Magnetic catalysis in nuclear matter

Alexander Haber, Florian Preis, and Andreas Schmitt

Phys. Rev. D 90, 125036 – Published 30 December 2014

Abstract

A strong magnetic field enhances the chiral condensate at low temperatures. This so-called magnetic catalysis thus seeks to increase the vacuum mass of nucleons. We employ two relativistic field-theoretical models for nuclear matter, the Walecka model and an extended linear sigma model, to discuss the resulting effect on the transition between vacuum and nuclear matter at zero temperature. In both models we find that the creation of nuclear matter in a sufficiently strong magnetic field becomes energetically more costly due to the heaviness of magnetized nucleons, even though it is also found that nuclear matter is more strongly bound in a magnetic field. Our results are potentially important for dense nuclear matter in compact stars, especially since previous studies in the astrophysical context have always ignored the contribution of the magnetized Dirac sea and thus the effect of magnetic catalysis.

Received 27 October 2014

DOI:https://doi.org/10.1103/PhysRevD.90.125036

Authors & Affiliations

Alexander Haber^*, Florian Preis^†, and Andreas Schmitt^‡

Institut für Theoretische Physik, Technische Universität Wien, 1040 Vienna, Austria

^*ahaber@hep.itp.tuwien.ac.at
^†fpreis@hep.itp.tuwien.ac.at
^‡aschmitt@hep.itp.tuwien.ac.at

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Vol. 90, Iss. 12 — 15 December 2014

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Images

Figure 1
Left panel: Dependence of the vacuum nucleon mass on the magnetic field in the Walecka model and the extended linear sigma model (eLSM). The increase of the vacuum mass is expected from magnetic catalysis (MC); neglecting the contribution of the Dirac sea that is responsible for magnetic catalysis leads to an incorrect constant vacuum mass (horizontal thin dashed line). The thick dashed line is the result of the extended linear sigma model without the sea contribution of the chiral partner of the nucleon $N^{*}$ , showing that the main difference between the two models originates from that contribution. Right panel: Vacuum mass of the nucleon $M_{N}$ and its chiral partner $M_{N^{*}}$ according to the extended linear sigma model on a larger scale for the magnetic field, showing a linear behavior for very strong fields. The dashed lines are the quadratic approximations for small fields. (If $q = e ≃ 0.30$ , then $q B = 0.1 {GeV}^{2}$ in natural Heaviside-Lorentz units corresponds to $B = 1.7 \times 10^{19} G$ in Gaussian units.)
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Figure 2
Zero-temperature solutions for the nucleon mass in the Walecka model in the vicinity of the onset of nuclear matter for two different magnetic fields, compared to the solution in the absence of a magnetic field. The vertical dashed lines indicate the onset of nuclear matter, where the effective mass decreases discontinuously. The vacuum mass (horizontal segments of the curves) is increased for both magnetic fields due to magnetic catalysis. With respect to the onset, the two panels show two different cases: in the left (right) panel, the critical chemical potential for the onset is smaller (larger) than without magnetic field. The (black) dashed line is defined by $μ みゅー = M_{N}$ , such that the shaded area corresponds to the vacuum. In the extended linear sigma model, the results look qualitatively always like in the right panel.
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Figure 3
Onset for nuclear matter in the presence of a background magnetic field. The thick lines show our results for the Walecka model and the extended linear sigma model (eLSM). For comparison, the two thin dashed lines (barely distinguishable from each other) show the result within the same models, but without magnetic catalysis; i.e., ignoring the $B$ -dependent sea contribution, as done in the previous literature. The right panel is a zoom-in to small magnetic fields and shows the oscillations due to the Landau levels (here, ${μ みゅー}_{0} ≃ 922.7 MeV$ is the chemical potential for the onset in the absence of a magnetic field).
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Figure 4
Binding energy (left) and baryon density (right) along the onset of nuclear matter for both models (solid lines). Again, the thin dashed lines show the incorrect result with a $B$ -independent vacuum mass of the nucleons. If rotated by 90° and shifted by $m_{N}$ , the dashed curves for the binding energy are identical to the dashed onset curves in Fig. 3 because the entire effect of the magnetic field is given by the binding energy.
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Figure 5
Effect of the $B$ -independent sea contributions to the vacuum mass (left) and the onset of nuclear matter (right) in the Walecka model. In both panels, the solid line is the result shown in the main text, i.e., without $B$ -independent sea contributions. In the left panel we show the effect of the renormalization of the nucleon sector (dashed line) and of the renormalization of both the nucleon and meson sectors (dashed-dotted line). The right panel compares the result for the onset with and without renormalizing the nucleon sector, showing that both results are barely distinguishable.
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