arXiv subjects

Mathias P. Nødtvedt

Publications and source records attributed to Mathias P. Nødtvedt.

5 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.

hep-ph↗

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.

hep-ph↗

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.

hep-ph↗

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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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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