Fermionic bound states in Minkowski-space: Light-cone singularities and structure

The Bethe-Salpeter equation for two-body bound system with spin $1/2$ constituent is addressed directly in the Minkowski space. In order to accomplish this aim we use the Nakanishi integral representation of the Bethe-Salpeter amplitude and exploit the formal tool represented by the exact projection onto the null-plane. This formal step allows one i) to deal with end-point singularities one meets and ii) to find stable results, up to strongly relativistic regimes, that settles in strongly bound systems. We apply this technique to obtain the numerical dependence of the binding energies upon the coupling constants and the light-front amplitudes for a fermion-fermion $0^+$ state with interaction kernels, in ladder approximation, corresponding to scalar-, pseudoscalar- and vector boson exchanges, respectively. After completing the numerical survey of the previous cases, we extend our approach to a quark-antiquark system in $0^-$ state, taking both constituent-fermion and exchanged boson masses, from lattice calculations. Interestingly, the calculated light-front amplitudes for such a mock pion show peculiar signatures of the spin degrees of freedom.Comment: 22 pages, 7 figures, bst file include

Bethe-Salpeter bound-state structure in Minkowski space

The quantitative investigation of the scalar Bethe-Salpeter equation in Minkowski space, within the ladder-approximation framework, is extended to include the excited states. This study has been carried out for an interacting system composed by two massive bosons exchanging a massive scalar, by adopting (i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and (ii) the formally exact projection onto the null plane. Our analysis, on one hand, confirms the reliability of the method already applied to the ground state and, on the other one, extends the investigation from the valence distribution in momentum space to the corresponding quantity in the impact-parameter space, pointing out some relevant features, like (i) the equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and (ii) the leading exponential fall-off of the valence wave function in the impact-parameter space.Comment: 15 pages, 7 figure

Transversity studies with a polarized 3He target

A realistic study of the SiDIS process 3He(e , e π)X in the Bjorken limit is briefly reviewed, showing that the nuclear effects, present in the extraction of the neutron information, are largely under theoretical control, within an ImpulseApproximation approach. In view of the forthcoming experimental data, we shortly present a novel Poincar´e covariant description of the nuclear target, implementing a Light-Front analysis at finite Q2, within the Bakamijan-Thomas construction of the Poincar´e generators. Furthermore, as a by-product of the introduction of a LightFront spin-dependent spectral function for a J = 1/2 system, we straightforwardly extend our analysis to the quark-quark correlator, obtaining three new exact relations between the six leading-twist Transverse-Momentum–Dependent distributions

Exact response of the non-relativistic harmonic oscillator

Using Green$'$s function and operator techniques we give a closed expression for the response of a non-relativistic system interacting through confining, harmonic forces. The expression for the incoherent part permits rapid evaluation of coefficients in a 1/q expansion. A comparison is made with standard approximation methods.Comment: 9p.; INFN-ISS 93/2; WIS-93/50/Jun-P