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In this paper, we explore the discriminatory power of the matrix elementmethod (MEM) in constraining the $L_\mu-L_\tau$ model at the LHC. The $Z'$gauge boson associated with the spontaneously broken $U(1)_{L_\mu-L_\tau}$symmetry only interacts with the second and third generation of leptons at treelevel, and is thus difficult to produce at the LHC. We argue that the bestchannels for discovering this $Z'$ are in $Z \to 4\mu$ and$2\mu+\displaystyle{\not}E_T$. Both these channels have a large number ofkinematic observables, which strongly motivates the usage of a multivariatetechnique. The MEM is a multivariate analysis that uses the squared matrixelement to quantify the likelihood of the testing hypotheses. We find that with$300 \, \text{fb}^{-1}$ of integrated luminosity, we are sensitive to thecouplings of $ g_{Z'} \gtrsim 0.002 ~ g_1$ and $M_{Z'} < 20 \text{ GeV}$, and$g_{Z'} \gtrsim 0.005 g_1$ and $20\, \text{GeV} <M_{Z'} < 40 ~ \text{GeV}$,which is about an order of magnitude improvement over the cut-and-count methodfor the same amount of data.

Using the (Modified) Matrix Element Method to constrain $L_\mu - L_\tau$ Interactions