Asymptotic Freedom in Strong Magnetic Fields

Abstract

Perturbative gluon exchange interaction between quark and antiquark, or in a 3q system, is enhanced in a magnetic field and may cause vanishing of the total qq[over ¯] or 3q mass, and even unlimited decrease of it-recently called the magnetic collapse of QCD. The analysis of the one-loop correction below shows a considerable softening of this phenomenon due to qq[over ¯] loop contribution, similar to the Coulomb case of QED, leading to approximately logarithmic damping of gluon exchange interaction (<V>≈O(1/ln|eB|)) at large magnetic field.

The evolution of meson masses in a strong magnetic field

“…A sample of light neutral meson masses in MF (actually, the meson energies for zero longitudial momentum) has been calculated with PIH framework in [62][63][64], and the NambuGoldstone (NG) modes in MF have been studied in [69]. In all cases the resulting values of M i (B) are in reasonable agreement with lattice data from [23,24]- [25].…”

“…To simplify calculations we chose the confining term in the variable quadratic form [63,64], restoring its original linear form at the stationary point (it was checked to be accurate within about 5%), namely…”

“…motion from the relative motion in the nonrelativistic Hamiltonian for the neutral system in MF. This approach was extended to the relativistic sector in the PIH framework for two-body systems in [62][63][64] and for three-body systems in [81]. The Pseudomomentum approach is applicable only for electrically neutral systems, and for the charged ones an exact analytical answer was obtained only in an unphysical model of charged meson with equally charged quark constituents [63].…”

“…As will be shown, the CS method allows to study charged and neutral systems in the same way. To introduce it, we first write the relativistic Hamiltonian in MF within PIH formalism and exploit the oscillator representation for the confinement interaction used before in [62][63][64] with 5% accuracy. This allows to split the Hamiltonian into transversal and longitudial (with respect to the MF direction) parts analytically.…”

One-loop QCD thermodynamics in a strong homogeneous and static magnetic field

“…and M B is taken as an infrared mass that can be interpreted as the ground-state mass of two gluons connected by the fundamental string (∼ 1 GeV), with the string tension, τ = 0.18 GeV 2 , Λ V and µ 0 are taken as 0.385 GeV and 1.1 GeV, respectively [56][57][58]. We now revisit the quark and gluon propagators at the vacuum in a strong magnetic field and then thermalize them in a hot QCD medium, which are the ingredients to compute the quark self-energy.…”