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Short Note on Spin Magnetization in QGP

Andrew Steinmetz, Johann Rafelski

TL;DR

The paper investigates a primordial mechanism for generating cosmic magnetic fields by invoking spin magnetization in the quark-gluon plasma epoch. It develops a grand partition-function framework for a spin-polarized fermion gas in a magnetic field, incorporating Landau quantization and a spin-polarization potential $\Pi$, and analyzes the massless limit to obtain analytic magnetization results. The authors obtain upper bounds on the maximum fields that could be produced by quarks and leptons (e.g., $\mathcal{B}_{q\bar{q}}(300{\rm MeV})<9.1\times10^{15}$ T and $\mathcal{B}_{\ell\bar{\ell}}(300{\rm MeV})<1.6\times10^{16}$ T) and show that the required polarization fraction scales as $f(T)\propto 1/T$, with plausible values as low as $10^{-12}$ to $10^{-4}$ at $T=300$ MeV. The analysis reveals that the magnetization grows as $\mathcal{M}\sim T^{2}$ in the massless limit, suggesting that a minute spin alignment in the early Universe could seed the large-scale magnetic fields observed today, potentially aided by color ferromagnetism near hadronization. The work connects cosmological magnetogenesis with QGP phenomenology and motivates further exploration in laboratory QGP experiments and color-mferromagnetism dynamics.

Abstract

We outline the theory of spin magnetization applicable to the QGP (quark-gluon plasma) epoch of the Universe. We show that a fully spin-polarized single flavor up-quark gas could generate a cosmic magnetic fields in excess of $10^{15}$ Tesla, far in excess of a possible upper limit to the primordial field. The complete multi component ferro-magnetized primordial fermion gas we consider consists of (five) nearly free electrically charged quarks, and leptons (electrons, muons, tau). We present details of how the magnetization is obtained using a grand partition function approach and point to the role of the nonrelativistic particle component. In the range of temperature 150 MeV to 500 MeV our results are also of interest to laboratory QGP experiments. We show that the required polarization capable to explain large scale structure magnetic fields observed has $1/T$ scaling in the limit of high $T$, and could be very small, at pico-scale. In the other limit, as temperature decreases in the expanding Universe, we show that any magnetic fields present before hadronization can be carried forward to below quark confinement condition temperature by polarization of electrons and muons.

Short Note on Spin Magnetization in QGP

TL;DR

The paper investigates a primordial mechanism for generating cosmic magnetic fields by invoking spin magnetization in the quark-gluon plasma epoch. It develops a grand partition-function framework for a spin-polarized fermion gas in a magnetic field, incorporating Landau quantization and a spin-polarization potential , and analyzes the massless limit to obtain analytic magnetization results. The authors obtain upper bounds on the maximum fields that could be produced by quarks and leptons (e.g., T and T) and show that the required polarization fraction scales as , with plausible values as low as to at MeV. The analysis reveals that the magnetization grows as in the massless limit, suggesting that a minute spin alignment in the early Universe could seed the large-scale magnetic fields observed today, potentially aided by color ferromagnetism near hadronization. The work connects cosmological magnetogenesis with QGP phenomenology and motivates further exploration in laboratory QGP experiments and color-mferromagnetism dynamics.

Abstract

We outline the theory of spin magnetization applicable to the QGP (quark-gluon plasma) epoch of the Universe. We show that a fully spin-polarized single flavor up-quark gas could generate a cosmic magnetic fields in excess of Tesla, far in excess of a possible upper limit to the primordial field. The complete multi component ferro-magnetized primordial fermion gas we consider consists of (five) nearly free electrically charged quarks, and leptons (electrons, muons, tau). We present details of how the magnetization is obtained using a grand partition function approach and point to the role of the nonrelativistic particle component. In the range of temperature 150 MeV to 500 MeV our results are also of interest to laboratory QGP experiments. We show that the required polarization capable to explain large scale structure magnetic fields observed has scaling in the limit of high , and could be very small, at pico-scale. In the other limit, as temperature decreases in the expanding Universe, we show that any magnetic fields present before hadronization can be carried forward to below quark confinement condition temperature by polarization of electrons and muons.

Paper Structure

This paper contains 7 sections, 35 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Estimation of maximum plasma spin magnetization
  3. Theory of a spin magnetized gas
  4. Magnetized grand partition function
  5. Sum of Landau states
  6. Evaluation of magnetization in the massless limit
  7. Conclusions

Figures (1)

  • Figure 1: Temperature dependence of several key magnetic field contributions in the early Universe during the QGP epoch. The primordial epoch magnetic fields range (grey band) was obtained from Eq. (\ref{['eq:PMF']}). The maximum possible spin magnetization for quarks are plotted with the following curves: light $u+d$ quarks (orange), strange (bright red), charm (dark red), and bottom (brown). Lepton curves are given by: electrons (dark blue), muons (blue), and tau (light blue). The maximum magnetic field strengths from spin polarization $\mathcal{B}$ for charged leptons and quarks was determined by Eq. (\ref{['eq:HeavyNumberDensity']}) (summing over the first ten terms with $k=10$) and Eq. (\ref{['eq:UpperLimitMagnetization']}) respectively.