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Accessing Sivers gluon distribution via transverse single spin asymmetries in p(transv. polarized) p --> D X processes at RHIC

M. Anselmino, M. Boglione, U. D'Alesio, E. Leader, F. Murgia

TL;DR

The paper addresses how to access the Sivers gluon distribution through transverse single-spin asymmetries in D meson production in p^↑ p collisions at RHIC. It adopts a generalized TMD factorization including intrinsic k_perp in PDFs, FFs, and hard scatterings, and analyzes A_N for p^↑ p → DX, noting that gg → cc̄ dominates at RHIC energies up to x_F ≈ 0.6, making A_N a direct probe of the gluon Sivers function. By deriving the SSA as a convolution of Sivers functions with partonic cross sections and fragmentation, and employing a Gaussian k_perp model with two extreme Sivers scenarios, the study shows that sizable A_N would indicate a nonzero Δ^N f_{g/p^↑}. The work highlights the crucial role of intrinsic transverse momentum in generating SSA and suggests RHIC measurements could constrain the gluon Sivers distribution for D mesons across multiple species.

Abstract

The production of D mesons in the scattering of transversely polarized protons off unpolarized protons at RHIC offers a clear opportunity to gain information on the Sivers gluon distribution function. D production at intermediate rapidity values is dominated by the elementary g g --> c cbar channel; contributions from q qbar --> c cbar s-channel become important only at very large values of x_F. In both processes there is no single spin transfer, so that the final c or cbar quarks are not polarized. Therefore, any transverse single spin asymmetry observed for D's produced in p(transv. polarized) p interactions cannot originate from the Collins fragmentation mechanism, but only from the Sivers effect in the distribution functions. In particular, any sizeable spin asymmetry measured in p(transv. polarized) p --> D X at mid-rapidity values will be a direct indication of a non zero Sivers gluon distribution function. We study the p(transv. polarized) p --> D X process including intrinsic transverse motion in the parton distribution and fragmentation functions and in the elementary dynamics, and show how results from RHIC could allow a measurement of the Sivers gluon distribution function.

Accessing Sivers gluon distribution via transverse single spin asymmetries in p(transv. polarized) p --> D X processes at RHIC

TL;DR

The paper addresses how to access the Sivers gluon distribution through transverse single-spin asymmetries in D meson production in p^↑ p collisions at RHIC. It adopts a generalized TMD factorization including intrinsic k_perp in PDFs, FFs, and hard scatterings, and analyzes A_N for p^↑ p → DX, noting that gg → cc̄ dominates at RHIC energies up to x_F ≈ 0.6, making A_N a direct probe of the gluon Sivers function. By deriving the SSA as a convolution of Sivers functions with partonic cross sections and fragmentation, and employing a Gaussian k_perp model with two extreme Sivers scenarios, the study shows that sizable A_N would indicate a nonzero Δ^N f_{g/p^↑}. The work highlights the crucial role of intrinsic transverse momentum in generating SSA and suggests RHIC measurements could constrain the gluon Sivers distribution for D mesons across multiple species.

Abstract

The production of D mesons in the scattering of transversely polarized protons off unpolarized protons at RHIC offers a clear opportunity to gain information on the Sivers gluon distribution function. D production at intermediate rapidity values is dominated by the elementary g g --> c cbar channel; contributions from q qbar --> c cbar s-channel become important only at very large values of x_F. In both processes there is no single spin transfer, so that the final c or cbar quarks are not polarized. Therefore, any transverse single spin asymmetry observed for D's produced in p(transv. polarized) p interactions cannot originate from the Collins fragmentation mechanism, but only from the Sivers effect in the distribution functions. In particular, any sizeable spin asymmetry measured in p(transv. polarized) p --> D X at mid-rapidity values will be a direct indication of a non zero Sivers gluon distribution function. We study the p(transv. polarized) p --> D X process including intrinsic transverse motion in the parton distribution and fragmentation functions and in the elementary dynamics, and show how results from RHIC could allow a measurement of the Sivers gluon distribution function.

Paper Structure

This paper contains 3 sections, 13 equations, 2 figures.

Table of Contents

  1. Introduction and formalism
  2. Numerical estimates
  3. Comments and conclusions

Figures (2)

  • Figure 1: The unpolarized cross section for the process $pp \to DX$ at $\sqrt s = 200$ GeV, as a function of $E_D$ and $p_T$ at fixed pseudo-rapidity $\eta=3.8$ (a), and as a function of $x_F$ at fixed transverse momentum $p_T=1.5$ GeV/$c$ (b), calculated according to Eqs. (\ref{['final-unp']}) and (\ref{['unp-pdf']}). The solid line is the full cross section, whereas the dashed and dotted lines show the $q\bar{q} \to c\bar{c}$ and $gg \to c\bar{c}$ contributions separately.
  • Figure 2: Maximized values of $|A_N|$ for the process $p^\uparrow p \to DX$ as a function of $E_D$ and $p_T$ at fixed pseudo-rapidity (a), and as a function of $x_F$ at fixed transverse momentum (b), calculated using saturated Sivers functions, according to Eq. (\ref{['sat']}) of the text. The dashed line corresponds to a maximized quark Sivers function (with the gluon Sivers function set to zero), while the dotted line corresponds to a maximized gluon Sivers function (with the quark Sivers function set to zero).