Abstract
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 {\Lambda}QCD and are fine-tuned to reproduce the pion weak decay constant, within a range suggested by lattice calculations. Besides f{\pi}, 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.
Highlights
The pion plays a pivotal role within quantum chromodynamics (QCD), since its Goldstone boson nature is associated with the dynamical generation of the mass of the hadrons and nuclei constituting the visible universe
In the perspective of exploring dynamical models, incorporating as much as possible nonperturbative features of QCD in Minkowski space, and to take advantage of the results for building useful hadron imaging, we study the response of the pion valence momentum distribution to the variation of (i) the effective masses of both quark and gluon and (ii) the scale governing the size of the interaction quarkgluon vertex
Within the light-front framework, where the physical intuition based on the Fock-space expansion of the hadron wave function can be used at large extent, we have studied the strongly bound qqsystem that generates the pion
Summary
The pion plays a pivotal role within quantum chromodynamics (QCD), since its Goldstone boson nature is associated with the dynamical generation of the mass of the hadrons and nuclei constituting the visible universe. At the initial scale, even the simplified calculation of the PDF, based on the Mandelstam formula involving the BS amplitude, will include partons from Fock-state components beyond the valence one This is an immediate consequence of the solution of the BS equation in Minkowski space. In the perspective of exploring dynamical models, incorporating as much as possible nonperturbative features of QCD in Minkowski space, and to take advantage of the results for building useful hadron imaging, we study the response of the pion valence momentum distribution to the variation of (i) the effective masses of both quark and gluon and (ii) the scale governing the size of the interaction quarkgluon vertex. VII, drawing our conclusions and presenting perspectives of future developments
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