# Bachelor thesis with Priv.-Doz. Worek in 2018

Lorentz Invariant Phase-Space Integrals for Multiparticle Systems

An important numerical problem in particle physics is the computation of cross sections. Those are usually very complicated integrals over the square matrix element and the phase-space volume of momenta of the final state particles. Such cross sections exhibit strong peaks in many different regions of the phase space. Additionally, the presence of complicated kinematical cuts render an analytic treatment impossible. The Monte Carlo methods of integration are often used instead. In the Monte Carlo approach, a huge effort must be made to reduce the variance of the integrand. One of the popular approaches of variance reduction is the so-called stratified sampling technique, another approach is that of importance sampling.

The goal of this bachelor thesis will be to calculate phase-space integrals using Monte Carlo techniques together with different methods to minimise the integration error. These approaches will be applied to the real-life calculation of a cross section in electron-positron collisions. A comparative study of various methods for variance reduction will be made for one particular process. Finally, a comparison to existing Monte Carlo programs will be performed to cross-check the efficiency of the implemented methods.

The student will learn:

1. The basic of Monte Carlo methods
2. How to reduce the variance of the integrand (stratified sampling, importance sampling, other methods)
3. How to efficiently calculate phase-space volume of momenta of the final state particles

Requirements:

1. Basic understanding of particle physics is required and can be obtained during the work on the thesis
2. Programming skills e.g. in Fortran, C/C++ that can be easily learned during the time of the thesis

The associated production of a Higgs boson with a top quark-antiquark pair at the LHC

The observation of a Higgs boson with a mass of approximately 125 GeV at the Large Hadron Collider marked the starting point of a broad program to determine the properties of the newly discovered particle. To date, all measured properties, including couplings, spin, and parity are consistent with the SM expectations within experimental uncertainties. Among many production processes the Higgs boson in association with a top-quark pair (ttH) is very important. For the Higgs boson mass mH = 125 GeV a wealth of different Higgs boson decay channels is available, among others the bb final state. However, the pp → ttH → ttbb production channel is very challenging. Since the top quark decays into t → Wb the final state that in reality has to be studied is pp → WWbbH → WWbbbb. We have two main problems in this channel:

• the so called combinatorial problem with b-­jets → the bb pair that builds the Higgs boson can be chosen incorrectly.
• the so called combinatorial problem with b-­jets → the bb pair that builds the Higgs boson can be chosen incorrectly.
• the b-jet tagging efficiency → at the LHC the b-tagging efficiency is not 100% so the b-jets for Higgs candidate can arise from mis-tagged QCD light jet

As a consequence the Higgs boson has not yet been discover in this channel.

The goal of this bachelor thesis will be to understand the main phenomenological features of the ttH production process, with H → bb. In a next step, Higgs production in this channel will be studied in more detail together with two main background processes, which are the top quark-pair production process with additional jets (b-jets or light jets), i.e. pp → ttbb and pp → ttjj production. Main obstacles to correctly reconstruct the Higgs boson will be examined. To this end various observables and phase space cuts will be introduced to suppress these two background production modes as compared to the signal process. The phenomenological studies will be carried out with the publicly available Monte Carlo program HELAC-PHEGAS.

The student will learn:

1. How to perform phenomenological analyses for the LHC.
2. How to use publicly available Monte Carlo programs.
3. How to efficiently reduce background processes to enhance the signal process.

Requirements:

1. Basic understanding of particle physics is required and can be obtained during the work on the thesis.
2. Programming skills in Fortran that can be easily learned during the time of the thesis.