Nuclear effects in the Drell-Yan process at very high energies

TL;DR

This work develops and applies the light-cone color-dipole formalism to nuclear Drell-Yan processes at very high energies, enabling explicit, impact-parameter dependent predictions of shadowing and transverse-momentum broadening in pA, DA, and AA collisions. The authors compute the DY cross section and $q_T$ distributions by eikonalizing the dipole cross section with gluon shadowing implemented through a Green-function approach, and they separate transversely and longitudinally polarized contributions, predicting polarization effects and Lam-Tung-violation signals. A key finding is that valence-quark shadowing can dominate over sea-quark shadowing in nuclei, and gluon shadowing significantly enhances suppression in heavy-ion collisions, with substantial centrality and energy dependence. The work also develops detailed appendices on gluon shadowing and the DY $q_T$ distribution, providing analytic and numerical tools for incorporating higher Fock-state dynamics and nonperturbative effects within a coherent, high-energy framework.

Abstract

We study Drell-Yan (DY) dilepton production in proton(deuterium)-nucleus and in nucleus-nucleus collisions within the light-cone color dipole formalism. This approach is especially suitable for predicting nuclear effects in the DY cross section for heavy ion collisions, as it provides the impact parameter dependence of nuclear shadowing and transverse momentum broadening, quantities that are not available from the standard parton model. For p(D)+A collisions we calculate nuclear shadowing and investigate nuclear modification of the DY transverse momentum distribution at RHIC and LHC for kinematics corresponding to coherence length much longer than the nuclear size. Calculations are performed separately for transversely and longitudinally polarized DY photons, and predictions are presented for the dilepton angular distribution. Furthermore, we calculate nuclear broadening of the mean transverse momentum squared of DY dileptons as function of the nuclear mass number and energy. We also predict nuclear effects for the cross section of the DY process in heavy ion collisions. We found a substantial nuclear shadowing for valence quarks, stronger than for the sea.

Figures (18)

• Figure 1: In the target rest frame, DY dilepton production looks like bremsstrahlung. A quark or an anti-quark from the projectile hadron scatters off the target color field (denoted by the shaded circles) and radiates a massive photon, which subsequently decays into the lepton pair. The photon decay is not shown. The photon can be radiated before or after the quark scatters.
• Figure 2: The eikonal formula (\ref{['eq:signuc']}) takes only multiple rescatterings of the $|q\bar{q}\rangle$-Fock component into account. This figure illustrates the amplitude for double scattering (left). When the amplitude is squared (middle), the gluon rungs combine into gluon ladders (Pomerons), which are enclosed into each other. In Regge theory, this contribution to the cross section is expressed in terms of the Pomeron-Pomeron-Reggeon vertex (right).
• Figure 3: At high energy, the lifetime of higher Fock states becomes long enough for multiple scattering. Shown here is the double-scattering amplitude for the $|q\bar{q}G\rangle$-Fock state. In Regge theory, this process is expressed in terms of the triple-Pomeron vertex (right). The eikonal formula (\ref{['eq:signuc']}) is improved by multiplying $\sigma_{q\bar{q}}$ by the gluon shadowing ratio $R_G$, Eq. (\ref{['eq:sigmanuc']}), to include these contributions also.
• Figure 4: The figure on the left shows the $q\bar{q}$-nucleus cross section (\ref{['eq:sigmanuc']}) divided by the nuclear mass number $A$ for two different values of $x$. The two lower curves (solid and dashed) are calculated for gold ($A=197$) and the two upper curves for a proton. The figure on the right shows the $q\bar{q}$-nucleus cross section divided by $A$ times the dipole cross section (\ref{['eq:wuestsigma']}). While large separations are strongly suppressed, small size dipoles are much less affected by the nucleus. Nuclear gluon shadowing is included in the calculation, as explained in the text. It slowly vanishes at small $q\bar{q}$ separations, which correspond to high $\widetilde{Q}^2$.
• Figure 5: Gluon shadowing vs. the length of the nuclear medium $L=2\sqrt{R_A^2-b^2}$, where $b$ is the impact parameter and $R_A$ the nuclear radius. All curves are for $Q^2=20$ GeV$^2$ but for different values of $x$.