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Register a new userHow to measure the linear polarization of gluons in unpolarized proton using the heavy-quark pair leptoproduction
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We study the azimuthal $cos varphi$ and $cos 2varphi$ asymmetries in heavy-quark pair leptoproduction, $lNrightarrow l^{prime}Qbar{Q}X$, as probes of linearly polarized gluons inside unpolarized proton, where the azimuth $varphi$ is the angle between the lepton scattering plane $(l,l^{prime})$ and the heavy quark production plane $(N,Q)$. First, we determine the maximal values for the $cos varphi$ and $cos 2varphi$ asymmetries allowed by the photon-gluon fusion with unpolarized gluons; these predictions are large, $(sqrt{3}-1)/2$ and $1/3$, respectively. Then 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 values of the azimuthal distributions depend strongly on the gluon polarization; they vary from 0 to 1 depending on $h_{1}^{perp g}$. We conclude that the azimuthal $cos varphi$ and $cos 2varphi$ asymmetries in heavy-quark pair leptoproduction are predicted to be large and very sensitive to the contribution of linearly polarized gluons. For this reason, future measurements of the azimuthal distributions in charm and bottom production at the proposed EIC and LHeC colliders seem to be very promising for determination of the linear polarization of gluons inside unpolarized proton.
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We consider the azimuthal $cos varphi$ and $cos 2varphi$ distributions and the Callan-Gross ratio $R={rm d}sigma_L/{rm d}sigma_T$ in heavy-quark pair electroproduction, $lNrightarrow l^{prime}Qbar{Q}X$, as probes of linearly polarized gluons in unpolarized nucleons. Our analysis shows that the azimuthal asymmetries and Callan-Gross ratio are predicted to be large and very sensitive to the contribution of the gluonic counterpart of the Boer-Mulders function, $h_{1}^{perp g}$, describing the linear polarization of gluons inside unpolarized nucleon. In particular, the maximum values of the azimuthal distributions vary from 0 to 1 depending on $h_{1}^{perp g}$. We conclude that future measurements of these quantities at the proposed EIC and LHeC colliders could clarify in details the proton spin decomposition puzzle.
We study the Callan-Gross ratio $R={rm d}sigma_L/{rm d}sigma_T$ in heavy-quark pair leptoproduction, $lNrightarrow l^{prime}Qbar{Q}X$, 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 $gamma^*Nrightarrow Qbar{Q}X$ 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.
We use the Color Glass Condensate (CGC) framework to study the production of forward heavy quark-antiquark pairs in unpolarized proton-nucleus or proton-proton collisions in the small-x regime. In the limit of nearly back-to-back jets, the CGC result simplifies into the transverse-momentum dependent (TMD) factorization approach. For massless quarks, the TMD factorization formula involves three unpolarized gluon TMDs: the Weizs{a}cker-Williams gluon distribution, the adjoint-dipole gluon distribution, and an additional one. When quark masses are kept non-zero, three new gluon TMDs appear -- each partnered to one of the aforementioned distributions -- which describe the distribution of linearly-polarized gluons in the unpolarized small-x target. We show how these six gluon TMDs emerge from the CGC formulation and we determine their expressions in terms of Wilson line correlators. We calculate them analytically in the McLerran-Venugopalan model, and further evolve them towards smaller values of x using a numerical implementation of JIMWLK evolution.
We study the perturbative and parametric stability of the QCD predictions for the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and azimuthal $cos(2varphi)$ asymmetry, $A(x,Q^2)$, in heavy-quark leptoproduction. We review the available theoretical results for these quantities and conclude that, contrary to the production cross sections, the ratios $R(x,Q^2)$ and $A(x,Q^2)$ are stable under radiative QCD corrections in wide region of the variables $x$ and $Q^2$. This implies that large radiative contributions to the structure functions cancel each other in the ratios $R(x,Q^2)$ and $A(x,Q^2)$ with good accuracy. Then we consider some experimental and phenomenological applications of the observed perturbative stability. We provide compact analytic predictions for $R(x,Q^2)$ and azimuthal $cos(2varphi)$ asymmetry in the case of low $xll 1$. It is demonstrated that our obtained results will be useful in the extraction of the structure functions from measurements of the reduced cross sections. Finally, we analyze the properties of $R(x,Q^2)$ and $A(x,Q^2)$ within the variable-flavor-number scheme (VFNS) of QCD. We conclude that the Callan-Gross ratio and azimuthal asymmetry are perturbatively stable but sensitive to resummation of the mass logarithms of the type $alpha_{s}lnleft( Q^{2}/m^{2}right)$. For this reason, the quantities $R(x,Q^2)$ and $A(x,Q^2)$ will be good probes of the heavy-quark content of the proton.
We propose a unified new approach to describe polarized and unpolarized quark distributions in the proton based on the gauge-gravity correspondence, light-front holography, and the generalized Veneziano model. We find that the spin-dependent quark distributions are uniquely determined in terms of the unpolarized distributions by chirality separation without the introduction of additional free parameters. The predictions are consistent with existing experimental data and agree with perturbative QCD constraints at large longitudinal momentum $x$. In particular, we predict the sign reversal of the polarized down-quark distribution in the proton at $x=0.8pm0.03$, a key property of nucleon substructure which will be tested very soon in upcoming experiments.
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