Constraining the minimal supergravity model parameter $\tan \beta$ by measuring the dilepton mass distribution at CERN LHC

We study the dependence on $\tan \beta$ of the event kinematics of final states with $e^{+}{e}^{-}/{\mu }^{+}{\mu }^{-}{/e}^{\pm }{\mu }^{\mp }{+E}_T^{\mathrm{miss}}+\mathrm{jets},$ as expected in $\mathrm{pp}$ collisions at CERN LHC, within the framework of the minimal supergravity model. With an increase of $\tan \beta ,$ the third generation sparticle masses $m_{{\tilde{\tau }}_1}$ and $m_{b_1}$ decrease due to the increase of the tau and bottom Yukawa couplings. As a result, the gluino, top squark, sbottom, chargino, and neutralino decays to third generation particles and sparticles are enhanced. With $\tan \beta$ rising, we observe a characteristic change in the shape of the dilepton mass spectra in $e^{+}{e}^{-}/{\mu }^{+}{\mu }^{-}{+E}_T^{\mathrm{miss}}+\mathrm{jets}$ versus $e^{\pm }{\mu }^{\mp }{+E}_T^{\mathrm{miss}}+\mathrm{jets}$ final states, reflecting the presence of the decays ${\tilde{\chi }}_2^0\to l_{L,R}^{\pm }{l}^{\mp }\to {\tilde{\chi }}_1^0{l}^{+}{l}^{-},\hspace{0.5em}{\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0{l}^{+}{l}^{-},$ and ${\tilde{\chi }}_2^0\to {\tilde{\tau }}_1^{\pm }{\tau }^{\mp }\to {\tilde{\chi }}_1^0{\tau }^{+}{\tau }^{-},$ ${\tilde{\chi }}_2^0\to {\tau }^{+}{\tau }^{-}{\tilde{\chi }}_1^0,$ respectively. We exploit this effect for constraining the value of $\tan \beta .$