A note on renormalon models for the determination of alpha_s(M_tau)

Understand

The tau hadronic width provides a determination of the strong coupling constant alpha_s at low energies, since it can be related to a weighted integral of the Adler function in the complex energy plane.

• Using Operator Product Expansion, one sees that the sensitivity to alpha_s comes from the perturbative contribution, which can be obtained by integrating the perturbative expansion of the Adler function.
• Two different prescriptions proposed to perform this integral, called Fixed-Order Perturbation Theory and Contour-Improved Perturbation Theory (FOPT and CIPT), yield different results for the strong coupling constant.
• Recently, models for the Adler function based on renormalon calculus have been proposed to determine which of the two methods is the most accurate, by comparing the resulting asymptotic series with the true value of the integral.