Understanding and improving the Effective Mass for LHC searches

A handy and extensively used kinematic variable in LHC analyses, especially for golden SUSY signals of multijets plus missing energy, is the Effective Mass, M_eff = sum_j |p_T^j|+ |p_T^miss|. Empirically, the value of M_eff at which the histogram of events has a maximum is correlated with the SUSY spectrum, M_eff|_max ~ 80% M_susy, where M_susy is essentially the sum of the masses of the SUSY particles initially created. In this paper we explain the reason for such strong correlation, pointing out the cases where the correlation is not good. Besides, we propose a new variable, the Effective Transverse Energy, E_T^eff, which shows an even better and more direct correlation E_T^eff|_max ~ M_susy, and is independent of the procedure followed to identify the jets. E_T^eff and M_eff are complementary variables, rather than competitors; and plotting histograms in both can be useful to cross-check the results, allowing a better and more robust identification of M_susy. The extension of this procedure to other scenarios of new physics (not necessarily SUSY) is straightforward.