Quadrupole moments of spin-1 systems: the rho meson, the S-wave deuteron and some general constraints

TL;DR

This paper develops a relativistic operator for the quadrupole moment of spin-1 systems, calculates specific values for the rho meson and deuteron, and explores bounds on quadrupole moments for such systems.

Contribution

It introduces a new relativistic operator for quadrupole moments and provides the first bounds for these moments in two-particle systems with spin-1.

Findings

Calculated Q_rho = -0.158 ± 0.04 GeV^-2

Calculated Q_deuteron = -1.4×10^-4 GeV^-2

Formulated bounds for quadrupole moments in two-particle 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 rho meson and of the S-wave deuteron without any free parameters, using our unified pi&rho model (Phys. Rev.D 93, 036007 (2016); 97, 033007 (2018)) and our previous results on deuteron. Our calculation gives Q_rho=-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.