Anatomy of real intermediate state-subtraction scheme

TL;DR

This paper analyzes the origin of the real intermediate state subtraction problem, compares existing solutions, and proposes a new scheme that avoids negative scattering rates and assesses the on-shell approximation's validity.

Contribution

It introduces a novel subtraction scheme that prevents negative scattering rates and provides a quantitative measure of the on-shell approximation's validity.

Findings

The ambiguity in subtraction schemes stems from the on-shell approximation.

The new scheme avoids negative scattering rates.

Quantifies the validity of the on-shell limit using an effective weight function.

Abstract

We study the origin of the real intermediate state subtraction problem and compare its different solutions. We show that the ambiguity in subtraction schemes arises from the on-shell approximation for the 2-point functions that reduces the Schwinger-Dyson equations to the Boltzmann limit. We also suggest a new subtraction scheme which, unlike the earlier definitions, never leads to negative scattering rates. This scheme also quantifies the validity of the on-shell limit in terms of an effective one-particle weight function $R(\Delta )$, where $\Delta$ measures the region around the resonance associated with the real state.