Confluent Padé approximant and their applications

Abstract

New variants of the Padé approximants (PA) are defined aiming to reproduce the correct hierarchy of the renormalon behavior. These types of PAs are motivated by the appearance of branch cuts instead of poles in the Borel plane of the perturbative series. The first variant of PAs wants to highlight dominant cuts in the Borel plane and it is called D-Log Padé approximant. This method converts the original branch cut into poles through derivatives, where we implement the PA to finally return to the original function. The second method is named Confluent Padé approximant and takes the approximants to the subdominant confluent singularities in the Borel plane which must be considered before moving to the other singular values. We apply the method to the Bjorken Sum Rule, giving a prediction of the next coefficient in the perturbation series.