Light-Front Transverse Momentum Distributions for ${\cal J}$=1/2 Hadronic Systems in Valence Approximation

The European Muon Collaboration effect in Light-Front Hamiltonian Dynamics

“…The trace is obviously independent of S and M. It is worth noticing that, in our Poincaré-covariant framework, the momentum distribution fulfills both normalization (i.e. the baryon number sum rule) and momentum sum rule [14,15]. Finally, in the Bjorken limit, the evaluation of the nuclear SF is simplified, since n N (ξ, k ⊥ ) can be obtained more directly from the nucleus wf in momentum space [15], rather than through the cumbersome LF spectral-function.…”

“…In particular, notice that we use nonsymmetric intrinsic variables, which disentangle the internal motion of the interacting (A − 1)-nucleon system from that of the struck nucleon and hence are able to implement the macroscopic locality [13]. Recently, in this framework, the six 3 He leading-twist transverse-momentum distributions have been evaluated in valence approximation [15].…”

“…This quantity is the trace of the momentum-distribution 2 × 2 matrix, N N M (ξ, k ⊥ , S) [15], with S the polarization of the nucleus and M the component of the total angular momentum J along S (in general S = ẑ). The trace is obviously independent of S and M. It is worth noticing that, in our Poincaré-covariant framework, the momentum distribution fulfills both normalization (i.e.…”

“…the baryon number sum rule) and momentum sum rule [14,15]. Finally, in the Bjorken limit, the evaluation of the nuclear SF is simplified, since n N (ξ, k ⊥ ) can be obtained more directly from the nucleus wf in momentum space [15], rather than through the cumbersome LF spectral-function. Hence, once the ground-state of a nucleus is calculated with a realistic interaction, the corresponding nuclear structure function can be affordably evaluated in the Bjorken limit, through Eqs.…”

“…Analogously, one can evaluate the longitudinally and transversely polarized nucleon distributions, g N 1 and h N 1 , by using the spin-dependent nucleon momentum distribution, n N σ,σ (ξ, k ⊥ , S), i.e. the elements of N N M (ξ, k ⊥ , S) [15]. These distributions are given by…”