arXiv subjects

Jens O. Andersen

Publications and source records attributed to Jens O. Andersen.

At least 37 records · Page 2Linked to original sources

arXiv2020

Quark and pion condensates at finite isospin density in chiral perturbation theory

In this paper, we consider two-flavor QCD at zero temperature and finite isospin chemical potential ($μ_I$) using a model-independent analysis within chiral perturbation theory at next-to-leading order. We calculate the effective potential, the chiral condensate and the pion condensate in the pion-condensed phase at both zero and nonzero pionic source. We compare our finite pionic source results for the chiral condensate and the pion condensate with recent (2+1)-flavor lattice QCD results and find that they are in excellent agreement.

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arXiv2020

Pion and kaon condensation at zero temperature in three-flavor $χ$PT at nonzero isospin and strange chemical potentials at next-to-leading order

We consider three-flavor chiral perturbation theory ($χ$PT) at zero temperature and nonzero isospin ($μ_{I}$) and strange ($μ_{S}$) chemical potentials. The effective potential is calculated to next-to-leading order (NLO) in the $π^{\pm}$-condensed phase, the $K^{\pm}$-condensed phase, and the $K^0/\bar{K}^0$-condensed phase. It is shown that the transitions from the vacuum phase to these phases are second order and take place when, $|μ_I|=m_π$, $|{1\over2}μ_I+μ_S|=m_K$, and $|-{1\over2}μ_I+μ_S|=m_K$, respectively at tree level and remains unchanged at NLO. The transition between the two condensed phases is first order. The effective potential in the pion-condensed phase is independent of $μ_S$ and in the kaon-condensed phases, it only depends on the combinations $\pm{1\over2}μ_I+μ_S$ and not separately on $μ_I$ and $μ_S$. We calculate the pressure, isospin density and the equation of state in the pion-condensed phase and compare our results with recent $(2+1)$-flavor lattice QCD data. We find that the three-flavor $χ$PT results are in good agreement with lattice QCD for $μ_I<200$ MeV, however for larger values $χ$PT produces values for observables that are consistently above lattice results. For $μ_I>200$ MeV, the two-flavor results are in better agreement with lattice data. Finally, we consider the observables in the limit of very heavy $s$-quarks, where they reduce to their two-flavor counterparts with renormalized couplings. The disagreement between the predictions of two and three flavor $χ$PT can largely be explained by the differences in the experimental values of the low-energy constants.

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arXiv2020

QCD at finite isospin density: chiral perturbation theory confronts lattice data

We consider the thermodynamics of three-flavor QCD in the pion-condensed phase at nonzero isospin chemical potential ($μ_I$) and vanishing temperature using chiral perturbation theory in the isospin limit. The transition from the vacuum phase to a superfluid phase with a Bose-Einstein condensate of charged pions is shown to be second order and takes place at $μ_I=m_π$. We calculate the pressure, isospin density, and energy density to next-to-leading order in the low-energy expansion. Our results are compared with recent high-precision lattice simulations as well as previously obtained results in two-flavor chiral perturbation theory. The agreement between the lattice results and the predictions from three-flavor chiral perturbation theory is very good for $μ_I<200$ MeV. For larger values of $μ_I$, the agreement between lattice data and the two-flavor predictions is surprisingly good and better than with the three-flavor predictions. Finally, in the limit $m_{s}\gg m_{u}=m_{d}$, we show that the three-flavor observables reduce to the two-flavor observables with renormalized parameters. The disagreement between the results for two-flavor and three-flavor $χ$PT can largely be explained by the differences in the measured low-energy constants.

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arXiv2019

Two-flavor chiral perturbation theory at nonzero isospin: Pion condensation at zero temperature

In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at next-to-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state. We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2+1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in $χ$PT.

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arXiv2019

Thermodynamics and phase diagrams of Polyakov-loop extended chiral models

We study the thermodynamics and phase diagrams of two-flavor quantum chromodynamics using the Polyakov-loop extended quark-meson (PQM) model and the Pisarski-Skokov chiral matrix ($χM$) model. At temperatures up to $T\approx2T_c$ and baryon chemical potentials up to $μ_B=400\ \rm{MeV}$, both models show reasonable agreement with the pressure, energy density, and interaction measure as calculated on the lattice. The Polyakov loop is found to rise significantly faster with temperature in models than on the lattice. In the low-temperature and high baryon density regime, the two models predict different states of matter; The PQM model predicts a confined and chirally restored phase, while the $χM$ model predicts a deconfined and chirally restored phase. At finite isospin density and zero baryon density, the onset of pion condensation at $T=0$ is at $μ_I={1\over2}m_π$, and the transition is second order at all temperatures. The transition temperature for pion condensation coincides with that of the chiral transition for values of the isospin chemical potential larger than approximately $110\ \rm{MeV}$. In the $χM$ model they also coincide with the transition temperature for deconfinement. The results are in good overall agreement with recent lattice simulations of the $μ_I$--$T$ phase diagram.

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arXiv2018

Nonperturbative Analysis of the Electroweak Phase Transition in the Two Higgs Doublet Model

We perform a nonperturbative study of the electroweak phase transition (EWPT) in the two Higgs doublet model (2HDM) by deriving a dimensionally reduced high-temperature effective theory for the model, and matching to known results for the phase diagram of the effective theory. We find regions of the parameter space where the theory exhibits a first-order phase transition. In particular, our findings are consistent with previous perturbative results suggesting that the primary signature of a first-order EWPT in the 2HDM is $m_{A_0} > m_{H_0} + m_Z$.

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arXiv2018

Pion condensation and phase diagram in the Polyakov-loop quark-meson model

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the $μ_I$--$T$ plane where $μ_I$ is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At $T=0$, the onset of pion condensation is at $μ_I={1\over2}m_π$ in accordance with exact results. The phase transition to a Bose-condensed phase is of second order for all values of $μ_I$ and in the $O(2)$ universality class. The chiral critical line joins the critical line for pion condensation at a point whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of $μ_I$ these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken $O(2)$ symmetry. We compare our results with recent lattice simulations and find overall good agreement.

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arXiv2018

Pion condensation and QCD phase diagram at finite isospin density

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study 1) the possibility of inhomogeneous chiral condensates and its competition with a homogeneous pion condensate in the $μ$--$μ_I$ plane at $T=0$ and 2) the phase diagram in the $μ_I$--$T$ plane. In the $μ$--$μ_I$ plane, we find that an inhomogeneous chiral condensate only exists for pion masses lower that 37.1 MeV and does not coexist with a homogeneous pion condensate. In the $μ_I$--$T$ plane, we find that the phase transition to a Bose-condensed phase is of second order for all values of $μ_I$ and we find that there is no pion condensation for temperatures larger than approximately 187 MeV. The chiral critical line joins the critical line for pion condensation at a point, whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of $μ_I$ these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken $O(2)$ symmetry. We compare our results with recent lattice simulations and find overall good agreement

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arXiv2018

Bose-Einstein condensation and pion stars

Pion stars consisting of Bose-Einstein condensed charged pions have recently been proposed as a new class of compact stars. We use the two-particle irreducible effective action to leading order in the $1/N$-expansion to describe charged and neutrals pions as well as the sigma particle. Tuning the parameters in the Lagrangian correctly, the onset of Bose-Einstein condesation of charged pions is exactly at $μ_I=m_π$, where $μ_I$ is the isospin chemical potential. We calculate the pressure, energy density, and equation of state, which are used as input to the Tolman-Oppenheimer-Volkov equations. Solving these equations, we obtain the mass radius-relation for pion stars. Global electric charge neutrality is ensured by adding the contribution to the pressure and energy density from a gas of free relativistic leptons. We compare our results with those of recent lattice simulations and find good agreement. The masses of the pion stars are up to approximately 200 solar masses while the corresponding radii are of the order of $10^5$ km.

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arXiv2018

Chiral density wave versus pion condensation at finite density

The quark-meson model is often used as an effective low-energy model for QCD to study the chiral transition at finite temperature $T$, baryon chemical potential $μ_B$, and isospin chemical potential $μ_I$. The parameters of the model are determined by matching the meson and quark masses, as well as the pion decay constant to their physical values using the on-shell and modified minimal subtraction schemes. In this paper, we study the possibility of different phases at zero temperature. In particular, we investigate the competition between an inhomogeneous chiral condensate and a pion condensate. For the inhomogeneity, we use a chiral-density wave ansatz. For a sigma mass of $600$ MeV, we find that an inhomogeneous chiral condensate exist only for pion masses below approximately 37 MeV. We also show that due to our parameter fixing, the onset of pion condensation takes place exactly at $μ_I={1\over2}m_π$ in accordance with exact results.

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arXiv2017

Inhomogeneous phases at finite density in an external magnetic field

The two-flavor quark-meson model is used as a low-energy effective model for QCD to study inhomogeneous chiral condensates at finite quark chemical potential $μ$ in a constant magnetic background $B$. We determine the parameters of the model by matching the meson and quark masses, and the pion decay constant to their physical values using the on-shell and modified minimal subtraction schemes. We calculate the free energy in the mean-field approximation for a chiral density wave using dimensional regularization. The system has a surprisingly rich phase structure.

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arXiv2017

Inhomogeneous chiral condensate in the quark-meson model

The two-flavor quark-meson model is used as a low-energy effective model for QCD to study inhomogeneous chiral condensates at finite %temperature $T$ baryon chemical potential $μ_B$. The parameters of the model are determined by matching the meson and quark masses, and the pion decay constant to their physical values using the on-shell and modified minimal subtraction schemes. Using a chiral-density wave ansatz for the inhomogeneity, we calculate the effective potential in the mean-field approximation and the result is completely analytic. The size of the inhomogeneous phase depends sensitively on the pion mass and whether one includes the vacuum fluctuations or not. Finally, we briefly discuss the mean-field phase diagram.

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arXiv2017

Consistent regularization and renormalization in models with inhomogeneous phases

In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different consistent ways of regularizing and renormalizing quantum fluctuations, focusing on a symmetric energy cutoff scheme and dimensional regularization. We apply these techniques calculating the vacuum energy in the NJL model in 1+1 dimensions in the large-$N_c$ limit and the 3+1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.

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arXiv2017

Chiral density wave versus pion condensation in the 1+1 dimensional NJL model

In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $μ$ using dimensional regularization. The phase diagram in the $μ$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $μ>μ_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a constant pion condensate at finite isospin chemical potential $μ_I$. The phase diagram in the $μ_I$--$μ$ plane is mapped out and shows a rich phase structure.

hep-th↗

arXiv2017

On-shell parameter fixing in the quark-meson model

The quark-meson model is often used as an effective low-energy model for QCD to study the chiral transition at finite temperature $T$ and baryon chemical potential $μ_B$. The parameters in the quark-meson model can be found by expressing them in terms of the sigma mass $m_σ$, the pion mass $m_π$, the constituent quark mass $m_q$ and the pion decay constant $f_π$. In practice, this matching is done at tree level, which is inconsistent once we take loop effects of the effective potential into account. We show how to properly perform the matching in the quark-meson model by using the on-shell and the modified minimal subtraction renormalization schemes relating the physical masses and the pion decay constant to the running mass parameter and couplings. We map out the phase diagram in the $μ_B$--$T$ plane and compare our results with other approximations.

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arXiv2016

Three-loop hard-thermal-loop perturbation theory thermodynamics at finite temperature and finite baryonic and isospin chemical potential

In a previous paper (JHEP {\bf 05} (2014) 27), we calculated the three-loop thermodynamic potential of QCD at finite temperature $T$ and quark chemical potentials $μ_q$ using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and isospin chemical potential $μ_I$. We calculate the pressure, energy density, and entropy density, the trace anomaly, and the speed of sound at zero and nonzero $μ_I$. The second, fourth, and sixth-order isospin susceptibilities are calculated at zero $μ_I$. Our results can be directly compared to lattice QCD without Taylor expansions around $μ_q=0$ since QCD has no sign problem at finite isospin chemical potential.

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arXiv2015

Confronting effective models for deconfinement in dense quark matter with lattice data

Ab initio numerical simulations of the thermodynamics of dense quark matter remain a challenge. Apart from the infamous sign problem, lattice methods have to deal with finite volume and discretization effects as well as with the necessity to introduce sources for symmetry-breaking order parameters. We study these artifacts in the Polyakov-loop-extended Nambu-Jona-Lasinio model, and compare its predictions to existing lattice data for cold and dense two-color matter with two flavors of Wilson quarks. To achieve even qualitative agreement with lattice data requires the introduction of two novel elements in the model: (i) explicit chiral symmetry breaking in the effective contact four-fermion interaction, referred to as the chiral twist, and (ii) renormalization of the Polyakov loop. The feedback of the dense medium to the gauge sector is modeled by a chemical-potential-dependent scale in the Polyakov-loop potential. In contrast to previously used analytical ansaetze, we determine its dependence on the chemical potential from lattice data for the expectation value of the Polyakov loop. Finally, we propose to add a two-derivative operator to our effective model. This term acts as an additional source of explicit chiral symmetry breaking, mimicking an analogous term in the lattice Wilson action.

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arXiv2014

Phase diagram of QCD in a magnetic field: A review

We review in detail recent advances in our understanding of the phase structure and the phase transitions of hadronic matter in strong magnetic fields $B$ and zero quark chemical potentials $μ_f$. Many aspects of QCD are described using low-energy effective theories and models such as the MIT bag model, the hadron resonance gas model, chiral perturbation theory, the Nambu-Jona-Lasinio (NJL) model, the quark-meson (QM) model and Polyakov-loop extended versions of the NJL and QM models. We critically examine their properties and applications. This includes mean-field calculations as well as approaches beyond the mean-field approximation such as the functional renormalization group (FRG). Renormalization issues are discussed and the influence of the vacuum fluctuations on the chiral phase transition is pointed out. Magnetic catalysis at $T=0$ is covered as well. We discuss recent lattice results for the thermodynamics of nonabelian gauge theories with emphasis on $SU(2)_c$ and $SU(3)_c$. In particular, we focus on inverse magnetic catalysis around the transition temperature $T_c$ as a competition between contributions from valence quarks and sea quarks resulting in a decrease of $T_c$ as a function of $B$. Finally, we discuss recent efforts to modify models in order to reproduce the behavior observed on the lattice.

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