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.

In this article we have investigated the effects of strong magnetic field on the properties of quarkonia immersed in a thermal medium of quarks and gluons and studied its quasi-free dissociation due to the Landau-damping. Thermalizing the Schwinger propagator in the lowest Landau levels for quarks and the Feynman propagator for gluons in real-time formalism, we have calculated the resummed retarded and symmetric propagators, which in turn give the real and imaginary components of dielectric permittivity, respectively. Thus the effect of a strongly magnetized hot QCD medium have been encrypted into the real and imaginary parts of heavy quark interaction in medium, respectively. The magnetic field affects the large-distance interaction more than the short-distance interaction, as a result, the real part of potential becomes more attractive and the magnitude of imaginary part too becomes larger, compared to the thermal medium in absence of strong magnetic field. As a consequence the average size of J/ψ's and ψ ′ 's are increased but χ c 's get shrunk. Similarly the magnetic field affects the binding of J/ψ's and χ c 's discriminately, i.e. it decreases the binding of J/ψ and increases for χ c . However, the further increase in magnetic field results in the decrease of binding energies. On contrary the magnetic field increases the width of the resonances, unless the temperature is sufficiently high. We have finally studied how the presence of magnetic field affects the dissolution of quarkonia in a thermal medium due to the Landau damping, where the dissociation temperatures are found to increase compared to the thermal medium in absence of magnetic field. However, further increase of magnetic field decreases the dissociation temperatures. For example, J/ψ's and χ c 's are dissociated at higher 1 hasan.dph2014@iitr.ac.in 2 binoyfph@iitr.ac.in 3 bhaswar.mph2016@iitr.ac.in 4 p.bagchi@vecc.gov.in 1 temperatures at 2 T c and 1.1 T c at a magnetic field eB ≈ 6 and 4 m 2 π , respectively, compared to the values 1.60 T c and 0.8 T c in the absence of magnetic field, respectively.

We examined the effects of the weak magnetic field on the properties of heavy quarkonia immersed in a thermal medium of quarks and gluons and studied how the magnetic field affects the quasifree dissociation of quarkonia in the aforementioned medium. For that purpose, we have revisited the general structure of gluon self-energy tensor in the presence of a weak magnetic field in thermal medium and obtained the relevant structure functions using the imaginary-time formalism. The structure functions give rise to the real and imaginary parts of the resummed gluon propagator, which further give the real and imaginary parts of the dielectric permittivity. The real and imaginary parts of the dielectric permittivity will be used to evaluate the real and imaginary parts of the complex heavy quark potential. We have observed that the real part of the potential is found to be more screened, whereas the magnitude of the imaginary part of the potential gets increased on increasing the value of both temperature and magnetic field. In addition to this, we have observed that the real part gets slightly more screened while the imaginary part gets increased in the presence of a weak magnetic field as compared to their counterparts in the absence of a magnetic field (pure thermal). The increase in the screening of the real part of the potential leads to the decrease of binding energies of J=Ψ and ϒ, whereas the increase in the magnitude of the imaginary part leads to the increase of thermal width with the temperature and magnetic field both. Also the binding energy and thermal width in the presence of a weak magnetic field become smaller and larger, respectively, as compared to that in the pure thermal case. With the observations of binding energy and thermal width in hand, we have finally obtained the dissociation temperatures for J=Ψ and ϒ, which become slightly lower in the presence of a weak magnetic field. For example, with eB ¼ 0m 2 π the J=ψ and ϒ are dissociated at 1.80T c and 3.50T c , respectively, whereas with eB ¼ 0.5m 2 π they dissociated at slightly lower values 1.74T c and 3.43T c , respectively. This observation leads to the slightly early dissociation of quarkonia because of the presence of a weak magnetic field.

The equation of state, the magnetic moment, as well as a Curie-type law for the susceptibility parameter of a system of particles of spin 1/2 in the presence of an external magnetic field are calculated assuming that these particles obey generalized statistics. Here one assumes that the occupation number of an energy state can take the values 0, 1, 2, ..., 1 and no more, where I is an integer greater than unity. This is a direct consequence of the generalized method of field quantization originally due to Green. Exact expressions for the thermodynamic and magnetic properties due to the generalized nature of the statistics are given, and the characteristic departures of the present results from those of the Fermi-Dirac case are pointed out. Our results are useful for investigating the thermodynamic state and spontaneous magnetization of the highly compressed state of matter, presumably of quarks, obtained in a star in gravitational collapse. The quarks are assumed to obey generalized F e m i statistics known in the literature as para-Fermi statistics.

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