Pade Theory applied to the vacuum polarization of a heavy quark

TL;DR

This paper demonstrates how Pade Approximants can reconstruct the vacuum polarization function of a heavy quark from low-energy data, providing a method to determine key constants at higher orders.

Contribution

It applies Pade Theory to the vacuum polarization of a heavy quark, enabling reconstruction of the full function from low-energy expansion data.

Findings

Successfully determined the constant K^(2) at order O(alpha_s^2)

Validated the use of Pade Approximants for heavy quark vacuum polarization

Showed the function's reconstruction is possible away from the physical cut

Abstract

The vacuum polarization of a quark, when considered in terms of the external momentum q^2, is a function of the Stieltjes type. Consequently, the mathematical theory of Pade Approximants assures that the full function, at any finite value of q^2 away from the physical cut, can be reconstructed from its low-energy power expansion around q^2=0. We illustrate this point by applying this theory to the vacuum polarization of a heavy quark and obtain the value of the constant K^(2) governing the threshold expansion at order O(alpha_s^2).