Classification of four-quark operators with $ΔF\le 2$ under flavor symmetry and their renormalization in a gauge-invariant scheme
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| Format: | Preprint |
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2025
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| _version_ | 1866917064928657408 |
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| author | Spanoudes, Gregoris Costa, Marios Mitsidi, Kyproulla Panagopoulos, Haralambos |
| author_facet | Spanoudes, Gregoris Costa, Marios Mitsidi, Kyproulla Panagopoulos, Haralambos |
| contents | In this paper we study a complete set of scalar and pseudoscalar four-quark operators, with a particular emphasis on their renormalization within a Gauge-Invariant Renormalization Scheme (GIRS). We focus on operators that do not mix with lower-dimensional operators by virtue of their transformation properties under the flavor-symmetry group. This class includes all $ΔF = 2$ operators, as well as their partners that transform under the same irreducible representations of the flavor group. These encompass a substantial subset of $ΔF = 1$ and $ΔF = 0$ operators. The present analysis provides a detailed classification of all four-quark operators, exploring their Fierz identities, symmetry properties, and mixing patterns. Different variants of GIRS are explored, including a democratic version that treats all mixing operators uniformly. For selected variants, which exhibit smaller mixing effects, we present the conversion matrices from GIRS to the $\overline{\text{MS}}$ scheme at next-to-leading order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of four-quark operators with $ΔF\le 2$ under flavor symmetry and their renormalization in a gauge-invariant scheme Spanoudes, Gregoris Costa, Marios Mitsidi, Kyproulla Panagopoulos, Haralambos High Energy Physics - Lattice High Energy Physics - Phenomenology In this paper we study a complete set of scalar and pseudoscalar four-quark operators, with a particular emphasis on their renormalization within a Gauge-Invariant Renormalization Scheme (GIRS). We focus on operators that do not mix with lower-dimensional operators by virtue of their transformation properties under the flavor-symmetry group. This class includes all $ΔF = 2$ operators, as well as their partners that transform under the same irreducible representations of the flavor group. These encompass a substantial subset of $ΔF = 1$ and $ΔF = 0$ operators. The present analysis provides a detailed classification of all four-quark operators, exploring their Fierz identities, symmetry properties, and mixing patterns. Different variants of GIRS are explored, including a democratic version that treats all mixing operators uniformly. For selected variants, which exhibit smaller mixing effects, we present the conversion matrices from GIRS to the $\overline{\text{MS}}$ scheme at next-to-leading order. |
| title | Classification of four-quark operators with $ΔF\le 2$ under flavor symmetry and their renormalization in a gauge-invariant scheme |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2511.04305 |