### Bachelor thesis topics

Students interested in a bachelor thesis in the group T30f are strongly advised to attend this list of lectures.

##### Topics

The topics offered for a bachelor thesis are

*Wilson loop and confinement**X, Y, Z states*

Quark and gluons interact strongly. At low energy in particular
their interaction coupling constant becomes large, giving origin to the
property
of confinement: quarks are therefore confined into hadrons.
The field theory describing the strong interactions, QCD (Quantum
Chromodynamics)
displays such a property.
However, the study of confinement should be performed with nonperturbative
methods. Lattice QCD is such a method, in which the Lagrangian of QCD is
discretized on a space-time lattice and field theoretical calculations are
reduced to the numerical computation of multidimensional integrals.
An object of particular interest in relation to confinement studies is a
correlator called the Wilson loop.
The scope of this thesis is to test and optimize a code for the calculation of
the Wilson loop in QCD and to understand how confinment arises from the
behaviour of the Wilson loop.
.

**Advisors:** Prof. N. Brambilla, Pd. A. Vairo, Dr. J. Weber

X, Y, Z states are exotics states observed in the heavy quarkonium
sector at several high energy accelerator experiments (Belle in Japan,
BES in China and experiments at the Large Hadron Collider at CERN).
They are formed by a heavy quark, a heavy antiquark and some other
component (gluonic-hybrids or light-quarks-tetraquarks)
that make them non-standard.
The properties of these states are directly related to the
nonperturbative nature of low energy QCD and to
the confinement mechanism of strong interactions.
Lattice calculations of the hybrid and tetraquark static energies are
available. The scope of the thesis is to use these lattice
curves together with elementary notions of nonrelativistic effective
field theories to obtain interaction potentials and
solve numerically appropriate Schrödinger
equations to obtain information on the masses and transitions of these
exotic states.

**Advisors:** Prof. N. Brambilla, PD Dr. A. Vairo, Dr. Jorge Segovia, Dr. Wai Kin
Lai

##### Previous Theses

Some previous bachelor theses (found here) included these topics:

*Aspects of Van der Waals Interactions*
Van der Waals interactions play an important role throughout large parts of physics. Although
their origin is very well-understood in terms of quantum physics, calculating them in a precise
way remained an important topic in research. Through Effective Field Theories (EFT) it is now
possible to consider the so-called gluonic Van der Waals interactions (strong interaction between
colour-neutral objects) as well. A very important quantity to determine the strength of these
long-range forces is the polarizability. This thesis is first going to study Van der Waals interactions
in terms of non-relativistic quantum mechanics and then to present methods to calculate the
polarizability of an object. These methods are applied to obtain an elementary expression for the
static polarizability of the hydrogen atom in arbitrary bound states.*Quarkonium dissociation at the Large Hadron Collider*
Heavy quarkonia,
namely bound states of a heavy quark and antiquark, turn out to be
useful systems to probe the QGP. In particular the hot state of matter
can induce thermal modifications to the quarkonium states.
Experimentally we can see such effects either in the quarkonium
suppression or in changes in the bound state properties
(masses and widths). From a theoretical point of view,
effective field theories give us the possibility
to study in detail what happens to heavy quarkonia
in this extremely hot state of matter.
The goal of this thesis is to get a better understanding of the QGP by numerically solving
the Schrödinger equation for heavy quark-antiquark potentials obtained within the framework
of effective field theories.
*Application of Hydrodynamics to Heavy Ion Collisionns*
At the typical temperatures that are found on earth, quarks and gluons are confined inside hadrons. However, it is predicted that at very high energies QCD will have a transition into a deconfined phase. In order to reach such high temperatures in the laboratory heavy ions are collided at high energies. One of the biggest surprises was that the time evolution of the fireball created in these experiments is very well described by ideal hydrodynamics. Indeed the matter created in heavy ion collisions is the most perfect liquid ever known. In the limit in which the size of the ion is infinitely large and when looking at particles at midrapidity, the hydrodynamics equation can be solved analytically (when the viscosity is zero) following what is called Bjorken evolution. However, in the case these conditions are not meet the only possibility is to solve the hydrodynamics equation numerically. The task in this bachelor thesis is to investigate the applicability of the different codes available in the literature and understand for which initial conditions and which values of the viscosity there is an important departure from Bjorken evolution.*Quarkonium dissociation at the Large Hadron Collider*
Ongoing experiments at the Large Hadron Collider (LHC) at CERN explore heavy ion collisions in an unprecedented energy window, with lead nuclei colliding now at a centre-of-mass energy of 2.76 TeV per colliding nucleon pair. The aim of these experimental investigations is the formation of the Quark Gluon Plasma (QGP), a new state of matter that should originate when nuclear matter undergoes a phase transition from its normal hadronic state to a deconfined partonic phase. This transition is predicted by QCD, the theory of strong interactions, at a temperature of about 170 MeV. Such studies have important cosmological and astrophysical implications, given that we believe that the QGP was existing in the early universe, filling all space a few microseconds after the Big-Bang.*Hybrid Masses in QCD*
Hybrid mesons are states formed by a quark and an antiquark and some gluonic degrees of freedom. They are searched at particle accelerator experiments and some candidates for heavy hybrids have recently been observed at B-factories.-
*Van der Waals interaction in QCD*
In QuantumChromoDynamics (QCD, the theory of strong interactions) the interaction arising from the exchange of two or more gluons between color singlet hadrons is contained in gluonic van der Waals potentials, in a way similar to the Van der Waals interaction among molecules. The color van der Waals potential is expected to be the dominant contribution in the case of the interaction of heavy quarkonium states with hadrons or nuclei at low energies. *Thermal production of dark matter*

Dark matter should account for about the 21% of the matter components, but it cannot be explained inside the Standard model of particle physics. Part of the solution of the problem of dark matter may come from right-handed neutrinos. In some scenarios of physics beyond the Standard Model dark matter is accounted for by one generation of right-handed neutrinos. An important ingredient of these scenarios is the production rate of right-handed neutrinos from the thermal medium made by the Standard Model particles. In the literature there are diverse results on this issue and scope of the thesis is to analyze and review the state of the art.

**Advisors:**Prof. N. Brambilla; PD Dr. A. Vairo; Dr. M. Escobedo; S. Biondini.*Quirky Composite Dark Matter*

"Quirky dark matter" is a proposed new dark matter candidate, a scalar baryonic bound state of a new non-abelian force that becomes strong at the electroweak scale. The bound state is made of chiral quirks: new fermions, acquiring mass from the Higgs mechanism. A novel method to search for quirky dark matter is to look for a gamma-ray “dark line” spectroscopic feature in galaxy clusters that result from the quirky Lyman-alpha or quirky hyperfine transitions.

Scope of the thesis is to address the quantum mechanical energy spectrum calculation of the quirky dark matter solving a Schroedinger-like equation with a quirkcolor force potential. Prospects for direct and indirect detection of quirky dark matter will be discussed in relation to experimental data.

**Advisor:**Prof. N. Brambilla; PD Dr. A. Vairo; Jacopo Ghiglieri*String Contribution to the Quark-Antiquark Potentials*

The dynamics of heavy quarkonium systems in the strong coupling regime reduces to a quantum mechanical problem with a number of potentials which may be organized in powers of 1/m, m being the heavy quark mass. The potentials must be calculated non-perturbatively, for instance in lattice QCD. It is well known that the long distance behavior of the static potential is well reproduced by an effective string theory. Scope of this thesis is to address the calculation of the long distance behaviour of the 1/m and 1/m^2 suppressed potential using an effective string description. This amounts to establishing a correspondence between the fields and the string degrees of freedom, solving some string differential equations and calculating the corresponding Green's functions and potentials. A comparison of the obtained potential with the lattice data is planned.

**Advisors:**Prof. N. Brambilla; PD Dr. A. Vairo; Piotr Pietrulewicz

**Advisors:**Prof. N. Brambilla

**Advisors:**Prof. N. Brambilla

**Advisors:**Prof. N. Brambilla; PD Dr. A. Vairo; Dr. Miguel Escobedo; Simoe Biondini

Heavy quarkonium dissociation is one of the phenomena used to obtain information about the quark-gluon plasma formation in heavy-ion collisions. Recent theory results based on effective field theories gives a description of this phenomenon inside a Schrödinger equation with a complex potential. The aim of this thesis is to study the correct way of defining the eigenfunctions and eigenvalues for this problem and write a computer program able to find them numerically at different temperatures.

**Advisors:**Prof. N. Brambilla; PD Dr. A. Vairo; Dr. Miguel Escobedo

The properties of these states are directly related to the nonperturbative nature of low energy QCD and to the confinement mechanism of strong interactions. Lattice calculations of the hybrids' static energies are available. The scope of the thesis is to use these lattice hybrids curves together with elementary notions of nonrelativistic effective field theories to solve numerically an appropriate Schrödinger equation and obtain information on the masses and transitions of the hybrids.

**Advisors:**Prof. N. Brambilla; PD Dr. A. Vairo; Matthias Berwein

The properties of quarkonia in a nuclear medium are still poorly known, yet they are very important for the description of photo- and hadro-production of quarkonium on nuclear targets (at the planned experiments at the FAIR facility at GSI) as well as for the diagnostic of hadronic final states in heavy ion collisions at the Large Hadron Collider at CERN. The aim of this thesis is to study quarkonium-quarkonium Van der Waals interactions using a novel nonrelativistic effective field theory of QCD and study the related impact on quarkonium-nuclei interaction.

**Advisors:**Prof. N. Brambilla; PD Dr. A. Vairo; Dr. M. Escobedo; Vladyslav Shtabovenko