Scaling for deuteron structure functions in a relativistic light-front model.

Abstract

Scaling limits of the structure functions [B.D. Keister, Phys. Rev. C 37, 1765 (1988)], ${W}_{1}$ and ${W}_{2}$, are studied in a relativistic model of the two-nucleon system. The relativistic model is defined by a unitary representation, $U(\ensuremath{\Lambda}, a)$, of the Poincar\'e group which acts on the Hilbert space of two spinless nucleons. The representation is in Dirac's [P.A.M. Dirac, Rev. Mod. Phys. 21, 392 (1949)] light-front formulation of relativistic quantum mechanics and is designed to give the experimental deuteron mass and $n\ensuremath{-}p$ scattering length. A model hadronic current operator that is conserved and covariant with respect to this representation is used to define the structure tensor. This work is the first step in a relativistic extension of the results of Hueber, Gl\"ockle, and Boemelburg [D. Hueber et al. Phys. Rev. C 42, 2342 (1990)]. The nonrelativistic limit of the model is shown to be consistent with the nonrelativistic model of Hueber, Gl\"ockle, and Boemelburg. The relativistic and nonrelativistic scaling limits, for both Bjorken and $y$ scaling are compared. The interpretation of $y$ scaling in the relativistic model is studied critically. The standard interpretation of $y$ scaling requires a soft wave function which is not realized in this model. The scaling limits in both the relativistic and nonrelativistic case are related to probability distributions associated with the target deuteron.