Journal
PHYSICAL REVIEW D
Volume 106, Issue 11, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.106.116013
Keywords
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [398579334 (Gi328/9-1), 406116891, RTG 2522/1]
- European Union [754496]
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In this paper, we combine a construction of BRST-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting functional preserves the background-field invariance and BRST invariance of the quantum field. We verify the theory by computing the one-loop effective action and the beta function of the gauge coupling. We also study off-shell one-loop contributions and the application of the decoupling solution.
We combine a recent construction of a Becchi-Rouet-Stora-Tyutin (BRST)-invariant, nonlinear massive gauge fixing with the background field formalism. The resulting generating functional preserves background -field invariance as well as BRST invariance of the quantum field manifestly. The construction features BRST-invariant mass parameters for the quantum gauge and ghost fields. The formalism employs a background Nakanishi-Lautrup field which is part of the nonlinear gauge-fixing sector and thus should not affect observables. We verify this expectation by computing the one-loop effective action and the beta function of the gauge coupling as an example. The corresponding Schwinger functional generating connected correlation functions acquires additional one-particle reducible terms that vanish on shell. We also study off-shell one -loop contributions in order to explore the consequences of a nonlinear gauge fixing scheme involving a background Nakanishi-Lautrup field. As an application, we show that our formalism straightforwardly accommodates nonperturbative information about propagators in the Landau gauge in the form of the so-called decoupling solution. Using this nonperturbative input, we find evidence for the formation of a gluon condensate for sufficiently large coupling, whose scale is set by the BRST-invariant gluon mass parameter.
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