The renormalization of non-Abelian gauge theories is studied in the background-field gauge by means of Ward-Slavnov identities derived from supergauge transformations and with use of 't Hooft and Veltman's renormalization. As a result, the counterterm depending on the background field only is shown to be (gg₀)²L(→Aᶜˡ).
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Kluberg-Stern et al. (1975) studied this question.