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

Abstract

We costruct the relativistic operator of the quadrupole moment of two-particle composite spin one systems with zero orbital moment of the relative motion and derive explicit analytical expression for the quadrupole moment using the approach to relativistic composite systems based on our version of the instant-form relativistic quantum mechanics (RQM). We calculate the quadrupole moments of the ρ meson and of the S-wave deuteron without any free parameters, using our unified π&ρ model (Phys. Rev.D 93, 036007 (2016); 97, 033007 (2018)) and our previous results on deuteron. Our calculation gives Qρ = −0.158 ± 0.04 GeV −2 and Q d = −1.4 · 10 −4 GeV −2 . Having in our disposition the rather general form of the quadrupole-moment operator we for the first time formulate the problem of the upper and lower bounds for possible values of the quadrupole moment of a two-particle system with indicated quantum numbers for a large range of constituent masses, and partially solve it.

Pion gravitational form factors in a relativistic theory of composite particles

“…To obtain the pion form factor A we use directly the equations ( 18), ( 51), (36) while in the case of the form factor D, which is ill-defined, we involve an anzatz described in detail in Section III. We obtain the pion D form factor in the vicinity of t = 0 using ( 18), (51) and assuming (39) (the form factor D (πa) (t)).…”

“…Here b is the parameter of the model along with the quark-mass M . The best results for electroweak properties of light mesons [30][31][32][33][34][35][36][37][38] were obtained for the following values of these parameters:…”

“…The model [27,28] was successfully used for various composite two-particle systems, namely, the deuteron [29], the pion [30][31][32][33], the ρ meson [34][35][36] and the kaon [37]. This model had predicted, with surprising accuracy, the values of the form factor F π (Q 2 ), which were measured later in JLab experiments (see the discussion in Ref.…”