Sill distribution: genesis and salient features

TL;DR

The paper introduces the Sill distribution, a new mathematical model for resonance energy line shapes that accounts for threshold effects, applicable to mesons and baryons, and demonstrates its use on the $ ext{psi}(3770)$ resonance.

Contribution

It presents the Sill distribution as a natural, normalized, and extendable model for resonance line shapes, incorporating threshold effects in both nonrelativistic and relativistic contexts.

Findings

Sill distribution correctly normalizes broad states.

It remains continuous at thresholds.

Successfully applied to describe $ ext{psi}(3770)$ resonance.

Abstract

We present the so-called Sill distribution, both in the nonrelativistic and relativistic cases, as a natural and simple way to include the effect of threshold(s) on the energy line shapes of resonances. The Sill is correctly normalized (even for broad states), is continuous at threshold(s), does not require any modification to the `mass part', is easily extendable to the multichannel case, and can be applied to both mesons and baryons. Here, as a novel example, we employ the Sill to describe the resonance $\psi(3770)$.