We present a comment on the kinematic variable $m_{CT2}$ recently proposed in Amplification of endpoint structure for new particle mass measurement at the LHC. The variable is designed to be applied to models such as R-parity conserving Supersymmetry
(SUSY) when there is pair production of new heavy particles each of which decays to a single massless visible and a massive invisible component. It was proposed in Amplification of endpoint structure for new particle mass measurement at the LHC that a measurement of the peak of the $m_{CT2}$ distribution could be used to precisely constrain the masses of the SUSY particles. We show that when Standard Model backgrounds are included in simulations, the sensitivity of the $m_{CT2}$ variable to the SUSY particle masses is more seriously impacted for $m_{CT2}$ than for other previously proposed variables.
Since Baades photographic study of M32 in the mid 1940s, it has been accepted as an established fact that M32 is a compact dwarf satellite of M31. The purpose of this paper is to report on the findings of our investigation into the nature of the exis
ting evidence. We find that the case for M32 being a satellite of M31 rests upon Hubble Space Telescope (HST) based stellar population studies which have resolved red-giant branch (RGB) and red clump stars in M32 as well as other nearby galaxies. Taken in isolation, this recent evidence could be considered to be conclusive in favour of the existing view. However, the conventional scenario does not explain M32s anomalously high central velocity dispersion for a dwarf galaxy (several times that of either NGC 147, NGC 185 or NGC 205) or existing planetary nebula observations (which suggest that M32 is more than twice as distant as M31) and also requires an elaborate physical explanation for M32s inferred compactness. Conversely, we find that the case for M32 being a normal galaxy, of the order of three times as distant as M31, is supported by: (1) a central velocity dispersion typical of intermediate galaxies, (2) the published planetary nebula observations, and (3) known scaling relationships for normal early-type galaxies. However, this novel scenario cannot account for the high apparent luminosities of the RGB stars resolved in the M32 direction by HST observations. We are therefore left with two apparently irreconcilable scenarios, only one of which can be correct, but both of which suffer from potentially fatal evidence to the contrary. This suggests that current understanding of some relevant fields is still very far from adequate.
