Last Call for RHIC Predictions
This paper contains the individual contributions of all speakers of the session on 'Last Call for RHIC Predictions' at Quark Matter 99, and a summary by the convenor.
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arXiv subjects
D. Kharzeev
Publications and source records attributed to D. Kharzeev.
Scalar Glueball--Quarkonium Mixing and the Structure of the QCD Vacuum
We use Ward identities of broken scale invariance to infer the amount of scalar glueball--$\bar{q}q$ meson mixing from the ratio of quark and gluon condensates in the QCD vacuum. Assuming dominance by a single scalar state, as suggested by a phase-shift analysis, we find a mixing angle $γ\sim 36^{\circ}$, corresponding to near-maximal mixing of the glueball and $\bar{s}s$ components.
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Long-Range Forces of QCD
We consider the scattering of two color dipoles (e.g., heavy quarkonium states) at low energy - a QCD analog of Van der Waals interaction. Even though the couplings of the dipoles to the gluon field can be described in perturbation theory, which leads to the potential proportional to (N_c^2-1)/R^{7}, at large distances R the interaction becomes totally non-perturbative. Low-energy QCD theorems are used to evaluate the leading long-distance contribution \sim (N_f^2-1)/(11N_c - 2N_f)^2 R^{-5/2} exp(-2 μR) (μis the Goldstone boson mass), which is shown to arise from the correlated two-boson exchange. The sum rule which relates the overall strength of the interaction to the energy density of QCD vacuum is derived. Surprisingly, we find that when the size of the dipoles shrinks to zero (the heavy quark limit in the case of quarkonia), the non-perturbative part of the interaction vanishes more slowly than the perturbative part as a consequence of scale anomaly. As an application, we evaluate elastic πJ/ψand πJ/ψ\to πψ' cross sections.
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Interactions of quarkonium at low energies
We present two examples of the short-distance QCD calculations for the quarkonium (Φ) interactions; 1) πΦelastic and πΦ-> πΦ' cross sections, and 2) the potential between two Φ's. The former is relevant for the Φsuppression in heavy ion collisions; we find that the corresponding cross sections are very small. For the latter we derive the sum rule which relates the strength of the potential to the energy density of the QCD vacuum. The key starting point in both cases is that the leading operator in the operator product expansion (OPE) for the low--energy scattering amplitude is the trace of the QCD stress tensor whose matrix elements are unambiguously fixed by the low energy theorem. The resonances in the two-pion scalar channel are taken into account as a formfactor.
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Quarkonium Formation Time in a Model-Independent Approach
We use dispersion relations to reconstruct, in a model-independent way, the formation dynamics of heavy quarkonium from the experimental data on e+ e- annihilation to Q-bar Q. We extract a distribution of formation times with a mean value for the J/psi, tau{J/psi} = 0.44 fm; and for the Upsilon, tau{Upsilon} = 0.32 fm. The corresponding widths of these distributions are given by Delta-tau{J/psi} = 0.31 fm and Delta-tau{Upsilon} = 0.28 fm. This information can be used as an input in modeling of heavy quarkonium production on nuclear targets.
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Chi_2 production in polarized pp collisions at RHIC: measuring ΔG and testing the color octet model
We consider the production and decay of the $χ_2$ charmonium state in polarized and unpolarized $pp$ collisions at RHIC in the framework of an effective theory based on the QCD multipole expansion. We find that the angular distribution in the decay of the produced charmonium, $χ_2 \to J/ψ+ γ$, in the unpolarized case allows us to distinguish clearly between the color singlet and color octet production mechanisms. Once the production mechanism is known, the angular distribution in the polarized case can be used to measure the polarized gluon distribution in the proton, $ΔG(x)$.
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$J/ψ$ Photoproduction and the Gluon Structure of the Nucleon
Using short distance QCD methods based on the operator product expansion, we calculate the $J/ψ$ photoproduction cross section in terms of the gluon distribution function of the nucleon. Comparing the result with data, we show that experimental behaviour of the cross section correctly reflects the $x$-dependence of the gluon distribution obtained from deep inelastic scattering.
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Parity odd bubbles in hot QCD
We consider the topological susceptibility for an SU(N) gauge theory in the limit of a large number of colors, $N \to \infty$. At nonzero temperature, the behavior of the topological susceptibility depends upon the order of the deconfining phase transition. The most interesting possibility is if the deconfining transition, at $T=T_d$, is of second order. Then we argue that Witten's relation implies that the topological susceptibility vanishes in a calculable fashion at $T_d$. As noted by Witten, this implies that for sufficiently light quark masses, metastable states which act like regions of nonzero $θ$ --- parity odd bubbles --- can arise at temperatures just below $T_d$. Experimentally, parity odd bubbles have dramatic signatures: the $η'$ meson, and especially the $η$ meson, become light, and are copiously produced. Further, in parity odd bubbles, processes which are normally forbidden, such as $η\to π^0 π^0$, are allowed. The most direct way to detect parity violation is by measuring a parity odd global asymmetry for charged pions, which we define.
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Possibility of spontaneous parity violation in hot QCD
We suggest that for QCD in the limit of a large number of colors, N, the axial U(1) symmetry of massless quarks is effectively restored at the deconfining=chiral phase transition. If the deconfining transition is of second order, then the chiral transition is weakly first order. In this case, metastable states in which parity is spontaneously broken appear at temperatures below the phase transition. The production of these metastable states would have dramatic signatures, including enhanced production of eta and eta' mesons, which can decay through parity violating decay processes such as eta -> pi^0 pi^0, and global parity odd asymmetries for charged pions. Using a nonlinear sigma model, in QCD these metastable states only appear rather near the phase transition.
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Long-Range Interactions of Small Color Dipoles
We study the scattering of small color dipoles (e.g., heavy quarkonium states) at low energies. We find that even though the couplings of color dipoles to the gluon field can be described in perturbation theory, at large distances the interaction becomes totally non--perturbative. The structure of the scattering amplitude, however, is fixed by the (broken) chiral and scale symmetries of QCD; the leading long--distance contribution arises from the correlated two--pion exchange. We use the spectral representation technique to evaluate both perturbative and non-perturbative contributions to the scattering amplitude. Our main result is the sum rule which relates the overall strength of the non--perturbative interaction between color dipoles to the energy density of QCD vacuum.
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Theoretical Interpretations of J/Psi Suppression: A Summary
The strong "anomalous" J/Psi suppression observed recently by the NA50 Collaboration at CERN SPS has attracted considerable attention. Is it the first signature of a long-awaited quark-gluon plasma, or just a peculiar combination of "conventional" effects acting together to produce the puzzling pattern observed experimentally? This talk is an attempt to summarize the theoretical explanations proposed during the last two years.
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Anomalous J/Psi suppression and the nature of deconfinement
We study the characteristic features of J/Psi suppression by deconfinement. A first order phase transition leads to an essentially discontinuous onset of anomalous J/Psi suppression. The different energy densities required for the dissociation of different charmonium states result in a two-step suppression pattern, in which first the J/Psi's from chi decays are suppressed and subsequently the directly produced J/Psi states. Combining both features leads to a unique form of J/Psi suppression in a deconfining medium.
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The Transverse Momentum Dependence of Anomalous $J/ψ$ Suppression
In proton-nucleus and nucleus-nucleus collisions up to central $S-U$ interactions, the $P_T$-dependence of $J/ψ$ production is determined by initial state parton scattering and pre-resonance nuclear absorption (``normal" $J/ψ$ suppression). The ``anomalous" $J/ψ$ suppression in $Pb-Pb$ collisions must reduce the normal $P_T$ broadening, since it occurs mainly in the central part of the interaction region, where also initial state parton scattering and nuclear absorption are strongest. We thus expect for $< P_T^2 >$ in $Pb-Pb$ collisions a turn-over and decrease with increasing $E_T$.
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A Quantitative Analysis of Charmonium Suppression in Nuclear Collisions
Data from J/psi and psi' production in p-A collisions are used to determine the cross section for absorption of pre-resonance charmonium in nuclear matter. The J/psi suppression in O-Cu, O-U and S-U collisions is fully reproduced by the corresponding nuclear absorption, while Pb-Pb collisions show an additional suppression increasing with centrality. We study the onset of this change in terms of hadronic comover interactions and conclude that so far no conventional hadronic description can consistently account for all data. Deconfinement, starting at a critical point determined by central S-U collisions, is in accord with the observed suppression pattern.
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On the Sum Rule Approach to Quarkonium-Hadron Interactions
We extend a recent sum rule calculation for inelastic quarkonium-hadron interactions to realistic parton distribution functions; we also include finite target-mass corrections. Both modifications are shown to have no significant effect on the resulting cross section behaviour but the performed analysis gives useful insights on the sum-rule approach in general.
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Quarkonium Production and Color Deconfinement in Nuclear Collisions
The suppression of quarkonium production in nucleus-nucleus collisions was originally proposed as a signal of colour deconfinement. Strong ``anomalous" J/ψsuppression in Pb-Pb collisions has been reported at this Conference by the NA50 Collaboration. Is this suppression really anomalous? Can we conclude that the quark-gluon plasma is already discovered? What has to be done next? I address these questions basing on the current theoretical understanding of quarkonium production and new precise experimental information.
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Can Gluons Trace Baryon Number?
QCD as a gauge non-Abelian theory imposes severe constraints on the structure of the baryon wave function. We point out that, contrary to a widely accepted belief, the traces of baryon number in a high-energy process can reside in a non-perturbative configuration of gluon fields, rather than in the valence quarks. We argue that this conjecture can be tested experimentally, since it can lead to substantial baryon asymmetry in the central rapidity region of ultra-relativistic nucleus-nucleus collisions.
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