Calculation of tensor susceptibility beyond rainbow-ladder approximation of Dyson-Schwinger equations approach

TL;DR

This paper investigates the impact of vertex dressing effects on tensor vacuum susceptibility within the Dyson-Schwinger approach, finding a modest 10% reduction when using the Ball-Chiu vertex compared to the rainbow-ladder approximation.

Contribution

It extends previous calculations by incorporating the Ball-Chiu vertex, revealing the dressing effect's limited influence on tensor vacuum susceptibility.

Findings

Tensor vacuum susceptibility is reduced by about 10% with BC vertex.

Dressing effects of the quark-gluon vertex are not large in this calculation.

The study provides insights into vertex dressing effects beyond rainbow-ladder approximation.

Abstract

In this paper, we extend the calculation of tensor vacuum susceptibility in the rainbow-ladder approximation of the Dyson-Schwinger (DS) approach in [Y.M.Shi, K.P.Wu, W.M.Sun, H.S.Zong, J.L.Ping, Phys. Lett. B $\bf{639}$, 248 (2006)] to that of employing the Ball-Chiu (BC) vertex. The dressing effect of the quark-gluon vertex on the tensor vacuum susceptibility is investigated. Our results show that compared with its rainbow-ladder approximation value, the tensor vacuum susceptibility obtained in the BC vertex approximation is reduced by about 10%. This shows that the dressing effect of the quark-gluon vertex is not large in the calculation of the tensor vacuum susceptibility in the DS approach.