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Register a new userOn the Perturbative Stability of the QCD Predictions for the Ratio $R=F_L/F_T$ in Heavy-Quark Leptoproduction
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We analyze the perturbative and parametric stability of the QCD predictions for the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ in heavy-quark leptoproduction. We consider the radiative corrections to the dominant photon-gluon fusion mechanism. In various kinematic regions, the following contributions are investigated: exact NLO results at low and moderate $Q^2lesssim m^2$, asymptotic NLO predictions at high $Q^2gg m^2$, and both NLO and NNLO soft-gluon (or threshold) corrections at large Bjorken $x$. Our analysis shows that large radiative corrections to the structure functions $F_T(x,Q^2)$ and $F_L(x,Q^2)$ cancel each other in their ratio $R(x,Q^2)$ with good accuracy. As a result, the NLO contributions to the Callan-Gross ratio are less than 10% in a wide region of the variables $x$ and $Q^2$. We provide compact LO predictions for $R(x,Q^2)$ in the case of low $xll 1$. A simple formula connecting the high-energy behavior of the Callan-Gross ratio and low-$x$ asymptotics of the gluon density is derived. It is shown that the obtained hadron-level predictions for $R(xto 0,Q^2)$ are stable under the DGLAP evolution of the gluon distribution function. Our analytic results simplify the extraction of the structure functions $F_2^c(x,Q^2)$ and $F_2^b(x,Q^2)$ from measurements of the corresponding reduced cross sections, in particular at DESY HERA.
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We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and/or azimuthal $cos(2varphi)$ asymmetry in deep inelastic lepton-nucleon scattering. Our approach is based on the perturbative stability of the QCD predictions for these two quantities. We resume the mass logarithms of the type $alpha_{s}lnleft( Q^{2}/m^{2}right)$ and conclude that heavy-quark densities in the nucleon can, in principle, be determined from data on the Callan-Gross ratio and/or azimuthal asymmetry. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.
We present the QCD predictions for the azimuthal $cos 2varphi$ asymmetry in charm leptoproduction for the kinematics of the COMPASS experiment at CERN. The asymmetry is predicted to be large, about 15%. The radiative corrections to the QCD predictions for the $cos 2varphi$ distribution are estimated to be small, less than 10%. Our calculations show that the azimuthal asymmetry in charm production is well defined in pQCD: it is stable both perturbatively and parametrically, and practically insensitive to theoretical uncertainties in the input parameters. We analyze the nonperturbative contributions to the $cos 2varphi$ distribution due to the gluon transverse motion in the target and the $c$-quark fragmentation. Because of the $c$-quark low mass, the nonperturbative contributions are expected to be sizable, about (30--40)%. We conclude that extraction of the azimuthal asymmetries from available COMPASS data will provide valuable information about the transverse momentum dependent distribution of the gluon in the proton and the $c$-quark hadronization mechanism. Finally, we discuss the $cos 2varphi$ asymmetry as a probe of the gluonic analogue of the Boer-Mulders function, $h_{1}^{perp g}$, describing the linear polarization of gluons inside unpolarized proton.
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 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.
Following the procedure and motivations developed by Richardson, Buchmuller and Tye, we derive the potential of static quarks consistent with both the three-loop running of QCD coupling constant under the two-loop perturbative matching of V and MS-bar schemes and the confinement regime at long distances. Implications for the heavy quark masses as well as the quarkonium spectra and leptonic widths are discussed.
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