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Register a new userAzimuthal Asymmetry and Ratio $R= F_L / F_T$ as Probes of the Charm Content of the Proton
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N.Ya. Ivanov
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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.
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We calculate the azimuthal dependence of the heavy-quark-initiated ${cal O}(alpha_{s})$ contributions to the lepton-nucleon deep inelastic scattering (DIS). It is shown that, contrary to the photon-gluon fusion (GF) component, the photon-quark scattering (QS) mechanism is practically $cos2phi$-independent. We investigate the possibility to discriminate experimentally between the GF and QS contributions using their strongly different azimuthal distributions. Our analysis shows that the GF and QS predictions for the azimuthal $cos2phi$ asymmetry are quantitatively well defined in the fixed flavor number scheme: they are stable, both parametrically and perturbatively. We conclude that measurements of the azimuthal distributions at large Bjorken $x$ could directly probe the intrinsic charm content of the proton. As to the variable flavor number schemes, the charm densities of the recent CTEQ and MRST sets of parton distributions have a dramatic impact on the $cos2phi$ asymmetry in the whole region of $x$ and, for this reason, can easily be measured.
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.
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.
Constraints on the intrinsic charm probability $wccm = P_{{mathrm{c}bar mathrm{c}} / mathrm{p}}$ in the proton are obtained for the first time from LHC measurements. The ATLAS Collaboration data for the production of prompt photons, accompanied by a charm-quark jet in pp collisions at $sqrt s = 8 $ TeV, are used. The upper limit mbox{$wccm < 1.93$~%} is obtained at the 68~% confidence level. This constraint is primarily determined from the theoretical scale and systematical experimental uncertainties. Suggestions for reducing these uncertainties are discussed. The implications of intrinsic heavy quarks in the proton for future studies at the LHC are also discussed.
We investigate the charm sector of the nucleon structure phenomenologically, using the most up-to-date global QCD analysis. Going beyond the common assumption of purely radiatively generated charm, we explore possible degrees of freedom in the parton parameter space associated with nonperturbative (intrinsic) charm in the nucleon. Specifically, we explore the limits that can be placed on the intrinsic charm (IC) component, using all relevant hard-scattering data, according to scenarios in which the IC has a form predicted by light-cone wave function models; or a form similar to the light sea-quark distributions. We find that the range of IC is constrained to be from zero (no IC) to a level 2--3 times larger than previous model estimates. The behaviors of typical charm distributions within this range are described, and their implications for hadron collider phenomenology are briefly discussed.
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