Four-quark operators with $ΔF = 2$ in the GIRS scheme
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912202213031936 |
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| author | Constantinou, M. Costa, M. Herodotou, H. Panagopoulos, H. Spanoudes, G. |
| author_facet | Constantinou, M. Costa, M. Herodotou, H. Panagopoulos, H. Spanoudes, G. |
| contents | We calculate the mixing matrices of four-quark operators that change flavor numbers by two units. Our approach employs two schemes: the coordinate-space Gauge Invariant Renormalization Scheme (GIRS) and the Modified Minimal Subtraction scheme. From our perturbative computations, we extract the conversion factors between these two renormalization schemes at the next-to-leading order. A significant challenge in the study of four-quark operators is that they mix among themselves upon renormalization. Additionally, computations in GIRS at a given order in perturbation theory require Feynman diagrams with at least one additional loop. The extraction of the conversion factors involves calculating two-point Green's functions, which include products of two four-quark operators, and three-point Green's functions, which involve one four-quark operator and two bilinear operators, with all operators located at distinct spacetime points. We investigate both parity-conserving and parity-violating four-quark operators. This calculation is relevant to the determination of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements from numerical simulations using the GIRS scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Four-quark operators with $ΔF = 2$ in the GIRS scheme Constantinou, M. Costa, M. Herodotou, H. Panagopoulos, H. Spanoudes, G. High Energy Physics - Lattice High Energy Physics - Phenomenology We calculate the mixing matrices of four-quark operators that change flavor numbers by two units. Our approach employs two schemes: the coordinate-space Gauge Invariant Renormalization Scheme (GIRS) and the Modified Minimal Subtraction scheme. From our perturbative computations, we extract the conversion factors between these two renormalization schemes at the next-to-leading order. A significant challenge in the study of four-quark operators is that they mix among themselves upon renormalization. Additionally, computations in GIRS at a given order in perturbation theory require Feynman diagrams with at least one additional loop. The extraction of the conversion factors involves calculating two-point Green's functions, which include products of two four-quark operators, and three-point Green's functions, which involve one four-quark operator and two bilinear operators, with all operators located at distinct spacetime points. We investigate both parity-conserving and parity-violating four-quark operators. This calculation is relevant to the determination of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements from numerical simulations using the GIRS scheme. |
| title | Four-quark operators with $ΔF = 2$ in the GIRS scheme |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2501.13939 |