cross section. We find that as the integrated luminosity exceeds an inverse femtobarn, the LHC is close to tightening the LEP bound of ${m_{{{\widetilde{\tau}}}_1}}\gtrsim 100{\ensuremath{\,\textnormal{GeV}}}$, which currently remains the best limit on the direct production of long-lived sleptons. If the $7{\ensuremath{\,\textnormal{TeV}}}$ run reaches $10{\ensuremath{\,\textnormal{fb}}}^{-1}$, one will be able to exclude stau masses up to roughly $170{\ensuremath{\,\textnormal{GeV}}}$.

Optimized $\boldsymbol{{p_\text{T}}}$-cut {#optimized-boldsymbolp_textt-cut .unnumbered}
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Looking at the ${p_\text{T}}$-distribution of the staus (figure \[fig:distau-obs\], bottom) and the ${p_\text{T}}$-cut dependence of the di-muon cross section (figure \[fig:dimu\], right) we see that we can improve the search by optimizing the ${p_\text{T}}$-cut according to the stau mass hypothesis being considered. In other words, we repeat the previous analysis with an additional ${p_\text{T}}$-cut (again on both stau candidates) that grows linearly with ${m_{{{\widetilde{\tau}}}_1}}$, [p\_]{}&gt; [p\_]{}\^=0.4[m\_[\_1]{}]{}. The stau cross section after applying this additional cut is nearly identical to the lowermost curve in figure \[fig:sigma-mass\]. We emphasize that the result is not sensitive to the choice of the factor $0.4$. Choosing $0.5$ instead gives almost the same result.

(0.68,0.55) (0.005,0.03) (0.63,0.447)[$\mbox{\small{${\color{green} 10^{-10}}$}}$]{} (0.56,0.447)[$\mbox{\small{${\color{green}10^{-7}}$}}$]{} (-0.038,0.116) (0.303,-0.006)[$m_{{{\widetilde{\tau}}}_1}\;[$GeV$]$]{} (0.43,0.3233) (0.13,0.2507) (0.086,0.3) (0.546,0.081)[$14{\ensuremath{\,\textnormal{TeV}}}$]{}

The dependence of the background cross section on this optimized ${p_\text{T}}$-cut is shown in the right panel of figure \[fig:dimu\]. 