Diquark condensate and quark interaction with an instanton liquid

The interaction of light quarks with an instanton liquid is considered at nonzero density of quark/baryon matter in a phase where the diquark condensate is nonzero. It is shown that the inclusion of the relevant perturbation of the instanton liquid leads to an increase in the quark chemical potential μ_c. This in turn induces a considerable growth of the threshold quark-matter density at which one expects the emergence of color superconductivity.     

Instantons and meson correlation functions in QCD

Various QCD correlators are calculated in the instanton liquid model in zeromode approximation and 1/N _c expansion. Previous works are extended by including dynamical quark loops. In contrast to the original “perturbative” 1/N _c approximation, not all quark loops are suppressed. Renormalization of the instanton density allows the identification of the density with the gluon condensate even in presence of dynamical quark loops. In the flavor singlet meson correlators a chain of quark bubbles survives the N _c → ∞ limit causing a massive η′ in the pseudoscalar correlator while keeping massless pions in the triplet correlator. The correlators are plotted and meson masses and couplings are obtained from a spectral fit. They are compared to the values obtained from numerical studies of the instanton liquid and to experimental results.     

Instantons: Dynamical mass generation,chiral Ward identities and the topological charge correlation function

When dynamical mass generation resulting from the breakdown of chiral symmetry is taken into account, instanton dynamics treated within the dilute gas approximation may satisfy the constraints on the quark condensates and the topological charge correlation function derived by Crewther from an analysis of the chiral Ward identities assuming the absence of a physical axial U(1) Goldstone boson. From a consideration of the contribution of the η′ to the topological charge correlation function, a relationship is derived in which m_η′²f_η′² is proportional to the vacuum energy density.     

The structure of the multi-instanton gas

We parametrize the q-instanton solutions of an SU(2) gauge theory in terms of the positions of 2q constituent particles or “instanton quarks”. Explicit computations of lowest order quantum fluctuations about the q = 1 and q = 2 solutions show that the short-distance interaction between instanton quark pairs is logarithmic. Extending these interactions to arbitrary q, we describe the multi-instanton gas as a plasma of instanton quarks.     

Instanton effects on the interaction potential between light quarks and the isomultiplet mass splitting of baryons

On the basis of current assumptions of instanton theory we derive strictly the explicit dependence on the masses and spins of the instanton induced potential between a pair of light quarks in baryons, namelyV ₁₂=γ+β(m _* ^1+α )(m _* ^2+α )η(1-σ ₁ησ ₁), wherem _i ^* andσ _i (i=1.2) are respectively the mass and Pauli spin of theith quark. On the additional basis of the MIT bag model, we obtain γ=c/R ³ and β=b/R ³>0, and α>0 is independent of the radiusR of the baryon. The magnitudes of the parametersb and α are also estimated. The MIT bag model is improved by taking into account this potential. Isomultiplet mass splitting formulas are derived in good agreement with experiment.     

Instanton vacuum in thermal QCD

The effects of instanton-anti-instanton interactions in high-temperature QCD with colour SU(2) are studied with and without quarks. The instanton potential proves to have no repulsive core, thus creating troubles with the definition of nonperturbative contributions to physical quantities. Also the chiral condensate is calculated, and it is shown to vanish if number of quark flavoursN _f≧2, whereas forN _f=1 it is nonzero for the arbitrary high temperature.     

Instantons and the hyperfine splitting ofB andB Smesons

In this short note we wish to point out that the instanton model, which was theoretically fascinating, has recently found application in explaining the hyperfine splitting of mesons and baryons. In particular, the flavour independence ofM _v ² -M _P ² (i.e. the squared mass difference of the vector and the pseudoscalar mesons), known to be constant for the strange and non-strange mesons in theu,d and the charm quark sectors, have recently been shown to be the same for the beauty sector through experiments. This flavour independence and the magnitude of the splitting agrees remarkably well with the instanton model.     

Understanding of radial and elliptic expansion with quark number scaling and blast wave model in 200 GeV Au+Au at RHIC-PHENIX

Measurement of azimuthal anisotropy is one of the most important study because of its relation to the initial stage. Especially, the elliptical anisotropy which is measured as the second coefficient of Fourier expansion of particle azimuthal distribution is believed to carry the information about the initial geometrical anisotropy. It seems the identified hadron v ₂ depends on the number of quark contents of the hadron. The experimental result of quark number scaling of v ₂ suggests quark level collectivity in the hot dense matter and quark coalescence mechanism to form hadron from quark matter via quark-gluon phase transition. The measured v ₂ and p _T spectra are analyzed with various assumptions based on the blast wave model in order to understand the freeze-out temperature and collective flow after the system expansion.     

$VA\widetilde{V}$ correlator within the instanton vacuum model

The correlator of vector and non-singlet axial-vector currents in the external electromagnetic field is calculated within the instanton liquid model of the QCD vacuum. In general the correlator has two Lorentz structures: longitudinal, w_L, and transversal, w_T, with respect to the axial-vector index. Within the instanton model the saturation of the anomalous w_L structure is demonstrated. It is known that in the chiral limit the transversal structure w_T is free from perturbative corrections. In this limit within the instanton model we calculate the transversal invariant function w_T at arbitrary space-like momentum transfer q and show the absence of power corrections to this structure at large q². Instead there arise exponential corrections to w_T at large q² reflecting non-local properties of the QCD vacuum. The slope of w_T at zero virtuality, the QCD vacuum magnetic susceptibility of the quark condensate and its momentum dependence are estimated.Received: 7 May 2005, Published online: 6 July 2005     

On constrained instantons

A simple method is presented for doing systematic constrained instanton calculations in models such as φ⁴ or Higgs theories where the presence of a mass term prevents the existence of a classical solution. As an application, instanton estimates of the large-order behavior of the perturbation series in massive φ₄⁴ theory are derived. (These estimates agree with those of Frishman and Yankielowicz.)     

Instanton effects in supersymmetric gauge theories

We investigate how in supersymmetric gauge theories non-perturbative effects are able to generate non-trivial vacuum properties otherwise forbidden by perturbative non-renormalization theorems. This conclusion can be reliably drawn since the constancy of certain Green functions — due to supersymmetry (SUSY) — allows one to connect vacuum-dominated large distances with short-distance behaviour which is reliably computed by instanton methods. In all the cases we discuss (without matter, with massive or massless matter in real representations and, finally, with matter in complex representations) instanton calculations imply the occurrence of a variety of condensates. For the pure SUSY gauge theory, a gluino condensate induces the spontaneous breaking of Z_2N. For massive super-quantum chromodynamics (SQCD) we find a peculiar mass dependence of matter condensates whose origin is traced to mass singularities of non-zero mode instanton contributions. These contributions force the massless limit of SQCD to differ from the strictly massless case, in which the spontaneous breaking of chiral symmetries is induced. Inconsistency with an anomaly equation forces either infinite matter condensates or spontaneous SUSY breaking in the massless cases. For non-constant Green functions, instantons are shown to provide new calculable short-distance singularities of an obvious non-perturbative nature.     

Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q² dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F₂ will, at large Q², exceed the free quark result by a factor 1.751, while for x = 0.5, F₂ is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.     

Formation of highly excited states of 6He in the 9Be(π−, tt)t reaction

The hypothesis of a heavy stable quark of the fourth family can provide a nontrivial solution for cosmological dark matter if baryon asymmetry in the fourth family has a negative sign and an excess of ū antiquarks with charge (?2/3) is generated in the early Universe. Excessive ū antiquarks form (ūūū) antibaryons with electric charge ?2, which are all captured by ⁴He and trapped in a [⁴He⁺⁺(ūūū)^??] O-helium OHe “atom” as soon as ⁴He is formed in Big Bang nucleosynthesis. Interaction of O-helium with nuclei opens a new path to the creation of heavy nuclides in Big Bang nucleosynthesis. Due to the large mass of the U quark, OHe “atomic” gas decouples from baryonic matter and plays the role of dark matter in large-scale structure formation with structures on small scales being suppressed. Owing to nuclear interaction with matter, cosmic O-helium from the galactic dark matter halo is slowed in the Earth below the thresholds of underground dark matter detectors. However, an experimental test of this hypothesis is possible in the search for OHe in balloon-borne experiments and for U hadrons in cosmic rays and accelerators. OHe “atoms” might form anomalous isotopes and could cause cold nuclear transformations in matter, offering a possible way to exclude (or prove) their existence.     

Stars of strange matter?

We investigate suggestions that quark matter with strangeness per baryon of order unity may be stable. We model this matter at nuclear matter densities as a gas of close packed Λ-particles. From the known mass of the Λ-particle we obtain an estimate of the energy and chemical potential of strange matter at nuclear densities. These are sufficiently high to preclude any phase transition from neutron matter to strange matter in the region near nucleon matter density. Including effects from gluon exchange phenomenologically, we investigate higher densities, consistently making approximations which underestimate the density of transition. In this way we find a transition density ρ_tr≳7ρ₀, where ρ₀ is nuclear matter density is not far from the maximum density in the center of the most massive neutron stars that can be constructed. Since we have underestimated ρ_tr and still find it to be ∼7ρ₀, we do not believe that the transition from neutron to quark matter is likely in neutron stars. Moreover, measured masses of observed neutron stars are ≅1.4 M_⊙, where M_⊙ is the solar mass. For such masses, the central (maximum) density is ρ_c<5ρ₀. Transition to quark matter is certainly excluded for these densities.     

Leading logarithms of heavy quark masses in processes with light and heavy quarks

The matrix elements of operators containing both heavy quark (Q) and light quark (q) fields can contain large logarithms of the type ln(m_Q²/μ²), where μ is a typical QCD mass scale and m_Q is the heavy quark mass. We outline a method for summing leading logarithms of this type. We apply it to the decay constant f_M of a low lying pseudoscalar meson M with Q̄q flavor quantum numbers and predict the ratios of decay constants for mesons with different heavy flavors. We also apply it to a matrix element of a four-quark operator which is relevant for B⁰−B̄⁰ mixing.     

BCS Theory of Hadronic Matter at High Densities

The equilibrium between the so-called 2SC and CFL phases of strange quark matter at high densities is investigated in the framework of a simple schematic model of the NJL type. Equal densities are assumed for quarks u,d and s. The 2SC phase is here described by a color-flavor symmetric state, in which the quark numbers are independent of the color-flavor combination. In the CFL phase the quark numbers depend on the color-flavor combination, that is, the number of quarks associated with the color-flavor combinations ur,dg,sb is different from the number of quarks associated with the color flavor combinations ug,ub,dr,db,sr,sg. We find that the 2SC phase is stable for a chemical potential μ below μ _c ?=?0.505 GeV, while the CFL phase is stable above, the equilibrium pressure being P _c ?=?0.003 GeV⁴. We have used a 3-momentum regularizing cutoff Λ?=?0.8 GeV, which is somewhat larger than is usual in NJL type models. This should be adequate if the relevant chemical potential does not exceed 0.6 GeV.     

Is heavy lepton pair production on nuclei really independent of nuclear size?

We investigate the nuclear size dependence of the distribution of massive lepton pairs produced by hadronic beams. Our principle conclusion is that <p ² _T > of the lepton pair should have a substantial and readily observable component from nuclear rescattering even though the nuclear enhancement exponent α(p _T ) lies within present experimental limits. We indicate the relevance of these effects to the study of quark propagation through nuclear matter.     

Hadron spectroscopy with instanton induced quark forces

It is shown that within the framework of a non-relativistic quark model with string-like confinement and an instanton induced residual quark-quark interaction it is possible to account simultaneously for the baryon and the meson spectra, including theπ- η- η′ splitting for pseudoscalar mesons, up to energies of roughly 2 GeV.     

Magnetic catalysis of stability of quark matter in the Nambu-Jona-Lasinio model

The effect of an external magnetic field H on the stability of quark matter is studied on the basis of the Nambu-Jona-Lasinio model. It is shown that, at H = 0, droplets of quark matter are stable only in the case where the coupling constant G is greater than some value G_bag. If H ≠ 0, stable multiquark formations may exist even for G ≤ G_bag (magnetic catalysis of stability). For G > G_bag, a magnetic field facilitates the formation of stable quark matter.