Testing Supersymmetry in $A H^\pm$ Associated Production

In the Minimal Supersymmetric Standard Model, the masses of the charged Higgs boson ($H^\pm$) and the CP-odd scalar ($A$) are related by $M_{H^+}^2=M_A^2+m_W^2$ at the Born level. Because the coupling of $W^-$-$A$-$H^+$ is fixed by gauge interaction, the Born level production rate of $q \bar q' \to W^{\pm \ast} \to A H^\pm$ depends only on one supersymmetry parameter -- the mass ($M_A^{}$) of $A$. We illustrate how to test the mass relation between $A$ and $H^+$ in case that the signal is found at the LHC. If the signal is not found, the product of the decay branching ratios of $A$ and $H^\pm$ predicted by the MSSM is bounded from above as a function of $M_A$.