Eur. Phys. J. C (2013) 73: 2353
https://doi.org/10.1140/epjc/s10052-013-2353-6

Regular Article - Theoretical Physics

Consistency of loop regularization method and divergence structure of QFTs Beyond one-loop order

¹ Kavli Institute for Theoretical Physics China (KITPC) at the CAS, State Key Laboratory of Theoretical Physics (SKLTP), Institute of Theoretical Physics, Chinese Academy of Science, Beijing, 100190, China
² University of Chinese Academy of Sciences, Beijing, 100049, China
⁴ Department of Physics, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

^* e-mail: dahuang@phys.nthu.edu.tw

Received: 18 October 2012
Revised: 13 January 2013
Published online: 10 April 2013

Abstract

We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the general procedure. In the processes, we find a new divergence structure: the regulated result for each two-loop diagram contains a gauge-violating quadratic harmful divergent term even combined with their corresponding counterterm insertion diagrams. Only when we sum up over all the relevant diagrams do these quadratic harmful divergences cancel, recovering the gauge invariance and locality.