Sign-posting the phase diagram of quantum chromodynamics

The good agreement between lattice predictions and data for the shape of the distribution of event-by-event fluctuations of the baryon number is discussed. Such comparisons can give fine probes of thermalization, and can be used to provide a direct determination of the cross-over temperature T _c of QCD. The logic of these comparisons and the systematics involved are discussed. The same methods can be used to further explore the phase diagram.     

Net-proton measurements at RHIC and the quantum chromodynamics phase diagram

Two measurements related to the proton and antiproton production near midrapidity in \(\sqrt {s_{{NN}}} = 7.7\) , 11.5, 19.6, 27, 39, 62.4 and 200 GeV Au+Au collisions using the STAR detector at the Relativistic Heavy Ion Collider (RHIC) are discussed. At intermediate impact parameters, the net-proton midrapidity dv ₁/dy, where v ₁ and y are directed flow and rapidity, respectively, shows non-monotonic variation as a function of beam energy. This non-monotonic variation is characterized by the presence of a minimum in dv ₁/dy between \(\sqrt {s_{NN}} = 11.5\) and 19.6 GeV and a change in the sign of dv ₁/dy twice between \(\sqrt {s_{{NN}}}\) = 7.7 and 39 GeV. At small impact parameters the product of the moments of net-proton distribution, kurtosis × variance (κ σ ²) and skewness × standard deviation (S σ) are observed to be significantly below the corresponding measurements at large impact parameter collisions for \(\sqrt {s_{{NN}}}\) = 19.6 and 27 GeV. The κ σ ² and S σ values at these beam energies deviate from the expectations from Poisson statistics and that from a hadron resonance gas model. Both these measurements have implications towards understanding the quantum chromodynamics (QCD) phase structures, the first-order phase transition and the critical point in the high baryonic chemical potential region of the phase diagram.     

The deconfining phase transition in lattice quantum chromodynamics

We present a large-scale Monte Carlo calculation of the deconfining phase transition temperature in lattice quantum chromodynamics without fermions. Using the Wilson action, the transition temperature as a function of the lattice couplingg is consistent with scaling behavior dictated by the perturbativeα function for 6/g²>6.15. Speaker at the conference; on leave from CRIP, Budapest.     

Photon structure functions in quantum chromodynamics: (II). Feynman diagram method

We compute the strong interaction corrections to the polarized photon structure functions using perturbative chromodynamics. The results agree with those of our previous calculations with the operator product expansion method.     

Perturbative quantum chromodynamics

A large variety of modern perturbative aspects of QCD is critically reviewed from a theoretical as well as phenomenological point of view. The first part of this review is devoted to the classical more formal approach of summing leading logs: After a brief discussion of the basic concepts of renormalization theory, we review the renormalization group and its predictions for the effective (running) coupling constant in any field theory (asymptotic freedom as well as ‘fixed point’ theories). Using, in addition, the operator product expansion for deep inelastic scattering we calculate scaling violations of structure functions and show how to compare these results with experiment. Furthermore, dynamical calculations of parton distributions are discussed, as well as σ_L/σ_T, jets in leptoproduction and subleading corrections. We then proceed to show how these renormalization group improved results can be also derived using a simple perturbative language (Kogut-Susskind; Altarelli-Parisi) or by summing parton (Bethe-Salpeter) ladders. The universal validity (process independence) of the resulting Q² dependencies of parton distributions is emphasized and their factorization from the uncalculable non-perturbative piece (infrared divergences) is discussed. These latter results enable us to make rather unambiguous predictions for processes other than deep inelastic scattering, to which the remainder of this review is devoted. The hard scattering processes discussed indetail include hadronic (Drell-Yan) production of lepton pairs as well as their transverse momenta, the hadronic production of heavy quark flavors, semi-inclusive processes and fragmentation functions, high-p_T reactions and some recent topics and problems of jet production in e⁺e^? annihilation.     

The static potential in quantum chromodynamics

The effective interaction between a static quark-antiquark pair is computed within the framework of 〈G_μv^aG_a^μv〉 ≠ 0. Due to the static approximation the interaction takes the form of a potential, which is in striking agreement with phenomenological potentials.     

Deconfining and chiral phase transitions in quantum chromodynamics at finite temperature

We give further arguments to support the claim of Svetitsky and Yaffe that the finite-temperature transition in 4-dimensional SU(N) gauge theories is in the universality class of 3-dimensional Z_N spin models. We show that this implies a smoothing out of the transition when quarks are added to the system as long as N ≠ 3. For N = 3 the pure gauge transition is expected to be first order and will be smoothed by quarks only if the quark contribution to the internal energy is larger than the latent heat of transition.     

Condensates in quantum chromodynamics

The paper presents a short review of our knowledge today on vacuum condensates in quantum chromodynamics (QCD). The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determining physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of the quark condensate, connected to the existence of baryon masses, is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic τ decay. In theoretical analysis, the terms of perturbation theory (PT) up to α _s ³ are accounted for; in the operator product expansion (OPE), those up to dimension 8. The total probability of the decay τ → hadrons (with zero strangeness) and of the τ-decay structure functions are best described at α _s (m _τ ² )=0.330±0.025. It is shown that the Borel sum rules for τ-decay structure functions along the rays in the q ²-complex plane are in agreement with experiment, having an accuracy of ～2% at the values of the Borel parameter |M ²|>0.8 GeV². The magnitudes of dimension 6 and 8 condensates were found, and the limitations on gluon condensates were obtained. The sum rules for the charmed-quark vector-current polarization operator were analyzed in three loops (i.e., in order α _s ² ). The value of the charmed-quark mass (in an \(\overline {MS} \) regularization scheme) was found to be \(\bar m_c (\bar m_c^2 ) = 1.275 \pm 0.015\) GeV, and the value of gluon condensate was estimated as 〈0|(α _s/π)G ²|0〉=0.009±0.007 GeV⁴. The general conclusion is that the QCD described by PT + OPE is in good agreement with experiment at Q ²?1 GeV².     

The bose form of two-dimensional quantum chromodynamics

By means of a special choice of gauge QCD₂ [SU(N)] with one flavor of quarks is recast into the Bose form. Weak (g m) and strong (gm) coupling regimes are studied. The former is shown to be the SU(N)-symmetric confining phase in which bound states possess stringlike configurations with strings being represented by electric vortex lines; the ordinary mesons and baryons appear as longitudinal modes of electric strings. The strong coupling regime describes the Higgs phase with the residual symmetry [U(1)]^N−1 S_N where the left and right factors are the maximal abelian subgroup of SU(N) and the permutation group of N quarks, respectively; the particle spectrum consists of S_N multiplets and the [Uw(1)]^N−1 charges are trapped.     

The quark form factor in quantum chromodynamics

It is shown how leading logarithmic predictions of certain quark form factor effects in QCD, such as the suppression of the Drell-Yan process at small transverse momenta and of the collinear energy-energy correlation in e⁺e^? annihilation, are invalidated by non-leading logarithms corresponding to the vectorial cancellation of gluon transverse momenta. Simple improved expressions incorporating this phenomenon are presented.     

Charmed baryons in quantum chromodynamics

We consider a three-phase model of strongly interacting matter, treating each phase as an ideal gas modified by a simple phenomenological interaction feature. For nuclear matter, we take into account the baryonic repulsion; for the quark-gluon plasma, we include the bag pressure; the constituent quark phase has a non-zero effective quark mass as well as an independent bag pressure. By studying which phase dominates thermodynamically in what region of temperature and baryon number density, we obtain a phase diagram for strongly interacting matter and gain some insight on the relation between deconfinement and chiral symmetry restoration.     

Scaling violations and perturbative quantum chromodynamics

We try to understand the meaning of the recent data on scaling violations of the moments of the structure function F₃ measured in ν and $\text{ν}$ deep inelastic scattering, and their relevance as a test of QCD. We do this by reducing to the minimum the theoretical machinery and prejudices and stressing the perturbative nature of the problem. We are led to a definition of the perturbation coupling constant σ_S(Q = 2.5 GeV) = 0.61 ± 0.06, in termas of which the corrective terms for all quantities computed so far turn out to be relatively small.     

On de-globalization in quantum chromodynamics

The recent discovery and resummation of a class of single logarithmic effects (non-global logs), has a significant impact on several QCD observables ranging from the classic Sterman-Weinberg jet definition to currently studied event shapes and rapidity gap observables. The discovery of the above effects overturns, for example, the common wisdom that hadronic energy flow in limited inter-jet regions is dictatedprimarily by the colour flow of the underlying hard partonic subprocess. We discuss some features of non-global logs and the rapid progress being made in estimating and controlling such corrections.     

Multijet structure in quantum chromodynamics

Field theories naturally give rise to multiple jets of hadrons in short-distance processes, such as e⁺ e^? annihilation. In particular, a low-energy jet of hadrons distributed in some cone of opening angle δ would be naively expected to evolve at high energies into multiple jets within the angle δ. We explore to what extent this will happen in quantum chromodynamics.     

The short-range nucleon-nucleon interaction from nonrelativistic quantum chromodynamics

A careful derivation of the nucleon-nucleon (NN) interaction from nonrelativistic quantum chromodynamics is presented. The theory predicts the short-range repulsion. Both the spin-orbit and the tensor interactions, given by the theory, have the right signatures but are too weak. It is also found that the theory is unable to give sufficient attraction in the intermediate range.     

Quantum phase diagram of granular superconducting quantum dots array

We study the quantum phase diagram of granular superconducting quantum dots (GSQD) array. We implement the physics of granularity by considering site dependent Josephson couplings, on-site charging energies and the intersite interactions. We predict dimer density wave and staggered phases at the insulating state for higher order commensurability. Several parts of the quantum phase diagram of GSQD are in contrast with the clean superconducting quantum dots array. We also obtain the superconducting phase of GSQD. We develop the theory for weak tunneling conductance and the Coulomb energy is smaller than the superconducting gap.