Hydrodynamic models for heavy-ion collisions and beyond

A generic property of a first-order phase transition in equilibrium, and in the limit of large entropy per unit of conserved charge, is the smallness of the isentropic speed of sound in the “mixed phase”. A specific prediction is that this should lead to a non-isotropic momentum distribution of nucleons in the reaction plane (for energies ≈ 40 A GeV in our model calculation). On the other hand, we show that from present effective theories for low-energy QCD one does not expect the thermal transition rate between various states of the effective potential to be much larger than the expansion rate, questioning the applicability of the idealized Maxwell/Gibbs construction. Experimental data could soon provide essential information on the dynamics of the phase transition.     

Pseudoscalar mesons in the c-c and b-b systems

It is shown that the pseudoscalar η_c and “η_c” (η_b and “η_b”) with M ≈ 2.80 and 3.51 GeV (9.17 and 9.88 GeV) can be predicted by using the radial mixing model, where the “η_c” and “η_b” are the excited 0^- states in the $\text{c-}\text{c}$ and $\text{b-}\text{b}$ systems, respectively, and the former would correspond to the observed 0^- meson with M ≈ 3.45 GeV in charmonium.     

“Massive” perturbative QCD, Regular in the IR limit

The goal of the research is to devise a modification of the perturbative QCD (pQCD) that should be regular in the low-energy region and could serve as a practical means for the analysis of data below 1 GeV down to the IR limit. Recent observation of the four-loop pQCD series “blow-up” in the region below 1 GeV for the Bjorken Sum Rule gave an impetus to this attempt. The proposed “massive” analytic pQCD has two sources. It can be treated as the common logarithmic pQCD with only one parameter added, the effective “glueball mass” m _gl ? 1 GeV, serving as an IR regulator. At the same time, it looks like a modification of Analytic Perturbation Theory (APT) comprising nonpower perturbative expansion that makes it compatible with linear integral transformations. Figuratively (with minor reservations), the proposed MAPT differs from the minimal APT by simple ansatz Q ² → Q ² + m _g1 ² .     

Comparison of e+e− annihilation with QCD and determination of the strong coupling constant

We have analyzed 1113 events of the reaction e⁺e^? → hadrons at CM energies of 12 and 30 GeV in order to make a detailed comparison with QCD. Perturbative effects can be well separated from effects depending on the quark and gluon fragmentation parameters to yield a reliable measurement of the coupling constant α_S. At 30 GeV, the result is α_S = 0.17 ± 0.02 (statistical) ± 0.03 (systematic). QCD model predictions, using the fragmentation parameters determined along with α_S, agree with both gross properties of the final states and with detailed features of the three-jet states.     

Exotic mesons withJ PC=1−+, strange and non-strange

We analyse the QCD sum rules for the exotic quark-antiquark-gluon states called “glukonium” or “hermaphrodite” mesons. We predict a non-strange resonance of this type at ～1.5 GeV, a strange one at ～1.6 GeV and a strange-antistrange one at ～1.75 GeV. It should be noted that the above values of masses depend crucially on the vacuum expectation value of the gluon field operator <g ³ f _abc ·G _μv ^a G _vλ ^b G _λμ ^c >.     

Polarization in charge exchange reaction π−+p→π0+n at 40 GeV/c for the 4-momentum transfer range 0<|t|<2 (GeV/c)2

The results on measuring polarization in charge exchange reaction π^?+p→π⁰+n at 40 GeV/c are presented for the 4-momentum transfer range from 0 up to 2 (GeV/c)². At |t|≦0.4 (GeV/c)² the polarization has a positive sign. In the “crossover” region of π^± elastic scattering a possible minimum in the polarization behaviour has been seen for the first time. the polarization is zero within the statistical accuracy near this point. In the “deep” region of the charge-exchange differential cross-section the polarization has a negative sign. The presented data are not in agreement with the modern theoretical models.     

Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice

The Hubbard model is investigated for a halffilled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the “metallic” phase at small U and a complementary wave function for the insulating regime at large values of U. The comparison of the two variational ground states at the mean-field level yields a Mott transition at U _c /t ≈ 5:3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the “metallic” wave function with respect to antiferromagnetism. The critical value U _m/t ≈ 3:7 obtained in this way is considered to be a lower bound for the true critical point for antiferromagnetism, whereas there are good arguments that the mean-field value U _c/t ≈ 5:3 represents an upper bound for the Mott transition. Therefore the “metal”- insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon.     

Two-photon exchange in p⊆)p→ℓ+ℓ−X and a comparison with QCD

A thorough study of lepton-pair production from two-photon annihilation in p?)p collisions is presented. The differential cross section is calculated over a large range of energies (27?√s?800 GeV as a function of the dilepton mass M as well as the dilepton transverse momentum Q_T and the Feynman variable x_F. No kinematical approximations (such as the equivalent photon approximation) are made. For Q_T ≈ 0 the two-photon mechanism represents an important fraction of the pp→e⁺e^?X cross section already at ISR energies, whereas at ISABELLE energies it dramatically dominates in the interval 0?Q_T?1 GeV. At ISR energies these conclusions follow from a direct comparison of the two-photon contribution with pp→e⁺e^?X data. For the ISABELLE energy range the expected O(α_s) QCD contribution to pp→?⁺?^?X, corrected for soft gluon radiation to all orders (in leading bilogarithmic approximation), was taken as a reference. At larger Q_T and ISR energies the γγ contribution is negligible, whereas at √s = 800 GeV γγ/QCD? 10–20% almost everywhere. Furthermore, two-photon candidate events from the ISR are shown to be in reasonable agreement with theory. A decomposition of the γγ cross section into contributions from both proton vertices being elastic, inelastic and of mixed configuration is given. The results provide important clues for a future isolation of the two-photon mechanism.     

Perturbative thermalisation in nuclear collisions at very high energies?

According to lowest order perturbation theory more than one hundred gluons and quarks with p_T > p₀ ≈2 GeV are produced per unit rapidity within a time of 0.1 fm in an average collision of two large nuclei at a CMS energy/particle in the few 100 GeV range. We show, including longitudinal expansion and QCD branching, that before a time of about 0.4 fm each of these will experience more than one collision with one of the other gluons and quarks. Without any assumptions concerning soft QCD one thus concludes that the quark-gluon subsystem is driven towards thermalisation.     

TheJ/ψ→η c γ decay in QCD sum rules

In QCD sum rules, including power correction ≈G ², the amplitudes and decay rates of “magnetic-dipole” (M1) types radiative transition in charmonium are obtained.     

Baryon spectrum and the forces between quarks

We study the effect of confinement on gluon bremsstrahlung. A natural infrared cutoff emerges both at small gluon momenta and at small angles. If the confinement potential is of the linear “string” type, the cutoff is controlled by the tension parameter and is thus about 1GeV for the transverse momentum of a hard gluon relative to its parent quark. We propose that this confinement effect may remove the necessity for introducing ad hoc cutoffs by a large “intrinsic partonp _T ” in phenomenological applications of perturbative QCD.     

Diffraction dissociation,the deck mechanism and diffractive resonance production

We have constructed a model amplitude for the diffractive production of resonant states in the presence of Deck amplitudes: rescattering corrections to the Deck amplitudes are included. We have found that gross distortion of the resonance may occur and also that the phase of the diffractively produced system may vary very slowly, despite the existence of resonances: the only requirement is that the phase of the Deck amplitude leads the production phase of the resonance by ≈40°. Our model simultaneously accommodates the well established lack of phase variation in the diffractively produced 1⁺ s-wave (A1) ?π system and the details of the variation of intensity with mass, with resonance parameters M_A1 ≈ 1.3 GeV/c² and Γ_A1 ≈ 240 MeV/c². The analogous Kππ (Q) diffractive enhancement fits satisfactorily into the same framework. Our model also accounts for a number of features of diffractive N¹ production.     

Thermal multifragmentation of hot nuclei and liquid-fog phase transition

Multiple emission of intermediate-mass fragments (IMF) in the collisions of protons (up to 8.1 GeV), ⁴He (4 and 14.6 GeV), and ¹²C (22.4 GeV) on Au has been studied with the 4π setup FASA. In all the cases, thermal multifragmentation of the hot and diluted target spectator takes place. The fragment multiplicity and charge distributions are well described by the combined model including the modified intranuclear cascade followed by the statistical multibody decay of the hot system. IMF-IMF-correlation study supports this picture, giving a very short time scale of the process (≤70 fm/c). This decay process can be interpreted as the first-order nuclear “liquid-fog” phase transition inside the spinodal region. The evolution of the mechanism of thermal multifragmentation with increasing projectile mass was investigated. The onset of the radial collective flow was observed for heavier projectiles. The analysis reveals information on the fragment space distribution inside the breakup volume: heavier IMFs are formed predominantly in the interior of the fragmenting nucleus possibly due to the density gradient.     

Observation of QCD effects in transverse momenta of e+e− jets

Probability distributions of the total transverse momenta (K⊥) of charged particles produced in hadronic jets in e⁺e^? annihilations have been measured for center of mass energies in the range from 9.2 to 31.6 GeV. A linear increase of the average K_⊥² with Q² is observed. The data are successfully compared with high order QCD predictions (according to a simple q$\text{q}$ picture supplemented by multiple emission of soft gluons). Deviations from this picture at the highest energies and large K_⊥ are then analyzed in terms of hard gluon bremsstrahlung and qualitative agreement is found with first order QCD predictions. Scaling “in the mean” is found to be valid both for jet and single particle transverse momenta.     

A new study of Kπ scattering between 0.7 and 2 GeV/c2

We present new data on the reaction K⁺d → K⁺π^?p(p), at 5.44 GeV/c. This reaction is dominated by absorbed pion exchange and we have used the data to study K⁺π^? scattering between 0.7 and 2 GeV/c². We find the $\text{I=}\text{1}\text{2}$ s-wave Kπ phase shift increases approximately linearly with mass up to 1.45 GeV/c², and have evidence for a more rapid variation of the s-wave amplitude in the region of 1.5 GeV/c². The so-called “up” branches in the region of the K¹(890) and K¹(1400) are excluded, save for the possibility of narrow s-wave resonances of width <10 MeV/c². We have explained quantitatively every aspect of the data up to 2 GeV/c² with s-, p-, d- and f-waves, finding an f-wave resonance at a mass of ≈1.76 GeV/c² and with a width ≈300 MeV/c². We have obtained new resonance parameters for the K¹(1400) which differ substantially from the currently accepted values.     

The hypothesis of statistical jet evolution confronted withe + e − annihilation data

We describe the processe ⁺ e ^?→ hadrons in a “dynamical” phase space, where energy and momentum are quantised in a volume, which expands with velocity of light in a sequence of discrete time steps. Our hypothesis of statistical evolution which is based on an appropriate application of the equipartition principle, determines uniquely the distribution over the resolvable states in this dynamical phase space and leads to a branching process. Neglecting all degrees of freedom except energy and momentum, and restricting to final state pions we arrive at a minimal model with no other parameters thanh, c andm _π. We compare this model in detail with data on multiplicities, inclusive spectra and energy-energy correlations; new energy flow measurements will be proposed. The low energy region (1<W<5 GeV) may provide a clue on the role of color as a new degree of freedom.     

Baryon-to-entropy ratio in very high energy nuclear collisions

We compute as a function of rapidity y the baryon number carried by quarks and antiquarks with p _T > p ₀ ≈ 2 GeV produced in Pb+Pb collisions at TeV energies. The computation is carried out in lowest order QCD perturbation theory using structure functions compatible with HERA results. At p ₀ = 2 GeV the initial gluon density is both transversally saturated and thermalised in the sense that the energy/gluon equals to that of an ideal gas with the same energy density. Even at these high energies the initial net baryon number density at y = 0 at τ = 0.1 fin will be more than the normal nuclear matter density but the baryon-toentropy ratio is only (B-B?)/S ～ 1/5000. Further evolution of the system is discussed and the final baryon-to-entropy ratio is estimated.     

Correlations of pions and kaons as a measure for delayed expansion due to the QCD phase transition

We study pion and kaon correlations in ultra-relativistic heavy ion collisions in a hydrodynamical model with transverse cylindrical and boost-invariant longitudinal symmetry. As a function of the initial energy density ε₀, the ratioR _out/R _side of the inverse widths of the two-particle correlation function in out- and side-direction reflects the behaviour of the lifetime of the system. The ratio shows an enhancement in the case of a delayed expansion caused by the QCD phase transition. We discuss how this time-delay signal depends on the average transverse momentum of the pair, and show that it appears particularly strong for pairs with large average transverse momentum,K _⊥～1 GeV and for initial energy densities ε₀ ? 10 ? 20 GeVfm^?3 GeVfm^?3, corresponding to nuclear collisions at RHIC.