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TMDs and SSAs in hadronic interactions

E. C. Aschenauer, U. D'Alesio, F. Murgia

TL;DR

The paper surveys transverse single spin asymmetries in high-$p_T$ hadronic processes, focusing on a generalised parton model (GPM) with TMDs and its comparison to collinear twist-3 formalisms. It analyzes how Sivers, Collins, and transversity–related effects manifest across inclusive and double-inclusive channels, including Drell–Yan and electroweak boson production, and discusses experimental RHIC results from PHENIX and STAR that constrain TMDs and their evolution. A key emphasis is on the potential sign change of the Sivers function between SIDIS and Drell–Yan, tests of TMD factorisation in various processes, and the role of gluon TMDs, particularly the gluon Sivers function, in midrapidity measurements. The paper also highlights ongoing theoretical developments (CGI-GPM, twist-3 connections) and outlines future experimental programs that will clarifying TMD evolution and universality, with broader implications for the 3D structure of the nucleon.

Abstract

We present an overview on the current experimental and phenomenological status of transverse single spin asymmetries (tSSAs) in proton-proton collisions. In particular, we focus on large-$p_T$ inclusive pion, photon, jet, pion-jet production and Drell-Yan processes. For all of them theoretical estimates are given in terms of a generalised parton model (GPM) based on a transverse momentum dependent (TMD) factorisation scheme. Comparisons with the corresponding results in a collinear twist-3 formalism and in a modified GPM approach are also made. On the experimental side, a selection of the most interesting and recent results from RHIC is presented.

TMDs and SSAs in hadronic interactions

TL;DR

The paper surveys transverse single spin asymmetries in high- hadronic processes, focusing on a generalised parton model (GPM) with TMDs and its comparison to collinear twist-3 formalisms. It analyzes how Sivers, Collins, and transversity–related effects manifest across inclusive and double-inclusive channels, including Drell–Yan and electroweak boson production, and discusses experimental RHIC results from PHENIX and STAR that constrain TMDs and their evolution. A key emphasis is on the potential sign change of the Sivers function between SIDIS and Drell–Yan, tests of TMD factorisation in various processes, and the role of gluon TMDs, particularly the gluon Sivers function, in midrapidity measurements. The paper also highlights ongoing theoretical developments (CGI-GPM, twist-3 connections) and outlines future experimental programs that will clarifying TMD evolution and universality, with broader implications for the 3D structure of the nucleon.

Abstract

We present an overview on the current experimental and phenomenological status of transverse single spin asymmetries (tSSAs) in proton-proton collisions. In particular, we focus on large- inclusive pion, photon, jet, pion-jet production and Drell-Yan processes. For all of them theoretical estimates are given in terms of a generalised parton model (GPM) based on a transverse momentum dependent (TMD) factorisation scheme. Comparisons with the corresponding results in a collinear twist-3 formalism and in a modified GPM approach are also made. On the experimental side, a selection of the most interesting and recent results from RHIC is presented.

Paper Structure

This paper contains 11 sections, 14 equations, 20 figures.

Table of Contents

  1. Introduction
  2. Experimental Results
  3. Access to Transversity: the Collins and Interference Fragmentation Functions
  4. Transverse Polarisation in the Proton; Sivers and Qiu-Sterman effects
  5. Theory and Phenomenology
  6. SSAs in $p^\uparrow p\to h\, X$ processes
  7. SSAs in $pp\to {\rm jet}\, X$ and in $pp \to \gamma \, X$
  8. SSAs in $pp\to {\rm jet}\, h\,X$
  9. SSAs in $pp\to \ell^+\ell^-\, X$ and $pp\to \ell \nu\, X$
  10. SSAs in double inclusive production in $pp$ collisions
  11. Conclusions and outlook

Figures (20)

  • Figure 1: Transverse single spin asymmetry measurements for charged and neutral pions at different center-of-mass energies as a function of Feynman-$x$, $x_F$.
  • Figure 2: (a): The Collins asymmetry $A_{UT}^{\sin(\phi_S-\phi_H)}$ vs. $z$ ($z=p_{\pi}/p_{\rm jet}$) for charged pions in jets at $0 <\eta <1$ from $pp$ collisions at $\sqrt{s}$ = 200 and 500 GeV by STAR Spin2014:Adkins. The $p_{T,\rm jet}$ ranges have been chosen to sample the same parton $x$ values for both beam energies. The angular cuts, characterised by the minimum distance of the charged pion from the jet thrust axis, have been chosen to sample the same $x_T$ values ($x_T=2p_T/\sqrt s$). (b): The di-hadron asymmetry $A_{UT}^{\sin(\phi)}$ (upper panel) and the corresponding $p_{T{\pi^+\pi^-}}$ (lower panel) as a function of the invariant mass $M_{\pi^+\pi^-}$ for $-1 < \eta < 1$. A clear enhancement of the signal around the $\rho$-mass region is observed both at $\sqrt{s}$ = 200 and 500 GeV by STAR Vossen:2012zz.
  • Figure 3: The Collins azimuthal asymmetry $A_{UT}^{\sin(\phi_S-\phi_H)}$ of a $\pi^0$ inside a calorimetric jet measured by the STAR FMS at $2.8 < \eta < 4.0$ as a function of $x_F$.
  • Figure 4: “Collins-like” asymmetry, $A_{UT}^{\sin(\phi_S-2\phi_h)}$, as a function of pion $z$. These results could provide the first experimental constraint on model predictions utilizing linearly polarised gluons. See also Sec. \ref{['pion-jet']}.
  • Figure 5: The amplitude of the transverse single spin asymmetry for $W^{\pm}$ (a) and $Z^0$ (b) -boson production measured by STAR in proton-proton collisions at $\sqrt{s}$ = 500 GeV for a recorded integrated luminosity of 25 pb$^{-1}$.
  • ...and 15 more figures