Parton model versus color dipole formulation of the Drell-Yan process

TL;DR

The paper addresses whether Drell–Yan production can be described equivalently by the color dipole formulation or by the conventional NLO parton model in the Regge regime, where the dilepton mass is small compared with the collider energy. It develops and tests a dipole-based description using σ^N_{q\bar q}(αρ,x) and the light-cone wavefunction Ψ_{γ^* q}, deriving the DY cross section in this framework and comparing it to NLO parton-model results across pp/pd data and RHIC energies. The main finding is that, at low x_2, the two approaches yield very similar predictions (within ~20–25%), with discrepancies growing at larger x_2 where valence effects become important; the DY transverse momentum distribution reveals larger differences at moderate q_⊥, providing a sensitive probe of the dipole cross section. The study highlights that most uncertainties arise from the dipole cross-section parameterization, scale choices, and PDF inputs, and argues that upcoming RHIC data could meaningfully constrain σ^N_{q\bar q} and test the validity of the dipole description as a complementary view of DY dynamics.

Abstract

In the kinematical region where the center of mass energy is much larger than all other scales, the Drell-Yan process can be formulated in the target rest frame in terms of the same color dipole cross section as low Bjorken-x deep inelastic scattering. Since the mechanisms for heavy dilepton production appear very different in the dipole approach and in the conventional parton model, one may wonder whether these two formulations really represent the same physics. We perform a comparison of numerical calculations in the color dipole approach with calculations in the next-to-leading order parton model. For proton-proton scattering, the results are very similar at low x_2 from fixed target to RHIC energies, confirming the close connection between these two very different approaches. We also compare the transverse momentum distributions of Drell-Yan dileptons predicted in both formulations. The range of applicability of the dipole formulation and the impact of future Drell-Yan data from RHIC for determining the color dipole cross section are discussed. A detailed derivation of the dipole formulation of the Drell-Yan process is also included.

Figures (5)

• Figure 1: In the target rest frame, DY dilepton production looks like bremsstrahlung. A quark or an antiquark 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 (antiquark) scatters.
• Figure 2: Calculations in the dipole approach to DY and its modification Eq. (\ref{['eq:modified']}) compared to NLO parton model results at fixed target energy ($\sqrt{s}=38.8$ GeV). The CTEQ5M parameterization cteq is used for the parton model calculation. The data are from E772 e772. The curves and data for the different mass bins have been rescaled for better visibility. In all calculations, none of the free parameters of the dipole approach were adjusted to DY data. Only DIS data have been used.
• Figure 3: The same as Fig. \ref{['fig:e772']}, but now at RHIC energy ($\sqrt{s}=500$ GeV), where much lower values of $x_2$ can be reached.
• Figure 4: The same as Fig. \ref{['fig:rhic']}, but with GRV PDFs grv. For the dipole approach, we employed the LO PDFs GRV98LO for the projectile parton distribution.
• Figure 5: Comparison of the DY transverse momentum distribution calculated in the dipole approach and in the NLO parton model. The parton model calculations have been performed for two different values of the quark's intrinsic momentum. The values of the kinematical variables for all curves in this figure are $\sqrt{s}=500$ GeV, $x_F=0$ and $M=4.25$ GeV.