Bb4l event generator, interferences and off-shell effects Leo Peyruchat University of Strasbourg Supervised by Jeremy Andrea, CMS, CERN (Dated: 9 ao^ut2017) Proton-proton collisions happening in LHC create lots of data. To understand the underlying physics behind these events, the real data must be compared to simulated events. A new generator, called the bb4l model, is able to simulate collisions happening in LHC with new interesting features regarding process creating two W bosons and two b quarks. One of them is that it takes interferences between different processes into account. Such effects have always been neglected in the case of top pair or single top production, but with the increasing sensitivity of the detectors it is becoming important to know precisely their amplitude. The goal of this study is to separate events generated with bb4l into different categories, and then to look at many variables and look for differences between categories. STANDARD MODEL which indicate that it is only a low energy effective theory of a more general theory. This is one of the main moti- The Standard Model (SM) of particle physics is the vation for current researches in particle physics. Because theoretical framework that describes the behaviour of ele- of its properties, the top quark is a good tool to probe mentary particles and their interactions (except via gra- new physics. vity) [1]. Particles are divided into different subsets. First one shall distinguish fermions (half-integer spin), which are the building blocks of matter, and bosons (integer TOP QUARK PHYSICS spin), which are the carrier of the interactions (except for the higgs boson). With its heavy mass (' 173 GeV) and its short life Then among fermions, one can make the distinction time (' 10−25s), the top quark has a peculiar role in the between quarks and leptons. The former carry a color SM [3]. charge, and therefore interacts via strong interaction, Because the strong force increases with distance, while the latter doesn't. Both have six particles and anti- quarks are always in bound states (also called confin- particles, divided into three generations. Each quark ge- ment). So when high energy quarks are created and ta- neration has two members, with spin 2/3 (eg. up quark) ken apart, they will create many composite particles (cal- and spin -1/3 (eg. down quark). A leptonic family consists led hadrons). This process is called hadronization, and is of an electrically charged particle (eg. electron) and its at the origin of the tight cones of particles (called jets) associated neutral particle, the neutrino. created in high energy collisions. But the time required The different gauge bosons have distinct properties to hadronize (' 10−24s) is bigger than the life-time of that specify how the associated interaction will work. the top quark. So top quarks, unlike other quarks, will Photons mediate electromagnetic force between electri- decay before hadronizing. Therefore top quarks can be cally charged particles, via processes described by quan- seen as 'bare quarks', allowing us to measure their mass tum electrodynamics (QED). W+− and Z bosons carry precisely and to study their properties directly from their weak force between all fermions, via respectively char- decay products. ged and neutral currents. These bosons can be associa- A single top quark will decay into a W boson and a b ted with photons in the electroweak (EW) interaction. quark in almost all cases. The b quark will form a jet, Strong force is mediated by eight gluons and is described and the W will decay into either a charged lepton and by quantum chromodynamics (QCD). neutrino pair, or into a quark and antiquark pair. If one With the help of quantum field theory, and by imposing then considers a double top process, the final products a local gauge invariance, one can build the SM lagrangian will consist of two b quark, and either two leptons pairs that describes all three fundamental interactions [2]. But ('dileptons'), two quarks pairs ('all jets'), or one of each this predicts only massless particles, which doesn't coin- ('lepton+jets'). cide with experimental observations. The Higgs mecha- nism must be introduced to give mass to particles. The associated particle is the Higgs boson, which has a unique LHC AND CMS role is the SM. It is the only elementary scalar particle (spin 0), and because it gives their mass to the particles The LHC, which first ran in 2008, is an hadron acce- it can be viewed as the building block of the SM. lerator that can reach an energy in the center of mass But this theory isn't perfect. Indeed, it has some flaws as high as 13 TeV [4]. It uses radiofrequency chambers 2 to accelerate particles, and superconducting electroma- gnets to control and focus the beam. The beam consists of many bunches of protons (about 106). The actual re- cord is 2556 simultaneous bunches, with correspond to a 25ns 'separation' between the bunches. Four main detectors are placed along the ring, where the bunches are brought together to collide. One of them is called CMS for Compact Muon Solenoid. It is a big cy- Figure 1: Feynmann diagram of an quark anti-quark linder (29x15 meters) consisting of multiple layers of de- pair annihilation leading to the creation of an electron tectors. The innermost part is a tracker [5] (silicium semi- positron pair conductor) which uses a strong magnetic field to bend the charged particles. It allows to reconstruct the trajectory and the momentum of the particles. Then there are two vertices. Particles are represented by an arrow pointing calorimeters, which measure their energy. The first one towards a vertex, whereas anti-particles have an arrow is for electron and photon, and the second one is for ha- pointing away from a vertex. The example shown in fi- drons. The last part is the muon chamber. Muons need gure 1 shows the annihilation of a quark anti-quark pair a specific detector because they are the only particles of into photon. The photon then decays into an electron and the SM that are able to reach the outermost part of the a positron. A basic diagram like this represent what is cal- detector. led an 'hard' process, and describes particles with a high Let's define two widely used parameters. The first one momentum. These hard process are calculated via exact is the transverse momentum (pt), which is simply the pro- fiexd-order perturbation theory. But corrections need to jection of the momentum of a particle in the transverse be done to have a good description of the experimental plan. The second one is the pseudo-rapidity (η), defined collisions. as : η = − ln(tan(θ=2)) with θ the angle between the Any particle with a colour charge (quarks and gluons) momentum of the particle and the direction of the beam. is called a parton, and can radiate virtual gluons. These Therefore a small rapidity corresponds to a particle emit- gluons can themselves turn into a quark and anti-quark ted close to the transverse plan, whereas a large rapidity pair or emit another gluon. This effect is particularly im- correspond to a particle going near the beam axis. portant with hadronic colliders, because there is always Raw data obtained from the detectors need to be car- multiple partons in the initial state. All these possible refully treated to determine which particles were created contributions are computed through a process called 'par- during a collision. Among the many reconstruction algo- ton shower', that uses approximate pertubation theory. rithms used, one is peculiar to CMS : the particle flow. It All the quarks and gluons produced will then hadronize combines data from different parts of the detector, thus because of QCD confinment, by creating additional jets. allowing a better identification of the different types of Another particular aspect of hadronic collisions is that particles. the initial state is not well known. Indeed, because of But experimental data alone are not enough to un- vacuum fluctuation, a proton of the beam, which usually derstand what is happening during collisions. Indeed, one contains two up quark and a down quark, can have virtual needs to compare them to numerical simulation. partons inside. These may interact during the collision. The probability to find a certain parton in the proton is called parton density function, and depends on the MONTE CARLO EVENT GENERATION energy of the initial proton. So the probability to find a certain final state is the sum of all the possible initial The purpose of simulating an event is to be able to states, times the probability to find it in the proton and compare it to the experimental data. If the two are si- also the probability associated to the process. milar, then the model you used to simulate the events Now, one has to generate many events with the pre- is effective at describing what's happening. If not, then viously calculated probability amplitude, with pseudo- there might be issues in the simulations or in the detec- random numbers to simulate the fluctuation associated tor, but it could also be a hint towards new physics. to quantum mechanics. This kind of methods are called If one wants to simulate a certain event, the first step is Monte Carlo (MC) generators, and compute the integral to simulate the matrix element associated to this process of the phase space associated to a given process. If the [6]. This element is directly related to the probability of number of generated events is sufficient, the probability it happening. Feynmann diagram are used to represent to find a certain configuration in the simulation should interactions, and allows to compute the matrix element correspond to the probability of finding it in the detector.