Heavy quark potential in a static and strong homogeneous magnetic field

Abstract

We have investigated the properties of quarkonia in a thermal QCD medium in the background of strong magnetic field. For that purpose, we employ the Schwinger proper-time quark propagator in the lowest Landau level to calculate the one-loop gluon self-energy, which in the sequel gives the effective gluon propagator. As an artifact of strong magnetic field approximation (eB >> T 2 and eB >> m 2 ), the Debye mass for massless flavors is found to depend only on the magnetic field which is the dominant scale in comparison to the scales prevalent in the thermal medium. However, for physical quark masses, it depends on both magnetic field and temperature in a low temperature and high magnetic field but the temperature dependence is very meager and becomes independent of the temperature beyond a certain temperature and magnetic field. With the above mentioned ingredients, the potential between heavy quark (Q) and anti-quark (Q) is obtained in a hot QCD medium in the presence of a strong magnetic field by correcting both short-and longrange components of the potential in the real-time formalism. It is found that the long-range part of the quarkonium potential is affected much more by magnetic field as compared to the short-range part. This observation facilitates us to estimate the magnetic field beyond which the potential will be too weak to bind QQ together. For example, the J/ψ is dissociated at eB ∼ 10 m 2 π and ϒ is dissociated at eB ∼ 100 m 2 π whereas its excited states, ψ and ϒ are dissociated at smaller magnetic field eB = m 2 π , 13m 2 π , respectively.

Gauge-invariant screening masses and static quark free energies in Nf=2+1 QCD at nonzero baryon density

“…Magnetic and electric screening masses in the presence of an external background field have been determined by lattice simulations in Ref. [10] and have indeed been shown to be increasing functions of B, in agreement with analytical studies of screening effects in the QGP [11][12][13].…”

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

“…Therefore the longitudinal component (3.36) gives the Debye mass (3.16) for the massless quarks, 38) which was recently obtained by one of us [64] and also by others using the different approaches [33,65]. Thus the Debye mass in the presence of a strong magnetic field depends…”

Hadronic Paschen–Back effect

“…Under such a situation, implementation of the potentials modified by both the temperature and the magnetic field as estimated in Refs. [24,27,28,30,31] would be important. When QGP is not produced after the collision (T < T c ), and the P-wave charmonia do not suffer from the thermal effects (or can be slightly affected by thermal hadronic matter), then we can measure almost pure HPBE.…”

“…We do not consider the B-dependence of the potentials. In fact, the anisotropy of the confinement potential in a magnetic field is indicated by phenomenological models [21][22][23][24][25][26][27][28] as well as lattice QCD simulations at zero [29] and finite temperature [30,31]. Implementation of such anisotropy on the potential model as Ref.…”