The 4-loop slope of the Dirac form factor

Stefano Laporta

doi:10.1051/epjconf/202023401009

All issues

Volume 234 (2020)

EPJ Web Conf., 234 (2020) 01009

Abstract

Open Access

Issue		EPJ Web Conf. Volume 234, 2020 International Workshop on “Flavour Changing and Conserving Processes” (FCCP2019)


Article Number		01009
Number of page(s)		5
DOI		https://doi.org/10.1051/epjconf/202023401009
Published online		27 April 2020

EPJ Web of Conferences 234, 01009 (2020)
https://doi.org/10.1051/epjconf/202023401009

The 4-loop slope of the Dirac form factor

Stefano Laporta¹^,2^a^,b

¹ Dipartimento di Fisica e Astronomia, Università di Padova, Via Marzolo 8, I-35131 Padova, Italy
² Istituto Nazionale Fisica Nucleare, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy

^a e-mail: stefano.laporta@pd.infn.it
^b Talk given at “Flavour changing and conserving processes” 2019 (FCCP2019), 29-31 August 2019, Villa Orlandi, Anacapri, Capri, Italy.

Published online: 27 April 2020

Abstract

The 4-loop contribution to the slope of the Dirac form factor in QED has been evaluated with 1100 digits of precision. The value is $m^{2} F_{1}^{(4)^{'}} (0) = 0 .886545673946443145836821730610315359390424032660064745 \dots {(\frac{α}{π})}^{4}$ ${m^2}F_1^{(4)'}(0) = {\rm{0}}{\rm{.886545673946443145836821730610315359390424032660064745}} \cdots {\left( {{\alpha \over \pi }} \right)^4}$ . We have also obtained a semi-analytical fit to the numerical value. The expression contains harmonic polylogiπ2iπ iπ arithms of argument $e^{\frac{i π}{3}}, e^{\frac{2 i π}{3}}, e^{\frac{i π}{2}}$ ${e^{{{i\pi } \over 3}}},{e^{{{2i\pi } \over 3}}},{e^{{{i\pi } \over 2}}}$ , one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. We show the correction to the energy levels of the hydrogen atom due to the slope.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.