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G. Salmè

Publications and source records attributed to G. Salmè.

14 recordsLinked to original sources
arXiv2023

The chiral limit of a fermion-scalar $(1/2)^+$ system in covariant gauges

The homogeneous Bethe-Salpeter equation (BSE) of a (1/2)$^+$ bound system, that has both fermionic and bosonic degrees of freedom, that we call a {\em mock nucleon}, is studied in Minkowski space, in order to analyse the chiral limit in covariant gauges. After adopting an interaction kernel built with a one-particle exchange, the $χ$-BSE is numerically solved by means of the Nakanishi integral representation and light-front projection. Noteworthy, the chiral limit induces a scale-invariance of the model and consequently generates a wealth of striking features: i) it reduces the number of non trivial Nakanishi weight functions to only one; ii) the form of the surviving weight function has a factorized dependence on the two relevant variables, compact and non-compact one; iii) the coupling constant becomes an explicit function of the real exponent governing the power-law fall-off of the non trivial Nakanishi weight function. The thorough investigation at large transverse-momentum of light-front Bethe-Salpeter amplitudes, obtained with massive constituents, provides a confirmation of the expected universal power-law fall-off, with exponents predicted by our non-perturbative framework. Finally, one can shed light on the exponents that govern the approach to the upper extremum of the longitudinal-momentum fraction distribution function of the {\em mock nucleon}, when the coupling constant varies.

hep-ph↗
arXiv2023

Unpolarized transverse-momentum dependent distribution functions of a quark in a pion with Minkowskian dynamics

The unpolarized twist-2 (leading) and twist-3 (subleading), T-even, transverse-momentum dependent quark distributions in the pion are evaluated for the first time by using the actual solution of a dynamical equation in Minkowski space. The adopted theoretical framework is based on the homogeneous Bethe-Salpeter integral equation with an interaction kernel given by a one-gluon exchange, featuring an extended quark-gluon vertex. The masses of quark and gluon as well as the interaction-vertex scale have been chosen in a range suggested by lattice-QCD calculations, and calibrated to reproduce both pion mass and decay constant. The sum rules to be fulfilled by the transverse-momentum dependent distributions are carefully investigated, particularly the leading-twist one, that has to match the collinear parton distribution function, and hence can be scrutinized in terms of existing data as well as theoretical predictions. Noteworthy, the joint use of the Fock expansion of the pion state facilitates a more in-depth analysis of the content of the pion Bethe-Salpeter amplitude, allowing for the first time to determine the gluon contribution to the quark average longitudinal fraction, that results to be $\sim 6\%$. The current analysis highlights the role of the gluon exchanges through quantitative analysis of collinear and transverse-momentum distributions, showing, e.g. for both leading and subleading-twists, an early departure from the widely adopted exponential fall-off, for $|k_\perp|^2 > m^2$, with the quark mass $\sim Λ_{QCD}$.

hep-ph↗
arXiv2022

The parton distribution function in a pion with Minkowskian dynamics

The parton distribution of the pion is obtained for the first time from the solution of a dynamical equation in Minkowski space. The adopted equation is the homogeneous Bethe-Salpeter one with a ladder kernel, described in terms of i) constituent quarks and gluons degrees of freedom, and ii) an extended quark-gluon vertex. The masses of quark and gluon as well as the interaction-vertex scale have been chosen in a range suggested by lattice QCD calculations, and calibrated to reproduce both pion mass and decay constant. Beside the full parton distribution, we have also calculated the contribution from the light-front valence wave function, corresponding to the lowest Fock component in the expansion of the pion state. After applying an evolution with an effective charge and a LO splitting function, a detailed and inspiring comparison with both the extracted experimental data ( with and without resummation effects) and other recent calculations obtained in different frameworks is presented. Interestingly, in a wide region of longitudinal-momentum fraction, the parton distribution function receives sizable contributions from the higher Fock-components of the pion state at the initial scale, while approaching the tail the light-front valence component dominates, as expected. Moreover, an exponent $\sim$ 3 is found suitable for describing the tail at the scale 5.2 GeV.

hep-ph↗
arXiv2020

Observing the Minkowskian dynamics of the pion on the null-plane

A dynamical model is applied to the study of the pion valence light-front wave function, obtained from the actual solution of the Bethe-Salpeter equation in Minkowski space, resorting to the Nakanishi integral representation. The kernel is simplified to a ladder approximation containing constituent quarks, an effective massive gluon exchange, and the scale of the extended quark-gluon interaction vertex. These three input parameters carry the infrared scale ΛQCD and are fine-tuned to reproduce the pion weak decay constant, within a range suggested by lattice calculations. Besides fπ, we present and discuss other interesting quantities on the null-plane, like: (i) the valence probability, (ii) the dynamical functions depending upon the longitudinal or the transverse components of the light-front (LF) momentum, represented by LF-momentum distributions and distribution amplitudes, and (iii) the probability densities both in the LF-momentum space and the 3D space given by the Cartesian product of the covariant Ioffe-time and transverse coordinates, in order to perform an analysis of the dynamical features in a complementary way. The proposed analysis of the Minkowskian dynamics inside the pion, though carried out at the initial stage, qualifies the Nakanishi integral representation as an appealing effective tool, with still unexplored potentialities to be exploited for addressing correlations between dynamics and observable properties.

hep-ph↗
arXiv2019

Solving the Bethe-Salpeter Equation in Minkowski Space for a Fermion-Scalar system

The ladder Bethe-Salpeter Equation of a bound (1/2)+ system, composed by a fermion and a scalar boson, is solved in Minkowski space, for the first time. The formal tools are the same already successfully adopted for two-scalar and two-fermion systems, namely the Nakanishi integral representation of the Bethe-Salpeter amplitude and the light-front projection of the fulfilled equation. Numerical results are presented and discussed for two interaction kernels: i) a massive scalar exchange and ii) a massive vector exchange, illustrating both the correlation between binding energies and the interaction coupling constants, as well as the valence content of the interacting state, through the valence probabilities and the light-front momentum distributions. In the case of the scalar exchange, an interesting side effect, to be ascribed to the repulsion generated by the small components of the Dirac spinor, is pointed out, while for the vector exchange the manifestation of the helicity conservation opens new interesting questions to be addressed within a fully non-perturbative framework, as well as the onset of a scale-invariant regime.

hep-ph↗
arXiv2017

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.

hep-ph↗
arXiv2017

Final state interactions and the extraction of neutron single spin asymmetries from SIDIS by a transversely polarized $^3$He target

The semi-inclusive deep inelastic electron scattering off transversely polarized $^3$He, i.e. the process, $e + \vec{^3 {\rm He}} \to e' + h+X$, with $h$ a detected fast hadron, is studied beyond the plane wave impulse approximation. To this end, a distorted spin-dependent spectral function of a nucleon inside an A=3 nucleus is actually evaluated through a generalized eikonal approximation, in order to take into account the final state interactions between the hadronizing system and the (A-1) nucleon spectator one. Our realistic description of both nuclear target and final state is a substantial step forward for achieving a reliable extraction of the Sivers and Collins single spin asymmetries of the free neutron. To illustrate how and to what extent the model dependence due to the treatment of the nuclear effects is under control, we apply our approach to the extraction procedure of the neutron single spin asymmetries from those measured for $^3$He for values of the kinematical variables relevant both for forthcoming experiments at Jefferson Lab and, with an exploratory purpose, for the future Electron Ion Collider.

nucl-th↗
arXiv2016

Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space

Actual solutions of the Bethe-Salpeter equation for a two-fermion bound system are becoming available directly in Minkowski space, by virtue of a novel technique, based on the so-called Nakanishi integral representation of the Bethe-Salpeter amplitude and improved by expressing the relevant momenta through light-front components, i.e. $k^\pm=k^0 \pm k^3$. We solve a crucial problem that widens the applicability of the method to real situations by providing an analytically exact treatment of the singularities plaguing the two-fermion problem in Minkowski space, irrespective of the complexity of the irreducible Bethe-Salpeter kernel. This paves the way for feasible numerical investigations of relativistic composite systems, with any spin degrees of freedom. We present a thorough comparison with existing numerical results, evaluated in both Minkowski and Euclidean space, fully corroborating our analytical treatment, as well as fresh light-front amplitudes illustrating the potentiality of non perturbative calculations performed directly in Minkowski space.

hep-th↗
arXiv2016

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.

hep-ph↗
arXiv2008

Time- and Spacelike Nucleon Electromagnetic Form Factors beyond Relativistic Constituent Quark Models

For the first time, a phenomenological analysis of the experimental electromagnetic form factors of the nucleon, both in the timelike and spacelike regions, is performed by taking into account the effects of nonvalence components in the nucleon state, within a light-front framework. Our model, based on suitable Ansatzes for the nucleon Bethe-Salpeter amplitude and a microscopic version of the well-known Vector Meson Dominance model, has only four free parameters (determined by the spacelike data with $χ^2/datum \sim 1.7$), and yields a nice description of the experimental electromagnetic form factors in the physical region in the range $-30 (GeV/c)^2 < q^2 < 20 (GeV/c)^2$, except for the neutron one in the timelike region. Valuable information can be gained in the timelike region on possible missing Vector Mesons around $q^2 \sim 4.5 (GeV/c)^2$ and $q^2 \sim 8.0 (GeV/c)^2$

hep-ph↗
arXiv1995

Nucleon and pion electromagnetic structure and constituent quark form factors

We have evaluated nucleon and pion electromagnetic form factors using for the first time eigenfunctions of a light-front mass operator, reproducing a large set of energy levels, and constituent quark form factors in the one-body current. The comparison with the experimental data yields valuable information on the electromagnetic structure of light constituent quarks and on the different role played by their Dirac and Pauli form factors.

nucl-th↗
arXiv1994

Investigation of the Neutron Form Factors by Inclusive Quasi-Elastic Scattering of Polarized Electrons off Polarized $^{3}$He: A Theoretical Overview

The theory of quasi-elastic inclusive scattering of polarized leptons off polarized $^3$He is critically reviewed and the origin of different expressions for the polarized nuclear response function appearing in the literature is explained. The sensitivity of the longitudinal asymmetry upon the neutron form factors is thoroughly investigated and the role played by the polarization angle for minimizing the proton contribution is illustrated.

nucl-th↗
arXiv1994

Hard Constituent Quarks and Electroweak Properties of Pseudoscalar Mesons

The high momentum components generated in the wave function of pseudoscalar mes* by the one-gluon-exchange interaction are investigated within a relativistic constituent quark model. Adopting the light-cone formalism, the sensitivity of the weak decay constant and the charge form factor to hard constituent quarks is illustrated.

nucl-th↗