Deep inelastic scattering on the deuteron in the Bethe-Salpeter formalism: Scalar meson exchange

The deep inelastic scattering on the deuteron is considered in a fully covariant field theoretical approach. All calculations are performed in the Bethe-Salpeter formalism and the Wilson operator product expansion method within an effective meson-nucleon theory. By the operator product expansion method we obtain an explicit form of the nucleon contribution and mesonic exchange corrections to moments of the deuteron structure function ${\mathit{F}}_2^{\mathit{D}}$. The structure function of the deuteron is recovered by the inverse Mellin transform of the moments and is presented as the sum of two convolution terms, viz. the nucleonic (relativistic impulse approximation) and mesonic (contribution of the meson exchange currents) ones. The sum rules for the baryon number and energy-momentum of the deuteron are derived using the normalization condition of the Bethe-Salpeter amplitude and virial theorem of field theory. The numerical estimates of the nuclear effects in the deuteron structure function in the Bethe-Salpeter formalism are also presented. It is found that the binding effects of the nucleons are significant and relativistic calculations within the Bethe-Salpeter formalism are compared with the previous nonrelativistic estimates.