We investigate the medium modifications of the masses of pseudoscalar open charm (<math><mi>D</mi></math> and <math><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>) mesons and the charmonium state [<math><mrow><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo></mrow></math>] in hot isospin asymmetric strange hadronic medium in the presence of an external magnetic field within a chiral effective model. The in-medium partial decay widths of <math><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo></math> to charged and neutral <math><mi>D</mi><mover><mi>D</mi><mo>¯</mo></mover></math> mesons are computed from the medium modifications of the masses of the initial and final state mesons. These are computed using two light quark pair creation models—(I) the <math><mrow><mmultiscripts><mrow><msub><mrow><mi>P</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow><mprescripts></mprescripts><none></none><mrow><mn>3</mn></mrow></mmultiscripts></mrow></math> model and (II) a field theoretical (FT) model of composite hadrons with quark (and antiquark) constituents. The production cross sections of <math><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo></math>, arising from scattering of the <math><mi>D</mi></math> and <math><mover><mi>D</mi><mo>¯</mo></mover></math> mesons, are computed from the relativistic Breit-Wigner spectral function expressed in terms of the in-medium masses and the decay widths of the charmonium state. The effects of the magnetic field are considered due to the Dirac sea (DS) of the baryons, the mixing of the pseudoscalar (<math><mi>S</mi><mo>=</mo><mn>0</mn></math>) and vector (<math><mi>S</mi><mo>=</mo><mn>1</mn></math>) meson (PV mixing), the Landau level contributions for the charged hadrons. The anomalous magnetic moments (AMMs) of the baryons are also taken into account in the present study. For magnetized nuclear matter, at <math><msub><mi>ρ</mi><mi>B</mi></msub><mo>=</mo><msub><mi>ρ</mi><mn>0</mn></msub></math>, the effect of Dirac sea leads to inverse magnetic catalysis (IMC), which is drop of the magnitude of the light quark condensates (proportional to the scalar fields) with increase in the magnetic field, contrary to the opposite effect of magnetic catalysis (MC) at <math><msub><mi>ρ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></math>. The inclusion of hyperons to the nuclear medium is observed to lead to magnetic catalysis. There are observed to be significant effects from the DS and PV mixing on the properties of the charm mesons. The production cross sections of <math><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo></math> arising due to scattering of <math><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>D</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup><mo>)</mo></mrow></math> mesons in the hot magnetized strange hadronic matter are observed to have distinct peak positions, when the magnetic field is large. This is because the production cross sections have contributions from the transverse as well as longitudinal components of <math><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo></math>, which have nondegenerate masses due to PV [<math><mrow><mi>ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo><mo>−</mo><msubsup><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>′</mo></mrow></msubsup></mrow></math>] mixing. These can have observable consequences on the dilepton spectra as well as on the production of the charm mesons in ultrarelativistic peripheral heavy ion collision experiments, where the produced magnetic field is huge.

India

Amruta Mishra

Arvind Kumar

S. P. Misra

Charmonium production in hot magnetized hyperonic matter: Effects of the baryonic Dirac sea and pseudoscalar-vector mixing

In-medium masses of the light vector <math><mi>ω</mi></math>, <math><mi>ρ</mi></math> and axial-vector <math><msub><mi>A</mi><mn>1</mn></msub></math> mesons are studied in the magnetized nuclear matter, accounting for the effects of (inverse) magnetic catalysis at finite temperature. The in-medium partial decay widths for the <math><msub><mi>A</mi><mn>1</mn></msub><mo>→</mo><mi>ρ</mi><mi>π</mi></math> channels are studied from the in-medium masses of the initial and the final state particles by applying a phenomenological Lagrangian to account for the <math><msub><mi>A</mi><mn>1</mn></msub><mi>ρ</mi><mi>π</mi></math> interaction vertices. The masses are calculated within the QCD sum rule framework, with the medium effects coming through the light quark (<math><mo>∼</mo><mo>⟨</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><mo>⟩</mo></math>) and the scalar gluon condensates (<math><mo>∼</mo><mo>⟨</mo><msup><mi>G</mi><mn>2</mn></msup><mo>⟩</mo></math>), as well as the light four-quark condensate (<math><mo>∼</mo><mo>⟨</mo><mover><mi>q</mi><mo>¯</mo></mover><mi>q</mi><msup><mo>⟩</mo><mn>2</mn></msup></math>). The condensates are calculated within the chiral <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> model in terms of the medium modified scalar fields: isoscalar <math><mi>σ</mi></math>, <math><mi>ζ</mi></math>, isovector <math><mi>δ</mi></math>, and the dilaton field <math><mi>χ</mi></math>. The effects of magnetic fields are incorporated through the magnetized Dirac sea contribution as well as the Landau energy levels of protons and anomalous magnetic moments (AMMs) of the nucleons at finite temperature nuclear matter. The effects of temperature are included through the Fermi distribution functions in the number (<math><msub><mi>ρ</mi><mrow><mi>p</mi><mo>,</mo><mi>n</mi></mrow></msub></math>) and scalar (<math><msubsup><mi>ρ</mi><mrow><mi>p</mi><mo>,</mo><mi>n</mi></mrow><mi>s</mi></msubsup></math>) densities of nucleons within the chiral effective model framework. The incorporation of the magnetic field through the Dirac sea of nucleons lead to an enhancement (reduction) of the light quark condensates with magnetic field, give rise to the phenomenon of magnetic (inverse) catalysis. The effects of (inverse) magnetic catalysis at finite temperature nuclear matter are studied on the spectral functions and production cross sections of the neutral <math><mi>ρ</mi></math> and <math><msub><mi>A</mi><mn>1</mn></msub></math> mesons. This may affect the production of the light vector and axial-vector mesons in the peripheral heavy-ion collision experiments, where estimated magnetic field is very large at the early stages of collisions with very high temperature.

Pallabi Parui

Spectral properties of <math><mi>ω</mi></math>, <math><mi>ρ</mi></math>, and <math><msub><mi>A</mi><mn>1</mn></msub></math> mesons in hot magnetized matter: Effects of the inverse magnetic catalysis

We investigate the in-medium masses of the pseudoscalar <math><mrow><mo>(</mo><mi>D</mi><mo>,</mo><mover><mi>D</mi><mo>¯</mo></mover><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mo>±</mo></msubsup><mo>)</mo></mrow></math>, and vector <math><mrow><mo>(</mo><msup><mi>D</mi><mo>*</mo></msup><mo>,</mo><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mrow><mo>*</mo><mo>±</mo></mrow></msubsup><mo>)</mo></mrow></math>, open charm mesons in isospin asymmetric magnetized nuclear matter, accounting for the effects of the Dirac sea. The masses are used to study the in-medium partial decay widths of <math><mrow><msup><mi>D</mi><mo>*</mo></msup><mo>→</mo><mi>D</mi><mi>π</mi></mrow></math> (<math><mrow><msup><mover><mi>D</mi><mo>¯</mo></mover><mo>*</mo></msup><mo>→</mo><mover><mi>D</mi><mo>¯</mo></mover><mi>π</mi></mrow></math>) and <math><mrow><mi>Ψ</mi><mrow><mo>(</mo><mn>3770</mn><mo>)</mo></mrow><mo>→</mo><mi>D</mi><mover><mi>D</mi><mo>¯</mo></mover></mrow></math>, using the <math><mmultiscripts><mi>P</mi><mn>0</mn><none></none><mprescripts></mprescripts><none></none><mn>3</mn></mmultiscripts></math> model. The in-medium masses of the open charm mesons are calculated from their interactions with the nucleons and scalar mesons within the generalized chiral effective model in terms of the scalar and number densities of nucleons and the scalar fields fluctuations. The free energy of the magnetized vacuum with Landau energy levels and anomalous magnetic moments (AMMs) of the charged fermions in the single fermion energies are taken into account in the Dirac sea contribution. The effects of Landau energy levels of protons and AMMs of the nucleons are also considered in the magnetized nuclear matter. The light quark condensates are modified considerably with magnetic field, leading to (inverse) magnetic catalysis due to the magnetized Dirac sea effects. The magnetic field causes modifications to occur due to the mixing of the pseudoscalar and longitudinal component of the vector mesons, along with the lowest Landau-level contribution to the ground-state energy of the charged mesons as point-particle correction. For the charmonium state <math><mrow><mi>Ψ</mi><mo>(</mo><mn>3770</mn><mo>)</mo></mrow></math>, the effects of the magnetized Dirac sea are incorporated to the mass modifications through the medium-modified scalar dilaton field <math><mi>χ</mi></math> within the chiral model. The in-medium masses and decay widths of the open charm and charmonium mesons thus obtained should have important observable consequences in the production of the open charm mesons and charmonia in noncentral ultrarelativistic heavy-ion collision experiments, where huge magnetic fields are expected to be created.

Sourodeep De

Charm mesons in magnetized nuclear matter: Effects of (inverse) magnetic catalysis

We study the partial decay widths of charmonium (bottomonium) states to <math><mrow><mi>D</mi><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>(</mo><mi>B</mi><mover><mrow><mi>B</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>)</mo></mrow></math> mesons in magnetized (nuclear) matter using a field theoretical model of composite hadrons with quark (and antiquark) constituents. These are computed from the mass modifications of the decaying and produced mesons within a chiral effective model, including the nucleon Dirac sea effects. The mass modifications of the open charm (bottom) mesons are calculated from their interactions with the nucleons and the scalar mesons, whereas the mass shift of the heavy quarkonium state is obtained from the medium change of a scalar dilaton field, <math><mi>χ</mi></math>, which mimics the gluon condensates of QCD. The Dirac sea contributions are observed to lead to a rise (drop) in the quark condensates as the magnetic field is increased; an effect called the (inverse) magnetic catalysis. These effects are observed to be significant, and the anomalous magnetic moments (AMMs) of the nucleons are observed to play an important role. For <math><msub><mi>ρ</mi><mi>B</mi></msub><mo>=</mo><mn>0</mn></math>, there is observed to be magnetic catalysis (MC) without and with AMMs, whereas, for <math><msub><mi>ρ</mi><mi>B</mi></msub><mo>=</mo><msub><mi>ρ</mi><mn>0</mn></msub></math>, the inverse magnetic catalysis is observed when the AMMs are taken into account, contrary to MC, when the AMMs are ignored. In the presence of a magnetic field, there are also mixings of spin 0 (pseudoscalar) and spin 1 (vector) states (PV mixing), which modify the masses of these mesons. The magnetic field effects on the heavy quarkonium decay widths should have observable consequences on the production the heavy flavor mesons, which are created in the early stage of ultrarelativistic peripheral heavy ion collisions, at RHIC and LHC, when the produced magnetic fields can still be extremely large.

Dirac sea effects on heavy quarkonia decay widths in magnetized matter: A field theoretical model of composite hadrons

In-medium masses of the <math><mn>1</mn><mi>S</mi></math> and <math><mn>1</mn><mi>P</mi></math> states of heavy quarkonia are investigated in the magnetized asymmetric nuclear medium, accounting for the Dirac sea effects, using a combined approach of chiral effective model and QCD sum rule method. Masses are calculated from the in-medium scalar and twist-2 gluon condensates, calculated within the chiral model. The gluon condensate is simulated through the scalar dilaton field, <math><mi>χ</mi></math> introduced in the model through a scale-invariance breaking logarithmic potential. Contribution of the Dirac sea is incorporated through the nucleonic tadpole diagrams. Treating the scalar fields as classical, the dilaton field, <math><mi>χ</mi></math>, the isoscalar nonstrange <math><mi>σ</mi><mo>(</mo><mo>∼</mo><mo>(</mo><mo>⟨</mo><mover><mi>u</mi><mo>¯</mo></mover><mi>u</mi><mo>⟩</mo><mo>+</mo><mo>⟨</mo><mover><mi>d</mi><mo>¯</mo></mover><mi>d</mi><mo>⟩</mo><mo>)</mo><mo>)</mo></math>, strange <math><mi>ζ</mi><mo>(</mo><mo>∼</mo><mo>⟨</mo><mover><mi>s</mi><mo>¯</mo></mover><mi>s</mi><mo>⟩</mo><mo>)</mo></math> and isovector <math><mrow><mi>δ</mi><mo>(</mo><mo>∼</mo><mo>(</mo><mo>⟨</mo><mover><mrow><mi>u</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>u</mi><mo>⟩</mo><mo>−</mo><mo>⟨</mo><mover><mrow><mi>d</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>d</mi><mo>⟩</mo><mo>)</mo><mo>)</mo></mrow></math> fields, are obtained by solving their coupled equations of motion as derived from the chiral model Lagrangian. The effects of magnetic field are incorporated through the Dirac sea as well as the Landau energy levels of the protons, and the anomalous magnetic moments of the nucleons. The scalar fields modify appreciably with magnetic field due to the Dirac sea contribution. In-medium masses of the charmonium and bottomonium ground states are observed to have significant modifications with magnetic field due to the effects of (inverse) magnetic catalysis. In presence of an external magnetic field, there is mixing between the longitudinal component of the vector and the pseudoscalar mesons (PV mixing) in both quarkonia sectors, leading to a rise (drop) of the masses of <math><mrow><mi>J</mi><mo>/</mo><msup><mrow><mi>ψ</mi></mrow><mrow><mo>|</mo><mo>|</mo></mrow></msup><mo>(</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo></mrow></math> and <math><mrow><msup><mrow><mi>ϒ</mi></mrow><mrow><mo>|</mo><mo>|</mo></mrow></msup><mo>(</mo><mn>1</mn><mi>S</mi><mo>)</mo><mo>(</mo><msub><mrow><mi>η</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>)</mo></mrow></math> states. These might show in the experimental observables, e.g., the dilepton spectra in the noncentral, ultrarelativistic heavy ion collision experiments at RHIC and LHC, where the produced magnetic field is huge.

Ankit Kumar

QCD sum rule analysis of heavy quarkonium states in magnetized matter: Effects of magnetic and inverse magnetic catalysis

We investigate the in-medium masses of open charm mesons (D(   $ D^0 $  ,   $ D^0 $  ),   $ D^0 $  (   $ D^0 $  ,   $ D^0 $  ),   $ D^0 $  (   $ D^0 $  ,   $ D^0 $  )) and charmonium states (   $ D^0 $  ,   $ D^0 $  ,   $ D^0 $  ,   $ D^0 $  ,   $ D^0 $  ) in strongly magnetized isospin asymmetric strange hadronic matter using a chiral effective model. In the presence of a magnetic field, the number and scalar densities of charged baryons have contributions from Landau energy levels. The mass modifications of open charm mesons result from their interactions with nucleons, hyperons, and the scalar fields (the non-strange field σ, strange field ζ, and isovector field δ) in the presence of a magnetic field. The mass modifications of the charmonium states result from the modification of gluon condensates in a medium simulated by the variation in the dilaton field (χ) in the chiral effective model. The effects of finite quark masses are also incorporated in the trace of the energy-momentum tensor in quantum chromodynamics to investigate the mass shifts of charmonium states. The in-medium masses of open charm mesons and charmonia are observed to decrease with an increase in baryon density. The charged   $ D^0 $  ,   $ D^0 $  ,   $ D^0 $  , and   $ D^0 $   mesons have additional positive mass shifts due to Landau quantization in the presence of a magnetic field. The effects of the strangeness fraction are observed to be more dominant for   $ D^0 $   mesons compared with D mesons. The mass shifts of charmonia are observed to be larger in hyperonic media compared with nuclear media when the effect of the finite quark mass term is neglected. These medium mass modifications can have observable consequences on the production of the open charm mesons and charmonia in high-energy asymmetric heavy-ion collision experiments.

Amal Jahan C. S.

Open charm mesons and charmonia in magnetized strange hadronic matter  

The in-medium properties of <math id="M2"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></math> mesons are investigated within the framework of an effective hadronic model, which is a generalization of a chiral <math id="M3"><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> model, to <math id="M4"><mi>S</mi><mi>U</mi><mo>(</mo><mn>4</mn><mo>)</mo></math>, in order to study the interactions of the charmed hadrons. In the present work, the <math id="M5"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></math> mesons are observed to experience net attractive interactions in a dense hadronic medium, hence reducing the masses of the <math id="M6"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> and <math id="M7"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>S</mi></mrow><mrow><mo>-</mo></mrow></msubsup></mrow></math> mesons from the vacuum values. While this conclusion holds in both nuclear and hyperonic media, the magnitude of the mass drop is observed to intensify with the inclusion of strangeness in the medium. Additionally, in hyperonic medium, the mass degeneracy of the <math id="M8"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>S</mi></mrow></msub></mrow></math> mesons is observed to be broken, due to opposite signs of the Weinberg-Tomozawa interaction term in the Lagrangian density. Along with the magnitude of the mass drops, the mass splitting between <math id="M9"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow></msubsup></mrow></math> and <math id="M10"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>S</mi></mrow><mrow><mo>-</mo></mrow></msubsup></mrow></math> mesons is also observed to grow with an increase in baryonic density and strangeness content of the medium. However, all medium effects analyzed are found to be weakly dependent on isospin asymmetry and temperature. We discuss the possible implications emanating from this analysis, which are all expected to make a significant difference to observables in heavy ion collision experiments, especially the upcoming Compressed Baryonic Matter (CBM) experiment at the future Facility for Antiproton and Ion Research (FAIR), GSI, where matter at high baryonic densities is planned to be produced.