The ratio $R={\rm d}\sigma_L/{\rm d}\sigma_T$ in heavy-quark pair leptoproduction as a probe of linearly polarized gluons in unpolarized proton

TL;DR

This paper investigates how the ratio of longitudinal to transverse cross sections in heavy-quark leptoproduction can serve as a sensitive probe for linearly polarized gluons within unpolarized protons, with implications for future collider experiments.

Contribution

It introduces a method to use the Callan-Gross ratio as a probe for gluon polarization, highlighting its sensitivity to the gluonic Boer-Mulders function and potential for experimental measurement.

Findings

The ratio R can reach values up to 2 with unpolarized gluons.

Maximum R varies from 0 to Q^2/4m^2 depending on gluon polarization.

Future collider measurements can determine gluon linear polarization.

Abstract

We study the Callan-Gross ratio $R={\rm d}\sigma_L/{\rm d}\sigma_T$ in heavy-quark pair leptoproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$, as a probe of linearly polarized gluons inside unpolarized proton, where ${\rm d}\sigma_T$ (${\rm d}\sigma_L$) is the differential cross section of the $\gamma^*N\rightarrow Q\bar{Q}X$ process initiated by a transverse (longitudinal) virtual photon. Note first that the maximal value for the quantity $R$ allowed by the photon-gluon fusion with unpolarized gluons is large, about 2. We calculate the contribution of the transverse-momentum dependent gluonic counterpart of the Boer-Mulders function, $h_{1}^{\perp g}$, describing the linear polarization of gluons inside unpolarized proton. Our analysis shows that the maximum value of the ratio $R$ depends strongly on the gluon polarization; it varies from 0 to $\frac{Q^2}{4m^2}$ depending on $h_{1}^{\perp g}$. We conclude that the Callan-Gross ratio in heavy-quark pair leptoproduction is predicted to be large and very sensitive to the contribution of linearly polarized gluons. For this reason, future measurements of the longitudinal and transverse components of the charm and bottom production cross sections at the proposed EIC and LHeC colliders seem to be very promising for determination of the linear polarization of gluons inside unpolarized proton.