Using subsystemM_T2for complete mass determinations in decay chains with missing energy at hadron colliders

Abstract

We propose to use the M T 2 concept to measure the masses of all particles in SUSY-like events with two unobservable, identical particles. To this end we generalize the usual notion of M T 2 and define a new M (n,p,c) T 2 variable, which can be applied to various subsystem topologies, as well as the full event topology. We derive analytic formulas for its endpoint M (n,p,c) T 2,max as a function of the unknown test massM c of the final particle in the subchain and the transverse momentum p T due to radiation from the initial state. We show that the endpoint functions M (n,p,c) T 2,max (M c , p T ) may exhibit three different types of kinks and discuss the origin of each type. We prove that the subsystem M (n,p,c) T 2 variables by themselves already yield a sufficient number of measurements for a complete determination of the mass spectrum (including the overall mass scale). As an illustration, we consider the simple case of a decay chain with up to three heavy particles, X 2 → X 1 → X 0 , which is rather problematic for all other mass measurement methods. We propose three different M T 2 -based methods, each of which allows a complete determination of the masses of particles X 0 , X 1 and X 2 . The first method only uses M (n,p,c) T 2 endpoint measurements at a single fixed value of the test massM c . In the second method the unknown mass spectrum is fitted to one or more endpoint functions M (n,p,c) T 2,max (M c , p T ) exhibiting a kink. The third method is hybrid, combining M T 2 endpoints with measurements of kinematic edges in invariant mass distributions. As a practical application of our methods, we show that the dilepton W + W − and tt samples at the Tevatron can be used for an independent determination of the masses of the top quark, the W boson and the neutrino, without any prior assumptions. 42 -2 - [18,19,27,38,39].• III. M T 2 methods. These methods explore the transverse invariant mass variable M T 2 originally proposed in [13] and later used and developed in [17,24,26,28,37,40,41,45].Recently it was shown that under certain circumstances, the endpoint of the M T 2 distribution, when considered as a function of the unknown test massM 0 of the lightest new particle X 0 , exhibits a kink and the true mass M 0 of X 0 , i.e. atM 0 = M 0 [29-32,36].One could also combine two or more of these techniques into a hybrid method, e.g. a mixed polynomial and endpoint method [34], a mixed M T 2 and endpoint method [33,43], or a mixed M T 2 and polynomial method [47,48]. In Section 2 we shall describe in detail each of these three basic approaches I -III. We shall then contrast them to each other and discuss their pros and cons. In particular, we shall concentrate on their applicability as a function of the length of the decay chain, i.e. the number n of intermediate resonances in Fig. 1. We shall find that for sufficiently long decay chains, namely n ≥ 3, each method I -III by itself is able to completely determine the unknown particle spectrum, at least as a matter of principle. Therefore, if Nature is so ki...

Determination of the top quark mass circa 2013: methods, subtleties, perspectives

“…This method is kinematical in nature and utilizes the correlation between the endpoints of the M b and the M 221 T2perp distributions and m t [95,96]. It gives a mass measurement m t = 173.90±0.90(stat.…”

Search for top-squark pair production in the single-lepton final state in pp collisions at $\sqrt{s}=8\ \mathrm{TeV}$

“…This variable is a variant of the M T2 observable [56][57][58], and is designed specifically to suppress the tt → background with one undetected lepton in the top squark search. By construction, for the dilepton tt background without mismeasurement effects, M W T2 has an endpoint at the top-quark mass.…”

Search for direct top-squark pair production in final states with two leptons in pp collisions at $ \sqrt{s} $ = 8 TeV with the ATLAS detector

“…The minimisation is performed over all the possible decompositions of q T . For tt or W W decays, if the transverse momenta of the two leptons in each event are taken as p T,1 and p T,2 , and E miss T as q T , m T2 ( , , E miss T ) is bounded sharply from above by the mass of the W boson [85,86]. In thet 1 → b +χ ± 1 decay mode the upper bound is strongly correlated with the mass difference between the chargino and the lightest neutralino.…”