On the analysis of lepton scattering on longitudinally or transversely polarized protons

TL;DR

The paper develops a comprehensive framework to analyze polarized lepton-proton scattering by carefully transforming target spin definitions between the lepton-beam frame and the virtual-photon frame. It derives a master cross-section structure and explicit relations between beam- and photon-frame asymmetries, enabling decomposition of the gamma*p subprocess into its helicity cross sections and interference terms. Applied to SIDIS, exclusive meson production, and DVCS, the approach clarifies how twist-two and twist-three contributions arise and how various observables project onto generalized parton distributions (GPDs) and transverse-momentum dependent functions (TMDs), including Sivers and Collins effects. The work also provides positivity bounds that constrain the size of interference terms and guides Rosenbluth-type separations to disentangle longitudinal and transverse photon contributions, with implications for accessing quark orbital angular momentum through E-type GPDs and related observables.

Abstract

We discuss polarized lepton-proton scattering with special emphasis on the difference between target polarization defined relative to the lepton beam or to the virtual photon direction. In particular, this difference influences azimuthal distributions in the final state. We provide a general framework of analysis and apply it to the specific cases of semi-inclusive deep inelastic scattering, of exclusive meson production, and of deeply virtual Compton scattering.

Figures (6)

• Figure 1: Kinematics of the process (\ref{['gen-proc']}) in the target rest frame. $\hbox{\boldmath{$P$}}_{hT}$ and $\hbox{\boldmath{$S$}}_T$ respectively are the components of $\hbox{\boldmath{$P$}}_h$ and $\hbox{\boldmath{$S$}}$ perpendicular to $\hbox{\boldmath{$q$}}$. (The target spin vector $\hbox{\boldmath{$S$}}$ is not shown.) $\phi$ and $\phi_S$ respectively are the azimuthal angles of $\hbox{\boldmath{$P$}}_h$ and $\hbox{\boldmath{$S$}}$ in the coordinate system with axes $x$, $y$, $z$, in accordance with the Trento conventions Bacchetta:2004jz.
• Figure 2: The lepton plane in the target rest frame. The $y$ and $y'$ axes coincide and point out of the paper plane.
• Figure 3: Semi-inclusive hadron production $\gamma^* p\to h X$ at large $Q^2$. (a) Born level graph. (b) A next-to-leading order graph where the hadron $h$ has transverse momentum of order $Q$.
• Figure 4: Example graphs for exclusive production of a meson $M$ at large $Q^2$. Instead of the proton there may be a different baryon in the final state. The lower blobs represent twist-two generalized parton distributions, and the upper blobs stand for the twist-two distribution amplitude of the meson.
• Figure 5: Region in the plane of $\sigma_{L}$ and $\mathrm{Im}\,\sigma_{00}^{+-}$ allowed by the positivity bounds (\ref{['long-pos']}) and (\ref{['hyp-bound']}).