Probing the Gluon Sivers Function with an Unpolarized Target: GTMD Distributions and the Odderons

Abstract

It is commonly believed that the Sivers function has uniquely to do with processes involving a transversely polarized nucleon. In this paper we show that this is not necessarily the case. We demonstrate that exclusive pion production in unpolarized electron-proton scattering in the forward region is a direct probe of the gluon Sivers function due to its connection to the QCD Odderon.

Spin-dependent Pomeron and Odderon in elastic proton–proton scattering

“…As usual, g and N c = 3 denote the QCD coupling and number of colors. Following [34], we parametrize the dipole amplitude as…”

“…The initial saturation scale Q s0 is expected to be around 1 GeV in the TeV region, while the strength of Odderon κ is an unknown parameter including its sign (see, however, [29]) which should be fitted to the data [34]. The other parameters in this model are m q , m s and c 2 s A (only this product enters our observables).…”

“…Yet, the exact treatment of the problem has been difficult due to the lack of a systematic way to connect the Pomeron and Odderon with the spin degrees of freedom of the scattering (composite) particles such as protons in QCD. 1 Recently, however, there has been a significant progress in our understanding of the interplay between the Odderon and the proton spin [29][30][31][32][33][34]. In the Deep Inelastic Scattering (DIS) at small-x, the Color Glass Condensate (CGC) framework [35] provides a consistent description of the Pomeron and Odderon in terms of Wilson line correlators.…”

“…In the Deep Inelastic Scattering (DIS) at small-x, the Color Glass Condensate (CGC) framework [35] provides a consistent description of the Pomeron and Odderon in terms of Wilson line correlators. Their couplings with various proton polarization states can be completely parametrized by the generalized transverse momentum dependent distributions (GTMDs) [34]. Indeed, the gluon Sivers function [36] at small-x is connected to the Odderon in the forward limit [29][30][31] and participates in the proton helicity-flip reactions including the unpolarised elastic scattering processes.…”

Phenomenology of the hadronic structure at small-$x$

“…Notably, in Ref. [17] it was argued that in the forward limit the Sivers function can be accessed in unpolarized electron-nucleon collisions via its connection with the QCD Odderon.…”