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Register a new userNuclear effects on the longitudinal structure function at small x
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We discuss the longitudinal structure function in nuclear DIS at small $x$. We work within the framework of universal parton densities obtained in DGLAP analyses at NLO. We show that the nuclear effects on the longitudinal structure function closely follow those on the gluon distribution. The error analyses available from newest sets of nuclear PDFs also allow to propagate the uncertainties from present data. In this way, we evaluate the minimal sensitivity required in future experiments for this observable to improve the knowledge of the nuclear glue. We further discuss the uncertainties on the extraction of $F_2$ off nuclear targets, introduced by the usual assumption that the ratio $F_L/F_2$ is independent of the nuclear size. We focus on the kinematical regions relevant for future lepton-ion colliders.
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We determine the small Bjorken $x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton in the double-logarithmic approximation (DLA), which resums powers of $alpha_s ln^2 (1/x)$ with $alpha_s$ the strong coupling constant. Starting with the operator definitions for the quark and gluon OAM, we simplify them at small $x$, relating them, respectively, to the polarized dipole amplitudes for the quark and gluon helicities defined in our earlier works. Using the small-$x$ evolution equations derived for these polarized dipole amplitudes earlier we arrive at the following small-$x$ asymptotics of the quark and gluon OAM distributions in the large-$N_c$ limit: begin{align} L_{q + bar{q}} (x, Q^2) = - Delta Sigma (x, Q^2) sim left(frac{1}{x}right)^{frac{4}{sqrt{3}} , sqrt{frac{alpha_s , N_c}{2 pi}} }, L_G (x, Q^2) sim Delta G (x, Q^2) sim left(frac{1}{x}right)^{frac{13}{4 sqrt{3}} , sqrt{frac{alpha_s , N_c}{2 pi}}} . end{align}
We consider the effect of higher twist operators of the Wilson operator product expansion in the structure function $F_{2}(x,Q^{2})$ at small-$x$, taking into account QCD effective charges whose infrared behavior is constrained by a dynamical mass scale. The higher twist corrections are obtained from the renormalon formalism. Our analysis is performed within the conventional framework of next-to-leading order, with the factorization and renormalization scales chosen to be $Q^{2}$. The infrared properties of QCD are treated in the context of the generalized double-asymptotic-scaling approximation. We show that the corrections to $F_{2}$ associated with twist-four and twist-six are both necessary and sufficient for a good description of the deep infrared experimental data.
Up to now, all charge radius measurements of the proton and deuteron assumed uniform spheroidal charge distribution. We investigate the nuclear deformation effects on these charge radius measurements by assuming a uniform prolate charge distribution for the proton and deuteron. We solve the energy levels of the corresponding muonic and electric atoms with such deformed nucleus and present how the purely quadruple deformation of proton and deuteron affects their Lamb shifts. The numerical results suggest that the deformation of proton and deuteron leads to that the charge radius extracted from the electronic measurement should be smaller than the corresponding one in the muonic measurement which assumed uniform spheroidal charge distribution. If the central values of newest measurements for the proton are adopted, the proton would have a prolate structure with the 0.91 $mathrm{fm}$ long axis and 0.73 $mathrm{fm}$ short axis. Further improved precise charge radius measurements of the proton and deuteron will help us to pin down their shape deformation.
In this work, the two-photon-exchange (TPE) effects in $e^+e^- rightarrow pi^+ pi^-$ at small $sqrt{s}$ are discussed within a hadronic model. In the limit $m_erightarrow 0$, the TPE contribution to the amplitude can be described by one scalar function $overline{c}_{1}^{(2gamma)}$. The ratio between this function and the corresponding contribution in one-photon exchange $c_{1}^{(1gamma)}$ reflects all the information of the TPE corrections. The numerical results on this ratio are presented and an artificial function is used to fit the numerical results. The latter can be used conveniently in the further experimental data analysis. The numerical results show the asymmetry of the differential cross sections in $e^+e^- rightarrow pi^+ pi^-$ is about $-4%$ at $sqrt{s}sim 0.7$ GeV.
Using QCD calculations of the cross section of inclusive dijet photoproduction in Pb-Pb ultraperipheral collisions in the LHC kinematics as pseudo-data, we study the effect of including these data using the Bayesian reweighting technique on nCTEQ15, nCTEQ15np, and EPPS16 nuclear parton distribution functions (nPDFs). We find that, depending on the assumed error of the pseudo-data, it leads to a significant reduction of the nPDF uncertainties at small values of the momentum fraction $x_A$. Taking the error to be 5%, the uncertainty of nCTEQ15 and nCTEQ15np nPDFs reduces approximately by a factor of two at $x_A=10^{-3}$. At the same time, the reweighting effect on EPPS16 nPDFs is much smaller due to the higher value of the tolerance and a more flexible parametrization form.
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