No Arabic abstract
The differential and partially integrated cross sections are considered for bremsstrahlung from high-energy electrons in atomic field with the exact account of this field. The consideration exploits the quasiclassical electron Greens function and wave functions in an external electric field. It is shown that the Coulomb corrections to the differential cross section are very susceptible to screening. Nevertheless, the Coulomb corrections to the cross section summed up over the final-electron states are independent of screening in the leading approximation over a small parameter $1/mr_{scr}$ ($r_{scr}$ is a screening radius, $m$ is the electron mass, $hbar=c=1$). Bremsstrahlung from an electron beam of the finite size on heavy nucleus is considered as well. Again, the Coulomb corrections to the differential probability are very susceptible to the beam shape, while those to the probability integrated over momentum transfer are independent of it, apart from the trivial factor, which is the electron-beam density at zero impact parameter. For the Coulomb corrections to the bremsstrahlung spectrum, the next-to-leading terms with respect to the parameters $m/epsilon$ ($epsilon$ is the electron energy) and $1/mr_{scr}$ are obtained.
The experimental results of the future electron -- ion ($e A$) collider are expected to constrain the dynamics of the strong interactions at small values of the Bjorken -- $x$ variable and large nuclei. Recently it has been suggested that Coulomb corrections can be important in inclusive and diffractive $eA$ interactions. In this paper we present a detailed investigation of the impact of the Coulomb corrections to some of the observables that will be measured in the future $eA$ collider. In particular, we estimate the magnitude of these corrections for the charm and longitudinal cross sections in inclusive and diffractive interactions. Our results demonstrate that the Coulomb corrections for these observables are negligible, which implies that they can be used to probe the QCD dynamics.
We obtain the following analytical formula which describes the dependence of the electric potential of a point-like charge on the distance away from it in the direction of an external magnetic field B: Phi(z) = e/|z| [ 1- exp(-sqrt{6m_e^2}|z|) + exp(-sqrt{(2/pi) e^3 B + 6m_e^2} |z|) ]. The deviation from Coulombs law becomes essential for B > 3pi B_{cr}/alpha = 3 pi m_e^2/e^3 approx 6 10^{16} G. In such superstrong fields, electrons are ultra-relativistic except those which occupy the lowest Landau level (LLL) and which have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For B > 3 pi B_{cr}/alpha, it substantially differs from the one obtained without accounting for the modification of the atomic potential.
We argue that contemporary jet substructure techniques might facilitate a more direct measurement of hard medium-induced gluon bremsstrahlung in heavy-ion collisions, and focus specifically on the soft drop declustering procedure that singles out the two leading jet substructures. Assuming coherent jet energy loss, we find an enhancement of the distribution of the energy fractions shared by the two substructures at small subjet energy caused by hard medium-induced gluon radiation. Departures from this approximation are discussed, in particular, the effects of colour decoherence and the contamination of the grooming procedure by soft background. Finally, we propose a complementary observable, that is the ratio of the two-pronged probability in Pb-Pb to proton-proton collisions and discuss its sensitivity to various energy loss mechanisms.
We calculate higher-order corrections to the quenching factor of heavy-quark jets due to hard, in-medium splittings in the framework of the BDMPS-Z formalism. These corrections turn out to be sensitive to a single mass-scale $m_ast = (hat q L)^{1/2}$, where $hat q$ is the medium transport coefficient and $L$ the path length, and allow to draw a distinction between the way light, with $m < m_ast$ (in contrast to massless $m=0$), and genuinely heavy, with $m > m_ast$, quark jets are quenched in the medium. We show that the corrections to the quenching factor at high energies are double-logarithmic and qualitatively of the same order as for the massless quark jet.
We present results for higher-order corrections to exclusive $mathrm{J}/psi$ production. This includes the first relativistic correction of order $v^2$ in quark velocity, and next-to-leading order corrections in $alpha_s$ for longitudinally polarized production. The relativistic corrections are found to be important for a good description of the HERA data, especially at small values of the photon virtuality. The next-to-leading order results for longitudinal production are evaluated numerically. We also demonstrate how the vector meson production provides complementary information to the structure functions for extracting the initial condition for the small-$x$ evolution of the dipole-proton scattering amplitude.