Spectral function of a scalar boson coupled to fermions

TL;DR

This paper calculates the spectral function of an unstable scalar boson coupled to fermions, showing how a high-energy cutoff influences the particle's width and suggesting experimental implications for detecting new physics.

Contribution

It introduces a method to compute the spectral function with a finite high-energy cutoff, revealing its impact on the width of unstable particles and potential experimental signatures.

Findings

Spectral function normalization is maintained with a finite cutoff.

Higher cutoffs lead to narrower Breit-Wigner widths at fixed coupling.

Line shape measurements could reveal the existence of a high-energy cutoff.

Abstract

We present the calculation of the spectral function of an unstable scalar boson coupled to fermions as resulting from the resummation of the one loop diagrams in the scalar particle self energy. We work with a large but finite high-energy cutoff: in this way, the spectral function of the scalar field is always correctly normalized to unity, independently on the value of the cutoff. We show that this high energy cutoff affects the Breit-Wigner width of the unstable particle: the larger the cutoff, the smaller is the width at fixed coupling. Thus, the existence of a high energy cutoff (alias minimal length), and for instance the possible opening of new degrees of freedom beyond that energy scale, could then be in principle proven by measuring, at lower energy scales, the line shape of the unstable scalar state. Although the Lagrangian here considered represents only a toy-model, we discuss possible future extensions of our work which could be relevant for particle physics phenomenology.