All-loop four-quark Bethe-Salpeter kernel
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915986444124160 |
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| author | Bargiela, Piotr |
| author_facet | Bargiela, Piotr |
| contents | We analytically calculate the all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel using modern scattering amplitude methods. We work to subleading order in the large number of quark flavors approximation of massless Quantum Chromodynamics, which simultaneously makes an all-loop calculation feasible, is systematically improvable, and preserves asymptotic freedom. It also allows for avoiding the ambiguity of choosing a truncation scheme in Dyson-Schwinger equations. We exploit state-of-the-art methods in Integration-By-Parts reduction of Lorentz scalar Feynman integrals into a minimal Master Integral basis, and direct integration into Generalized Polylogarithms. As a byproduct of our calculation, we also provide the result for the gluon and quark propagators. We discuss a path towards nonperturbative formulation and potential future phenomenological applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05349 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | All-loop four-quark Bethe-Salpeter kernel Bargiela, Piotr High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory We analytically calculate the all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel using modern scattering amplitude methods. We work to subleading order in the large number of quark flavors approximation of massless Quantum Chromodynamics, which simultaneously makes an all-loop calculation feasible, is systematically improvable, and preserves asymptotic freedom. It also allows for avoiding the ambiguity of choosing a truncation scheme in Dyson-Schwinger equations. We exploit state-of-the-art methods in Integration-By-Parts reduction of Lorentz scalar Feynman integrals into a minimal Master Integral basis, and direct integration into Generalized Polylogarithms. As a byproduct of our calculation, we also provide the result for the gluon and quark propagators. We discuss a path towards nonperturbative formulation and potential future phenomenological applications. |
| title | All-loop four-quark Bethe-Salpeter kernel |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.05349 |