QCD at non-zero baryon density is expected to have a critical point where the finite temperature crossover at zero density turns into a first order phase transition. To identify this point, we use the canonical ensemble approach to scan the temperaturedensity plane through lattice QCD simulations with Wilson-type fermions. In order to scan a wide range of the phase diagram, we develop an algorithm, the ”winding number expansion method” (WNEM) to fix the numerical instability problem due to the discrete Fourier transform for calculating the projected determinant. For a given temperature, we measure the chemical potential as a function of the baryon number and look for the signal of a first order phase transition. We carry out simulations using clover fermions with mπ ≈ 800MeV on 63 × 4 lattices. As a benchmark, we run simulations for the four degenerate flavor case where we observe a clear signal of the first order phase transition. In the two flavor case we do not see any signal for temperatures as low as 0.83 Tc. To gauge the discretization errors, we also run a set of simulations using Wilson fermions and compare the results to those from the clover fermion. The three flavor case is close to realistic QCD with two light u and d quarks and one heavier s quark. Any hint of the existence of the first order phase transition and, particularly, its critical end point will be valuable for the planned relativistic heavy-ion experiments to search for such a point. In the three flavor case we found a clear signal for the first order phase transition, the critical point is located at a temperature of 0.93(2) Tc and a baryon chemical potential of 3.25(7) Tc. Since the quark mass in our present simulation is relatively heavy, we would like to repeat it with lighter quark masses and larger volumes.

O decaimento do potencial de superfície de um isolante carregado por um pulso rápido de descarga corona é estudado supondo-se densidade finita de armadilhas profundas, o que generaliza o cálculo anterior de Rudenko. Supõe-se que uma fração da carga depositada na superfície é instantaneamente injetada, obtendo- se o potencial como função do tempo, bem como o potencial residual. O comportamento assintótico do potencial é estudado para o caso em que toda a carga da superfície é\' instantaneamente injetada. são apresentados alguns gráficos do transiente,correspondentes a particulares valores dos parâmetros que levam a expressões mais simples / The decay of the surface pontential of a sample,corona charged by a pulse, is studied. It is assumed a finite density of deep traps,and this makes our calculation a generalization of previous work by Rudenko. It is supposed that a fraction of the charge deposited on the surface moves inside the sample and the potential as a function of the time is obtained as well as the residual potential. The asymptotic behavior of the potential is also obtained when alI the charge is injected. Those transients leading to simples mathematical expressions are shown in graphs

O decaimento do potencial de superfície de um isolante carregado por um pulso rápido de descarga corona é estudado supondo-se densidade finita de armadilhas profundas, o que generaliza o cálculo anterior de Rudenko. Supõe-se que uma fração da carga depositada na superfície é instantaneamente injetada, obtendo- se o potencial como função do tempo, bem como o potencial residual. O comportamento assintótico do potencial é estudado para o caso em que toda a carga da superfície é\' instantaneamente injetada. são apresentados alguns gráficos do transiente,correspondentes a particulares valores dos parâmetros que levam a expressões mais simples / The decay of the surface pontential of a sample,corona charged by a pulse, is studied. It is assumed a finite density of deep traps,and this makes our calculation a generalization of previous work by Rudenko. It is supposed that a fraction of the charge deposited on the surface moves inside the sample and the potential as a function of the time is obtained as well as the residual potential. The asymptotic behavior of the potential is also obtained when alI the charge is injected. Those transients leading to simples mathematical expressions are shown in graphs

L'étude du diagramme des phases de la Chromodynamique Quantique (QCD) et des transitons associées (déconfinement et restoration de la symétrie chirale) représentent des défis majeurs de la Physique moderne et nombreuses sont les approches théoriques qui visent à en sonder les multiples facettes. Du fait de l'intensité de l'interaction forte dans les régimes d’énergie pertinents pour les transitions susmentionnées, ces approches sont en général de nature non-perturbative, la théorie des perturbations étant réputée inapplicable à ces échelles. Il est, cependant, bien établi que le point de départ de la théorie usuelle des perturbations, basée sur la procédure de fixation de jauge de Faddeev-Popov, est ambigu à ces échelles (ambiguïté de Gribov). Dans ce contexte, une approche perturbative modifiée, basée sur le Lagrangien de Curci et Ferrari, a été proposée, via l’ajout phénoménologique d'un terme de masse effectif pour le gluon en jauge de Landau. Cette approche a été testée avec succès, notamment dans sa capacité à reproduire les fonctions de corrélation de la théorie Yang-Mills (et QCD dans la limite de quarks lourds) et la thermodynamique à temperature et potentiel chimique non nuls.Dans cette thèse, nous avons testé la robustesse de ces résultats en évaluant la structure de phase de la QCD avec quarks lourds au deuxième ordre de la théorie des perturbations dans le modèle de Curci-Ferrari et en comparant nos résultats à ceux d'approches nonperturbatives. Nos résultats indiquent que, dans ce régime de quarks lourds, le diagramme de phases est contrôlée perturbativement. Nous avons égalementétendu notre étude au cas de la QCD avec quarks légers en utilisant un schéma de resommation qui exploite la présence de petits paramètres dans le régime infrarouge de la QCD. Dans le secteur des quarks, cette démarche donne lieu à la resommation des fameux diagrammes dits "arc-en-ciel”. Ici, nous généralisons ce formalisme à temperature et densité non nulles et en presence d'un champ de fond gluonique. Nous réalisons une toute première étude qualitative des prédictions du modèle CF concernant l’existence possible d’un point critique dans le diagramme de phases de QCD sur la base d’une version simplifiée des équations générales ainsi obtenues. / Unravelling the structure of the QCD phase diagram and its many aspects such as (de)confinementand chiral symmetry breaking, is one of the big challenges of modern theoretical physics, and manyapproaches have been devised to this aim. Since perturbation theory is believed to cease feasibilityat low energy scales, these approaches treat the relevant order parameters, the quark condensate andthe Polyakov loop, non-perturbatively. However, it is also well-established that the starting point forperturbation theory, the Fadeev-Popov gauge-fixing procedure, is inherently ill-defined in the infrareddue to the presence of Gribov ambiguities. In this context, a modified perturbative approach based onthe Curci-Ferrari Lagrangian has been introduced, where a phenomenologically motivated effective gluonmass term is added to the Landau gauge-fixed action. Prior to the beginning of the thesis, this approach hasproven extremely fruitful in its descriptions of (unquenched) Yang-Mills correlation functions and thermodynamics at (non)zero temperature and density.Throughout the thesis we extend this analysis to the entire phase structure of QCD and QCD-liketheories and test the validity of the model in various regimes of interest. For instance, to further aprevious one-loop study in the regime of heavy quark masses, we have computed the two-loop quarksunset diagram in the presence of a non-trivial gluon background in a finite temperature and densitysetting. We come to the conclusion that the physics underlying center symmetry is well-described by our perturbative model with a seemingly robust weak-coupling expansion scheme. Furthermore, we study the regime of light quarks by means of a recently proposed resummation scheme which exploits the presence of actual small parameters in the Curci-Ferrari description of infrared QCD. In the quark sector, this leads to the renown rainbow equations. We extend this first-principle setup to nonzero temperature, chemical potential, and gluon background. We perform a first qualitative analysis of the prediction of the model concerning the possible existence of a critical endpoint in the QCD phase diagram by using a simplified version of these general equations.

Das Zusammenspiel von Hadronen und Modifikationen ihrer Eigenschaften auf der einen Seite und spontaner chiraler Symmetriebrechung und Restauration auf der anderen Seite wird untersucht. Es werden die QCD Summenregeln für D und B Mesonen in kalter Materie berechnet. Wir bestimmen die Massenaufspaltung von D - D-bar und B - B-bar Mesonen als Funktion der Kerndichte und untersuchen den Einfluss verschiedener Kondensate in der Näherung linearer Dichteabhängigkeit. Die Analyse beinhaltet ebenfalls D_s und D^*_0 Mesonen. Es werden QCD Summenregeln für chirale Partner mit offenem Charmfreiheitsgrad bei nichtverschwindenden Nettobaryonendichten und Temperaturen vorgestellt. Es wird die Differenz sowohl von pseudoskalaren und skalaren Mesonen, als auch von Axialvektor- und Vektormesonen betrachtet und die entsprechenden Weinberg-Summenregeln hergeleitet. Basierend auf QCD Summenregeln werden die Auswirkungen eines Szenarios auf das rho Meson untersucht, in dem alle chiral ungeraden Kondensate verschwinden wohingegen die chiral symmetrischen Kondensate ihren Vakuumwert behalten. Die komplementären Folgerungen einer Massenverschiebung und Verbreiterung der rho Mesonanregung werden diskutiert. Ein alternativer Zugang basierend auf gekoppelten Dyson-Schwinger- und Bethe-Salpeter-Gleichungen für Quarkbindungszustände wird untersucht. Zu diesem Zwecke wird die analytische Struktur des Quarkpropagators in der komplexen Ebene numerisch untersucht und die Möglichkeit getestet die Anwendbarkeit auf den Sektor der schwer-leicht Quark Systeme im skalaren und pseudoskalaren Kanal, wie dem D Meson, durch Variation des Impulsteilungsparameters zu erweitern. Die Lösungen der Dyson-Schwinger-Gleichung in der Wigner-Weyl-Phase der chiralen Symmetrie bei nichtverschwindenden Stromquarkmassen wird benutzt um den Fall einer expliziten Symmetriebrechung ohne spontane Symmetriebrechung zu untersuchen. / The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D - D-bar and B - B-bar mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D_s and $D^*_0 mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the rho meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.

Das Zusammenspiel von Hadronen und Modifikationen ihrer Eigenschaften auf der einen Seite und spontaner chiraler Symmetriebrechung und Restauration auf der anderen Seite wird untersucht. Es werden die QCD Summenregeln für D und B Mesonen in kalter Materie berechnet. Wir bestimmen die Massenaufspaltung von D - D-bar und B - B-bar Mesonen als Funktion der Kerndichte und untersuchen den Einfluss verschiedener Kondensate in der Näherung linearer Dichteabhängigkeit. Die Analyse beinhaltet ebenfalls D_s und D^*_0 Mesonen. Es werden QCD Summenregeln für chirale Partner mit offenem Charmfreiheitsgrad bei nichtverschwindenden Nettobaryonendichten und Temperaturen vorgestellt. Es wird die Differenz sowohl von pseudoskalaren und skalaren Mesonen, als auch von Axialvektor- und Vektormesonen betrachtet und die entsprechenden Weinberg-Summenregeln hergeleitet. Basierend auf QCD Summenregeln werden die Auswirkungen eines Szenarios auf das rho Meson untersucht, in dem alle chiral ungeraden Kondensate verschwinden wohingegen die chiral symmetrischen Kondensate ihren Vakuumwert behalten. Die komplementären Folgerungen einer Massenverschiebung und Verbreiterung der rho Mesonanregung werden diskutiert. Ein alternativer Zugang basierend auf gekoppelten Dyson-Schwinger- und Bethe-Salpeter-Gleichungen für Quarkbindungszustände wird untersucht. Zu diesem Zwecke wird die analytische Struktur des Quarkpropagators in der komplexen Ebene numerisch untersucht und die Möglichkeit getestet die Anwendbarkeit auf den Sektor der schwer-leicht Quark Systeme im skalaren und pseudoskalaren Kanal, wie dem D Meson, durch Variation des Impulsteilungsparameters zu erweitern. Die Lösungen der Dyson-Schwinger-Gleichung in der Wigner-Weyl-Phase der chiralen Symmetrie bei nichtverschwindenden Stromquarkmassen wird benutzt um den Fall einer expliziten Symmetriebrechung ohne spontane Symmetriebrechung zu untersuchen. / The interplay of hadron properties and their modification in an ambient nuclear medium on the one hand and spontaneous chiral symmetry breaking and its restoration on the other hand is investigated. QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D - D-bar and B - B-bar mesons as a function of the nuclear matter density and investigate the impact of various condensates in linear density approximation. The analysis also includes D_s and $D^*_0 mesons. QCD sum rules for chiral partners in the open-charm meson sector are presented at nonzero baryon net density or temperature. We focus on the differences between pseudo-scalar and scalar as well as vector and axial-vector D mesons and derive the corresponding Weinberg type sum rules. Based on QCD sum rules we explore the consequences of a scenario for the rho meson, where the chiral symmetry breaking condensates are set to zero whereas the chirally symmetric condensates remain at their vacuum values. The complementarity of mass shift and broadening is discussed. An alternative approach which utilizes coupled Dyson-Schwinger and Bethe-Salpter equations for quark-antiquark bound states is investigated. For this purpose we analyze the analytic structure of the quark propagators in the complex plane numerically and test the possibility to widen the applicability of the method to the sector of heavy-light mesons in the scalar and pseudo-scalar channels, such as the D mesons, by varying the momentum partitioning parameter. The solutions of the Dyson-Schwinger equation in the Wigner-Weyl phase of chiral symmetry at nonzero bare quark masses are used to investigate a scenario with explicit but without dynamical chiral symmetry breaking.