A perturbative study of the chirally rotated Schrödinger Functional in QCD

The chirally rotated Schrödinger functional ($χ$SF) renders the mechanism of automatic $O(a)$ improvement compatible with the Schrödinger functional (SF) formulation. Here we report on the determination to 1-loop order in perturbation theory of the renormalization coefficients necessary to achieve automatic $O(a)$ improvement and the boundary improvement coefficients needed to eliminate the extra boundary $O(a)$ effects present in any SF formulation. After this is done, we perform a set of tests of automatic $O(a)$ improvement and of the universality between standard and chirally rotated SF formulations.

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