The electron self-energy in QED at two loops revisited
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2018
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| _version_ | 1866910571437228032 |
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| author | Hönemann, Ina Tempest, Kirsten Weinzierl, Stefan |
| author_facet | Hönemann, Ina Tempest, Kirsten Weinzierl, Stefan |
| contents | We reconsider the two-loop electron self-energy in quantum electrodynamics. We present a modern calculation, where all relevant two-loop integrals are expressed in terms of iterated integrals of modular forms. As boundary points of the iterated integrals we consider the four cases $p^2=0$, $p^2=m^2$, $p^2=9m^2$ and $p^2=\infty$. The iterated integrals have $q$-expansions, which can be used for the numerical evaluation. We show that a truncation of the $q$-series to order ${\mathcal O}(q^{30})$ gives numerically for the finite part of the self-energy a relative precision better than $10^{-20}$ for all real values $p^2/m^2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1811_09308 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The electron self-energy in QED at two loops revisited Hönemann, Ina Tempest, Kirsten Weinzierl, Stefan High Energy Physics - Phenomenology We reconsider the two-loop electron self-energy in quantum electrodynamics. We present a modern calculation, where all relevant two-loop integrals are expressed in terms of iterated integrals of modular forms. As boundary points of the iterated integrals we consider the four cases $p^2=0$, $p^2=m^2$, $p^2=9m^2$ and $p^2=\infty$. The iterated integrals have $q$-expansions, which can be used for the numerical evaluation. We show that a truncation of the $q$-series to order ${\mathcal O}(q^{30})$ gives numerically for the finite part of the self-energy a relative precision better than $10^{-20}$ for all real values $p^2/m^2$. |
| title | The electron self-energy in QED at two loops revisited |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/1811.09308 |