# Bachelor thesis with Prof. Czakon in 2016

Top quark transverse momentum distributions in the non-relativistic approximation

At the Large Hadron Collider, the top quark is often produced close to threshold. This means that the total energy of the top-anti-top system is close to 2*mt (mt is the top-quark mass). On the other hand, this also implies that the velocity of the quarks is much smaller than the speed of light. In consequence, one can treat the top-quarks as non-relativistic, and describe them with the ordinary Schroedinger equation, albeit with a suitably adapted potential. The purpose of the thesis is to use this approach to obtain the distribution of the top-quark transverse momentum, pT, at the LHC for small values of pT. This observable is measured to high precision and is the object of intense current research.

**The student will learn:**

- Why particles are usually produced close to thresholds, and what these thresholds are.
- How to solve the Schroedinger equation numerically including a description of the decay of the top-quark. This will be compared with analytic solutions.
- Why are transverse momentum distributions interesting and how to obtain them.

**Requirements:**

- Only a very basic understanding of particle physics is required and can be obtained during the work on the thesis.
- Good understanding of basics of Quantum Mechanics.
- Some programming skills, but the problem can be solved with a multitude of languages (certainly with C/C++, Fortran).

Color correlations in Quantum Chromodynamics

Strongly interacting elementary particles, quarks and gluons, poses a particular internal degree of freedom conventionally called color. This degree of freedom has some similarities to spin, but cannot be associated with space transformations. Observable objects, such as hadrons are effectively "colorless". Nevertheless, during high-energy collisions, color is exchanged in very complicated ways, which however follow well defined patterns. The purpose of this thesis is to develop a procedure, which will allow to evaluate color correlations, i.e. expectation values of color operators between physical states. Such color correlations drive the emission of very low energy gluons, which sometimes dominate the quantum effects in scattering processes.

**The student will learn:**

- Properties of the SU(3) group and its representations as required to describe color.
- How color enters physical transition probabilities and why it poses such a problem.
- How color is treated in actual applications for the Large Hadron Collider

**Requirements:**

- Good understanding of basics of Quantum Mechanics, in particular of the angular momentum and it relation to the SU(2) group (at the level of the Theo III lecture).
- Interest in mathematical structures, group theory and algorithms (besides knowledge related to a) no further knowledge is necessary at first).
- Some programming skills. The purpose is to develop an algorithm and test it. Preference will be given to an implementation in the object oriented Fortran 90 (a sufficient part of the language can be easily learned during the thesis)