How to test for mass degenerate Higgs resonances

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.