The stringy scaling loop expansion and stringy scaling violation

TL;DR

This paper introduces a systematic approximation scheme for calculating n-point functions in open bosonic string theory, revealing finite contributions at each loop order and explicitly computing next-to-leading order scaling violations.

Contribution

It develops a novel stringy scaling loop expansion with finite loop contributions and provides explicit calculations of next-to-leading order scaling violations.

Findings

Finite number of vacuum diagram terms at each loop order.

Explicit calculation of 4-point next-to-leading order scaling violation.

Development of Feynman rules for the expansion.

Abstract

We propose a systematic approximation scheme to calculate general $n$-point $HSSA$ of open bosonic string theory. This stringy scaling loop expansion contains finite number of vacuum diagram terms at each loop order of scattering energy due to a vacuum diagram contraint and a topological graph constraint. In addition, we calculate coefficient and give the vacuum diagram representation and its Feynman rules for each term in the expansion of the $HSSA$. As an application to extending our previous calculation of $n$-point leading order stringy scaling behavior of $HSSA$, we explicitly calculate some examples of $4$-point next to leading order stringy scaling violation terms.