Scattering off unstable states

TL;DR

This paper introduces a finite-time formalism in quantum field theory to accurately describe scattering processes involving long-lived unstable states, resolving singularities and justifying treating such particles as stable during interactions.

Contribution

It develops an analytic finite-time approach that removes t-channel singularities in unstable particle scattering, extending QFT applicability to long-lived states.

Findings

Finite-time formalism eliminates t-channel singularities.

Long-lived unstable particles can be treated as stable during strong interactions.

Provides a fundamental solution to scattering involving unstable states.

Abstract

Unstable states that live long enough may appear as in(out)going particles in scattering experiments. Yet, the standard QFT approach strictly applies only to fully stable asymptotic states. This is evident when scattering involving unstable particles develops a $t$-channel singularity at specific angles. We employ a finite-time formalism leading to analytic results without the singularity (even in the infinite-time limit), thus solving the problem at a fundamental level. In turn, the approach also justifies treating long-lived particles, like weakly decaying pions, as stable during strong interactions.