The hadron-quark/gluon phase transition is studied in the two-phase model. As a further study of our previous work, both the isoscalar and isovector vector interactions are included in the Polyakov loop modified Nambu--Jona-Lasinio model (PNJL) for the quark phase. The relevance of the exchange (Fock) terms is stressed and suitably accounted for. The calculation shows that the isovector vector interaction delays the phase transition to higher densities and the range of the mixed phase correspondingly shrinks. Meanwhile the asymmetry parameter of quark matter in the mixed phase decreases with the strengthening of this interaction channel. This leads to some possible observation signals being weakened, although still present. We show that these can be rather general effects of a repulsion in the quark phase due to the symmetry energy. This is also confirmed by a simpler calculation with the MIT--Bag model. However, the asymmetry parameter of quark matter is slightly enhanced with the inclusion of the isoscalar vector interaction, but the phase transition will be moved to higher densities. The largest uncertainty on the phase transition lies in the undetermined coupling constants of the vector interactions. In this respect new data on the mixed phase obtained from Heavy Ion Collisions at Intermediate Energies appear very important.
The fast simultaneous hadronization and chemical freeze out of supercooled quark-gluon plasma, created in relativistic heavy ion collisions, leads to the re-heating of the expanding matter and to the change in a collective flow profile. We use the assumption of statistical nature of the hadronization process, and study quantitatively the freeze out in the framework of hydrodynamical Bjorken model with different quark-gluon plasma equations of state.
Using updated gluon distributions from global fits to data, we investigate the sensitivity of direct photoproduction of heavy quarks and exclusive production of vector mesons to varying strength of gluon modifications. Implications of using these processes for constraining nuclear gluon distributions are discussed.
We investigate the hadronic cooling of a quark droplet within a microscopic model. The color flux tube approach is used to describe the hadronization of the quark phase. The model reproduces experimental particle ratios equally well compared to a static thermal hadronic source. Furthermore, the dynamics of the decomposition of a quark-gluon plasma is investigated and time dependent particle ratios are found.
One of the key signatures of the Quark Gluon Plasma (QGP) is the energy loss of high momentum particles as they traverse the strongly interacting medium. The energy loss of these particles is governed by the jet transport coefficient $\hat{q}/T^3$, wherein it has been thought that there is a large jump as the system transitions between the hadron gas and Quark Gluon Plasma phases. Here we calculate $\hat{q}/T^3$ within the Hadron Resonance Gas (HRG) model with the particle list PDG16+ and find that, if one incorporates the experimental error in the hadronic calculation of $\hat{q}/T^3$ and ass…
The productions of real photons from quark gluon plasma and hot hadronic matter formed after the nucleus - nucleus collisions at ultra-relativistic energies are discussed. The effects of the spectral shift of the hadrons at finite temperature on the production of photons are investigated. On the basis of the present analysis it is shown that the photon spectra measured by WA98 collaboration in Pb + Pb collisions at CERN SPS energies can be explained by both QGP as well as hadronic initial states if the spectral shift of hadrons at finite temperature is taken into account. Several other works o…
We review hadron formation from a deconfined quark gluon plasma (QGP) via coalescence or recombination of quarks and gluons. We discuss the abundant experimental evidence for coalescence from the Relativistic Heavy Ion Collider (RHIC) and compare the various coalescence models advocated in the literature. We comment on the underlying assumptions and remaining challenges as well as the merits of the models. We conclude with a discussion of some recent developments in the field.
We discuss recent data on particle production with emphasis on the degree of thermal and chemical equilibration achieved. The data are interpreted in terms of a resonance gas model. The phase boundary constructed between the resonance gas and the quark-gluon plasma is shown to be very close to the deduced parameters characterizing the hadronic fireball at freeze-out.
We evaluate the factor $κ$ appearing in Langer's expression for the nucleation rate extended to the case of hadron bubbles forming in zero baryon number cooled quark-gluon plasma. We consider both the absence and presence of viscosity and show that viscous effects introduce only small changes in the value of $κ$
A parton and hadron cascade model, PACIAE, is employed to investigate the net charge transfer fluctuation within $|η|$=1 in Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV. It is turned out that the observable of net charge transfer fluctuation, $κ$, in hadronic final state (HM) is nearly a factor of 3 to 5 larger than that in initial partonic state (QGM). However, only twenty percent of the net charge transfer fluctuation in the QGM can survive the hadronization
We present a simple model for the dimuon production from the decay of vector mesons which are hadronized from a baryon-free quark-gluon plasma. Continuous decay of vector mesons in the medium is known to enhance the dimuon production and in our model we can estimate the total yield of dimuons decayed from vector mesons through the rate equations for the number of vector mesons of interest. Muon pair production critically depends on the time duration of both the mixed and hadronic phases. Results are discussed in view of possible measurements in experiments.
Measured hadron yields from relativistic nuclear collisions can be equally well understood in two physically distinct models, namely a static thermal hadronic source vs.~a time-dependent, nonequilibrium hadronization off a quark-gluon plasma droplet. Due to the time-dependent particle evaporation off the hadronic surface in the latter approach the hadron ratios change (by factors of $<\approx 5$) in time. Final particle yields reflect time averages over the actual thermodynamic properties of the system at a certain stage of the evolution. Calculated hadron, strangelet and (anti-)cluster yields…
A popular derivation of the apparent temperature of the particle transverse momentum spectra and its inconsistency are considered. An improved formula for the apparent temperature is discussed. It is shown that recent results on transverse mass spectra of $J/ψ$ and $ψ^{\prime}$ mesons support a hypothesis of statistical production of charmonia at hadronization and suggest the early thermal freeze-out of these mesons. Using the apparent temperature formula the collective transverse velocity of the hadronizing quark gluon plasma is extracted to be $<v_T > \approx 0.2$. Predictions for transverse…
Recently we have reported the correct formulation of the lattice QCD method at the zero temperature to study the hadron formation from the quarks and gluons by incorporating the non-zero boundary surface term in QCD which arises due to the confinement of quarks and gluons inside the finite size hadron. In this paper we extend this to the finite temperature QCD and present the correct formulation of the lattice QCD method at the finite temperature to study the hadron formation from the quark-gluon plasma.
Assuming that quark and antiquark numbers are separately conserved during hadronization, we calculate Bremsstrahlung photon from a hadronizing quark-gluon plasma. The quark and antiquark numbers are obtained from the hadron numbers in the statistical model and the transition amplitudes for the hadronization from the constraint that all quarks and antiquarks must be consumed in the hadronization. Then Bremsstrahlung photon from the hadronization is obtained in the soft photon approximation, and we find that its contribution to the direct photon increases in low-energy heavy-ion collisions and i…
We numerically study the effects of high gluon density at small x on the evolution of gluon distribution function in both hadrons and nuclei. Using a newly derived, Wilson renormalization group-based evolution equation which includes n to 1 gluon ladder fusion, we find significant reduction in nuclear gluon distribution function for large nuclei at zero impact parameter at energies relevant for RHIC and LHC experiments.
We study the energy-momentum and baryonic number conservation laws for quark-gluon plasma discontinuity transitions into hadron matter states. We find that the time-like shock hadronization of a supercooled quark-gluon plasma (when the normal vector to the discontinuity hypersurface is time-like) should take place. We consider some properties of this process, which is different from the standard space-like shock hadronization.
We have carried out simulations of the hadronization of a hot, ideal but effectively massive quark-gluon gas into color neutral clusters in the framework of the semi-classical SU(3) chromodielectric model. We have studied the possible quark-gluon compositions of clusters as well as the final mass distribution and spectra, aiming to obtain an insight into relations between hadronic spectral properties and the confinement mechanism in this model.
Following an explicit example, we present the chain of steps required for an event-by-event description of hadron production in high energy hadronic and nuclear collisions. We start from incoming nuclei, described in the Color Glass Condensate effective theory, whose collision creates the gluon fields of the glasma. Individual gluons are then sampled from the gluon fields' Husimi (smeared Wigner) distributions, and clustered using a new spacetime based algorithm. Clusters are fed into the Herwig event generator, which performs the hadronization, conserving energy and momentum. We discuss the p…
We study the particle production in the early stage of the ultrarelativistic heavy-ion collisions. To this end the Boltzmann kinetic equations for gluons and pions with elastic rescattering are considered together with a simple model for the parton-hadron conversion process (hadronisation). It is shown that the overpopulation of the gluon phase space in the initial state leads to an intermediate stage of Bose enhancement in the low-momentum gluon sector which due to the gluon-pion conversion process is then reflected in the final distribution function of pions. This pattern is very similar to …
The gravitational form factors (GFFs) of hadrons encode the matrix elements of the energy momentum tensor of QCD. These quantities describe how energy, spin, and various mechanical properties of hadrons are carried by their quark and gluon constituents. We present the gluon GFFs of the pion, nucleon, $ρ$ meson, and $Δ$ baryon as functions of the squared momentum transfer $t$ in the region $0 \leq -t < 2 \; \text{GeV}^2$, as determined in a lattice QCD study with pion mass $m_π = 450(5) \; \text{MeV}$. By fitting the extracted GFFs using multipole and z-parameter expansion functional forms, we …
We estimate the energy loss distribution and investigate the quenching of hadron spectra in ultrarelativistic heavy-ion collisions due to the collisional energy loss of energetic partons from hard parton collisions in the initial stage.
The interaction of spatially extended heavy hadrons is investigated in the framework of lattice QCD with dynamical quarks. In addition to the baryon-baryon potential results for the baryon-antibaryon and for the meson-meson system are presented. It is shown that the expected dipole forces have a very short range and that sea quarks play a minor important role.
Final state medium-induced gluon radiation in ultradense nuclear matter is examined and shown to favor large angle emission when compared to vacuum bremsstrahlung due to the suppression of collinear gluons. Perturbative expression for the contribution of its hadronic fragments to the back-to-back particle correlations is derived. It is found that in the limit of large jet energy loss gluon radiation determines the yield and angular distribution of | Delta phi | > Pi/2 di-hadrons to transverse momenta pT2 of the associated particles. Clear transition from enhancement to suppression of the away-…
We modified the gluon saturation model by rescaling the momentum fraction according to saturation momentum and introduced the Cooper-Frye hydrodynamic evolution to systematically study the pseudo-rapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at BNL Relativistic Heavy Ion Collider (RHIC). The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.
We recently introduced a completely new way to study ultrarelativistic nuclear scattering by providing a link between the string model approach and a statistical description. A key issue is the microcanonical treatment of hadronizing individual quark matter droplets. In this paper we describe in detail the hadronization of these droplets according to n-body phase space, by using methods of statistical physics, i.e. constructing Markov chains of hadron configurations.
It has been predicted that dilepton production may be used as a quark-gluon plasma probe. We calculate the rapidity distributions of thermal dileptons produced by an evolving quark-gluon plasma assuming a longitudinal scaling expansion with initial conditions locally determined from the hadronic rapidity density. These distributions are compared with Drell-Yan production and semileptonic charm decays at invariant mass $M = 2$, 4, and 6 GeV.
Theoretical understanding of the observed jet quenching measurements at RHIC and LHC is challenging in QCD because it requires understanding of parton to hadron fragmentation function in non-equilibrium QCD. In this paper, by using closed-time path integral formalism, we derive the gauge invariant definition of the gluon to hadron fragmentation function in non-equilibrium QCD which is consistent with factorization theorem in non-equilibrium QCD from first principles.
The shear ($η$) and bulk ($ζ$) viscosities are calculated in a quasiparticle relaxation time approximation. The hadron phase is described within the relativistic mean field based model with scaled hadron masses and couplings. The quark phase is treated in terms of the heavy quark bag model fitted to the lattice data. A two-phase model allowing for the first order phase transition from the hadron phase to the strongly coupled quark gluon plasma is constructed by means of the Gibbs conditions. Temperature and baryon density dependence of the calculated viscosity-to-entropy ratios ($η/s$, $ζ/s$) …
We calculate the thermodynamic potential of bubbles of hadrons embedded in quark-gluon plasma, and of droplets of quark-gluon plasma embedded in hadron phase. This is a generalization of our previous results to the case of non-zero chemical potentials. As in the zero chemical potential case, we find that a quark-gluon plasma in thermodynamic equilibrium may contain stable bubbles of hadrons of radius $R \simeq 1$ fm. The calculations are performed within the MIT Bag model, using an improved multiple reflection expansion. The results are of relevance for neutron star phenomenology and for ultra…
Hypothesis of quark binding through condensation of gluons inside hadrons is formulated in the context of a renormalization group procedure for effective particles (RGPEP) in the light-front (LF) Hamiltonian approach to QCD. At the momentum scales of relative motion of hadronic constituents that are comparable with Lambda_QCD, the hypothetical boost-invariant constituent dynamics is identified using gauge symmetry. The resulting picture of mesons and baryons closely resembles constituent quark models with harmonic oscillator potentials, shares some features of AdS/QCD, and can be systematicall…
A transport model is developed to describe hadron emission from a strongly coupled quark-gluon plasma formed in relativistic heavy ion collisions. The quark-gluon plasma is controlled by ideal hydrodynamics, and the hadron motion is characterized by a transport equation with loss and gain terms. The two sets of equations are coupled to each other, and the hadronization hypersurface is determined by both the hydrodynamic evolution and the hadron emission. The model is applied to calculate the transverse momentum distributions of mesons and baryons, and most of the results agree well with the ex…
The energy densities achieved during central collisions of large nuclei at Brookhaven's AGS may be high enough to allow the formation of quark--gluon plasma. Calculations based on relativistic nucleation theory suggest that rare events, perhaps one in every 10$^2$ or 10$^3$, undergo the phase transition. Experimental ramifications may include an enhancement in the ratio of pions to baryons, a reduction in the ratio of deuterons to protons, and a larger source size as seen by hadron interferometry.
We study coherent and incoherent diffractive hadron production in high energy quarkonium--heavy nucleus collisions as a probe of the gluon saturation regime of QCD. Taking this process as a model for pA collisions, we argue that the coherent diffractive gluon production, in which the target nucleus states intact, exhibits a remarkable sensitivity to the energy, rapidity and atomic number dependence. The incoherent diffractive gluon production is less sensitive to the details of the low-x dynamics but can serve as a probe of fluctuations in the color glass condensate. As a quantitative measure …
We calculate the cross section for diffractive hadron production in deep inelastic scattering off heavy nuclei in the framework of gluon saturation/color glass condensate. We analyze the kinematic region of the future Electron-Ion Collider. We argue that coherent and incoherent diffractive channels are very sensitive to the structure of the nuclear matter at low $x$. This expresses itself in a characteristic dependence of the cross sections on rapidity and transverse momentum of the produced hadron and on the nuclear weight. We also discuss dependence on the scattering angle and argue that bot…
We review the methods and results obtained in an analysis of the experimental heavy ion collision research program at nuclear beam energy of 160-200A GeV. We study strange, and more generally, hadronic particle production experimental data. We discuss present expectations concerning how these observables will perform at other collision energies. We also present the dynamical theory of strangeness production and apply it to show that it agrees with available experimental results. We describe strange hadron production from the baryon-poor quark-gluon phase formed at much higher reaction energies…
We revisit the physical pictures for the hadronization of quark-gluon plasma, concentrating on the problem of entropy production during processes where the number of degrees of freedom is seemingly reduced due to color confinement. Based on observations on Regge trajectories we propose not having an infinite tower of hadronic resonances. We discuss possible entropy production mechanisms far from equilibrium in terms of stochastic dynamics.
We propose a new kind of two-particle correlation of identified hadrons in longitudinal rapidity space, called $G_{αβ}(y_α,y_β)$, which can reflect clearly the charge correlations of hot quark system produced in AA collisions at LHC energies. It is derived from the basic scenario of quark combination mechanism of hadron production. Like the elliptic flow of identified hadrons at intermediate transverse momentum, this correlation is independent of the absolute hadronic yields but dependent only on the flavor compositions of hadrons, and thus exhibits interesting properties for different kinds o…
We investigate the relativistic equation of state of hadronic matter and quark-gluon plasma at finite temperature and baryon density in the framework of the nonextensive statistical mechanics, characterized by power-law quantum distributions. We study the phase transition from hadronic matter to quark-gluon plasma by requiring the Gibbs conditions on the global conservation of baryon number and electric charge fraction. We show that nonextensive statistical effects play a crucial role in the equation of state and in the formation of mixed phase also for small deviations from the standard Boltz…
We study saturation effects in the production of dijets in p-p and p-Pb collisions using the framework of high energy factorization. We focus on central-forward jet configurations, which allow for probing gluon density at low longitudinal momentum fraction. We find significant suppression of the central-forward jet decorrelations in p-Pb compared to p-p, which we attribute to saturation of gluon density in nuclei.
Hadron multiplicity in the central rapidity region of high-energy heavy-ion collisions is investigated within a two-component mini-jet model which consists of soft and semi-hard particle production. The hard contribution from mini-jets is reevaluated using the latest parameterization of parton distributions and nuclear shadowing. The energy dependence of the experimental data from RHIC requires a strong nuclear shadowing of the gluon distribution in this model. The centrality dependence of the hadron multiplicity at $\sqrt{s}=130$ GeV is reproduced well with the impact-parameter dependent part…
We show that the boundary between quark-dominated and hadron-dominated regions of nuclear structure may be blurred by multi-nucleon quark clusters arising from color percolation. Recent experiments supporting partial percolation in cold nuclei and full percolation in hot/dense nuclear matter include: deep inelastic lepton-nucleus scattering, relativistic heavy-ion collisions and the binding energy in $^5 He_Λ$.
The formulation of the real and virtual photon production rate from strongly interacting matter is presented in the framework of finite temperature field theory. The changes in the hadronic spectral function induced by temperature are discussed within the ambit of the Walecka type model, gauged linear and non-linear sigma models, hidden local symmetry approach and QCD sum rule approach. Possibility of observing the direct thermal photon and lepton pair from quark gluon plasma has been contrasted with those from hot hadronic matter with and without medium effects for various mass variation scen…
The nuclear parton distribution functions (nPDFs) of gluons are known to be difficult to determine with fits of deep inelastic scattering (DIS) and Drell-Yan (DY) data alone. Therefore, the nCTEQ15 analysis of nuclear PDFs added inclusive neutral pion production data from RHIC to help in constraining the gluon. In this analysis, we present a new global analysis of nuclear PDFs based on a much larger set of single inclusive light hadron data from RHIC and the LHC. Using our new nCTEQ code (nCTEQ++) with an optimized version of INCNLO we study systematically the limitations of the theory and the…
Effective chiral Lagrangians involving constituent quarks, Goldstone bosons and long-distance gluons are believed to describe the strong interactions in an intermediate energy region between the confinement scale and the chiral symmetry breaking scale. Baryons and mesons in such a description are bound states of constituent quarks. We discuss the combined use of the techniques of effective chiral field theory and of the field theoretic method known as Fock-Tani representation to derive effective hadron interactions. The Fock-Tani method is based on a change of representation by means of a unit…
Consequences of the constraint of SU(3) colour singletness of quark-gluon plasma are studied. This restriction increases the free energy barrier for the formation of hadronic bubble in supercooled phase and influences significantly the dynamics of the initial stage of quark-hadron phase transition. It also introduces terms dependent on the volume occupied by the plasma in the energy density and the pressure. These modifactions vanish in the limit of an infinite volume. The last stage of the hadronization of the QGP likely to be formed in relativistic heavy ion collisions is necessarily charact…
Chiral-odd gluon transversity distribution could shed light on a new aspect of hadron physics. Although we had much progress recently on quark transversity distributions, there is no experimental measurement on the gluon transversity. The gluon trasversity does not exist in the spin-1/2 nucleons and it exists in the spin-1 deuteron. Therefore, it could probe new hadron physics in the deuteron beyond the basic bound system of a proton and a neutron because the nucleons cannot contribute directly. Here, we explain that the gluon transversity can be measured at hadron accelerator facilities, such…
We propose a new model for a homogeneous description of hadron-hadron and hadron-nucleus collisions, the Gluon Exchange Model, fundamentally based on color octet (gluon) exchange. In proton-proton collisions we provide an exact description of the final state proton and neutron spectrum including the proton diffractive peak. In proton-nucleus reactions we find that the projectile proton diquark cannot survive in more than about half of multiple proton-nucleon processes and consequently must be very frequently disintegrated, leading to long transfers of baryon number over rapidity space.
$SU(N_c)$ colour-singlet restriction, along with flavour and spin symmetry, on thermal partonic ensemble is shown to recombine the partons with internal colour structure into colour-singlet multi-quark clusters which can be identified with various hadronic modes at a given temperature. This provides a possible basis for recombination model for hadronization of quark-gluon plasma. This also leads to a natural explanation for the ratio of (anti)protons to pions and the quark number scaling of the elliptic flow coefficient in relativistic heavy-ion collisions.
Hardening of cosmic proton- and nuclei-spectra is explained by using the gluon condensation (GC) model, which states that a large amount of gluons in proton may condense near the high energy threshold. The results present the GC-effect as common origin of a series of anomalous astrophysical phenomena including the broken power-law in gamma-ray spectra, the excess in positron- and electron-spectra and hardening of proton- and nuclei-spectra.
We argue that gluon saturation effects may be visible in Large Hadron Collider (LHC) data. We look at the centrality dependence of the away-side peak of two-particle correlations measured in p-Pb collisions, using both ALICE data at midrapidity, and LHCb data at forward rapidity. Once the collective flow-like signal measured at the near-side peak is removed from the correlation function, the centrality dependence of the away-side peak turns out to be much stronger in the forward region than at midrapidity. We argue that this is a very specific prediction of the saturation framework, and we com…
The properties of the quark and hadron Universe are explored. Kinetic theory considerations are presented proving that hadron abundances after phase transformation from quarks to hadrons remain intact till abundances of hadrons become irrelevant. The hadronization process and the evolution of hadron yields is described in detail.
We present an analysis of the dynamics of two-flavour QCD in the vacuum. Special attention is payed to the transition from the high energy quark-gluon regime to the low energy regime governed by hadron dynamics. This is done within a functional renormalisation group approach to QCD amended by dynamical hadronisation techniques. The latter allow us to describe conveniently the transition from the perturbative high-energy regime to the nonperturbative low-energy limit without suffering from a fine-tuning of model parameters. In the present work, we apply these techniques to two-flavour QCD with …
We investigate the hadron production from the vortical quark-gluon plasma created in heavy-ion collisions. Based on the quark-coalescence and statistical hadronization models, we show that total hadron yields summed over the spin components are enhanced by the local vorticity with quadratic dependence. The enhancement factor amounts to be a few percent and may be detectable within current experimental sensitivities. We also show that the effect is stronger for hadrons with larger spin, and thus propose a new signature of the local vorticity, which may be detected by the yield ratio of distinct…
We introduce a combined macroscopic/microscopic transport approach employing relativistic hydrodynamics for the early, dense, deconfined stage of the reaction and a microscopic non-equilibrium model for the later hadronic stage where the equilibrium assumptions are not valid anymore. Within this approach we study the dynamics of hot, bulk QCD matter, which is expected to be created in ultra-relativistic heavy ion collisions at the SPS, the RHIC and the LHC. Our approach is capable of self-consistently calculating the freeze-out of the hadronic system, while accounting for the collective flow o…
In high density QCD the hadron production stems from decay of mini-jets that have the transverse momenta of the order of the saturation scale. It is shown in this paper that this idea is able to describe in a unique fashion both the inclusive hadron production for \sqrt{s} \geq 546 GeV including the first data from LHC and the deep inelastic scattering at HERA. Recently reported data from ALICE, CMS and ATLAS including inclusive charged-hadron transverse-momentum and multiplicity distribution in pp collisions are well described in our approach. We provide predictions for the upcoming LHC measu…
We discuss the role of noise and dissipation in the explosive spinodal decomposition scenario of hadron production during the chiral transition after a high-energy heavy ion collision. We use a Langevin description inspired by nonequilibrium field theory to perform real-time lattice simulations of the behavior of the chiral fields. Preliminary results for the interplay between additive and multiplicative noise terms, as well as for non-Markovian corrections, are also presented.
The upcoming p+Pb run at the LHC will probe the nuclear gluon distribution at very small Bjorken x (from $x \sim 10^{-4}$ at mid-rapidity down to $x \sim 10^{-6}$ in the proton fragmentation region) and will allow to test approaches based on parton saturation. Here, we present the predictions of the KLN model for hadron multiplicities and multiplicity distributions in p+Pb collisions at a center-of-mass energy of 4.4 TeV. We also compare the model to the existing pp, dA and AA data from RHIC and LHC.
The exclusive vector meson production cross section is one of the most promising observables to probe the high energy regime of the QCD dynamics. In particular, the squared momentum transfer ($t$) distributions are an important source of information about the spatial distribution of the gluons in the hadron and about fluctuations of the color fields. In this paper we complement previous studies on exclusive vector meson photoproduction in hadronic collisions presenting a comprehensive analysis of the $t$ - spectrum measured in exclusive $ρ$, $ϕ$ and $J/Ψ$ photoproduction in $pp$ and $PbPb$ col…
