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In this paper we explore how different regularization prescriptions affectthe counterterms in the renormalization of the galaxy bias expansion. We workin the context of primordial local non-Gaussianity including non-lineargravitational evolution. We carry out the one-loop renormalization of the field$\delta_\rho^2$ (i.e. the square of the matter overdensity field) up to thirdorder in gravitational evolution. Three regularization schemes are consideredand their impact on the values of the counterterms is studied. We explicitlyverify that the coefficients of the non-boost invariant operators areregularization scheme independent.

Regularization Scheme Dependence of the Counterterms in the Galaxy Bias Expansion