Boson Mass Spectrum and Pion Form Factor fromSO(5,2). Generalization toSO(m,2)

Abstract

The $\mathrm{SO}(5,2)$ representation whose basis functions are the solutions of the Bethe-Salpeter equation for two scalar quarks interacting via the exchange of a scalar zero-mass boson to form a bound state of zero mass is written as an infinite-dimensional representation for bosons. A general second-order, infinite-component wave equation is given with a reasonable mass spectrum. The ground-state form factor corresponding to this representation is calculated by identifying the electromagnetic current with the current of the equation, in which case the pion form factor is given by $G(t)=\frac{[\frac{1\ensuremath{-}b{(cosh\ensuremath{\theta})}^{2}t}{2m}]}{{[\frac{1\ensuremath{-}{(cosh\ensuremath{\theta})}^{2}t}{4{m}^{2}}]}^{\frac{5}{2}}}$. The mass spectrum and the form factor can easily be generalized to the group $\mathrm{SO}(m,2)$ by a simple substitution, and the mass spectra and form factors obtained before in the framework of the group $\mathrm{SO}(4,2)$ appear as special cases.