A possible determination of the quark radiation length in cold nuclear matter

TL;DR

The paper develops a next-to-leading order Drell-Yan framework including cold nuclear matter effects to study initial-state parton energy loss in nuclei. By comparing to fixed-target data and exploiting the low beam energy of Fermilab E906, it demonstrates that shadowing and energy loss can be disentangled and uses this to extract the quark radiation length $X_0$ in cold nuclear matter, with estimates in the tens-to-hundreds of femtometers and a potential precision of about 20% for $X_0$. The work introduces a probabilistic energy loss distribution $P_{q,g}(\epsilon)$ folded into PDFs and emphasizes the linear $A^{1/3}$ path-length dependence of initial-state energy loss as a key discriminant from final-state mechanisms. If confirmed by E906 data, these results would provide the first quantitative measure of quark stopping power in cold nuclei and establish a standard candle for nuclear responses to hard probes.

Abstract

We calculate the differential Drell-Yan production cross section in proton-nucleus collisions by including both next-to-leading order perturbative effects and effects of the nuclear medium. We demonstrate that dilepton production in fixed target experiments is an excellent tool to study initial-state parton energy loss in large nuclei and to accurately determine the stopping power of cold nuclear matter. We provide theoretical predictions for the attenuation of the Drell-Yan cross section at large values of Feynman $x_F$ and show that for low proton beam energies experimental measurements at Fermilab's E906 can clearly distinguish between nuclear shadowing and energy loss effects. If confirmed by data, our results may help determine the quark radiation length in cold nuclear matter $X_0 \sim 10^{-13}$ m.

Figures (4)

• Figure 1: Neutral pion suppression in minimum bias d+Au collisions at $y=4$ at RHIC. Theoretical calculations that include known nuclear matter effects are shown. A complete simulation gives a good description of the experimental data.
• Figure 2: Next-to-leading order calculations for the muon pair production cross section in p+D collisions at $\sqrt{s_{NN}} = 38.8$ GeV is compared to Fermilab E772 experimental data. The yellow bands represent the theoretical uncertainty due to choice of factorization and renormalization scales. We have only included isospin effects for the deuterium target.
• Figure 3: Plot of the ratio of the dimuon cross section $\sigma(\text{p+W})/\sigma(\text{p+A})$, where A = D,Be, from both experiment and theory for 800 GeV protons colliding with a fixed nuclear target. The theory curves are the NLO Drell-Yan cross section calculation, including shadowing effects and initial-state energy loss, respectively. The yellow bands indicate a five-fold variation of the mean quark medium-induced energy loss.
• Figure 4: Next-to-leading order theoretical predictions for the Drell-Yan dimuon cross section attenuation $\sigma(\text{p+A})/\sigma(\text{p+D})$ at Fermilab's E906. As with Figure \ref{['pA800']}, the curves include shadowing effects (dashed line) or initial-state energy loss (solid lines), respectively. We have considered three different radiation lengths $X_0$ of quarks in large nuclei, ranging from 30 fm to 160 fm. The lower right panel highlights the difference between the two physics scenarios at large $x_F$ as a function of $A^{1/3}$.