Perturbative renormalization of ΔF = 2 four-fermion operators with the chirally rotated Schrödinger functional

2016/05/29 by Mattia Dalla Brida, Brida, Mattia Dalla, Mauro Papinutto +3
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions

paper · doi:10.48550/arxiv.1605.09053

openalex publication_date 2016/05/29 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The chirally rotated Schrödinger functional (χSF) renders the mechanism of automatic O(a) improvement compatible with Schrödinger functional (SF) renormalization schemes. Here we define a family of renormalization schemes based on the χSF for a complete basis of ΔF = 2 parity-odd four-fermion operators. We compute the corresponding scale-dependent renormalization constants to one-loop order in perturbation theory and obtain their NLO anomalous dimensions by matching to the \textrmMS scheme. Due to automatic O(a) improvement, once the χSF is renormalized and improved at the boundaries, the step scaling functions (SSF) of these operators approach their continuum limit with O(a²) corrections without the need of operator improvement.

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