Updating Boer-Mulders functions from unpolarized pd and pp Drell-Yan data

TL;DR

This work updates the extraction of the proton Boer-Mulders functions by combining unpolarized $p d$ and $pp$ Drell-Yan data from E866/NuSea, incorporating $x_f$ and $Q$ dependencies under the assumption that the $\cos 2\phi$ asymmetry originates from $h_1^{\perp}$. It employs a Gaussian $p_T$-dependent model with flavor-dependent $x$-scaling $h_1^{\perp q}(x)=H_q\,x^{c^q}\,(1-x)^b\,f_1^q(x)$, and performs a global LO fit to the data, yielding parameter values that respect positivity bounds. The resulting Boer-Mulders functions are used to predict future $\cos 2\phi$ asymmetries in $pp$ collisions at J-PARC and in $p\bar p$ collisions at PANDA and PAX, with the findings indicating stronger signals in $pp$ than in $p\bar p$ and providing a testable framework for upcoming experiments. The work highlights the role of TMDs in describing azimuthal asymmetries and extends the phenomenology of $h_1^{\perp}$ to new kinematic regimes.

Abstract

We extract the Boer-Mulders functions for the proton by combining the unpolarized pd and pp Drell-Yan data measured by the E866/NuSea Collaboration by the assumption that the $\cos 2φ$ asymmetry is from the Boer-Mulders function. Using the extracted Boer-Mulders functions, we present the predictions for the $\cos 2 φ$ asymmetries in future pp experiments at J-PARC and $p \bar{p}$ experiments at PANDA and PAX.

Figures (8)

• Figure 1: The $q_T$-dependent $\cos 2 \phi$ asymmetries for unpolarized $p\,d$ (left) and $pp$ (right) Drell-Yan process calculated from our fitted results. The region between the two dotted line corresponds to the uncertainty of the parameters. Data are from the FNAL E866/NuSea experiments. Here we exclude data with $p_T >2$ GeV.
• Figure 2: The $x_1$-dependent $\cos 2 \phi$ asymmetries for unpolarized $p\,d$ (left) and $pp$ (right) Drell-Yan process calculated from our fitted results. The region between the two dotted line corresponds to the uncertainty of the parameters. Data are from the FNAL E866/NuSea collaboration.
• Figure 3: The $x_2$-dependent $\cos 2 \phi$ asymmetries for unpolarized $p\,d$ (left) and $pp$ (right) Drell-Yan process calculated from our fitted results. The region between the two dotted line corresponds to the uncertainty of the parameters. Data are from the FNAL E866/NuSea collaboration.
• Figure 4: The $x_F$-dependent $\cos 2 \phi$ asymmetries for unpolarized $p\,d$ (left) and $pp$ (right) Drell-Yan process calculated from our fitted results. The region between the two dotted line corresponds to the uncertainty of the parameters. Data are from the FNAL E866/NuSea collaboration.
• Figure 5: The $Q$-dependent $\cos 2 \phi$ asymmetries for unpolarized $p\,d$ (left) and $pp$ (right) Drell-Yan process calculated from our fitted results. The region between the two dotted line corresponds to the uncertainty of the parameters. Data are from the FNAL E866/NuSea collaboration.