Invariant mass | EPFL Graph Search

The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center-of-momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that "rest frame". In other reference frames, where the system's momentum is nonzero, the total mass (a.k.a. relativistic mass) of the system is greater than the invariant mass, but the invariant mass remains unchanged. Because of mass–energy equivalence, the rest energy of the system is simply the invariant mass times the speed of light squared. Similarly, the total energy of the system is its total (relativistic) mass times the speed of light squared. Systems whose four-momentum is

A search for heavy long-lived staus in the LHCb detector at √s = 7 and 8 TeV

Thi Viet Nga La

The Large Hadron Collider (LHC) has been producing pp collisions at 7 and 8 TeV since 2010 and promises a new era of discoveries in particle physics. One of its experiments, the Large Hadron Collider beauty (LHCb) experiment, was constructed to study CP violation in the B meson system. In addition to B physics, new Physics beyond the Standard Model can also be searched for at this single-arm forward spectrometer. With the different sub-detectors and the high resolution of the tracking system, the LHCb detector has the ability to search for heavy, long-lived and charged particles, which are predicted by extensions of the Standard Model. One of these extensions, the minimal Gauge Mediated Supersymmetry Breaking (mGMSB), proposes such a particle, named stau (τ~) - the SUSY bosonic counterpart of the heavy lepton tau (τ). The theory proposes that the staus may be pair-produced in pp collisions or in the decays of heavier particles, and have only electromagnetic interactions with the atoms of the medium like the muons. Therefore, we expect that at the energy of the LHC these particles can be produced if they do exist and that we have a chance to discover them at LHCb, as well as at the other experiments of the LHC. This thesis is dedicated to the search for stau pairs produced in pp collisions at the centre-of-mass energies √s = 7 and 8 TeV in the LHCb detector. For this purpose, we generated the stau pairs with seven different particle masses ranging from 124 to 309 GeV/c2 and simulated their path through the LHCb detector, as well as their muon background from the decays Z0, γ∗ → μ+μ−. Based on the results from the simulation, a set of cuts are then defined to select the stau pairs. Some muon pairs at high energies will also pass the selection cuts. Thus, to separate the stau pairs from the muon pairs, the Neural Network technique has been used. A first Neural Network has been used to distinguish the stau tracks from the muon tracks using their signals left in the sub-detectors: the VELO silicon detector, the electromagnetic calorimeter, the hadron calorimeter and the RICH detectors. Then, two methods to select the stau pairs have been developed: the first one is based on the product of the two responses from the first Neural Network (NN1) for the two tracks, the second one employs a second Neural Network to separate the stau pairs from the muon pairs by using the above product of the two NN1 responses and the invariant mass of pair. Finally, a favourable region for the staus finding has been defined and the expected numbers of stau and muon pairs in this region have been evaluated. The training of the Neural Network has been achieved with the Monte Carlo variables, then the trained Neural Network has been used to classify the data. The data used in our work were collected by the LHCb experiment in 2011 and 2012 and correspond to integrated luminosities of 1 fb−1 at √s = 7 TeV and of 2 fb−1 at √s = 8 TeV. No significant excess of signal has been observed. Upper limits at 95% CL on the cross section for stau pair production in pp collisions at √s = 7 and 8 TeV have been computed by using the profile likelihood method, which is derived from the well known Feldman and Cousins method.

EPFL2013

A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities

Adrien Giuliano Marcone

The purpose of this thesis is to provide an intrinsic proof of a Gauss-Bonnet-Chern formula for complete Riemannian manifolds with finitely many conical singularities and asymptotically conical ends. A geometric invariant is associated to the link of both the conical singularities and the asymptotically conical ends and is used to quantify the Gauss-Bonnet defect of such manifolds. This invariant is constructed by contracting powers of a tensor involving the curvature tensor of the link. Moreover this invariant can be written in terms of the total Lipschitz-Killing curvatures of the link. A detailed study of the Lipschitz-Killing curvatures of Riemannian manifolds is presented as well as a complete modern version of Chern's intrinsic proof of the Gauss-Bonnet-Chern Theorem for compact manifolds with boundary.

EPFL2019

A search for heavy long-lived staus in the LHCb detector at √s = 7 and 8 TeV

Thi Viet Nga La

EPFL2013