Master Courses & Projects

The dynamics of heavy-flavor particles in a thermal medium can be described by the Langevin equation, which incorporated several transport coefficients as parameters. To be respectful with the special relativity principles, a recent study has considered a causal version of the Langevin equation which requires an additional coefficient, the memory time [1]. In this project, the nature of the memory time will be studied from microscopic interactions of heavy particles. By applying the theory of hydrodynamic fluctuations, this parameter will be extracted for realistic systems performing numerical simulations.

[1] M.Rugieri et al. Phys.Rev.D 106 (2022) 3, 034032

The X(3872) is an exotic quarkonium state which can not be explained within the quark model. Several configurations have been proposed for the internal structure of this state, being the most popular ones the compact tetraquark and the hadronic molecule. Recently, the X(3872) has been observed in heavy-ion collisions, in which a hot QCD medium is created. Studying how the medium modifies the properties of the X(3872) we can obtain additional information that might allow us to determine whether this state is a tetraquark or a molecule. In this thesis, we are going to build on the results of Phys. Rev. D 107, 054014 that studied this mysterious bound state within the molecule approximation using an approach based on chiral perturbation theory. The goal is to obtain the finite temperature potential of the X(3872), allowing us to make phenomenological predictions. On one hand, we will be able to determine up to which temperatures the bound state solution is still valid. On the other hand, the wave function of the state can be used to analyze recombination within the coalescence model.

[1] Phys. Rev. D 107, 054014 (https://arxiv.org/abs/2211.01896), 

[2] Phys.Lett.B 854 (2024) 138760 (https://arxiv.org/abs/2401.10125)

In this work the student will focus on the pion-nucleon interaction, as parametrized by the SAID model, in all available partial waves [1,2]. This information will be used to reconstruct the asymptotic pair wave function and the final femtoscopy correlation function using the Koonin-Pratt formula [3]. The student will present a prediction of the p-pi+ and p-pi- correlation functions [4] including partial waves beyond L=0 (thus incorporating the prominent Delta resonances), and compare with the results of the Lednický approximation in s-wave. The use of scattering data (with asymptotic quantum states) into the correlation function will be compared against possible off-shell effects which take into account the complete wave function (not just asymptotically). The deviations will be analyzed as a function of the size of the source function, which weights the pair wave function around the origin or away from it.

[1] R.L. Workman et al., Parameterization dependence of T matrix poles and eigenphases from a fit to πN elastic scattering data, Phys.Rev.C 86 (2012) 035202, e-Print: 1204.2277 [hep-ph]

[2] JPAC Collaboration, https://www.jpac-physics.org/ 

[3] L. Fabbietti et al., Study of the Strong Interaction Among Hadrons with Correlations at the LHC, Annu. Rev. Nucl. Part. Sci. 2021. 71, 377:402 (2021) 

[4] Á. Peña, Meson-baryon femtoscopy studies in the S = 0 and S = −2 sectors using a T-matrix approach, Master thesis, Universitat de Barcelona (2024).

This project will employ the Polyakov-Nambu-Jona-Lasinio model of quarks to study the strong interaction and construct diquarks and baryons using few-body methods. Baryons will be modeled as bound states of a quark and a diquark, with the SU(3) flavor octet masses reproduced as a first benchmark. Then, the formalism will be extended to finite density to include medium corrections of diquark and baryon masses.

Since at some value of the chemical potential the diquarks can decay into quarks, their full spectral function will be incorporated into the calculation. The results will provide insight into how the masses of nucleons and other baryons are modified in baryon-rich environments such as neutron stars. This study is key in the refinement of the equation of state of the strong interaction by consistently including baryonic effects.

[1] Torres-Rincon, Aichelin, Phys.Rev.C 96 (2017) 4, 045205 https://arxiv.org/abs/1704.07858

[2] Torres-Rincon, Sintes, Aichelin, Phys.Rev.C 91 (2015) 6, 065206 https://arxiv.org/abs/1502.03459