arXiv subjects

Jens O. Andersen

Publications and source records attributed to Jens O. Andersen.

At least 19 recordsLinked to original sources

arXiv2026

Massive hybrid stars within the extended three-flavor quark-meson diquark model

We discuss the properties of the extended three-flavor quark-meson diquark (EQMD) model as a renormalizable low-energy effective model for QCD. The effective degrees of freedom are quarks, scalar- and pseudoscalar mesons, diquarks, vector- and axial-vector mesons. We calculate the equation of state (EoS) in the mean-field approximation at $T=0$ imposing charge neutrality for electric and color charges. We match the EoS with a low-density nuclear equation of state. We discuss how the choice of parameters in the model affects the EoS and thereby the mass-radius for hybrid stars. We show that it is possible to construct hybrid stars whose masses and radii are in agreement with recent astrophysical observations and perturbative QCD (pQCD). The addition of vector and axial vector mesons to the quark-meson diquark is essential, since it makes the EoS sufficiently stiff for intermediate densities. Our results suggest that stars with a mass larger than $M\sim2M_{\odot}$ have a quark core with a central density $n_B\geq 3.9n_{\rm sat}$, where $n_{\rm sat}\approx0.165$fm$^{-3}$ is the saturation density. The speed of sound has a double-peak structure and relaxes to the conformal limit from above for large baryon chemical potentials $μ_B$. This structure is caused by the decrease in the mass of the $s$ quark as $μ_B$ increases.

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arXiv2026

Quark-meson diquark model and color superconductivity in dense quark matter

We consider the two- and three-flavor QMD models as renormalizable low-energy models for QCD at finite quark chemical potentials with quarks, mesons, and diquarks as effective degrees of freedom. Using the on-shell scheme the parameters in the scalar sector can be fixed and expressed in terms of observed meson masses and decay constants. The remaining parameters can be varied. In the QMD models, all the symmetries are global, including the $SU(N_c)$ symmetry. The breaking of the global symmetries gives rise to a number of Goldstone bosons depending on the symmetry-breaking pattern, i.e. whether the system is in the 2SC phase or the color-flavor-locked (CFL) phase. This is in contrast to perturbative QCD, where some of the gauge bosons become massive via the Higgs mechanism. We classify the Goldstone bosons and show that their type and number are in accordance with general counting rules. The thermodynamic potential $Ω$ is calculated in the mean-field approximation, where we include quark loops, while mesons and diquarks are treated at tree level. As important applications, we study the properties of the pion-condensed phase at finite isospin chemical potential, and the 2SC and CFL phases at finite baryon chemical potential. We present a few numerical results focusing on the speed of sound, gaps, and condensates. It is shown that the BCS gaps approaches a constant for large isospin and baryon chemical potentials and that the speed of sound approaches the conformal value from above in the same limit.

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arXiv2025

Renormalization of the three-flavor quark-meson diquark model

We discuss the properties of the two- and three-flavor quark-meson diquark (QMD) model as a renormalizable low-energy effective model for color superconductivity in dense QCD. The effective degrees of freedom are scalars, pseudo-scalars, diquarks, and quarks. The parameters in the scalar/pseudo-scalar sector can be determined by matching the meson pole masses and decay constants to their observed values using the on-shell renormalization scheme. The remaining parameters are in the diquark sector and a priori unknown. In principle, they can be calculated from QCD, but we consider them free. We renormalize the thermodynamic potential in the 2SC phase for two flavors and in the color-flavor-locked (CFL) phase for three flavors, determining the counterterms of the couplings in the diquark sector. We derive a set of renormalization group equations for these couplings that are used to improve the thermodynamic potential. As an application, we calculate the gap and the speed of sound in the ideal CFL phase. It is shown that the gap approaches a constant as $μ_B\rightarrow\infty$ and that the speed of sound relaxes to the conformal limit from above.

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arXiv2025

Pion condensation versus 2SC, speed of sound, and charge neutrality effects in the quark-meson diquark model

We employ the two-flavor quark-meson diquark model as a low-energy model for QCD at non-zero quark and isospin chemical potentials $μ$ and $μ_I$, and at zero temperature. We map out the phase diagram in the $μ$-$μ_I$ plane, which has four phases: a vacuum phase, a phase with condensed charged pions/Cooper pairs of $u$ and $\bar{d}$ quarks, a normal quark matter phase, and a color superconducting phase (2SC phase). %In the 2SC phase, we study the effects of imposing color and %electric charge neutrality. The global symmetry breaking $SU(3)_c\rightarrow SU(2)_c$ in the 2SC phase gives rise to a number of Nambu-Goldstone bosons. We classify them and briefly discuss their properties. We calculate the speed of sound $c_s$ in the two special cases, finite $μ_I$ and $μ=0$, and finite $μ$ and $μ_I=0$. In both cases, the speed of sound exhibits a maximum and approaches the conformal limit from above as the density increases. For non-zero isospin $μ_I$, this behavior is in agreement with the speed of sound obtained from lattice simulations. In the 2SC phase, the behavior is qualitatively the same if we impose local charge neutrality. Finally, we discuss the possibility of having a mixed phase of negatively charged normal quark matter and positively charged 2SC matter with global color charge neutrality imposed on the latter.

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arXiv2025

Chiral perturbation theory and Bose-Einstein condensation in QCD

We present recent results in three-flavor chiral perturbation theory at finite isospin $μ_I$ and strangeness $μ_s$ chemical potentials at zero temperature. The phase diagram to ${\cal O}(p^2)$ in the $μ_I$--$μ_S$ plane is mapped out with and without electromagnetic effects. The phase diagram consists of a vacuum phase and three Bose-condensed phases with condensates of $π^{\pm}$, $K^{\pm}$, and $K^{0}/\bar{K}^0$, respectively. Including electromagnetic interactions, the Bose-condensed phases become Higgs phases via the Higgs mechanism. The tree-level spectrum for the mesons and gauge bosons is also derived. We calculate the pressure, energy density, isospin density, and speed of sound in the pion-condensed phase to ${\cal O}(p^4)$ for three-flavor $χ$PT. The results are compared with recent lattice simulations and the agreement is very good for isospin chemical potentials up to approximately 200 MeV. Moreover, by integrating out the $s$-quark, we show that the thermodynamic quantities can be mapped onto their two-flavor counterparts with renormalized parameters. %to ${\cal O}(p^6)$ for two-flavor $χ$PT in the chiral limit. We also consider the nonrelativistic limit. It is shown that the energy density can be matched onto the classic result by Lee, Huang and Yang (LHY) for a dilute Bose, with an $s$-wave scattering length that includes radiative corrections. The breaking of the $U(1)$ symmetry in the Bose-condensed phases gives rise to a Goldstone bosons, whose dispersion is linear for momenta $p\llμ_I$. In this regime, we use Son's prescription to construct an effective theory for the Goldstone field which is valid in this regime. It is shown that its damping rate is of order $p^5$. This result is in agreement with Beliav's for a dilute Bose gas.

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arXiv2024

Color superconductivity and speed of sound in the two-flavor quark-meson diquark model

We discuss the properties of the two-flavor quark-meson diquark (QMD) model as a renormalizable low-energy model for QCD in the 2SC phase of QCD. The effective degrees of freedom are the mesons (sigma and pions), quarks, and diquarks. Some of the parameters of the model can be determined by expressing them in terms of the vacuum meson masses and the pion decay constant using the on-shell renormalization scheme. The remaining parameters are considered free, although they in principle can be calculated from QCD. The thermodynamic potential is calculated in a mean-field approximation taking only quark loops into account. In this approximation, we derive a set of renormalization group equations for the running masses and couplings. The solutions to these equations are used to improve the thermodynamic potential $Ω$ and thereby thermodynamic quantities. Four parameter sets are chosen and the phase diagram in the $\barμ$--$T$ plane is obtained (with $\barμ={1\over3}μ_B$). We also calculate the speed of sound $c_s$ as a function of $\barμ$ at vanishing temperature. For large values of $\barμ$, the speed of sound approaches the conformal limit $c_s={1\over\sqrt{3}}$ from above, in disagreement with perturbative calculations, but agreement with hard-dense-loop resummed perturbation theory.

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arXiv2024

Pion condensation in dense QCD, the dilute Bose gas, and speedy Goldstone bosons

We consider pion condensation in QCD at finite isospin density $μ_I$ and zero temperature using two-flavor chiral perturbation theory ($χ$PT). The pressure is calculated to next-to-leading order (NLO) in the low-energy expansion. In the nonrelativistic limit, we recover the classic result by Lee, Huang, and Yang for the energy density of a dilute Bose gas with an $s$-wave scattering length that includes loop corrections from $χ$PT. In the chiral limit, higher-order calculations are tractable. We calculate the pressure to next-to-next-to-leading order (NNLO) in the low-energy expansion, which is an expansion in powers of $μ_I^2/(4π)^2f^2$, where $f$ is the (bare) pion decay constant. The spontaneous breakdown of the global internal symmetry $U(1)_{I_3}$ gives rise to a massless Goldstone boson or phonon. We discuss the properties of the low-energy effective theory describing this mode. Finally, we compare our results for the pressure and the speed of sound with recent lattice simulations with 2+1 flavors. The agreement is very good for isospin chemical potentials up to 180-200 MeV, depending on the physical quantity.

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arXiv2022

Thermodynamics and quark condensates of three-flavor QCD at low temperature

We use three-flavor chiral perturbation theory ($χ$PT) to calculate the pressure, light and $s$-quark condensates of QCD in the confined phase at finite temperature to ${\cal O}(p^6)$ in the low-energy expansion. We also include electromagnetic effects to order $e^2$, where the electromagnetic coupling $e$ counts as order $p$. Our results for the pressure and the condensates suggest that $χ$PT converges very well for temperatures up to approximately 150 MeV. We combine $χ$PT and the Hadron Resonance Gas (HRG) model by adding heavier baryons and mesons. Our results are compared with lattice simulations an d the agreement is very good for temperatures below {170} MeV, in contrast to the results from $χ$PT which agree with the lattice only up to $T\approx120$ MeV. Our value for the chiral crossover temperature is 160.1 MeV, which compares favorably to the lattice result of $157.3$ MeV.

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arXiv2022

Phases and condensates in zero-temperature QCD at finite $μ_I$ and $μ_S$

I discuss pion and koan condensation and the the properties of the phases of QCD at finite isospin chemical potential $μ_I$ and strangeness chemical potential $μ_S$ at zero temperature using three-flavor chiral perturbation theory. Electromagnetic effects are included in the calculation of the phase diagram, which implies that the charged meson condensed phases become superconducting phases of QCD with a massive photon via the Higgs mechanism. Without electromagnetic effects, we show results for the light quark condensate and the pion condensate as functions of $μ_I$ at next-to-leading (NLO) order in the low-energy expansion. The results are compared with recent lattice simulations and by including the NLO corrections, one obtains very good agreement.

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arXiv2022

Phases of QCD at nonzero isospin and strangeness chemical potentials with application to pion stars

We study pion and kaon condensation using three-flavor chiral perturbation theory at finite isospin and strangeness quark chemical potentials μI and μS . The phase diagram consists of a vacuum phase and three distinct Bose condensed phases with condensates of charged pions as well as charged and neutral kaons. Adding electromagnetic interactions, a phase with a charged condensate becomes a Higgs phase and the resulting phase diagram is modified due to the electromagnetic mass splittings of the mesons. The results for the pion-condensed phase are applied to calculate mass-radius relation of pion stars. Local electric charge neutrality is imposed by adding electrons, muons together with their neutrionos. Finally, we compare our results for the mass-radius relations with those from recent lattice simulations, and find very good agreement.

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arXiv2022

Effective field theory treatment of ${\cal N}=4$ supersymmetric Yang-Mills thermodynamics

At finite temperature the free energy density of ${\cal N}=4$ supersymmetric Yang-Mills can be calculated using resummed perturbation theory through the order $λ^{5/2}$. Effective field theory methods provide a useful alternative approach to streamline these calculations. In this proceedings contribution, I review recent work with my collaborators where we used effective field theory methods to calculate the free energy density of ${\cal N}=4$ supersymmetric Yang-Mills in four spacetime dimensions through second order in the 't Hooft coupling $λ$. At this order the contributions to the free energy density come from the hard scale $T$ and the soft scale $\sqrtλT$. The contribution from the scale $T$ enters through the coefficients in the effective Lagrangian obtained by dimensional reduction and the effects of the scale $gT$ can be calculated using perturbative methods in the effective theory.

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arXiv2022

Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude

The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into the long-wavelength domain. The effective evolution may be derived from first principles quantum field theory in an expanding background, through a sequence of approximations calling for additional scrutiny. We perform such an analysis, putting particular emphasis on the amplitude of the stochastic noise, which ultimately determines the cosmological correlations and provides a non-perturbative IR regulator to the dynamics.

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arXiv2022

${\cal N}=4$ supersymmetric Yang-Mills thermodynamics from effective field theory

The free energy density of ${\cal N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions is derived through second order in the 't Hooft coupling $λ$ at finite temperature using effective-field theory methods. The contributions to the free energy density at this order come from the hard scale $T$ and the soft scale $\sqrtλ T$. The effects of the scale $T$ are encoded in the coefficients of an effective three-dimensional field theory that is obtained by dimensional reduction at finite temperature. The effects of the electric scale $\sqrtλ T$ are taken into account by perturbative calculations in the effective theory.

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arXiv2021

QCD phase diagram in a constant magnetic background. Inverse magnetic catalysis: where models meet the lattice

Magnetic catalysis is the enhancement of a condensate due to the presence of an external magnetic field. Magnetic catalysis at $T=0$ is a robust phenomenon in low-energy theories and models of QCD as well as in lattice simulations. We review the underlying physics of magnetic catalysis from both perspectives. The quark-meson model is used as a specific example of a model that exhibits magnetic catalysis. Regularization and renormalization are discussed and we pay particular attention to a consistent and correct determination of the parameters of the Lagrangian using the on-shell renormalization scheme. A straightforward application of the quark-meson model and the NJL model leads to the prediction that the chiral transition temperature $T_χ$ is increasing as a function of the magnetic field $B$. This is in disagreement with lattice results, which show that $T_χ$ is a decreasing function of $B$, independent of the pion mass. The behavior can be understood in terms of the so-called valence and sea contributions to the quark condensate and the competition between them. We critically examine these ideas as well recent attempts to improve low-energy models using lattice input.

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arXiv2021

Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory

We calculate the light quark condensate, the strange quark condensate, the pion condensate, and the axial condensate in three-flavor chiral perturbation theory ($χ$PT) in the presence of an isospin chemical potential at next-to-leading order at zero temperature. It is shown that the three-flavor $χ$PT effective potential and condensates can be mapped onto two-flavor $χ$PT ones by integrating out mesons with strange quark content (kaons and eta), with renormalized couplings. We compare the results for the light quark and pion condensates at finite pseudoscalar source with ($2+1$)-flavor lattice QCD, and we also compare the axial condensate at zero pseudoscalar and axial sources with lattice QCD data. We find that the light quark, pion, and axial condensates are in very good agreement with lattice data. There is an overall improvement by including NLO effects.

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arXiv2021

Quantum corrections to slow-roll inflation: scalar and tensor modes

Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified as the expectation value of a quantum field, evolving in a quantum effective potential. The shape of this potential is determined by the underlying tree-level potential, dressed by quantum corrections from the scalar field itself and the metric perturbations. Following [1], we compute the effective scalar field equations and the corrected Friedmann equations to quadratic order in both scalar field, scalar metric and tensor perturbations. We identify the quantum corrections from different sources at leading order in slow-roll, and estimate their magnitude in benchmark models of inflation. We comment on the implications of non-minimal coupling to gravity in this context.

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arXiv2021

Condensates and pressure of two-flavor chiral perturbation theory at nonzero isospin and temperature

We consider two-flavor chiral perturbation theory ($χ$PT) at finite isospin chemical potential $μ_I$ and finite temperature $T$. We calculate the effective potential and the quark and pion condensates as functions of $T$ and $μ_I$ to next-to-leading order in the low-energy expansion in the presence of a pionic source. We map out the phase diagram in the $μ_I$--$T$ plane. Numerically, we find that the transition to the pion-condensed phase is second order in the region of validity of $χ$PT, which is in agreement with model calculations and lattice simulations. Finally, we calculate the pressure to two-loop order in the symmetric phase for nonzero $μ_I$ and find that $χ$PT seems to be converging very well.

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arXiv2021

Quark condensates and magnetization in chiral perturbation theory in a uniform magnetic field

We reconsider the problem of calculating the vacuum free energy (density) of QCD and the shift of the quark condensates in the presence of a uniform background magnetic field using two-and-three-flavor chiral perturbation theory ($χ$PT). Using the free energy, we calculate the degenerate, light quark condensates in the two-flavor case and the up, down and strange quark condensates in the three-flavor case. We also use the vacuum free energy to calculate the (renormalized) magnetization of the QCD vacuum, which shows that it is paramagnetic. We find that the three-flavor light-quark condensates and (renormalized) magnetization are improvements on the two-flavor results. We also find that the average light quark condensate is in agreement with the lattice up to $eB=0.2 {\rm\ GeV^{2}}$, and the (renormalized) magnetization is in agreement up to $eB=0.3 {\rm\ GeV^{2}}$, while three-flavor $χ$PT, which gives a non-zero shift in the difference between the light quark condensates unlike two-flavor $χ$PT, underestimates the difference compared to lattice QCD.

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