6533b856fe1ef96bd12b2915
RESEARCH PRODUCT
The electron self-energy in QED at two loops revisited
Ina HönemannStefan WeinzierlKirsten TempestKirsten Tempestsubject
Physics010308 nuclear & particles physicsModular formBoundary (topology)Order (ring theory)FOS: Physical sciencesElectron01 natural sciencesTruncation (geometry)High Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)Self-energyIterated integrals0103 physical sciencesRelative precision010306 general physicsMathematical physicsdescription
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 $p^2/m^2$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-12-19 |