Giovanni Salmè

Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane

The Nakanishi perturbative integral representation of the four-dimensional T-matrix is investigated in order to get a workable treatment for scattering states, solutions of the inhomogeneous Bethe-Salpeter Equation, in Minkowski space. The projection onto the null-plane of the four-dimensional inhomogeneous Bethe-Salpeter Equation plays a key role for devising an equation for the Nakanishi weight function (a real function), as in the homogeneous case that corresponds to bound states and it has been already studied within different frameworks. In this paper, the whole formal development is illustrated in detail and applied to a system, composed by two massive scalars interacting through the exchange of a massive scalar. The explicit expression of the scattering integral equations are also obtained in ladder approximation, and, as simple applications of our formalism, some limiting cases, like the zero-energy limit and the Wick-Cutkosky model in the continuum, are presented.

Quantitative studies of the homogeneous Bethe-Salpeter equation in Minkowski space

The Bethe-Salpeter Equation for a bound system, composed by two massive scalars exchanging a massive scalar, is quantitatively investigated in ladder approximation, within the Nakanishi integral representation approach. For the S-wave case, numerical solutions with a form inspired by the Nakanishi integral representation, have been calculated. The needed Nakanishi weight functions have been evaluated by solving two different eigenequations, obtained directly from the Bethe-Salpeter equation applying the Light-Front projection technique. A remarkable agreement, in particular for the eigenvalues, has been achieved, numerically confirming that the Nakanishi uniqueness theorem for the weight functions, demonstrated in the context of the perturbative analysis of the multi-leg transition amplitudes and playing a basic role in suggesting one of the two adopted eigenequations, can be extended to a non perturbative realm. The detailed, quantitative studies are completed by presenting both probabilities and Light-Front momentum distributions for the valence component of the bound state.

Neutron Transverse-Momentum Distributions and Polarized 3 He within Light-Front Hamiltonian Dynamics

The possibility to extract the quark transverse-momentum distributions in the neutron from semi-inclusive deep inelastic electron scattering off polarized 3He is illustrated through an impulse approximation analysis in the Bjorken limit. The generalization of the analysis at finite momentum transfers in a Poincaré covariant framework is outlined. The definition of the light-front spin-dependent spectral function of a J = 1/2 system allows us to show that within the light-front dynamics only three of the six leading twist T-even transverse-momentum distributions are independent.

Light-front spin-dependent spectral function and nucleon momentum distributions for a three-body system

Poincare covariant definitions for the spin-dependent spectral function and for the momentum distributions within the light-front Hamiltonian dynamics are proposed for a three-fermion bound system, starting from the light-front wave function of the system. The adopted approach is based on the Bakamjian-Thomas construction of the Poincare generators, that allows one to easily import the familiar and wide knowledge on the nuclear interaction into a light-front framework. The proposed formalism can find useful applications in refined nuclear calculations, like the ones needed for evaluating the EMC effect or the semi-inclusive deep inelastic cross sections with polarized nuclear targets, since remarkably the light-front unpolarized momentum distribution by definition fulfills both normalization and momentum sum rules. It is also shown a straightforward generalization of the definition of the light-front spectral function to an A-nucleon system.

Towards an Improved Description of SiDIS by a Polarized 3He Target

The possibility of improving the description of the semi-inclusive deep inelastic electron scattering off polarized 3He, that provides information on the neutron single spin asymmetries, is illustrated. In particular, the analysis at finite momentum transfers in a Poincaré covariant framework is outlined and a generalized eikonal approach to include final state interaction is presented.

Solutions of the Bethe-Salpeter Equation in Minkowski Space: A Comparative Study

The Bethe–Salpeter equation for a two-scalar, S-wave bound system, interacting through a massive scalar, is investigated within the ladder approximation. By assuming a Nakanishi integral representation of the Bethe–Salpeter amplitude, one can deduce new integral equations that can be solved and quantitatively studied, overcoming the analytic difficulties of the Minkowski space. Finally, it is shown that the Light-front distributions of the valence state, directly obtained from the Bethe–Salpeter amplitude, open an effective window for studying the two-body dynamics.

Y-scaling analysis of inclusive electron scattering and the nucleon momentum distribution in few-body systems and complex nuclei

Abstract The basic assumptions underlying the y-scaling analysis of inclusive electron scattering by nuclei are summarized, and the nucleon momentum distribution in 2 H, 3 He, 4 He and 12 C obtained from available experimental data are presented and compared with the results of (e,e′p) reactions.

Two-Fermion Bethe–Salpeter Equation in Minkowski Space: The Nakanishi Way

The possibility of solving the Bethe–Salpeter equation in Minkowski space, even for fermionic systems, is becoming actual, through the applications of well-known tools: (1) the Nakanishi integral representation of the Bethe–Salpeter amplitude and (2) the light-front projection onto the null-plane. The theoretical background and some preliminary calculations are illustrated, in order to show the potentiality and the wide range of application of the method.

Light-Front Dynamics and the {{^{3}He}} Spectral Function

Two topics are presented. The first one is a novel approach for a Poincaré covariant description of nuclear dynamics based on light-front Hamiltonian dynamics. The key quantity is the light-front spectral function, where both normalization and momentum sum rule can be satisfied at the same time. Preliminary results are discussed for an initial analysis of the role of relativity in the EMC effect in