoff model and from the solution of the Balitsky-Kovchegov evolution equation, we are able to compute and predict the forward correlations between the lepton-pair and associated hadron in Drell-Yan process at RHIC and LHC. Similar to the forward dihadron correlation in d-Au collisions measured at RHIC, the Drell-Yan type correlation also implies a strong suppression of the away side hadron at forward rapidity due to the strong interaction between the forward quark from the projectile proton and the gluon density from the target nucleus. Another feature of this process is that the correlation contains a double-peak structure in the away side, which makes it a unique observable.

Figures (6)

• Figure 1: The Drell-Yan scattering process, with several of the momentum variables used in our calculation labeled. $p_p$ and $p_A$ are respectively the momenta of the proton and the nucleus from which the gluon was emitted. $p_\gamma$ is the momentum of the virtual photon as reconstructed from the lepton pair, and $p_\pi$ is the measured momentum of the pion. $x_p$ and $x_g$ are the longitudinal momentum fractions of the quark relative to the proton and the gluon relative to the nucleon, $z = p_\gamma^+/q^+$ is the fraction of total momentum taken by the photon, and $z_2 = p_\pi^+/k_q^+$ is the fraction of the momentum of the quark jet that is carried by the pion.
• Figure 2: The gluon distribution from the GBW model \ref{['eq:gbwfg']}, on top, and the output of the numerical BK evolution with fixed coupling \ref{['eq:fgfromphi']}, on bottom, for central p--Pb collisions. Each curve shows $F_{x_g}(k)$ for $x_g = \exp(Y_\text{init} - n\delta Y)$, where $n$ is the number that labels the curve and $\delta Y = \frac{1}{400}\ln(10^8) \approx 0.04605$ is the step size in rapidity used by the numerical integrator. The curve labeled 0 is the initial condition. Note the transient "spike" at the low $k^2$ region of the solution to the BK evolution, and the significant enhancement at large $k^2$ relative to the GBW model.
• Figure 3: This plot shows the peak of the momentum distribution, $k_\text{max} = \max k\phi(k^2, Y)$, computed from the analytic formula for the GBW model, from the fixed coupling BK evolution for selected values of $\alpha_s$, and from the running coupling BK evolution with selected values of $\Lambda_\text{QCD}^2$. For the BK evolution curves, the slope in the upper range of rapidities decreases as $\alpha_s$ or $\Lambda_\text{QCD}^2$ decreases, and the closest match to the slope of the GBW model curve at $Y > 15$ is achieved with $\alpha_s = 0.062$ for fixed coupling or $\Lambda_\text{QCD}^2 = 0.001$ for running coupling. The jagged "steps" in the curves reflect the finite spacing of the momentum grid used in the evolution.
• Figure 4: The gluon distribution from the numerical BK evolution with the running coupling for central p--Pb collisions. This is a continuation of figure \ref{['fig:fgplot']}, and the labels have the same interpretation. As is well known, the running coupling slows down the evolution of the wavefront. Otherwise, the plots are similar to the fixed-coupling BK evolution, though there is some erratic behavior at lower momenta especially at high rapidities which was not seen to such a large extent in the fixed coupling case.
• Figure 5: The angular correlations between the virtual photons and pions at RHIC, at medium rapidity, $Y_{\gamma} = Y_{\pi} = 2.5$. The upper graph shows the correlation for a virtual photon mass of $M = 0.5GeV$, and the lower one, for $M = 4GeV$. In each case, the three curves for GBW, fixed coupling BK, and running coupling BK, exhibit basically the same double-peak structure around $\Delta\phi = \pi$, but they show differing behavior near $\Delta\phi = 0,2\pi$, the near side correlation. This relates to the large-$k^2$ behavior of the corresponding gluon distributions.