The ratio R = dσL/dσT in heavy-quark pair leptoproduction as a probe of linearly polarized gluons in unpolarized proton

A.V Efremov,N.Ya Ivanov,O.V Teryaev

doi:10.1016/j.physletb.2018.03.008

Abstract

We study the Callan–Gross ratio R=dσL/dσT in heavy-quark pair leptoproduction, lN→l′QQ¯X, as a probe of linearly polarized gluons inside unpolarized proton, where dσT (dσL) is the differential cross section of the γ⁎N→QQ¯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, h1⊥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 Q24m2 depending on h1⊥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.

Highlights

Introduction and notationIt is well-known that the heavy flavor production in lepton-proton DIS offers direct probe of the gluon distributions in the proton
We study the contribution of linearly polarized gluons to the Callan-Gross ratio R = dσL/dσT in the reaction lN → l′QQ X with unpolarized initial states, where dσL is the differential cross section of the γ∗N → QQ X process initiated by a longitudinal virtual photon
Our analysis shows that the quantity R is expected to be large in wide kinematic ranges and very sensitive to the density h⊥1 g(ζ, kT2 )

Summary

Introduction and notation

It is well-known that the heavy flavor production in lepton-proton DIS offers direct probe of the gluon distributions in the proton. The transverse momentum dependent (TMD) density of the linearly polarized gluons inside unpolarized proton, h⊥1 g(ζ, kT2 ), can directly be measured in heavy-quark pair electroproduction. In Refs.[3,4,5], it was proposed to study the linearly polarized gluons in unpolarized nucleon using the heavy-quark pair production in the reaction l(l) + N(P) → l′(l − q) + Q(pQ) + Q (pQ ) + X(pX). To describe this process, the following hadron-level variables are used:.

Production cross section

The Callan-Gross ratio

R exp B T 2 R exp BhT

Conclusions and Outlook