Gravitational Form Factors of Pseudoscalar Mesons, Stress-Tensor-Current Commutation Relations, and Deviations from Tensor- and Scalar-Meson Dominance

Abstract

The low-momentum-transfer behavior of the gravitational form factors of the pseudoscalar mesons is derived, starting with the model-independent equal-time commutation relations between the stress tensor and the axial-vector current. The results indicate significant deviations from tensor-meson pole dominance and scalar-meson pole dominance of the matrix elements of the traceless part and the trace, respectively, of the stress tensor. An expression is derived for the stress-tensor-$\ensuremath{\epsilon}$-meson coupling in terms of ${g}_{{A}_{1}\ensuremath{\epsilon}\ensuremath{\pi}}$. With additional assumptions, a phenomenological result is obtained for the scale dimension of the pion field. Possible mechanisms are discussed which may give rise to large values of the rms radii of the form factors. As an example of additional phenomenological results obtainable from the scheme discussed here, a result is derived for the $f{A}_{1}\ensuremath{\pi}$ coupling.