The saturation scale and its x-dependence from Lambda polarization studies

TL;DR

This paper explores how Lambda hyperon polarization in high-energy p-A collisions can reveal the x-dependence of the saturation scale, offering a novel method to probe gluon saturation effects at the LHC.

Contribution

It demonstrates that Lambda polarization measurements can directly probe the x dependence of the saturation scale, extending previous models to more realistic x-dependent scenarios.

Findings

Polarization exhibits an extremum around the saturation scale.

Measurement feasibility at LHC is discussed, but challenging.

At RHIC, the peak occurs at too low transverse momentum for reliable measurement.

Abstract

The transverse polarization of forward Lambda hyperons produced in high-energy p-A collisions is expected to display an extremum at a transverse momentum around the saturation scale. This was first observed within the context of the McLerran-Venugopalan model which has an x-independent saturation scale. The extremum arises due to the k_t-odd nature of the polarization dependent fragmentation function, which probes approximately the derivative of the dipole scattering amplitude. The amplitude changes most strongly around the saturation scale, resulting in a peak in the polarization. We find that the observation also extends to the more realistic case in which the saturation scale Q_s is x dependent. Since a range of x and therefore Q_s values is probed at a given transverse momentum and rapidity, this result is a priori not expected. Moreover, the measurement of Lambda polarization over a range of x_F values actually provides a direct probe of the x dependence of the saturation scale. This novel feature is demonstrated for typical LHC kinematics and for several phenomenological models of the dipole scattering amplitude. We show that although the measurement will be challenging, it may be feasible at LHC. The situation at RHIC is not favorable, because the peak will likely be at too low transverse momentum of the Lambda to be a trustworthy measure of the saturation scale.