Transverse single-spin asymmetries in $\ell \,p^\uparrow \to h \,X$ within a TMD approach: Role of quasireal photon exchange

TL;DR

The work investigates transverse SSAs in lepton-proton collisions within a unified TMD framework, incorporating quasireal photon exchange via the Weizsäcker-Williams mechanism. It derives full TMD expressions for WW contributions to both unpolarized and spin-dependent cross sections and applies updated Sivers and Collins functions to data from HERMES, JLab, COMPASS, and projections for an Electron-Ion Collider (EIC). The WW term is found to substantially affect unpolarized cross sections and to improve the description of SSAs, notably aligning LO predictions with measurements, while gluon Sivers effects are typically small. The study also assesses how new Sivers/Collins extractions modify predictions across facilities, highlighting large-$x$ uncertainties and guiding future experimental tests of the unified TMD picture. Overall, the results support the relevance of quasireal photon exchange in a coherent TMD treatment of SSAs and provide concrete predictions for current and future experiments.

Abstract

We present an updated study of transverse single-spin asymmetries for the inclusive large-$P_T$ processes $\ell \, p^\uparrow \to h\, X$ and $\ell\, p^\uparrow \to {\rm jet}\,X$, within a transverse momentum-dependent approach, including the contribution of quasireal (Weizsäcker-Williams) photons. In the spirit of a unified transverse momentum-dependent scheme, predictions are obtained adopting the Sivers and transversity distributions and the Collins fragmentation functions as extracted from fits to the azimuthal asymmetries measured in semi-inclusive deep inelastic scattering and $e^+e^-$ annihilation processes. The description of the available data is extremely good, showing a clear general improvement with respect to the previous leading-order analysis. Predictions for unpolarized cross sections and single-spin asymmetries for ongoing and future experiments are also given.

Figures (13)

• Figure 1: Estimates of the unpolarized cross sections at $x_F=0.2$ as a function of $P_T$ for $\pi^+$ (left panel) and $\pi^-$ (right panel) production in $\ell\, p\to \pi\,X$, at HERMES, $\sqrt{s} = 7.25$ GeV, adopting two sets for the fragmentation functions: Kretzer set (blue dashed lines) and DSS set (red solid lines). The thin curves represent the LO calculation, while the thick curves the total (LO+WW) result.
• Figure 2: Estimates of the unpolarized cross sections at $P_T=1.4$ GeV as a function of $x_F$ for $\pi^+$ (left panel) and $\pi^-$ (right panel) production in $\ell\, p\to \pi\,X$, at HERMES, $\sqrt{s} = 7.25$ GeV. Curves have the same meaning as in Fig. \ref{['fig:unp-herm-xf02']}.
• Figure 3: Estimates of the unpolarized cross sections per nucleon at $x_F=0.2$ as a function of $P_T$ for $\pi^+$ (left panel) and $\pi^-$ (right panel) production in $\ell\,^3$He $\to \pi\,X$, at JLab-12, $\sqrt{s} = 4.84$ GeV. Curves have the same meaning as in the previous figures.
• Figure 4: Estimates of the unpolarized cross sections per nucleon at $P_T=1.5$ GeV as a function of $x_F$ for $\pi^+$ (left panel) and $\pi^-$ (right panel) production in $\ell \,^3$He $\to \pi\,X$, at JLab-12, $\sqrt{s} = 4.84$ GeV. Curves have the same meaning as in the previous figures.
• Figure 5: Estimates of the unpolarized cross sections at $P_T=2$ GeV as a function of $\eta$ for $\pi^+$ (left panel) and $\pi^-$ (right panel) production in $\mu \, p \to \pi\,X$, at COMPASS, $\sqrt{s} = 17.4$ GeV. Curves have the same meaning as in the previous figures.