Extracting Boer-Mulders functions from $p+D$ Drell-Yan processes

TL;DR

This study extracts the proton's Boer-Mulders functions $h_1^{\perp}$ for valence and sea quarks from unpolarized $p+D$ Drell–Yan data using a Gaussian TMD ansatz that ties $h_1^{\perp}$ to $f_1$. A MINUIT fit to E866/NuSea data provides flavor-dependent coefficients $H_q$ and a transverse-momentum width $p_{bm}^2$, enabling predictions of the $\cos 2\phi$ asymmetry in unpolarized $pp$, $pD$, and $p\bar{p}$ Drell–Yan across FNAL, RHIC, and GSI kinematics. The results agree with SIDIS expectations regarding sign and magnitude and offer testable predictions that can constrain the flavor decomposition of $h_1^{\perp}$ with future data. This work advances TMD phenomenology of spin-momentum correlations in hadrons and guides measurements toward disentangling valence and sea contributions.

Abstract

We extract the Boer-Mulders functions of valence and sea quarks in the proton from unpolarized $p+D$ Drell-Yan data measured by the FNAL E866 Collaboration. Using these Boer-Mulders functions, we calculate the $\cos 2 φ$ asymmetries in unpolarized $pp$ Drell-Yan processes, both for the FNAL E866/NuSea and the BNL Relativistic Heavy Ion Collider (RHIC) experiments. We also estimate the $\cos 2 φ$ asymmetries in the unpolarized $p\bar{p}$ Drell-Yan processes at GSI.

Figures (6)

• Figure 1: Fits to the $p_T$,$x_1$, $x_2$-dependent $\cos 2 \phi$ asymmetries $\nu_{pD}$ for Drell-Yan processes. Data are from the FNAL E866/NuSea collaboration.
• Figure 2: Comparison of $|p_{T} x h^\perp_1(x,\mathbf{p} _{T}^2)|/M$ and $x f_1(x,\mathbf{p}_{T}^2)$ for $u$ and $d$ quarks at $p_{T}=0.45$ GeV and $Q= 1$ GeV. Here $f_1$ is a combination of valence and sea quark distributions.
• Figure 3: The $Q$-dependent $\cos 2 \phi$ asymmetry $\nu_{pD}$ for Drell-Yan processes at FNAL E866/NuSea, presenting both the experimental data and the results we estimate with the best fit values of the Boer-Mulders functions in Table \ref{['tab']} (line).
• Figure 4: The $p_T$-dependent $\cos 2 \phi$ asymmetries $\nu$ in both $pp$ (dotted curve)and $pD$(solid curve) Drell-Yan processes at FNAL E866/NuSea, calculated with the fitted Boer-Mulders functions presented in Table \ref{['tab']}.
• Figure 5: The $y$-dependent $\cos 2 \phi$ asymmetries $\nu$ for $pp$ Drell-Yan process at RHIC, with the kinematical conditions $\sqrt{s}=200$ GeV, $-1< y <2$, and calculated with the Boer-Mulders functions that we got. The dotted and dashed lines show the asymmetries at $Q=4$ and 20 GeV, respectively.