On Gauge Consistency In Gauge-Fixed Yang-Mills Theory

Abstract

We investigate BRST invariance in Landau gauge Yang-Mills theory with functional methods. To that end, we solve the coupled systems of functional renormalisation group for the momentumdependent ghost and gluon propagator, ghost-gluon, and three-and four-gluon vertex dressings. The equations for both, transverse and longitudinal correlation functions are solved self-consistently: all correlation functions are fed back into the loops. Additionally, we also use the Slavnov-Taylor identities for computing the longitudinal correlation functions on the basis of the above results. Then, the gauge consistency of the solutions is checked by comparing the respective longitudinal correlation functions. We find good agreement of these results, hinting at the gauge consistency of our setup.

Gluon condensates and effective gluon mass

“…Accordingly, we exclude as many incompatible data points as possible from the extrapolation fit regime while keeping enough data for a meaningful prediction of Z cond (p = 0). As the data from [47] are relatively sparse and hence the respective Z cond (p min ) and the extrapolation show large error bars, we support this extrapolation with one obtained from dense fRG data provided in [108,109]. While the approximation used in the latter computations is not as sophisticated as that used in [47], it allows for a relatively quick production of dense data.…”

“…While the approximation used in the latter computations is not as sophisticated as that used in [47], it allows for a relatively quick production of dense data. The scaling solution of [108] yields Z cond = 0.166 (33), which agrees extremely well with the scaling solution estimate of [47], comp. Table 1.…”

Theory introduction to baryon spectroscopy

“…We could employ ansätze for those, or we could solve also their DSEs which depend on higher n-point functions, and so on. By systematically enlarging the set of computed n-point functions in this way, one should eventually get more and more precise results, and to some extent this is already seen in the existing calculations [51][52][53][54]. The n-point functions are not merely a means to do spectroscopy but also interesting in their own right.…”

QCD at finite temperature and density within the fRG approach: An overview

“…Significant progresses have been made in relevant studies, see [55] for a recent overview, and also e.g. [70,108,[201][202][203][204][205][206][207][208][209][210][211][212][213][214][215][216].…”

“…The quark-gluon coupling in Equation ( 53), the ghostgluon coupling in Equation ( 54), and the three-gluon or four-gluon coupling in Equation ( 50), etc., are consistent with one another in the perturbative regime of high energy, due to the Slavnov-Taylor identities (STIs) resulting from the gauge symmetry. However, when the momenta or the RG scale are decreased to k 1 ∼ 3 GeV, the gluon mass gap begins to affect the running of strong couplings, and also the transversal strong couplings can not be identified with the longitudinal ones via the modified STIs, see, e.g., [56,216,223,224] for more details. Consequently, different strong couplings deviate from one another in the low energy regime of k 1 ∼ 3 GeV [56][57][58]61], and thus it is necessary to distinguish them by adding appropriate suffixes.…”