In this work, we have studied the dissociation behavior of 1S and 2S states of quarkonium using quasiparticle approach where the Debye mass depends on baryonic chemical potential. The binding energies of the quarkonium states has been obtained by using quasiparticle Debye mass which further depends on temperature and baryonic chemical potential (<ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M1"><ns0:msub><ns0:mrow><ns0:mi>&#956;</ns0:mi></ns0:mrow><ns0:mrow><ns0:mi>b</ns0:mi></ns0:mrow></ns0:msub></ns0:math>). The effect of <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M2"><ns0:msub><ns0:mrow><ns0:mi>&#956;</ns0:mi></ns0:mrow><ns0:mrow><ns0:mi>b</ns0:mi></ns0:mrow></ns0:msub></ns0:math> on the binding energies and the dissociation temperature have been also studied. The binding energy and dissociation temperature of heavy quarkonia decrease as <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M3"><ns0:msub><ns0:mrow><ns0:mi>&#956;</ns0:mi></ns0:mrow><ns0:mrow><ns0:mi>b</ns0:mi></ns0:mrow></ns0:msub></ns0:math> increases. The effect of <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M4"><ns0:msub><ns0:mrow><ns0:mi>&#956;</ns0:mi></ns0:mrow><ns0:mrow><ns0:mi>b</ns0:mi></ns0:mrow></ns0:msub></ns0:math> on the mass spectra of quarkonium states has been studied well.

India

Vineet Kumar Agotiya

Siddhartha Solanki

Manohar Lal

Heavy Quarkonium States With Baryonic Chemical Potential

The analytical exact iteration method (AEIM) has been widely used to calculate <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M4"><ns0:mi>N</ns0:mi></ns0:math>-dimensional radial Schrodinger equation with medium-modified form of Cornell potential and is generalized to the finite value of magnetic field (eB) with quasiparticle approach in hot quantum chromodynamics (QCD) medium. In <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M5"><ns0:mi>N</ns0:mi></ns0:math>-dimensional space, the energy eigenvalues have been calculated for any states (<ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M6"><ns0:mi>n</ns0:mi></ns0:math>, <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M7"><ns0:mi>l</ns0:mi></ns0:math>). These results have been used to study the properties of quarkonium states (i.e, the binding energy and mass spectra, dissociation temperature, and thermodynamical properties in the <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M8"><ns0:mi>N</ns0:mi></ns0:math>-dimensional space). We have determined the binding energy of the ground states of quarkonium with magnetic field and dimensionality number. We have also determined the effects of magnetic field and dimensionality number on mass spectra for ground states of quarkonia. But the main result is quite noticeable for the values of dissociation temperature in terms of magnetic field and dimensionality number for ground states of quarkonia after using the criteria of dissociation energy. At last, we have also calculated the thermodynamical properties of QGP (i.e., pressure, energy density, and speed of sound) using the parameter eB with ideal equation of states (EoS). A preprint has previously been published (Solanki et al., 2023).

Dissociation of <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M1"><ns0:mi>J</ns0:mi><ns0:mo>/</ns0:mo><ns0:mi>&#968;</ns0:mi></ns0:math> and <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M2"><ns0:mi>Y</ns0:mi></ns0:math> Using Dissociation Energy Criteria in <ns0:math xmlns:ns0="http://www.w3.org/1998/Math/MathML" id="M3"><ns0:mi>N</ns0:mi></ns0:math>-Dimensional Space

Background: In the production of hot quark gluon plasma in high-energy heavy-ion collisions, the charmonium binding in the deconfined interior is prevented by color screening. The formation of deconfining plasma was found as a signature of reduction of the charmonium (a bound state of charm and anticharm quark) production. A significant amount of charm suppression has been observed in heavy-ion collisions <math><mo>(</mo><mi>p</mi><mtext>−</mtext><mi>A</mi><mo>)</mo></math> in various experimental investigations. Some of the issues are still not clear in this area of research, such as the study of hadronic properties in dense nuclear matter, the deconfinement phase transition from hadronic to quark gluon matter, etc. We follow up on the recently published work of Jamal et al. [M. Y. Jamal, I. Nilima, V. Chandra, and V. K. Agotiya, Phys. Rev. D 97, 094033 (2018)]; in this work the authors calculated the properties of quarkonia [i.e., potential, binding energy, and dissociation temperature (using thermal width criteria)] in the presence of temperature and anisotropy. Purpose: To investigate the properties of quarkonia, namely, potential, binding energy, mass spectra, dissociation temperature (using thermal width and thermal energy criteria), and thermodynamical properties of quark gluon plasma (i.e., pressure, energy density, and speed of sound) in the presence of baryonic chemical potential <math><mo>(</mo><msub><mi>μ</mi><mi>b</mi></msub><mo>)</mo></math> and anisotropy <math><mo>(</mo><mi>ξ</mi><mo>)</mo></math>. Methods: The properties of quarkonia and the thermodynamical properties of quark gluon plasma (QGP) are calculated by using the quasiparticle approach with <math><msub><mi>μ</mi><mi>b</mi></msub></math> in hot quantum chromodynamics medium. The medium modified form of heavy-quark potential at finite values of <math><msub><mi>μ</mi><mi>b</mi></msub></math> and <math><mi>ξ</mi></math> is considered. The calculations have been done by considering the real and imaginary parts of the potential with a static gluon propagator. The real part of the potential has been used in solving the Schrödinger equation to obtain the binding energy of quarkonia, and the imaginary part gives rise to the thermal width of heavy quarkonia. Results: The binding energy and the dissociation temperature of <math><mi>S</mi></math> states of charmonia and bottomonia for <math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math> and <math><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></math> (radial quantum number) and the mass spectra of <math><mrow><mn>1</mn><mi>S</mi></mrow></math> states of quarkonia with the effects of <math><msub><mi>μ</mi><mi>b</mi></msub></math> and <math><mi>ξ</mi></math> were calculated. The thermodynamical properties of QGP using the parameters <math><mi>ξ</mi></math> and <math><msub><mi>μ</mi><mi>b</mi></msub></math> were also determined. It was noticed that, with an increase in the value of <math><msub><mi>μ</mi><mi>b</mi></msub></math>, the values of the associated properties of quarkonia decrease. On the other hand, by increasing the value of <math><mi>ξ</mi></math>, the values of the properties of quarkonia increase. The extracted values of mass spectra and the variation of thermodynamical properties of QGP are also compared with the recently published theoretical and experimental data and a reasonable agreement between these values is observed. Conclusions: We have studied the properties of quarkonium state (i.e., <math><mn>1</mn><mi>S</mi></math> and <math><mn>2</mn><mi>S</mi></math>-states) and the thermodynamical properties of QGP with <math><msub><mi>μ</mi><mi>b</mi></msub></math> and <math><mi>ξ</mi></math> in hot and dense quantum chromodynamics medium. Finally with this, we may conclude that the obtained result (mention in result section) might be helpful for enhancing studies of the highly dense object (because Compressed Baryonic Matter experiment at the Facility for Anti-proton and ion Research in exploring QGP at higher baryon densities).

Rishabh Sharma

Dissociation and thermodynamical properties of heavy quarkonia in an anisotropic strongly coupled hot quark gluon plasma: Using a baryonic chemical potential

We studied the effect of momentum space anisotropy on heavy quarkonium states using an extended magnetized effective fugacity quasiparticle model (EQPM). Both the real and imaginary part of the potential has been modified through the dielectric function by including the anisotropic parameter <math id="M1"><mi>ξ</mi></math>. The real part of the medium-modified potential becomes more attractive in the presence of the anisotropy and constant magnetic field. The binding energy of the 1S, 2S, and 1P quarkonium states including anisotropy effects for both the oblate and the isotropic case were studied. We find that the binding energy of <math id="M2"><mi>Q</mi><mover><mi>Q</mi><mo>¯</mo></mover></math> states becomes stronger in the presence of anisotropy. However, the magnetic field is found to reduce the binding energy. The thermal width of the charmonium and bottomonium <math id="M3"><mn>1</mn><mi>S</mi></math> states has been studied at constant magnetic field <math id="M4"><mi>e</mi><mi>B</mi><mo>=</mo><mn>0.3</mn><mtext> </mtext><mi>G</mi><mi>e</mi><msup><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msup></math> for isotropic and prolate cases. The effect of magnetic field on the mass spectra of the 1P state for the oblate case was also examined. The dissociation temperature for the 1S, 2S, and 1P states of charmonium and bottomonium has been determined to be higher for the oblate case with respect to the isotropic case.

Anisotropic Behavior of S-Wave and P-Wave States of Heavy Quarkonia at Finite Magnetic Field

In the present work, we have studied the differential scattering cross-section for ground states of charmonium and bottomonium in the frame work of the medium-modified form of quark-antiquark potential and Born approximation using the nonrelativistic quantum chromodynamics approach. To reach this end, quasiparticle (QP) Debye mass depending upon baryonic chemical potential (<math id="M1"><msub><mrow><mi>μ</mi></mrow><mrow><mi>b</mi></mrow></msub></math>) and temperature has been employed, and hence the variation of differential scattering cross-section with baryonic chemical potential and temperature at fixed value of the scattering angle (<math id="M2"><mi>θ</mi></math>=<math id="M3"><mn>9</mn><msup><mrow><mn>0</mn></mrow><mrow><mi>o</mi></mrow></msup></math>) has been studied. The variation of differential scattering cross-section with scattering angle <math id="M4"><mi>θ</mi></math> (in degree) at fixed temperature and baryonic chemical potential has also been studied. We have also studied the effect of impact parameter and transverse momentum on differential scattering cross-section at <math id="M5"><mi>θ</mi><mo>=</mo><msup><mrow><mn>90</mn></mrow><mrow><mi>o</mi></mrow></msup></math>.

Study of Differential Scattering Cross-Section Using Yukawa Term of Medium-Modified Cornell Potential

The present article is the follow-up of our work Bottomonium suppression in quasi-particle model, where we have extended the study for charmonium states using quasi-particle model in terms of quasi-gluons and quasi quarks/antiquarks as an equation of state. By employing medium modification to a heavy quark potential thermodynamic observables, viz., pressure, energy density, speed of sound, etc. have been calculated which nicely fit with the lattice equation of state for gluon, massless, and as well massive flavored plasma. For obtaining the thermodynamic observables we employed the debye mass in the quasi particle picture. We extended the quasi-particle model to calculate charmonium suppression in an expanding, dissipative strongly interacting QGP medium (SIQGP). We obtained the suppression pattern for charmonium states with respect to the number of participants at mid-rapidity and compared it with the experimental data (CMS JHEP) and (CMS PAS) at LHC energy (Pb+Pb collisions, <math id="M1"><mrow><msqrt><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt></mrow></math> = <math id="M2"><mrow><mn>2.76</mn></mrow></math> TeV).

Indrani Nilima

Equation of States and Charmonium Suppression in Heavy-Ion Collisions

We have studied the equation of state and dissociation temperature of bottomonium state by correcting the full Cornell potential in isotropic medium by employing the effective fugacity quasi-particle Debye mass. We had also calculated the bottomonium suppression in an expanding, dissipative strongly interacting QGP medium produced in relativistic heavy-ion collisions. Finally we compared our results with experimental data from RHIC 200GeV/nucleon Au-Au collisions, LHC 2.76 TeV/nucleon Pb-Pb, and LHC 5.02 TeV/nucleon Pb-Pb collisions as a function of number of participants.