Different types of phase transition from hadron to quark at high density near zero temperature may occur in the inner core of hybrid stars. We investigate the impacts of phase transition types and quark models on properties of hybrid star and quark cores. The quark-meson coupling (QMC) model is used to describe hadronic matter, and the MIT bag model as well as the Nambu-Jona-Lasinio (NJL) model are employed to describe quark matter for comparison. From the mass-radius curves obtained by using equations of state (EOS), we find that EOSs of hadron matter have a decisive influence on the maximum mass of a hybrid star in the first-order phase transition case, while quark matter EOSs have more impacts on results in the crossover transition case. It is also found in the present work that the thermodynamic correction arising from an interpolation scheme considerably stiffens the EOSs. Therefore the crossover type phase transition generally leads to hybrid stars with higher masses. In particular, by using the QMC model and the NJL model to construct crossover EOSs with thermodynamic correction, we discover that the maximum masses of hybrid stars can meet the recent observational constraint on mass from PSR J0952-0607, i.e., $2.35\pm0.17M_\odot$.
We investigate the possibility and consequences of phase transitions from an equation of state (EOS) describing nucleons and hyperons interacting via mean fields of sigma, omega, and rho mesons in the recently improved quark-meson coupling (QMC) model to an EOS describing a Fermi gas of quarks in an MIT bag. The transition to a mixed phase of baryons and deconfined quarks, and subsequently to a pure deconfined quark phase, is described using the method of Glendenning. The overall EOS for the three phases is calculated for various scenarios and used to calculate stellar solutions using the Tolm…
We report a first attempt (i) to derive constraints on the energy loss of charm quarks in a deconfined medium from the recent PHENIX data of single-electron transverse momentum spectra and (ii) to estimate the resulting suppression of dileptons from correlated semi-leptonic decays of open charmed mesons. The momentum imbalance of photon-tagged light-quark jets is also considered.
The medium modification of mesons in dense hadronic matter is discussed with a focus on the relationship to the chiral structure of the non-perturbative QCD vacuum.
An effective hadronic Lagrangian including the charm mesons is introduced to study their interactions in hadronic matter. Using coupling constants that are determined either empirically or by the SU(4) symmetry, we have evaluated the absorption cross sections of $J/ψ$ and the scattering cross sections of $D$ and $D^*$ by $π$ and $ρ$ mesons.
It occurs that when we attempt to melt the nucleon in order to obtain the free quark gas, or QGP fluid the mass of the heat quantum (heaton) is equal to the pi-meson mass. Key words: Heat quanta; Quantum heat transport; Quantum diffusion coefficient.
The scattering effects of charm mesons by hadrons such as the pion, rho meson and nucleon are studied in an effective Lagrangian, and are found to be important in heavy ion collisions. At the CERN-SPS energies, hadronic rescatterings are shown to harden the charm meson $m_T$ spectra, leading to a significant enhancement of the yield of intermediate-mass dimuons from charm meson decays.
The phi-charmonium dissociation reactions in hadronic matter are studied. Unpolarised cross sections for 12 reactions are calculated in the Born approximation, in the quark-interchange mechanism and with a temperature-dependent quark potential. The potential leads to remarkable temperature dependence of the cross sections. With the cross sections and the phi distribution function we calculate the dissociation rates of the charmonia in the interactions with the phi meson in hadronic matter. The dependence of the rates on temperature and charmonium momentum is meaningful to the influence of phi …
Recent progress in the field of meson production in hadron collisions is presented. Special emphasis is put new developments in the application of effective field theory methods to pion production, but also theoretical concepts for two-pion, eta, and vector-meson production will be presented.
We investigate in stable strange hadronic matter (SHM) the modification of the masses of the scalar ($σ$, $σ^*$) and the vector ($ω$, $ϕ$) mesons. The baryon ground state is treated in the relativistic Hartree approximation in the nonlinear $σ$-$ω$ and linear $σ^*$-$ϕ$ model. In stable SHM, the masses of all the mesons reveal considerable reduction due to large vacuum polarization contribution from the hyperons and small density dependent effects caused by larger binding.
The B_C meson is the bound state of b-cbar whose recent detection is the first step toward completion of the spectroscopy of heavy quark mesonic states. The b-c states have properties that conveniently fill the gap between the J/Psi and Upsilon states. Thus it is probable that at RHIC the B_c mesons will serve as a probe of deconfined matter. We find that significant differences arise for B_c formation in deconfined and confined matter. Our initial calculations suggest that: (a) The rates of normal hadronic production mechanisms at RHIC energies are not sufficient to produce a detectable numbe…
We develop a model-independent analysis of hadronic scattering data in the resonance region, where the resonance shape follows from the matrix elements of a Hamiltonian. We investigate the rho meson in the tau decay. We demonstrate that the rho meson resonance in the two-pion decay of the tau lepton is described well through the coupling of a bare rho meson to the two-pion and the four-pion continuum. Furthermore, this four-pion continuum corresponds with the data of the four-pion decay channel of the tau lepton at energies up to 1.1 GeV.
Phi meson-baryon cross sections, estimated within a one-boson-exchange model, serve as input for a calculation of the collision rates in hot hadronic matter. We find that the width of the ϕmeson is modified through collisions with baryons by 1-10 MeV at 160 MeV temperature depending on the baryon fugacity. Thermalization of the ϕin high energy heavy ion collisions is discussed.
We analyze the effect of color superconductivity in the transition from hot hadron matter to quark matter in the presence of a gas of trapped electron neutrinos. To describe strongly interacting matter we adopt a two-phase picture in which the hadronic phase is described by means of a non-linear Walecka model and just deconfined matter through the MIT bag model including color superconductivity. We impose flavor conservation during the transition in such a way that just deconfined quark matter is transitorily out of equilibrium with respect to weak interactions. Our results show that color sup…
We investigate the production of the Phi meson and the Omega baryon which interact weakly with hot hadronic matter, and thus their spectra reflect the early stage of the heavy ion collisions. Our analysis shows that the hadronization temperature, T_had, and the transverse flow, v_T, of the initial deconfined phase are strongly correlated: T_had + a * (v_T)**2 = 0.25 GeV, where a=0.37 GeV in the Pb+Pb collision at 158 AGeV/c. When choosing appropriate initial values of T_had and v_T from the temperature region T_had=175 +- 15 MeV, the measured Rho meson spectra was reproduced surprisingly well …
We discuss medium modification of the rho meson originating from its coupling to in medium quasi-pions and delta-hole states. This medium effect leads to a marked structure of the rho meson strength function in the $500 MeV$ invariant mass region. We suggest that this effect may provide an explanation of the structure observed by the DLS collaboration in the $Ca+Ca/C+C$ ratio at $1 GeV/u$.
We study the in-medium properties of $D$ and $\bar{D}$ mesons in isospin asymmetric hyperonic matter arising due to their interactions with the light hadrons. The interactions of $D$ and $\bar{D}$ mesons with these light hadrons are derived by generalizing the chiral SU(3) model used for the study of hyperonic matter to SU(4). The nucleons, the scalar isoscalar meson, $σ$ and the scalar-isovector meson, $δ$ as modified in the strange hadronic matter, modify the masses of $D$ and $\bar{D}$ mesons. It is found that as compared to the $\bar{D}$ mesons, the $D$ meson properties are more sensitive …
The most general spin structures of the spin-1/2 baryon and spinless meson production operator for both photon and nucleon induced reactions are derived from the partial-wave expansions of these reaction amplitudes. The present method provides the coefficients multiplying each spin operator in terms of the partial-wave matrix elements. The result should be useful in studies of these reactions based on partial-wave analyses, especially, when spin observables are considered.
The nucleation process of quark matter in both cold and hot dense hadronic matter is investigated using a chiral approach to describe the quark phase. We use the Nambu-Jona-Lasinio and the Chromo Dielectric models to describe the deconfined phase and the non-linear Walecka model for the hadronic one. The effect of hyperons on the transition phase between hadronic and quark matter is studied. The consequences of the nucleation process for neutron star physics are outlined.
Changes in the properties of the vector mesons in hot and dense hadronic matter, as produced in heavy ion collisions, lead to the intriguing possibility of the opening of the decay channel $ω\ra ρπ$, for the omega meson, which is impossible in free space. This along with the channel $ωπ\ra ππ$ would result in a decrease in its effective life-time enabling it to decay within the hot zone and act as a chronometer in contradiction to the commonly held opinion and would have implications vis a vis determination of the size of the region through pion interferometry. A new peak and a radically alter…
An Extended Chiral Mean-Field Model with Medium-Modified Thermal Mesons for Hot and Dense Hadronic Matter
Center for Nuclear Research, Department of Physics, Kent State University（肯特州立大学物理系核研究中心）；Punjab, 144216, India（印度旁遮普邦）；Department of Physics, University of Houston（休斯顿大学物理系）
The phase transition to a deconfined phase is studied and the consequences in the formation of neutron stars are investigated. We use the quark-meson-coupling model for the hadron matter and the MIT Bag model for the quark matter in order to build the appropriate equations of state for the hybrid stars. The properties of the stars are then calculated. The differences between unpaired and color-flavor locked quark matter are discussed.
Within an effective hadronic model including electromagnetic interactions via a U$_{\rm em}$(1) gauge, we reinvestigate photon Bremsstrahlung from a hot hadronic gas as expected to be formed in relativistic heavy-ion collisions at SPS energies. We calculate photon emission from the reactions $ππ\toππγ$ and $πK \toπKγ$ by an explicit (numerical) evaluation of the multi-dimensional phase space integral. This, in particular, allows to avoid the commonly employed soft photon approximation (SPA), as well as to incorporate final-state thermal enhancement factors. % during the hadronic stage of the f…
We present a potential of which the short-distance part is given by one gluon exchange plus perturbative one- and two-loop corrections and of which the large-distance part exhibits a temperature-dependent constant value. The Schrodinger equation with this temperature-dependent potential yields a temperature dependence of the mesonic quark-antiquark relative-motion wave function and of meson masses. The temperature dependence of the potential, the wave function and the meson masses brings about temperature dependence of cross sections for the nonresonant reactions pi pi -> rho rho for I=2, KK -…
We study quantitatively the formation and evolution of B_c bound states in a space-time domain of deconfined quarks and gluons (quark-gluon plasma, QGP). At the Relativistic Heavy Ion Collider (RHIC) one expects for the first time that typical central collisions will result in multiple pairs of heavy (in this case charmed) quarks. This provides a new mechanism for the formation of heavy quarkonia which depends on the properties of the deconfined region. We find typical enhancements of about 500 fold for the B_c production yields over expectations from the elementary coherent hadronic B_c-meson…
A recent solution of the hyperon puzzle by a first order phase transition to color superconducting quark matter is revisited in order to replace the Maxwell construction by an interpolation method which describes a mixed phase. To do this, we apply for the first time the finite-range polynomial interpolation method for constructing a transition between hadronic and quark matter phases to the situation that is characterized in the literature as the reconfinement problem. For the description of the hadronic phase the lowest order constrained variational method is used while for the quark phase t…
Dilepton production from hot hadronic matter is studied in an effective chiral Lagrangian with pions, $ρ$-mesons, and $a_1$ mesons, We find that the production rates from reactions that involve axial-vector mesons dominate over contributions from all other reactions when the dilepton invariant mass is above 1.5 GeV.
The drag and diffusion coefficients of a hot hadronic medium have been evaluated by using hidden charm mesons as probes. The matrix elements for the evaluation of these coefficients are calculated using an effective theory as well as from scattering lengths. Although the transport coefficients show a significant rise with temperature its effects on the suppression of $J/ψ$ in hadronic matter is not significant.
The one-loop self-energy of the $D$ and $D^*$ mesons in a hot hadronic medium is evaluated using the real time formalism of thermal field theory. The interaction of the heavy open-charm mesons with the thermalized constituents $(π,K,η)$ of the hadronic matter is treated in the covariant formalism of heavy meson chiral perturbation theory. The imaginary parts are extracted from the discontinuities of the self-energy function across the unitary and the Landau cuts. The non-zero contribution from the latter to the spectral density of $D$ and $D^*$ mesons opens a number of subthreshold decay chann…
Temporal meson correlators and their spectral functions are calculated in the deconfined phase using the hard thermal loop resummation technique. The spectral functions exhibit strong medium effects coming from the hard thermal loop approximation for the quark propagator. The correlators, on the other hand, do not differ significantly from free correlators, for which bare quark propagators are used. This is in contrast to lattice calculations showing a clear deviation from the free correlations functions.
The drag and diffusion coefficients of a hot hadronic medium consisting of pions, kaons and eta using open beauty mesons as a probe have been evaluated. The interaction of the probe with the hadronic matter has been treated in the framework of chiral perturbation theory. It is observed that the magnitude of both the transport coefficients are significant, indicating substantial amount of interaction of the heavy mesons with the thermal bath. The results may have significant impact on the experimental observables like the suppression of single electron spectra originating from the decays of hea…
We employ recently published cross sections for $D$-mesons with hadrons and calculate the drag and diffusion coefficients of $D$-mesons in hadronic matter as a function of the momentum of $D$-mesons as well as of the temperature of the medium. Calculating in our approach the spatial diffusion coefficient, $D_x$, at zero chemical potential we see a very smooth transition between our calculations for the hadron gas and the lattice QCD calculations. Applying the results for the transport coefficients of $D$-mesons in a Fokker-Planck equation, which describes the evolution of $D$-mesons during the…
The Hidden Local Symmetry Lagrangian is used to study the interactions of phi mesons with other pseudoscalar and vector mesons in a hadronic gas at finite temperature. We have found a significantly small phi mean free path (less than 2.4 fm at T > 170 MeV) due to large collision rates with rho mesons, kaons and predominantly K* in spite of their heavy mass. This implies that phi mesons produced after hadronization in relativistic heavy ion collisions will not leave the hadronic system without scattering. The effect of these interactions on the time evolution of the phi density in the expanding…
The scattering cross sections of charm mesons with hadrons such as the pion, rho meson, and nucleon are studied in an effective Lagrangian. In heavy ion collisions, rescattering of produced charm mesons by hadrons affects the invariant mass spectra of both charm meson pairs and dileptons resulting from their decays. These effects are estimated for heavy ion collisions at SPS energies and are found to be significant.
The effective masses of the neutral mesons in a hadronic medium and under an external magnetic field are evaluated as functions of the baryonic density and the field intensity. For this purpose the meson polarization is evaluated in the one loop approximation using a Quantum Hadrodynamics model which includes pions, sigma, omega, and rho mesons. The propagators of the baryons include the full effect of the coupling to the magnetic field through their charges and their anomalous magnetic moments. Within the range of magnetic intensities considered here $10^{17}$ G $< B < 10^{19}$ G, the depende…
We study the hadronic effects on the X(3872) meson abundance in heavy ion collisions. We evaluate the absorption cross sections of the X(3872) meson by pions and rho mesons in the hadronic stage of heavy ion collisions, and further investigate the variation in the X(3872) meson abundance during the expansion of the hadronic matter for its two possible quantum number states; $J^P=1^+$ and $2^-$. We show that the absorption cross sections and the time evolution of the X(3872) meson abundance are strongly dependent on the structure and quantum number of the X(3872) meson. We thus suggest that stu…
We review the recent results of heavy meson diffusion in thermal hadronic matter. The interactions of D and B-bar mesons with other hadrons (light mesons and baryons) are extracted from effective field theories based on chiral and heavy-quark symmetries. When these guiding principles are combined with exact unitarity, physical values of the cross sections are obtained. These cross sections (which contain resonant contributions) are used to calculate the drag and diffusion coefficients of heavy mesons immersed in a thermal and dense medium. The transport coefficients are computed using a Fokker…
There are generally two types of Wick contractions in lattice QCD calculations of a correlation function --- connected and disconnected ones. The disconnected contribution is difficult to calculate and noisy, thus it is often neglected. In the context of studying tetraquarks, hadronic molecules and meson-meson scattering, we show that whenever there are both connected and singly disconnected contractions, the singly disconnected part gives the leading order contribution, and thus should never be neglected. As an explicit example, we show that information about the scalar mesons sigma, f0(980),…
We have developed a self-consistent theoretical approach to study the modification of the properties of heavy mesons in hot mesonic matter which takes into account chiral and heavy-quark spin-flavor symmetries. The heavy-light meson-meson unitarized scattering amplitudes in coupled channels incorporate thermal corrections by using the imaginary-time formalism, as well as the dressing of the heavy mesons with the self-energies. We report our results for the ground-state thermal spectral functions and the implications for the excited mesonic states generated dynamically in the heavy-light molecu…
We extend a previous work on the study of heavy charmonia and bottomonia in a deconfined quark-gluon plasma by considering the Bc family of mesons. With the introduction of this bound state of a charm and a beauty quark, we investigate at finite temperature the behavior of the quarkonium, in an energy region between the ψ and the Υ states.
We study what happens to D and D_s mesons as the temperature increases, using lattice QCD simulations with N_f=2+1 dynamical flavours on anistropic lattices. We have access to five temperatures in the hadronic phase. Using the determined groundstate mass at the lowest temperature, we investigate the effect of rising temperature by analysing ratios of mesonic correlators, without the need for further fitting or spectral reconstruction. In the pseudoscalar and vector channels, we demonstrate that temperature effects are at the percent level and can be captured by a reduction of the groundstate m…
We study the properties of the light vector mesons ($ρ$, $ω$ and $ϕ$) in strange hadronic matter using the QCD sum rule approach. The in-medium masses of the vector mesons are calculated from the modifications of the light quark condensates and the gluon condensates in the hadronic medium. The light quark condensates in the hadronic matter are obtained from the values of the non strange and strange scalar fields of the explicit chiral symmetry breaking term in a chiral SU(3) model. The in-medium gluon condensate is calculated through the medium modification of a scalar dilaton field, which is …
We study the effect of a hot and dense medium on the binding energy of hadronic molecules with open-charm mesons. We focus on a recent chiral quark-model-based prediction of a molecular state in the $N \bar D$ system. We analyze how the two-body thresholds and the hadron-hadron interactions are modified when quark and meson masses and quark-meson couplings change in a function of the temperature and baryon density according to predictions of the Nambu--Jona-Lasinio model. We find that in some cases the molecular binding is enhanced in medium as compared to their free-space binding. We discuss …
We calculate the effects of finite density of isospin asymmetric strange hadronic matter, for different strangeness fractions, on the in-medium properties of vector $\left( D^{\ast}, D_{s}^{\ast}, B^{\ast}, B_{s}^{\ast}\right)$ and axial-vector $\left( D_{1}, D_{1s}, B_{1}, B_{1s}\right)$ mesons using chiral hadronic SU(3) model and QCD sum rules. We focus on the evaluation of in-medium mass-shift and shift of decay constant of above vector and axial vector mesons. In QCD sum rule approach the properties e.g. masses and decay constants of vector and axial vector mesons are written in terms of …
We present effective-field-theory results with unitarized interactions on the D-meson transport coefficients in a gas populated by light mesons and baryons at finite temperature and baryochemical potential. The Fokker-Planck equation is used to compute the drag force, the relaxation time and the diffusion coefficients of D mesons for collisions at FAIR. At finite baryochemical potential, the combined effect of net baryonic density and sizable meson-baryon interaction makes the D mesons to relax more efficiently than in the case at zero baryochemical potential. We also describe the connection w…
Flux tube zero-point motion produces quark displacements transverse to the flux tube which make significant contributions to hadronic charge radii. In heavy quark systems, these contributions can be related by Bjorken's sum rule to the rates for semileptonic decay to hybrid mesons. This connection can be generalized to other leptoproduction processes, where transverse contributions to elastic form factor slopes are related to the cross sections for the production of the associated hybrid states. I identify the flux tube overlap integral responsible for these effects as the strong QCD analogue …
The cross sections for $J/ψ$ absorption by $π$ and $ρ$ mesons are studied in a meson-exchange model that includes not only pseudoscalar-pseudoscalar-vector-meson couplings but also three-vector-meson and four-point couplings. We find that they are much larger than in a previous study where only pseudoscalar-pseudoscalar-vector-meson couplings were considered. Including form factors at interaction vertices, the $J/ψ$ absorption cross sections $σ_{πψ}$ and $σ_{ρψ}$ are found to have values on the order of 7 mb and 3 mb, respectively. Their thermal averages in hadronic matter at temperature T=150…
We study the $K^*$ meson reduction in heavy ion collisions by focusing on the hadronic effects on the $K^*$ meson abundance. We evaluate the absorption cross sections of the $K^*$ and $K$ meson by light mesons in the hadronic matter, and further investigate the variation in the meson abundances for both particles during the hadronic stage of heavy ion collisions. We show how the interplay between the interaction of the $K^*$ meson and kaon with light mesons in the hadronic medium determines the final yield difference of the statistical hadronization model to the experimental measurements. For …
Spin alignments of vector mesons and hyperons in relativistic heavy-ion collisions have been proposed as signals of the global polarization. The STAR experiment first observed the $\rm Λ$ polarization. Recently, the ALICE collaboration measured the transverse momentum ($p_T$) and the collision centrality dependence of $K^*$ and $ϕ$ spin alignments in Pb-Pb collisions at $\rm \sqrt{s_{NN}}$ = 2.76 TeV. A large signal is observed in the low $p_T$ region of mid-central collisions for $K^*$ while the signal is much smaller for $ϕ$, and these have not been understood yet. Since vector mesons have d…
The modification of the width of rho mesons due to in-medium decays and collisions is evaluated. The decay width is calculated from the imaginary part of the one-loop self-energy at finite temperature. The collision width is related to the cross sections of the $ρ$ + pion and the $ρ$ + nucleon reactions. A calculation based on an effective Lagrangian shows the importance of including the direct $ρπ\toρπ$ scattering which is dominated by the $a_1$ exchange. A large broadening of the spectral function is found, accompanied by a strength suppression at the pole.
We study the thermal evolution of neutron stars containing deconfined quark matter in their core. Such objects are generally referred to as quark-hybrid stars. The confined hadronic matter in their core is described in the framework of non-linear relativistic nuclear field theory. For the quark phase we use a non-local extension of the SU(3) Nambu Jona-Lasinio model with vector interactions. The Gibbs condition is used to model phase equilibrium between confined hadronic matter and deconfined quark matter. Our study indicates that high-mass neutron stars may contain between 35 and 40 % deconfi…
We describe the remarkable accomplishments of the current heavy ion Pb--Pb collision experiments involving strange particle production, carried out at 158A GeV at CERN--SPS. These experimental results, together with the earlier 200A GeV S-induced reactions, imply that, at central rapidity, a novel mechanism of strangeness production arises, accompanied by excess entropy formation. We argue that: These results are consistent with the formation of a space-time localized, highly excited, dense state of matter; The freeze-out properties of strange hadrons are suggestive of the formation of a color…
We evaluate the in-medium $D$ and $\bar D$-meson masses in hot hadronic matter induced by interactions with the light hadron sector described in a chiral SU(3) model. The effective Lagrangian approach is generalized to SU(4) to include charmed mesons. We find that the D-mass drops substantially at finite temperatures and densities, which open the channels of the decay of the charmonium states ($Ψ^\prime$, $χ_c$, $J/Ψ$) to $D \bar D$ pairs in the thermal medium. The effects of vacuum polarisations from the baryon sector on the medium modification of the $D$-meson mass relative to those obtained…
We calculate the effects of finite density and temperature of isospin asymmetric strange hadronic matter, for different strangeness fractions, on the in-medium properties of vector $\left( D^{\ast}, D_{s}^{\ast}, B^{\ast}, B_{s}^{\ast}\right)$ and axial-vector $\left( D_{1}, D_{1s}, B_{1}, B_{1s}\right)$ mesons, using chiral hadronic SU(3) model and QCD sum rules. We focus on the evaluation of in-medium mass-shift and shift in decay constant of above vector and axial-vector mesons. In QCD sum rule approach, the properties, e.g., the masses and decay constants of vector and axial-vector mesons …
We study unpolarized cross sections for the endothermic nonresonant reactions: pion pion to rho rho for I=2, KK to K*K* for I=1, KK* to K*K* for I=1, pion K to rho K* for I=3/2, pion K* to rho K* for I=3/2, rho K to rho K* for I=3/2, and pion K* to rho K for I=3/2, which take place in hadronic matter. We provide a potential that is given by perturbative QCD with loop corrections at short distances, becomes a distance-independent and temperature-dependent value at long distances, and has a spin-spin interaction with relativistic modifications. The Schrodinger equation with the potential yields …
K*-charmonium dissociation reactions in hadronic matter are studied in the Born approximation, in the quark-interchange mechanism, and with a temperature-dependent quark potential. We obtain the temperature dependence of unpolarized cross sections for K*-charmonium dissociation reactions which produce charmed mesons and charmed strange mesons. We use the cross sections for charmonium dissociation in collisions with pion, rho meson, kaon, vector kaon, and eta meson to calculate dissociation rates of charmonium with the five types of mesons. Because of the temperature dependence of the meson mas…
The $NDΛ_c$ and $ND^*Λ_c$ form factors are evaluated in a full QCD sum rule calculation. We study the double Borel sum rule for the three point function of one meson one nucleon and one $Λ_c$ current up to order six in the operator product expansion. The double Borel transform is performed with respect to the nucleon and $Λ_c$ momenta, and the form factor is evaluated as a function of the momentum $Q^2$ of the heavy meson. These form factors are relevant to evaluate the charmonium absorption cross section by hadrons. Our results are compatible with constant form factors in these vertices.
We argue that the ratio of $ϕ$ mesons multiplicity over cube of the mean $p_T$ is proportional to the degeneracy of the medium produced in ultra-relativistic heavy ion collisions. The ratio extracted from the existing $ϕ$ meson data in the energy range $\sqrt{s}$=6.3-200 GeV, indicate that beyond a threshold energy $\sqrt{s}_{th}=15.74\pm 8.10$ GeV, the medium crosses over from a confined phase to a deconfined phase.
