arXiv subjects

Jens Braun

Publications and source records attributed to Jens Braun.

87 records · Page 5Linked to original sources

arXiv2010

N=1 Wess Zumino Model in d=3 at zero and finite temperature

Supersymmetric renormalization group (RG) flow equations for the effective superpotential of the three-dimensional Wess-Zumino model are derived at zero and non-zero temperature. This model with fermions and bosons interacting via a Yukawa term possesses a supersymmetric analogue of the Wilson-Fisher fixed-point. At zero temperature we determine the phase-transition line in coupling-constant space separating the supersymmetric from the non-supersymmetric phase. At finite temperature we encounter dimensional reduction from 3 to 2 dimensions in the infrared regime. We determine the finite-temperature phase diagram for the restoration of the global $Z_2$-symmetry and show that for temperatures above the $Z_2$ phase transition the pressure obeys the Stefan-Boltzmann law of a gas of massless bosons in 2+1 dimensions.

hep-th↗

arXiv2009

Quark Confinement from Color Confinement

We relate quark confinement, as measured by the Polyakov-loop order parameter, to color confinement, as described by the Kugo-Ojima/Gribov-Zwanziger scenario. We identify a simple criterion for quark confinement based on the IR behaviour of ghost and gluon propagators, and compute the order-parameter potential from the knowledge of Landau-gauge correlation functions with the aid of the functional RG. Our approach predicts the deconfinement transition in quenched QCD to be of first order for SU(3) and second order for SU(2) -- in agreement with general expectations. As an estimate for the critical temperature, we obtain T_c=284MeV for SU(3).

hep-th↗

arXiv2009

The QCD Phase Boundary from Quark-Gluon Dynamics

We study one-flavor QCD at finite temperature and chemical potential using the functional renormalization group. We discuss the chiral phase transition in QCD and its order with its underlying mechanism in terms of quarks and gluons and analyze the dependence of the phase transition temperature on small quark chemical potentials. Our result for the curvature of the phase boundary at small quark chemical potential relies on only a single input parameter, the value of the strong coupling at the Z mass scale.

hep-ph↗

arXiv2009

Finite-Size Scaling behavior in the O(4)-Model

The exact nature of the QCD phase transition has still not been determined conclusively, and there are contradictory results from lattice QCD simulations about the scaling behavior for two quark flavors. Ultimately, this issue can be resolved only by a careful scaling and finite-size scaling analysis of the lattice results. We use a renormalization group approach to obtain finite-size scaling functions for the O(4)-model, which are relevant for this analysis. Our results are applicable to Lattice QCD studies of the QCD phase boundary.

hep-ph↗

arXiv2009

Thermodynamics of QCD low-energy models and the derivative expansion of the effective action

We study the equation of state of a strongly interacting theory of relativistic bosons and chiral fermions in the vicinity and above the chiral phase transition temperature. Our model resembles presently used low-energy models of QCD in many ways, but its simplicity allows us to study systematically various approximation schemes by means of a derivative expansion. In particular, we compare the results for the phase transition temperature, equation of state and the thermal mass of the scalar fields obtained in various approximations. We find that the large-N_c approximation, being the zeroth order of our approximation, deviates significantly from approximation schemes in which effects of (Pseudo-) Goldstone modes have been taken into account, even at high temperatures and even if we allow for a finite explicit symmetry breaking. The important role of the (Pseudo-) Goldstone modes is also manifested in the phenomenon of "local order" which is missing in large-N_c studies.

hep-ph↗

arXiv2009

On the relation of quark confinement and chiral symmetry breaking

We study the phase diagram of QCD with the help of order parameters for chiral symmetry breaking and quark confinement. We also introduce a new order parameter for the confinement phase transition, which is related to the quark density. It is easily accessible by different theoretical approaches, such as functional approaches or lattice simulations. Its relation to the Polyakov loop expectation value is discussed and the QCD phase diagram is analysed. Our results suggest a close relation between the chiral and the confinement phase transition.

hep-ph↗

arXiv2009

Finite-size and confinement effects in spin-polarized trapped Fermi gases

We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different-species fermions in asymmetric traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization. Our findings contribute to understanding some experimental discrepancies in spin-polarized Fermi gases as finite-size and confinement effects.

cond-mat.other↗

arXiv2007

Scaling functions for the O(4)-model in d=3 dimensions

A non-perturbative Renormalization Group approach is used to calculate scaling functions for an O(4) model in d=3 dimensions in the presence of an external symmetry-breaking field. These scaling functions are important for the analysis of critical behavior in the O(4) universality class. For example, the finite-temperature phase transition in QCD with two flavors is expected to fall into this class. Critical exponents are calculated in local potential approximation. Parameterizations of the scaling functions for the order parameter and for the longitudinal susceptibility are given. Relations from universal scaling arguments between these scaling functions are investigated and confirmed. The expected asymptotic behavior of the scaling functions predicted by Griffiths is observed. Corrections to the scaling behavior at large values of the external field are studied qualitatively. These scaling corrections can become large, which might have implications for the scaling analysis of lattice QCD results.

hep-th↗

arXiv2007

Finite Size Scaling for the O(N) universality class from Renormalization Group Methods

The QCD phase diagram at finite temperature and density is a topic of considerable interest. Although much progress has been made in recent years, some open questions remain. Even at zero density, the order of the transition for two light flavors of fermions has not yet been conclusively established. While considerable evidence exists in favor of a second-order transition for massless quarks and a crossover for massive quarks, some recent results with two flavors of staggered fermions suggest a transition of first order. Since lattice simulations are performed in finite simulation volumes, actual phase transitions cannot be observed directly. Thus, finite-size scaling is a very useful tool in the analysis of lattice data. By comparing the scaling behavior of observables to the expected scaling properties, values of critical exponents can be confirmed and the order as well as the universality class of a transition can be established. In the comparison to lattice QCD results, the critical exponents and the universal scaling functions have been obtained mainly by means of lattice simulations of O(N) spin models, and results are usually restricted to the critical temperature or the point at which the susceptibilities peak. We propose to use a non-perturbative Renormalization Group method for this purpose. We have calculated the critical finite-size scaling behavior and the universal scaling functions for the three-dimensional O(4)-model for a wide range of temperatures and values of the symmetry breaking parameter. Our results are suitable for a comparison to lattice QCD results for the chiral susceptibility and the order parameter and can be used to check the consistency of the finite-size scaling behavior with that of the O(N) universality class.

hep-lat↗

arXiv2007

Finite-Size Scaling from the non-perturbative Renormalization Group

The phase diagram of QCD at finite temperature and density and the existence of a critical point are currently very actively researched topics. Although tremendous progress has been made, in the case of two light quark flavors even the order of the phase transition at zero density is still under discussion. Finite-size scaling is a powerful method for the analysis of phase transitions in lattice QCD simulations. From the scaling behavior, critical exponents can be tested and the order as well as the universality class of a phase transition can be established. This requires knowledge of the critical exponents and the scaling behavior. We use a non-perturbative Renormalization Group method to obtain critical exponents and the finite-size scaling functions for the O(4) universality class in three dimensions. These results are useful for a comparison to the actual scaling behavior in lattice QCD simulations with two flavors, as well as for an estimate of the size of the scaling region and the deviations from the expected scaling behavior.

hep-ph↗

arXiv2007

Running coupling at finite temperature and chiral symmetry restoration in QCD

We analyze the running gauge coupling at finite temperature for QCD, using the functional renormalization group. The running of the coupling is calculated for all scales and temperatures. At finite temperature, the coupling is governed by a fixed point of the 3-dimensional theory for scales smaller than the corresponding temperature. The running coupling can drive the quark sector to criticality, resulting in chiral symmetry breaking. Our results provide for a quantitative determination of the phase boundary in the plane of temperature and number of massless flavors. Using the experimental value of the coupling at the tau mass scale as the only input parameter, we obtain, e.g., for N_f=3 massless flavors a critical temperature of T_cr ~ 148 MeV in good agreement with lattice simulations.

hep-ph↗

arXiv2006

Chiral Phase Boundary of QCD from the Functional Renormalization Group

We show how the functional renormalization group can be applied to a study of chiral symmetry breaking in QCD. We discuss the running gauge coupling at finite temperature for QCD. For scales smaller than the corresponding temperature, the coupling is governed by a fixed point of the 3-dimensional theory. Chiral symmetry breaking is approached if the running coupling drives the quark sector to criticality. We analyze the phase boundary in the plane of temperature and number of flavors. For small flavor-numbers, we find good agreement with lattice results. For flavor numbers near the critical flavor number, we find that the scaling of the critical temperature is determined by the zero-temperature IR critical exponent of the running coupling.

hep-ph↗

arXiv2006

Effects of the Running of the QCD Coupling on the Energy Loss in the Quark-Gluon Plasma

Finite temperature modifies the running of the QCD coupling alpha_s(k,T) with resolution k. After calculating the thermal quark and gluon masses selfconsistently, we determine the quark-quark and quark-gluon cross sections in the plasma based on the running coupling. We find that the running coupling enhances these cross sections by factors of two to four depending on the temperature. We also compute the energy loss dE/dx of a high-energy quark in the plasma as a function of temperature. Our study suggests that, beside t-channel processes, inverse Compton scattering is a relevant process for a quantitative understanding of the energy loss of an incident quark in a hot plasma.

hep-ph↗

arXiv2006

Chiral phase boundary of QCD at finite temperature

We analyze the approach to chiral symmetry breaking in QCD at finite temperature, using the functional renormalization group. We compute the running gauge coupling in QCD for all temperatures and scales within a simple truncated renormalization flow. At finite temperature, the coupling is governed by a fixed point of the 3-dimensional theory for scales smaller than the corresponding temperature. Chiral symmetry breaking is approached if the running coupling drives the quark sector to criticality. We quantitatively determine the phase boundary in the plane of temperature and number of flavors and find good agreement with lattice results. As a generic and testable prediction, we observe that our underlying IR fixed-point scenario leaves its imprint in the shape of the phase boundary near the critical flavor number: here, the scaling of the critical temperature is determined by the zero-temperature IR critical exponent of the running coupling.

hep-ph↗

arXiv2004

Linking the Quark Meson Model with QCD at High Temperature

We model the transition of a system of quarks and gluons at high energies to a system of quarks and mesons at low energies in a consistent renormalization group approach. Flow equations interpolate between the physics of the high-temperature degrees of freedom and the low-temperature dynamics at a scale of 1 GeV. We also discuss the dependence of the equation of state on baryon density and compare our results with recent lattice gauge simulations.

hep-ph↗