Abstract
In this paper we study the emergence of steady electric currents in QCD as a response to a non-uniform magnetic background using lattice simulations with 2 + 1 quark flavors at the physical point, as well as leading-order chiral perturbation theory. Using these currents, we develop a novel method to determine the leading-order coefficient of the equation of state in a magnetic field expansion: the magnetic susceptibility of the QCD medium. We decompose the current expectation value into valence- and sea-quark contributions and demonstrate that the dominant contribution to the electric current is captured by the valence term alone, allowing for a comparably cheap determination of the susceptibility. Our continuum extrapolated lattice results for the equation of state confirm the findings of some of the existing studies in the literature, namely that the QCD medium behaves diamagnetically at low and paramagnetically at high temperatures.
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Acknowledgments
This research was funded by the DFG (Collaborative Research Center CRC-TR 211 “Strong-interaction matter under extreme conditions” - project number 315477589 - TRR 211) and by the Helmholtz Graduate School for Hadron and Ion Research (HGS-HIRe for FAIR). The authors are grateful for inspiring discussions with Massimo D’Elia and Dmitri Kharzeev.
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Brandt, B.B., Endrődi, G., Markó, G. et al. Steady electric currents in magnetized QCD and their use for the equation of state. J. High Energ. Phys. 2024, 27 (2024). https://doi.org/10.1007/JHEP07(2024)027
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DOI: https://doi.org/10.1007/JHEP07(2024)027