How to test for mass degenerate Higgs resonances

TL;DR

This paper introduces a method to determine the number of mass degenerate Higgs resonances at the LHC by analyzing the rank of a production and decay rate matrix, accounting for interference effects.

Contribution

It establishes a rank-based framework to identify the number of degenerate resonances and explores the LHC's potential to distinguish multiple Higgs states using current and future data.

Findings

The rank of the rate matrix constrains the number of resonances.

Interference effects can increase the maximum rank.

Current data limits the number of degenerate Higgs resonances.

Abstract

The Higgs-like signal observed at the LHC could be due to several mass degenerate resonances. We show that the number of resonances is related to the rank of a "production and decay" matrix, $R_{if}$. Each entry in this matrix contains the observed rate in a particular production mode $i$ and final state $f$. In the case of $N$ non-interfering resonances, the rank of $R$ is, at most, $N$. If interference plays a role, the maximum rank is $N^2$ or in the CP limit $N(N+1)/2$. As an illustration we use the present experimental data to constrain the rank of the corresponding matrix. We estimate the LHC reach of probing two and three resonances under various speculations on future measurements and uncertainties.