# Bachelor thesis with Priv.-Doz. Worek in 2017

General Monte Carlo algorithm for Lorentz invariant Phase Space

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:**

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

**Requirements:**

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

Study of Higgs boson production via Vector Boson Fusion at the Large Hadron Collider

Higgs boson production via Vector Boson Fusion (VBF) is one of the four leading processes of Higgs boson production at the Large Hadron Collider (LHC). In this process, the Higgs boson is accompanied by two additional quarks, which leads to a very distinct event topology: two high-energetic jets in the forward regions of the detector and reduced jet activity in the central region. Additionally, the decay products from the Higgs boson are likely to be encountered in the central detector region, between the two jets. This unique signature allows to distinguish Higgs production in VBF processes from other production modes with the same final state, which are called background processes. For the Higgs boson mass m_{H} = 125 GeV a wealth of different Higgs boson decay channels is available. From the experimental point of view, however, the following two channels provide a very clean signature: H → ZZ* and H → gamma gamma.

The goal of this bachelor thesis will be to understand the main phenomenological features of VBF process. In the next step, Higgs production in VBF will be studied in more detail together with two main background processes, which are electroweak and QCD-induced VVjj production. To this end various observables and phase space cuts will be examined to suppress these two production modes as compared to the signal VBF process. The phenomenological studies will be carried out with two publicly available Monte Carlo programs, namely VBFNLO and HELAC-PHEGAS.

**The student will learn:**

- How to perform phenomenological analyses for the LHC
- How to use various Monte Carlo programs
- How to efficiently reduce background processes to enhance the signal process

**Requirements:**

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