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Register a new userTheoretical uncertainties in exclusive electroproduction S-wave heavy quarkonia
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In this work, we revise the conventional description of J/Psi(1S), Y(1S), Psi(2S) and Y(2S) elastic photo- and electroproduction off a nucleon target within the color dipole picture and carefully study various sources of theoretical uncertainties in calculations of the corresponding electroproduction cross sections. For this purpose, we test the corresponding predictions using a bulk of available dipole cross section parametrisations obtained from deep inelastic scattering data at HERA. Specifically, we provide the detailed analysis of the energy and hard-scale dependencies of quarkonia yields employing the comprehensive treatment of the quarkonia wave functions in the Schroedinger equation based approach for a set of available c-bar{c} and b-bar{b} interquark interaction potentials. Besides, we quantify the effect of Melosh spin rotation, the Q^2-dependence of the diffractive slope and an uncertainty due to charm and bottom quark mass variations.
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In this work we present for the first time the comprehensive study of the Melosh spin rotation effects in diffractive electroproduction of S-wave heavy quarkonia off a nucleon target. Such a study has been performed within the color dipole approach using, as an example and a reference point, two popular parametrizations of the dipole cross section and two potentials describing the interaction between Q and bar{Q} and entering in the Schroedinger equation based formalism for determination of the quarkonia wave functions. We find a strong onset of spin rotation effects in 1S charmonium photoproduction which is obviously neglected in present calculations of corresponding cross sections. For photoproduction of radially excited Psi(2S) these effects are even stronger leading to an increase of the photoproduction cross section by a factor of 2-3 depending on the photon energy. Even in production of radially excited Y(2S) and Y(3S) they can not be neglected and cause the 20-30% enhancement of the photoproduction cross section. Finally, we predict that the spin effects vanish gradually with photon virtuality Q^2 following universality properties in production of different heavy quarkonia as a function of Q^2 + M_V^2.
The differential cross section $dsigma/dq^2$ of diffractive electroproduction of heavy quarkonia on protons is a sensitive study tool for the interaction dynamics within the dipole representation. Knowledge of the transverse momentum transfer $vec q$ provides a unique opportunity to identify the reaction plane, due to a strong correlation between the directions of $vec q$ and impact parameter $vec b$. On top of that, the elastic dipole-proton amplitude is subject to a strong correlation between $vec b$ and dipole orientation $vec r$. Most of models for $b$-dependent dipole cross section either completely miss this information, or make unjustified assumptions. We perform calculations basing on a realistic model for $vec r$-$vec b$ correlation, which significantly affect the $q$-dependence of the cross section, in particular the ratio of $psi^{,prime}(2S)$ to $J/psi$ yields. We rely on realistic potential models for the heavy quarkonium wave function, and the Lorentz-boosted Schrodinger equation. Good agreement with data on $q$-dependent diffractive electroproduction of heavy quarkonia is achieved.
We discuss three theoretical schemes to describe charm quark electroproduction.
We analyze the validity of a commonly used identification between structures of the virtual photon $gamma^*to Qbar Q$ and vector meson $Vto Qbar Q$ transitions. In the existing studies of $S$-wave vector-meson photoproduction in the literature, such an identification is typically performed in the light-front (LF) frame while the radial component of the meson wave function is rather postulated than computed from the first principles. The massive photon-like $Vto Qbar Q$ vertex, besides the $S$-wave component, also contains an extra $D$-wave admixture in the $Qbar Q$ rest frame. However, the relative weight of these contributions cannot be justified by any reasonable nonrelativistic $Qbar Q$ potential model. In this work, we investigate the relative role of the $D$-wave contribution starting from the photon-like quarkonium $Vto Qbar Q$ transition in both frames: in the $Qbar Q$ rest frame (with subsequent Melosh spin transform to the LF frame) and in the LF frame (without Melosh transform). We show that the photon-like transition imposed in the $Qbar Q$ rest frame leads to significant discrepancies with the experimental data. In the second case we find that the corresponding total $J/psi(1S)$ photoproduction cross sections are very close to those obtained with the $S$-wave only $Vto Qbar Q$ transition, both leading to a good description of the data. However, we find that the $S$-wave only transition leads to a better description of photoproduction data for excited heavy quarkonium states, which represent a more effective tool for study of $D$-wave effects. Consequently, the predictions for production of excited states based on the photon-like structure of $Vto Qbar Q$ transition should be treated with a great care due to a much stronger sensitivity of the $D$-wave contribution to the nodal structure of quarkonium wave functions.
We compute the exclusive electroproduction, $gamma^* p rightarrow V p$, of heavy quarkonia $V$ to NLO in the collinear factorisation scheme, which has been formally proven for this process. The inclusion of an off-shell virtuality $Q^2$ carried by the photon extends the photoproduction phase space of the exclusive heavy quarkonia observable to electroproduction kinematics. This process is relevant for diffractive scattering at HERA and the upcoming EIC, as well as at the proposed LHeC and FCC.
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