A comparison of condensate mass of QCD vacuum between Wilson line approach and Schwinger effect * *Supported by the National Natural Science Foundation of China (11575254), the National Key Research and Development Program of China (2016YFE0130800), and the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34030301). ST is supported by the PIFI (2021PM0065)

Sara Tahery,Liping Zou,Xurong Chen

doi:10.1088/1674-1137/abe03b

Abstract

We studied the condensate mass of QCD vacuum through the duality approach via dilaton wall background in the presence of the parameter , which represents the condensation in a holographic set up. First, from Wilson line calculation, we found (i.e., the condensate parameter in mixed non-local condensation), whose behavior mimics that of QCD. The value of that we found by this approach is in agreement with QCD data. Second, we considered the produced mass via the Schwinger effect mechanism in the presence of the parameter . We show that vacuum condensation generally contributes the mass dominantly and that the produced mass via Schwinger effect is suppressed by .

Highlights

By duality approach, we study condensate mass of QCD vacuum via dilaton wall background in presence of parameter c which represents the condensation in holographic set up
Needless to say that what we have found in last section is very different in its nature with Schwinger effect produced mass. m20 which appears in non-local and mixed condensates is a constant of proportionality in the conventional parametrization 11
Gluon condensation is an important issue since it represents many phenomenological aspects of QCD

Summary

Mass from condensation

Before starting our calculation we review method of [18], so if the reader is familiar with this reference can skip this part and continue from (11). It is not clear how to do this but by considering two important limiting cases, long distances and short distances, we can analyze the behavior of the function. Combining (25) with (23) we find the desired behavior of the function Q at short distances as, Q. where R = r − ε and ε is a small constant value. In 4d QCD linear decay is expected, while (30) shows a faster decay according to quadratic term r2 It comes from the nature of the GeV 4 modification of background metric, which represents condensation in gravity dual. Having found an estimate for function Q at short distances and behavior of that at long distances, we close this section and in the step we will study produced mass by Schwinger effect in presence of condensation parameter

Mass from Schwinger effect

Conclusions