Nonperturbative relativistic approach to pion form factors: Predictions for future JLab experiments

Abstract

Some predictions concerning possible results of the future JLab experiments on the pion form factor Fπ(Q 2 ) are made. The calculations exploit the method proposed previously by the authors and based on the instant-form Poincaré invariant approach to pion considered as a quark-antiquark system. Long ago, this model has predicted with surprising accuracy the values of Fπ(Q 2 ) measured later in JLab experiment. The results are almost independent from the form of wave function. The pion mean square radius r 2 π and the decay constant fπ also agree with experimental values. The model gives power-like asymptotic behavior of Fπ(Q 2 ) at high momentum transfer in agreement with QCD predictions.

Quadrupole moments of the ρ meson and the S -wave deuteron and some general constraints on quadrupole moments of spin-1 systems

“…We show that in the framework of our approach, adding physical reasoning connected with the structure of our relativistic operator of the quadrupole moment, it occurs to be possible to obtain some constraints for the values of the quadrupole moment of the composite systems with quantum numbers indicated above. As our approach have demonstrated its effectiveness for relativistic theory of very different two-particle composite systems [35][36][37][38][39][40][41]49], it is plausible to expect that our constraints are of a rather general character.…”

“…This model has predicted with surprising accuracy the values of the form factor F π (Q 2 ), which were measured later in JLab experiments [43][44][45][46][47] (see discussion in Ref. [38]). All the new points fall, within the experimental uncertainties, on the initially calculated curve.…”

“…Here we use our version of RQM, -the modified instant form (mIF) of RQM , that was successfully used for various composite two-particle systems, namely, the deuteron [35], the pion [36][37][38][39], the ρ meson [40,41] and the kaon [42]. This model has predicted with surprising accuracy the values of the form factor F π (Q 2 ), which were measured later in JLab experiments [43][44][45][46][47] (see discussion in Ref.…”

Pion form factor in time like region in a framework of relativistic composite quark model

“…The numerical calculations with different wave functions shows, that wide class of the wave functions, constructed with taking into account the confinement, allows to fit the experimental points in space-like region (see, e.g. [11]). The results of calculation of expression (3.2) with ψ-functions (4.1) and (4.2) at space-like and time-like t are shown on figure 1.…”

Electromagnetic structure of pion

“…In the theory of light mesons, relevant problems considered in the literature concern, for instance, the calculation of the mass and decay constant of the pion in a relativistic potential model of independent quarks [8], the study of masses and electroweak properties of light mesons in a relativistic quark model [9] and the study of a relativistic treatment of pion wave functions in the annihilationpp → ππ + [10], beside a lot of other works in which are considered calculations involving light mesons, as in Refs. [11,12,13,14,15].…”