Gauge-invariant renormalization of four-quark operators

Constantinou, M.; Costa, M.; Herodotou, H.; Panagopoulos, H.; Spanoudes, G.

doi:10.1103/PhysRevD.110.074506

Title: Gauge-invariant renormalization of four-quark operators

Journal Article · 10 October 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.074506 · OSTI ID:2474489

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; Herodotou, H.;

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We study the renormalization of four-quark operators in one-loop perturbation theory. We employ a coordinate-space gauge-invariant renormalization scheme (GIRS), which can be advantageous compared to other schemes, especially in nonperturbative lattice investigations. From our perturbative calculations, we extract the conversion factors between GIRS and the modified minimal subtraction scheme ( $\bar{MS}$ ) at the next-to-leading order. As a by-product, we also obtain the relevant anomalous dimensions in the GIRS scheme. A formidable issue in the study of the four-quark operators is that operators with different Dirac matrices mix among themselves upon renormalization. We focus on both parity-conserving and parity-violating four-quark operators, which change flavor numbers by two units ( $Δ F = 2$ ). The extraction of the conversion factors entails the calculation of two-point Green’s functions involving products of two four-quark operators, as well as three-point Green’s functions with one four-quark and two bilinear operators. The significance of our results lies in their potential to refine our understanding of QCD phenomena, offering insights into the precision of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and shedding light on the nonperturbative treatment of complex mixing patterns associated with four-quark operators. Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0020405

OSTI ID:: 2474489

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 7 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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