Local and global duality and the determination of \alpha(M_Z)

TL;DR

This paper discusses a method to determine the fine structure constant at the Z boson mass resonance by addressing the breakdown of global duality using polynomial fits, providing a conservative and assumption-light approach.

Contribution

It introduces a polynomial fitting technique to circumvent the breakdown of global duality in determining t the Z resonance, clarifying the difference between local and global duality.

Findings

The polynomial fit effectively mimics the weight function.

The method is largely independent of specific assumptions.

It offers a conservative approach to  determination.

Abstract

This talk presents work concepts and results for the determination of the fine structure constant $\alpha$ at the $Z_0$ mass resonance. The problem consisting of the break-down of global duality for singular integral weights is circumvented by using a polynomial fit which mimics this weight function. This method is conservative in the sense that it is mostly independent of special assumptions. In this context the difference between local and global duality is explained.