Breit-Wigner approximation for propagators of mixed unstable states

TL;DR

This paper introduces a Breit-Wigner approximation for propagators of mixed unstable particles, simplifying calculations while accurately capturing complex pole structures and interference effects, demonstrated in the MSSM Higgs sector.

Contribution

The paper presents a novel approximation method for mixed unstable particle propagators that accounts for complex poles and interference effects, improving theoretical predictions.

Findings

Excellent numerical agreement with full propagator calculations.

Facilitates more precise total width implementations.

Simplifies treatment of off-diagonal propagator contributions.

Abstract

For systems of unstable particles that mix with each other, an approximation of the fully momentum-dependent propagator matrix is presented in terms of a sum of simple Breit-Wigner propagators that are multiplied with finite on-shell wave function normalisation factors. The latter are evaluated at the complex poles of the propagators. The pole structure of general propagator matrices is carefully analysed, and it is demonstrated that in the proposed approximation imaginary parts arising from absorptive parts of loop integrals are properly taken into account. Applying the formalism to the neutral MSSM Higgs sector with complex parameters, very good numerical agreement is found between cross sections based on the full propagators and the corresponding cross sections based on the described approximation. The proposed approach does not only technically simplify the treatment of propagators with non-vanishing off-diagonal contributions, it is shown that it can also facilitate an improved theoretical prediction of the considered observables via a more precise implementation of the total widths of the involved particles. It is also well-suited for the incorporation of interference effects arising from overlapping resonances.