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 (bar{Q}) is obtained in a hot QCD medium in the presence of a strong magnetic field by correcting both short- and long-range 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 Qbar{Q} together. For example, the J/psi is dissociated at eB sim 10 m_pi ^2 and Upsilon is dissociated at eB sim 100 m_pi ^2 whereas its excited states, psi ^prime and Upsilon ^prime are dissociated at smaller magnetic field eB= m_pi ^2, 13 m_pi ^2, respectively.
Highlights
To realize this predicted phase, current experimental program of ultra-relativistic heavy ion collisions (URHIC) have been designed at different colliders with different center of mass energies, viz. Relativistic Heavy Ion Co√llider (RHIC) at Brookhaven National Laboratory (BNL) at s= 200 GeV per nucleon in Au + Au collisions and Large Hadron Collider (LHC)√at European Organization for Nuclear Research (CERN) at s= 2.76 TeV per nucleon in Pb + Pb collisions.Recent analysis suggests that the events of URHIC should be analyzed by incorporating the effect of the magnetic field because an intensely strong magnetic field, perpendicular to the reaction plane, is expected to be produced at very early stages of collisions when the event is off-central [1–5]
As we understood earlier in Strong Magnetic Field Approximation (SMFA), the strongly magnetized thermal medium with massless quarks possesses only one scale related to the magnetic field so by the dimensional arguments the square of the Debye mass is linear in eB
We have explored the effects of strong and homogeneous magnetic fields on the properties of quarkonium states
Summary
To realize this predicted phase, current experimental program of ultra-relativistic heavy ion collisions (URHIC) have been designed at different colliders with different center of mass energies, viz. Relativistic Heavy Ion Co√llider (RHIC) at Brookhaven National Laboratory (BNL) at s= 200 GeV per nucleon in Au + Au collisions and Large Hadron Collider (LHC)√at European Organization for Nuclear Research (CERN) at s= 2.76 TeV per nucleon in Pb + Pb collisions. Magnetic field is produced at the early stages of the collisions, it becomes worthwhile to examine the effects of the magnetic field on the properties of quarkonia bound states, which is the central theme of our present work Quantum mechanically both the quarkonium and the heavy meson spectra have been analyzed through the solution of the non-relativistic Schrödinger equation with both harmonic oscillator and Cornell potential with an additional spin–spin interaction term [23,24]. We have first calculated the gluon self-energy at finite temperature in a strong magnetic background and obtain the heavy quark potential by taking the static limit of the effective gluon propagator to see the effects of the magnetic field alone on the quarkonium states even in a thermal medium.
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