arXiv subjects

Jens O. Andersen

Publications and source records attributed to Jens O. Andersen.

At least 55 records · Page 3Linked to original sources

arXiv2014

Equation of State for QCD at finite temperature and density. Resummation versus lattice data

The perturbative series for finite-temperature field theories has very poor convergence properties and one needs a way to reorganize it. In this talk, I review two ways of reorganizing the perturbative series for field theories at finite temperature and chemical potential, namely hard-thermal-loop perturbation theory (HTLpt) and dimensional reduction (DR). I will present results for the pressure, trace anomaly, speed of sound and the quark susceptibilities from a 3-loop HTLpt calculation and for the quark susceptibilities using DR at four loops. A careful comparison with available lattice data shows good agreement for a number of physical quantities.

hep-ph↗

arXiv2014

Inverse magnetic catalysis and regularization in the quark-meson model

Motivated by recent work on inverse magnetic catalysis at finite temperature, we study the quark-meson model using both dimensional regularization and a sharp cutoff. We calculate the critical temperature for the chiral transition as a function of the Yukawa coupling in the mean-field approximation varying the renormalization scale and the value of the ultraviolet cutoff. We show that the results depend sensitively on how one treats the fermionic vacuum fluctuations in the model and in particular on the regulator used. Finally, we explore a $B$-dependent transition temperature for the Polyakov loop potential $T_0(B)$ using the functional renormalization group. These results show that even arbitrary freedom in the function $T_0(B)$ does not allow for a decreasing chiral transition temperature as a function of $B$. This is in agreement with previous mean-field calculations.

hep-ph↗

arXiv2014

Three loop HTL perturbation theory at finite temperature and chemical potential

In this proceedings contribution we present a recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculation of the thermodynamic potential for a finite temperature and chemical potential system of quarks and gluons. We compare the resulting pressure, trace anomaly, and diagonal/off-diagonal quark susceptibilities with lattice data. We show that there is good agreement between the three-loop HTLpt analytic result and available lattice data.

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arXiv2014

Effective Lagrangians for quantum many-body systems

The low-energy and low-momentum dynamics of systems with a spontaneously broken continuous symmetry is dominated by the ensuing Nambu-Goldstone bosons. It can be conveniently encoded in a model-independent effective field theory whose structure is fixed by symmetry up to a set of effective coupling constants. We construct the most general effective Lagrangian for the Nambu-Goldstone bosons of spontaneously broken global internal symmetry up to the fourth order in derivatives. Rotational invariance and spatial dimensionality of one, two or three are assumed in order to obtain compact explicit expressions, but our method is completely general and can be applied without modifications to condensed matter systems with a discrete space group as well as to higher-dimensional theories. The general low-energy effective Lagrangian for relativistic systems follows as a special case. We also discuss the effects of explicit symmetry breaking and classify the corresponding terms in the Lagrangian. Diverse examples are worked out in order to make the results accessible to a wide theoretical physics community.

hep-ph↗

arXiv2014

Three-loop HTLpt thermodynamics at finite temperature and chemical potential

We calculate the three-loop thermodynamic potential of QCD at finite temperature and chemical potential(s) using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The resulting analytic thermodynamic potential allows us to compute the pressure, energy density, and entropy density of the quark-gluon plasma. Using these we calculate the trace anomaly, speed of sound, and second-, fourth-, and sixth-order quark number susceptibilities. For all observables considered we find good agreement between our three-loop HTLpt calculations and available lattice data for temperatures above approximately 300 MeV.

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arXiv2014

Three-loop HTLpt Pressure and Susceptibilities at Finite Temperature and Density

We present results of a three-loop hard-thermal-loop perturbation theory calculation of the thermodynamical potential of a finite temperature and baryon chemical potential system of quarks and gluons. We compare the resulting pressure and diagonal quark susceptibilities with available lattice data. We find reasonable agreement between our analytic results and lattice data at both zero and finite chemical potential.

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arXiv2013

Equation of State of hot and dense QCD: Resummed perturbation theory confronts lattice data

We perform a detailed analysis of the predictions of resummed perturbation theory for the pressure and the second-, fourth-, and sixth-order diagonal quark number susceptibilities in a hot and dense quark-gluon plasma. First, we present an exact one-loop calculation of the equation of state within hard-thermal-loop perturbation theory (HTLpt) and compare it to a previous one-loop HTLpt calculation that employed an expansion in the ratios of thermal masses and the temperature. We find that this expansion converges reasonably fast. We then perform a resummation of the existing four-loop weak coupling expression for the pressure, motivated by dimensional reduction. Finally, we compare the exact one-loop HTLpt and resummed dimensional reduction results with state-of-the-art lattice calculations and a recent mass-expanded three-loop HTLpt calculation.

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arXiv2013

Chiral and deconfinement transitions in a magnetic background using the functional renormalization group with the Polyakov loop

We use the Polyakov loop coupled quark-meson model to approximate low energy QCD and present results for the chiral and deconfinement transitions in the presence of a constant magnetic background $B$ at finite temperature $T$ and baryon chemical potential $μ_B$. We investigate effects of various gluoni potentials on the deconfinement transition with and without a fermionic backreaction at finite $B$. Additionally we investigate the effect of the Polyakov loop on the chiral phase transition, finding that magnetic catalysis at low $μ_B$ is present, but weakened by the Polyakov loop.

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arXiv2013

Two-color QCD in a strong magnetic field: The role of the Polyakov loop

We study two-color QCD in an external magnetic backround at finite temperature using the Polyakov-loop extended two-flavor two-color NJL model. At T=0, the chiral condensate is calculated and it is found to increase as a function of the magnetic field $B$. In the chiral limit the deconfinement transition lies below the chiral transition for nonzero magnetic fields $B$. At the physical point, the two transitions seem to coincide for field strengths up to $|qB|\approx 5m_π^2$ whereafter they split. The splitting between the two increases as a function of $B$ in both the chiral limit and at the physical point. In the range from zero magnetic field and $|qB|=20 m_π^2$, the transition temperature for the chiral transition increases by approximately 35 MeV, while the transition temperature for deconfinement is essentially constant.

hep-ph↗

arXiv2013

Quark number susceptibilities from resummed perturbation theory

We evaluate the second and fourth order quark number susceptibilities in hot QCD using two variations of resummed perturbation theory. On one hand, we carry out a one-loop calculation within hard-thermal-loop perturbation theory, and on the other hand perform a resummation of the four-loop finite density equation of state derived using a dimensionally reduced effective theory. Our results are subsequently compared with recent high precision lattice data, and their agreement thoroughly analyzed.

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arXiv2012

The chiral transition in a magnetic background: Finite density effects and the functional renormalization group

We compute the phase diagram of the quark-meson model at finite temperature, finite baryon chemical potential $μ_B=3μ$ and constant external magnetic field $B$, using the functional renormalization group. Our results show that the critical temperature increases as a function of $B$ at $μ=0$, but for values $μ$ larger than about 210-225 MeV, the opposite behavior is realized. As the magnetic field increases, the critical point $(T^*,μ^*)$ moves from large $μ$, small $T$ towards small $μ$, larger $T$ in the $μ$--$T$ phase diagram.

hep-ph↗

arXiv2012

Thermal pions in a magnetic background

We use chiral perturbation theory for SU(2) to compute the leading corrections to the thermal mass of the pions and the pion decay constant in the presence of the magnetic field in a low-temperature expansion. The magnetic field gives rise to a splitting between $M_{π^0}$ and $M_{π^{\pm}}$ as well as $F_{π^0}$ and $F_{π^{\pm}}$. We also calculate the free energy and the quark condensate to next-to- leading order. The results suggest that the critical temperature $T_c$ for the chiral transition is larger in the presence of a constant magnetic field, in agreement with most model calculations but in disagreement with recent lattice calculations.

hep-ph↗

arXiv2012

Chiral perturbation theory in a magnetic background - finite-temperature effects

We consider chiral perturbation theory for SU(2) at finite temperature $T$ in a constant magnetic background $B$. We compute the thermal mass of the pions and the pion decay constant to leading order in chiral perturbation theory in the presence of the magnetic field. The magnetic field gives rise to a splitting between $M_{π^0}$ and $M_{π^{\pm}}$ as well as between $F_{π^0}$ and $F_{π^{\pm}}$. We also calculate the free energy and the quark condensate to next-to-leading order in chiral perturbation theory. Both the pion decay constants and the quark condensate are decreasing slower as a function of temperature as compared to the case with vanishing magnetic field. The latter result suggests that the critical temperature $T_c$ for the chiral transition is larger in the presence of a constant magnetic field. The increase of $T_c$ as a function of $B$ is in agreement with most model calculations but in disagreement with recent lattice calculations.

hep-ph↗

arXiv2011

Chiral transition in a magnetic field and at finite baryon density

We consider the quark-meson model with two quark flavors in a constant external magnetic field $B$ at finite temperature $T$ and finite baryon chemical potential $μ_B$. We calculate the full renormalized effective potential to one-loop order in perturbation theory. We study the system in the large-$N_c$ limit, where we treat the bosonic modes at tree level. It is shown that the system exhibits dynamical chiral symmetry breaking, i. e. that an arbitrarily weak magnetic field breaks chiral symmetry dynamically, in agreement with earlier calculations using the NJL model. We study the influence on the phase transition of the fermionic vacuum fluctuations. For strong magnetic fields, $|qB|\sim5m_π^2$ and in the chiral limit, the transition is first order in the entire $μ_B-T$ plane if vacuum fluctuations are not included and second order if they are included. At the physical point, the transition is a crossover for $μ_B=0$ with and without vacuum fluctuations.

hep-ph↗

arXiv2011

The QCD trace anomaly

In this brief report we compare the predictions of a recent next-to-next-to-leading order hard-thermal-loop perturbation theory (HTLpt) calculation of the QCD trace anomaly to available lattice data. We focus on the trace anomaly scaled by T^2 in two cases: N_f=0 and N_f=3. When using the canonical value of mu = 2 pi T for the renormalization scale, we find that for Yang-Mills theory (N_f=0) agreement between HTLpt and lattice data for the T^2-scaled trace anomaly begins at temperatures on the order of 8 T_c while when including quarks (N_f=3) agreement begins already at temperatures above 2 T_c. In both cases we find that at very high temperatures the T^2-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.

hep-ph↗

arXiv2011

Three-loop HTL QCD thermodynamics

The hard-thermal-loop perturbation theory (HTLpt) framework is used to calculate the thermodynamic functions of a quark-gluon plasma to three-loop order. This is the highest order accessible by finite temperature perturbation theory applied to a non-Abelian gauge theory before the high-temperature infrared catastrophe. All ultraviolet divergences are eliminated by renormalization of the vacuum, the HTL mass parameters, and the strong coupling constant. After choosing a prescription for the mass parameters, the three-loop results for the pressure and trace anomaly are found to be in very good agreement with recent lattice data down to $T \sim 2-3\,T_c$, which are temperatures accessible by current and forthcoming heavy-ion collision experiments.

hep-ph↗

arXiv2011

Functional renormalization group at finite density and Bose condensation

We discuss the functional renormalization group and pion condensation in the presence of a finite isospin chemical potential $μ_I$. We calculate the phase diagram as function of temperature $T$ and $μ_I$. While the exact effective average action is invariant under certain gauge transformations, the effective action in the local-potential approximation is not. As a consequence, the critical chemical potential $μ_I^c$ for Bose-Einstein condensation at T=0 is no longer equal to the mass of the condensing mode. We discuss possible solutions to this problem.

hep-ph↗

arXiv2011

The chiral phase transition and the role of vacuum fluctuations

We apply optimized perturbation theory to the quark-meson model at finite temperature T and quark chemical potential mu. The effective potential is calculated to one loop both in the chiral limit and at the physical point and used to study the chiral dynamics of two-flavor QCD. The critical temperature and the order of the phase transition depends heavily on whether or not one includes the bosonic and fermionic vacuum fluctuations in the effective potential. A full one-loop calculation in the chiral limit predicts a first-order transition for all values of mu. At the physical point, one finds a crossover in the whole $μ-T$ plane.

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