An event mixing method with invariant-mass/energy hierarchy correspondence cut for Bose-Einstein correlations in $\pi \pi X$ system

A new event mixing constraint, namely invariant-mass/energy hierarchy correspondence (IMEHC) cut, is introduced for the low-multiplicity event mixing technique for the purpose of measuring Bose-Einstein correlations (BEC) in exclusive reactions with $\pi \pi X$ final state particles.The mixing cut is relevant to the hierarchy of the invariant mass of $\pi X$ system and two bosons energy hierarchy. Numerical tests are performed to check the validity of the new mixing method. As long as the measurements of BEC parameters $r_0$ and $\lambda_2$ are considered, this new mixing method is effective to observe BEC effects and the systematic bias of $r_0$ and $\lambda_2$ are smaller than the previously proposed mixing cut.