Constrained \( \sqrt{{\widehat{S}}_{\min }} \) and reconstructing with semi-invisible production at hadron colliders

Received: December Smin and reconstructing Open Access 0 c The Authors. 0 0 Ahmedabad , Gujarat - 380 009 , India Mass variable pSmin and its variants [1, 2] were constructed by minimising the parton level center of mass energy that is consistent with all inclusive measurements. They were proposed to have the ability to measure mass scale of new physics in a fully model independent way. In this work we relax the criteria by assuming the availability of partial informations of new physics events and thus constraining this mass variable even further. Starting with two different classes of production topology, i.e. antler and non-antler, we demonstrate the usefulness of these variables to constrain the unknown masses. of invisible particles and thus improving the measurements to reveal the properties of new physics. Hadronic Colliders Constrained discussion is illustrated with different examples, from the standard model Higgs production and beyond standard model resonance productions leading to semi-invisible production. We also utilise these constrains to reconstruct the semi-invisible events with the momenta 1 Introduction 2 3 s mass-bound variables without additional constraints Antler topology and constrained variable Non-antler topology and constrained variables Event reconstruction capability Summary and conclusions The Standard Model (SM) is now essentially complete after CMS [3] and ATLAS [4] found its last missing bit, lone neutral scalar of the model, the Higgs boson. The SM is so far extremely successful in explaining the fundamental particles and the interactions between them. However some of the unresolved theoretical questions together with very convincing experimental observations, such as dark matter, neutrino oscillation and several others compel us to believe that the SM can not be the complete description. Numerous models beyond Standard Model (BSM) was constructed to accommodate some of these phenomena with a general belief that the scale of new physics is just around the corner at few to multiTeV level. Unfortunately, large hadron collider (LHC) has not observed any indication of new physics so far. Now, if any of these TeV scale BSM theories exists in nature then it can manifest its signature at the next LHC run. A scenario with positive signal essentially necessitates the determination of the new particle mass, spin and coupling etc associated with that new physics. Recently popular theoretically appealing BSM theories are the ones which accommodate the thermal relic dark matter as stable and weakly interacting massive particle (WIMP) estimating the tightly constrained observed amount of dark matter density [5]. Hence, this stability of the dark matter in most of the BSM theory is ensured by some discrete symmetry, such as Z2 symmetry in supersymmetry or many other scenario. Once this symmetry is respected, all the heavy BSM particles in such model has to be produced in pairs; subsequently decaying into some lighter BSM resonance together with SM particles (which may or may not be detected and measured at the detector) in multiple steps of successive decay. Typically at the end of each decay chain lightest BSM particle is produced which is the dark matter particle of that model and escape the detection. Hence, at least two massive and lightest BSM particles remain hidden in these events. The only way to know their presence is the observation of sizable P6~T in the detector calculated from the imbalance of transverse visible momenta produced in such events. The reconstruction of a dark matter signal at hadronic collider is challenging because of the partial knowledge of the incoming parton momenta further burdened with multiple massive final state particles of unknown mass goes undetected keeping no individual momentum informations at the detector. There has been several studies under gone into mass and spin determination in the context of semi-invisible production at the hadronic collider1 and we classify them based on the topology information as follows: Exclusive variables are defined based on the topology of the production mechanism and decay processes under consideration. Identical signatures consists of visibles and invisibles in the final state can be originated from very different topologies which is deeply related to the stabilising symmetry of the dark matter (DM). Shape of the visible invariant mass can effectively carry informations on topology along with the mass spectrum [9] of the decay chain. Underlying DM stabilising symmetry can also be probed [1012] using kinematic edge and cusp in the invariant mass distributions and from the shapes of transverse mass variable MT 2. Even the assumption of one particular underlying symmetry allows some fixed number of different topologies from which the correct one can be identified comparing suitable kinematic variables [13]. One expects that the ignorance of the correct topology can add difficulties in solving combinatorial ambiguity [1417] which is one source of complexity in mass determination methods, more prominently available when associated with long decay chain. This ambiguity can be originated from two different sources. Firstly, allocation of the final state particles to the correct decay chain, i.e. from which side of the decay chain some particular states is produced. Secondly, the ordering of the assigned particle in a single decay chain. The hemisphere method [18] and PT vs M methods [15] are introduced to reduce the this ambiguity in assigning the correct final state particles to the corresponding decay chain. However, the ordering of the particles left unresolved. The MT 2 variable together with invariant mass are also shown to reduce the combinatorics significantly [16]. In the literature several classes of exclusive variables are defined assuming that the correct knowledge of topology is available and anticipating that the combinatorial ambiguity can be controlled. The exclusive mass determination methods can be categorised as follows Edge measurement method : based on the idea of constructing all possible invariant masses out of visible decay products in each decay chain [1925]. Each invariant mass has an endpoint which is experimentally observable and these endpoints are related to the unknown masses in the decay chain. To evaluate all the unknown masses by inverting the the equations in terms of measured endpoints, one needs sufficient number of independent endpoint measurements. So essentially a long decay chain in necessary to have unique measurement of all the unknown masses. However this criteria inevitably invites combinatorial ambiguity thereby reducing the effectiveness of the method. This method also does not use all the available informations like missing transverse momentum P6~T in the event. 1For some recent review, see refs. [68]. Polynomial method : one tries to utilise all the available information in the event of particular topology and solve for t (...truncated)