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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2511.17349 |
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| _version_ | 1866918213526224896 |
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| author | Schröder, Christoph L. Meyer, Harvey B. |
| author_facet | Schröder, Christoph L. Meyer, Harvey B. |
| contents | We develop elements of coordinate-space perturbation theory for massive quantum field theories in general $d$-dimensional Euclidean space. Using the expansion in Gegenbauer polynomials, we provide analytic expressions for several three-point correlation functions in theories with one massive and one massless field. To this end, a class of antiderivatives of products of two Bessel functions multiplied by a power of their common argument are studied systematically. We expect these results to be useful in perturbative calculations involving vertices of high degree, at finite temperature and/or in finite volume, as well as in auxiliary perturbative computations for a lattice QCD treatment of hadronic effects in precision observables. As an illustration, we compute the one-loop coordinate-space propagator of a massive particle coupled to a massless one, both in the vacuum and at finite temperature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Euclidean coordinate-space perturbation theory with a single mass scale Schröder, Christoph L. Meyer, Harvey B. High Energy Physics - Lattice High Energy Physics - Theory We develop elements of coordinate-space perturbation theory for massive quantum field theories in general $d$-dimensional Euclidean space. Using the expansion in Gegenbauer polynomials, we provide analytic expressions for several three-point correlation functions in theories with one massive and one massless field. To this end, a class of antiderivatives of products of two Bessel functions multiplied by a power of their common argument are studied systematically. We expect these results to be useful in perturbative calculations involving vertices of high degree, at finite temperature and/or in finite volume, as well as in auxiliary perturbative computations for a lattice QCD treatment of hadronic effects in precision observables. As an illustration, we compute the one-loop coordinate-space propagator of a massive particle coupled to a massless one, both in the vacuum and at finite temperature. |
| title | Euclidean coordinate-space perturbation theory with a single mass scale |
| topic | High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.17349 |