The QCD phase diagram for external magnetic fields (1111.4956v2)

Abstract: The effect of an external (electro)magnetic field on the finite temperature transition of QCD is studied. We generate configurations at various values of the quantized magnetic flux with $N_f=2+1$ flavors of stout smeared staggered quarks, with physical masses. Thermodynamic observables including the chiral condensate and susceptibility, and the strange quark number susceptibility are measured as functions of the field strength. We perform the renormalization of the studied observables and extrapolate the results to the continuum limit using $N_t=6,8$ and 10 lattices. We also check for finite volume effects using various lattice volumes. We find from all of our observables that the transition temperature $T_c$ significantly decreases with increasing magnetic field. This is in conflict with various model calculations that predict an increasing $T_c(B)$. From a finite volume scaling analysis we find that the analytic crossover that is present at B=0 persists up to our largest magnetic fields $eB \approx 1 \textmd{GeV}^2$, and that the transition strength increases mildly up to this $eB\approx1 \textmd{GeV}^2$.

• The paper demonstrates that the QCD transition temperature significantly decreases with increasing magnetic fields.
• Using lattice QCD with 2+1 flavors of stout smeared staggered quarks, the study meticulously controls finite volume and continuum limit effects.
• The results challenge existing model predictions and have broad implications for cosmology, neutron stars, and heavy ion collisions.

The QCD Phase Diagram for External Magnetic Fields

The paper in question presents a comprehensive paper on the effects of external electromagnetic fields on the quantum chromodynamics (QCD) phase diagram, focusing on finite temperature transitions. The paper employs lattice QCD techniques, a non-perturbative method suited for simulating the dynamics of quarks and gluons on a discretized space-time lattice. This work is significant due to its relevance to phenomena in cosmology, such as the early universe's phase transitions, and in astrophysical contexts like the environments of neutron stars, and experimental conditions like noncentral heavy ion collisions.

Methodology and Findings

The research utilizes $N_f=2+1$ flavors of stout smeared staggered quarks, with quark masses set to physical values. The configurations are produced at multiple values of the quantized magnetic flux using lattice spacings $N_t=6,8,$ and $10$, with care taken to address finite volume effects.

A key result of this paper is the observation that the QCD transition temperature $T_c$ decreases significantly as the magnetic field increases, contrasting with predictions from various model calculations that suggest $T_c$ should increase with the magnetic field. This discrepancy is highlighted as a bold divergence from the prevailing theoretical expectations.

The authors perform extensive renormalization of thermodynamic observables such as the chiral condensate, its susceptibility, and the strange quark number susceptibility. They ensure the accuracy of extrapolations to the continuum limit and account for finite volume effects with lattice volumes scaling to achieve this.

Implications of the Findings

The implications of a decreasing $T_c$ with increasing magnetic field are profound and multifaceted. Theoretically, this challenges the validity of several widely-used model approaches to QCD under strong external fields. Practically, this finding is crucial for understanding the behavior of matter under extreme magnetic fields, such as those possibly present in the early universe and in neutron stars.

Further investigations are warranted to explore the roots of this contradiction with model-based predictions, particularly examining how different assumptions or approximations in models contribute to divergent temperature predictions when magnetic fields are considered.

Future Directions in Research

Given the stark difference between lattice QCD outcomes and model predictions, a promising area of research involves refining low-energy effective models to align more closely with these lattice results. Additionally, expanding lattice QCD studies to include more flavors and varying quark masses could provide valuable insights into the interactions between magnetic fields and QCD phases.

The research directions may also focus on studying the implications in heavy ion collisions at facilities like RHIC and LHC, where magnetic fields on the order of the magnitudes discussed can occur transiently. Understanding how magnetic fields affect the QCD phase transition can offer crucial insights into the nature of quark-gluon plasma and its evolution in these environments.

In summary, this paper makes a significant contribution to our understanding of QCD in external magnetic fields by providing compelling lattice QCD evidence that challenges existing theoretical models. The reduction in transition temperature under strong magnetic fields invites further paper to reconcile these findings with theoretical models and explore their application in both cosmological and experimental contexts.