Relativistic nature of the EMC-effect

The deep inelastic scattering of leptons off nuclei is studied within the the BetheSalpeter formalism. It is shown that nuclear short-range structure can be expressed in terms of the nucleon structure functions and four-dimensional Fermi motion of the nucleons. The four-dimensional Fermi motion broadens the bound nucleon localization area, what leads to the observation of the nucleon structure change in nuclei – EMC effect. The He to deuteron structure functions ratio is found in good agreement with experimental data. It is shown that the pattern of the ratio is defined by dynamical properties of the nucleon structure and four-dimensional geometry of the bound state. The European Muon Collaboration (EMC) demonstrated in the experiments on deep inelastic scattering (DIS) of leptons off nuclei that nuclear environment modifies short range nucleon structure [1]. The modifications were observed as deviations from unity of the nuclear and deuteron DIS cross-sections ratio R= 2σ/(Aσ) to the values smaller than one. Since it was widely accepted that soft momentum nucleon-nucleon interaction in nuclei cannot modify a hard momenta distribution of nucleon partons, this phenomena was very unexpected. Later this effect was studied in a wide kinematic range in many experiments (c.f. review [2]). A wide variety of models was proposed to explain these modifications (c.f. reviews [2,3]). In different kinematic ranges the oscillations were considered as the different effects that are shadowing, antishadowing, EMC effect, and Fermi motion. No one of the models provided a quantitative explanation of the effect in the whole kinematic range, what led to the conclusion of the review [2] that origin of the EMC-effect stays unclear. So, the EMC-effect remains a topical subject up to now. Experimental study of nuclear hard structure provided opportunities to find important regularities that can give additional constrains on the models of the EMC-effect. Study of the EMC-effect dependence on the atomic number of the nucleus (Adependence) performed in the SLAC experiments [4] showed that amplitude 1 Partially supported by the Alexander von Humboldt Foundation, Germany Preprint submitted to Elsevier Science 8 February 2008 of the effect does not saturate with increase of A. The consequent analysis of the world data for the 2σ/(Aσ) ratio made in the paper [5] uncovered universality in the EMC-effect A-dependence for the all kinematic ranges. An another important result was obtained in the hard pA scattering performed in FNAL [6]. Analysis of the nuclear and deuteron Drell-Yan cross-sections ratio showed no excess of the antiquark component in nuclei. These results provided a basis for the critics of the most obvious explanations of the EMC-effect that were proposed by the binding [7] and mesonic exchange models [8]. In the paper [9] it was stressed that due to the Hugenholtz-van Hove theorem [10] the nuclear binding effect in DIS is defined by the mass defect in the nucleus. Thus, the binding effect has to saturate with increasing of A, while the systematic experimental study of the EMC-effect A-dependence [4] does not show such saturation. Results of the Drell-Yan experiment [6] prove that the mean mesonic field in the nucleus, which presumably consist of qq̄ fields, also cannot explain the EMC-effect [9]. This critics led to the conclusion that nucleon energy-momentum change due to the binding effects cannot be responsible alone for the EMC-effect. The analysis performed within the QMC model [11] pointed that the EMC-effect cannot be explained without introducing the hypothesis that nucleon structure is changed in nuclear media. This conclusion is consistent with the previously obtained resume of the calculation based on the quasi-potential approach [12] and supported recently by the light front analysis [13]. However, despite this critics, the binding model provided an important signal about nucleon structure change in nuclei. This model assumes the bound nucleon mass shift m → m∗ = m − ǫ, where ǫ is the binding energy of the nucleon. Due to the uncertainty relation the mass-shift changes the observed radius of the nucleon localization area in the four-dimensional (4D) space [14]. Thus, this mass-scale shift leads to the change of the quark confinement 4Dradius and, hence, to distortion of the partonic distribution inside the nucleon. This explanation coincides with the Q-rescaling model [15], which explains the EMC-effect as a change of the quark confinement radius in the bound nucleon. In that way, the explanations of the EMC–effect that are proposed by the binding and Q-rescaling models can be reduced to the distortions of the nucleon 4D-structure in the nuclei. Thus, a fully covariant 4D-treatment is essential for understanding of this phenomenon. In the present letter I would like to focus on the bound state relativistic properties that are important for understanding of the EMC-effect. To clarify the role played by the relativistic effects it is essential to consider the bound state within an explicitly covariant approach that can be developed in the relativistic field theory framework. Within the covariant field theory the spacetime distribution of the nucleons inside the nucleus is defined by the following