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Register a new userLandau levels in QCD in an external magnetic field
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We will discuss the issue of Landau levels of quarks in lattice QCD in an external magnetic field. We will show that in the two-dimensional case the lowest Landau level can be identified unambiguously even if the strong interactions are turned on. Starting from this observation, we will then show how one can define a lowest Landau level in the four-dimensional case, and discuss how much of the observed effects of a magnetic field can be explained in terms of it. Our results can be used to test the validity of low-energy models of QCD that make use of the lowest-Landau-level approximation.
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We present first evidence for the Landau level structure of Dirac eigenmodes in full QCD for nonzero background magnetic fields, based on first principles lattice simulations using staggered quarks. Our approach involves the identification of the lowest Landau level modes in two dimensions, where topological arguments ensure a clear separation of these modes from energetically higher states, and an expansion of the full four-dimensional modes in the basis of these two-dimensional states. We evaluate various fermionic observables including the quark condensate and the spin polarization in this basis to find how much the lowest Landau level contributes to them. The results allow for a deeper insight into the dynamics of quarks and gluons in background magnetic fields and may be directly compared to low-energy models of QCD employing the lowest Landau level approximation.
Using numerical simulations of lattice QCD we calculate the effect of an external magnetic field on the equation of state of the quark-gluon plasma. The results are obtained using a Taylor expansion of the pressure with respect to the magnetic field for the first time. The coefficients of the expansion are computed to second order in the magnetic field. Our setup for the external magnetic field avoids complications arising from toroidal boundary conditions, making a Taylor series expansion straightforward. This study is exploratory and is meant to serve as a proof of principle.
We study the influence of an external magnetic field on the deconfinement transition in two-flavour lattice QCD with physical quark charges. We use dynamical overlap fermions without any approximation such as fixed topology and perform simulations on a $16^3 times 6$ lattice and at a pion mass around $500MeV$. The pion mass (as well as the lattice spacing) was determined in independent runs on $12^3 times 24$ lattices. We consider two temperatures, one of which is close to the deconfinement transition and one which is above. Within our limited statistics the dependence of the Polyakov loop and chiral condensate on the magnetic field supports the inverse magnetic catalysis scenario in which the transition temperature decreases as the field strength grows for temperature not to far above the critical temperature.
We study the change of the QCD spectrum of low-lying mesons in the presence of an external magnetic field using Wilson fermions in the quenched approximation. Motivated by qualitative differences observed in the spectra of overlap and Wilson fermions for large magnetic fields, we investigate the dependence of the additive quark mass renormalisation on the magnetic field. We provide evidence that the magnetic field changes the critical quark mass both in the free case and on our quenched ensemble. The associated change of the bare quark mass with the magnetic field affects the spectrum and is relevant for the magnetic field dependence of a number of related quantities. We derive Ward identities for lattice and continuum QCD+QED from which we can extract the current quark masses. We also report on a first test of the tuning of the quark masses with the magnetic field using the current quark masses, and show that this tuning resolves the qualitative discrepancy between the Wilson and overlap spectra.
The recent PVLAS experiment observed the rotation of polarization and the ellipticity when a linearly polarized laser beam passes through a transverse magnetic field. The phenomenon cannot be explained in the conventional QED. We attempt to accommodate the result by employing an effective theory for the electromagnetic field alone. No new particles with a mass of order the laser frequency or below are assumed. To quartic terms in the field strength, a parity-violating term appears besides the two ordinary terms. The rotation of polarization and ellipticity are computed for parity asymmetric and symmetric experimental set-ups. While rotation occurs in an ideal asymmetric case and has the same magnitude as the ellipticity, it disappears in a symmetric set-up like PVLAS. This would mean that we have to appeal to some low-mass new particles with nontrivial interactions with photons to understand the PVLAS result.
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