Chiral quarks,chiral limit,nonanalytic terms and baryon spectroscopy

It is shown that the principal pattern in baryon spectroscopy, which is associated with the flavor-spin hyperfine interactions, is due to the spontaneous breaking of chiral symmetry in QCD and persists in the chiral limit. All corrections, which are associated with a finite quark (Goldstone boson) mass are suppressed by the factor (μ/Λ_χ)² and higher.     

Critical behaviour in baryonic matter

First we consider the phenomenology of deconfinement and chiral symmetry restoration for strongly interacting matter at non-vanishing baryon number density. Subsequently, we present numerical results obtained by a Monte Carlo evaluation of statistical QCD on an 8³×3 lattice, using Wilson fermions withN _f =2, in fourth order hopping parameter expansion, and suppressing the imaginary part of the fermion action. We consider baryonic chemical potentials up to μa=0.6μa=0.6 (μ/Λ _L ?200); in this range, the critical parameters for deconfinement and chiral symmetry restoration are found to coincide.     

Charmed Deuteron

Possible existence of bound states of a charmed baryon, Λ _c , Σ _c , Σ* _c with a nucleon, N, as well as two charmed baryons, Λ _c Λ _c , etc., are examined in the meson exchange potential approach. The heavy quark spin symmetry induces a strong tensor coupling between Λ _c N, Σ _c N and Σ* _c N states, which causes a bound state of Λ _c N (J = 0⁺ and 1⁺) states. Such a bound state is also seen in the spin-singlet Λ _c Λ _c channel, which resembles the H dibaryon in the strange sector.     

Some aspects of a unified approach to gauge,dual and Gribov theories

We consider quantum chromodynamics (QCD) with N_c colours and N_f flavours. Large N expansions for this theory are discussed and their advantages are pointed out, especially in relation to the possibility of unifying gauge, dual and Gribov theories of strong interactions. We first recall how the 1/N_c expansion of 't Hooft can be related to a dual loop expansion with a fixed coupling constant. We point out the necessity for quarkless (purely gluonic) bound states to appear and their importance in maintaining confinement at higher orders in 1/N_c. We show how non-orientable dual loops are reinterpreted in QCD and how a paradox appears when N_f is such that asymptotic freedom is lost. Some recent results of Cornwall and Tiktopoulos are analyzed in leading order in 1/N_c. We then introduce a 1/N expansion at ? ≡ N_f/N_c fixed and show how it is related to the hadronic topological expansion (TE). This allows an unambiguous definition of reggeon field theory concepts such as the bare pomeron and diffractive dissociation in QDC. We are able to relate the parameter ? to the clustering of hadronic final states into resonances. Decreasing ? corresponds to increasing cluster over gap size. Renormalization of the dual coupling constant as a function of ? is discussed and an apparent paradox is resolved. We are also able to shed some new light on the problem of f extinction in the TE.Finally, we compare our approach to other schemes trying to relate different aspects of hadron physics.     

Lepton pair production in two-dimensional QCD

Large q² lepton pair production is calculated in leading order in 1/N_c in two-dimensional quantum chromodynamics (QCD). From this confinement model the (Drell-Yan) parton model result is recovered.     

B c-meson decays and lifetime within QCD sum rules

On the basis of three-point sum rules, the form factors for the semileptonic decays B _c ⁺ → B _s(B _s ^* )l ⁺ ν _l are calculated with allowance for α _s/v Coulomb corrections for the heavy quarkonium. Generalized relations associated with spin symmetry within the approach combining heavy-quark effective theory and nonrelativistic QCD are derived for form factors in the region of recoil momenta close to zero. The nonleptonic decays of the B _c meson are studied on the basis of the factorization hypothesis. By summing the main exclusive modes of c-quark decays and by using the results of a previous analysis of b-quark decays, the B _c-meson lifetime is estimated within QCD sumrules and within nonrelativistic QCD.     

Towards a complete QFT treatment of monopole induced baryon number violating transitions

By showing that the radially reduced QCD of s-wave fermions outside the core of a GUT monopole can be treated in a way analogous to 't Hofft's QCD₂ in the large N_climit, we are able to give a complete QFT treatment of all the relevant long-range gauge fields outside the monopole core. We prove that the original cluster argument for the existence of baryon number violating fermion “condensates” around the core, gives in fact, the correct result, despite the neglect of QCD strong interactions, which prevent the propagation of isolated quarks. We discuss briefly how a complete computational framework for a monopole induced hadron-lepton transition might be derived.     

Semileptonic decays of the B c meson

The semileptonic decays of the B _c meson into heavy quarkonia J/ψ(η_c) and a pair of leptons are investigated on the basis of three-point sum rules of QCD and nonrelativistic QCD (NRQCD). Calculations of analytic expressions for the spectral densities of QCD and NRQCD correlation functions with allowance for Coulomb-like α_s/v terms are presented. At recoil momenta close to zero, generalized relations due to the spin symmetry of NRQCD are derived for the B _c → J/ψ(η_c)/ν_l form factors, with l denoting one of the leptons (e, μ, or τ). This allows one to express all NRQCD form factors in terms of a single universal quantity, an analog of the Isgur-Wise function at the maximal lepton-pair invariant mass. The gluon-condensate corrections to three-point functions are calculated both in full QCD in the Borel transform scheme and in NRQCD in the moment scheme. This enlarges the parametric-stability region of the sum-rule method, thereby rendering the results of the approach more reliable. Numerical estimates of the widths for the transitions B _c → J/ψ(η_c)lν_l are presented.     

Nonlocal PNJL model beyond mean field

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/N _c expansion scheme. It is found that the 1/N _c corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/N _c expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.     

The Gross-Neveu model at finite temperature at next-to-leading order in the 1/N expansion

We present new results on the Gross-Neveu model at finite temperature and at next-to-leading order in the 1/N expansion. In particular, a new expression is obtained for the effective potential which is explicitly invariant under renormalization group transformations. The model is used as a playground to investigate various features of field theory at finite temperature. For example we verify that, as expected from general arguments, the cancellation of ultraviolet divergences takes place at finite temperature without the need for introducing counterterms beyond those of zero temperature. As well known, the discrete chiral symmetry of the (1+1)-dimensional model is spontaneously broken at zero temperature and restored, in leading order, at some temperature T_c; we find that the 1/N approximation breaks down for temperatures below T_c: as the temperature increases, the fluctuations become eventually too large to be treated as corrections, and a Landau pole invalidates the calculation of the effective potential in the vicinity of its minimum. Beyond T_c, the 1/N expansion becomes again regular: it predicts that in leading order the system behaves as a free gas of massless fermions and that, at the next-to-leading order, it remains weakly interacting. In the limit of large temperature, the pressure coincides with that given by perturbation theory with a coupling constant defined at a scale of the order of the temperature, as expected from asymptotic freedom.     

Baryon–Baryon and Meson–Baryon Potentials with QCD-Based Short-Range Cores

A unified potential model of baryon–baryon and meson–baryon interactions at low energies is proposed. In this model, the short-range cores which simulate recent lattice QCD calculations are introduced. In baryon–baryon sector, our potentials give a very good agreement with NN and YN scattering data and have very similar behavior to those from the lattice QCD calculations. The π N and KN interactions are also well described in our model.     

The nonlocal chiral quark model and the muon <Emphasis Type="Italic">g</Emphasis> – 2 problem

In the first part of the review we discuss the effective nonlocal approach in the quantum field theory. It concerns primary the historical retrospective of this approach, and than we concentrate on the interaction of matter particles (fermions and bosons) with the (abelian and nonabelian) gauge fields. In the second part of the review we consider the hadronic corrections (vacuum polarization) to the anomalous magnetic moment of the muon g - 2 factor discussed within the SU_f(2) nonlocal chiral quark model. This is considered in the leading and, partially, in the next-to-leading orders (the effect of the fermion propagator dressing due to pion field) of expansion in small parameter 1/N_c (N_c is the number of colors in QCD).     

A small parameter in the 1Nc expansion and narrowness of hadronic resonances

The dynamical basis for the validity of the $\text{1}\text{N}{}_{\mathrm{c}}$ expansion is investigated in the context of QCD in 1 + 1 dimensions. This is carried out by studying the first non-leading corrections in $\text{1}\text{N}{}_{\mathrm{c}}$ to the mass operator in the space of physical states. The correction to the real part of the mass operator has a direct implication for the convergence of the $\text{1}\text{N}{}_{\mathrm{c}}$ expansion, since a small effective parameter is identified, where its smallness depends on the dynamical circumstances in a known way. The generated imaginary part of the mass operator provides us with an insight concerning the question of the narrowness of hadronic resonances. In order to have a more realistic contact with our world, we include also effects due to the flavor symmetry group SU(N_f). This allows us to understand better the validity and usefulness of the notions of resonance dominance and (smooth) Regge behavior. We also discuss the expansion with $\text{N}{}_{\mathrm{f}}\text{N}{}_{\mathrm{c}}$ fixed and compare the results with those obtained from Dual Resonance Model. It is remarked that a nonuniformity exists between the limits N_c → ∞, N_f = fixed and N_c → ∞, $\text{N}{}_{\mathrm{f}}\text{N}{}_{\mathrm{c}}\text{=}\text{fixed}$, which may affect physical quantities.     

Meson screening masses from lattice QCD with two light quarks and one strange quark

We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents N _τ =4, 6 and 8 and aspect ratios of N _s /N _τ ≥4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3T _c (T _c being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4T _c . Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3T _c , indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

The mass of the scalar boson beyond the large- N c limit

Within the framework of the 1/N_c expansion of four-fermion interaction models, we analyse the next to leading 1/N_c corrections to the well known large-N _c result M _S = 2M _Q where M _S is the mass of the scalar boson and M _Q is the constituent quark mass. The calculation is performed in the Extended Nambu-Jona Lasinio (ENJL) model which is suitable for describing low energy hadron properties. We treat the model as fully non renormalizable and discuss the comparison with approaches based on the equivalence with renormalizable Yukawa type models. We consider both the G _V = 0 and the G _V ≠ 0 cases with n _f = 2 flavours and study the dependence upon the regularization scheme. We find that pure next-to-leading 1/N _c corrections are large and negative, while a partially resummed treatment can induce positive and smaller corrections. A triplet-singlet states’ splitting is observed.     

Hadronization of quark systems

Hadronization in simple models of quark systems is discussed with emphasis on the combinatorial aspects. The numberN of quarks and the numberN _c of colours are the relevant variables. In onedimension and in the meson and baryon sector the problem is completely soluble. When multiquark hadrons are included an iterative procedure still allows a complete solution. Higher dimensions are difficult to treat but global hadronization, without dimensionality constraints, is again soluble. As a general result the baryon/meson ratio is, for large quark densities, rather large, ?1/3 and may grow without limit asN→∞.     

Meson-loop effects in the NJL model at zero and nonzero temperature

We compare two different possibilities of including meson-loop corrections in the Nambu-Jona-Lasinio model: a strict 1/N _c expansion in the next-to-leading order and a nonperturbative scheme corresponding to a one-meson-loop approximation to the effective action. Both schemes are consistent with chiral symmetry, in particular, with the Goldstone theorem and the Gell-Mann-Oakes-Renner relation. The numerical part at zero temperature focuses on the pion and the ρ-meson sector. For the latter, meson-loop corrections are crucial in order to include the dominant ρ → ππ-decay channel, while the standard Hartree + RPA approximation only contains unphysical $m_\pi ,f_\pi ,\left\langle {\bar \psi \psi } \right\rangle $ -decay channels. We find that $q\bar q$ , and quantities related to the ρ-meson self-energy can be described reasonably with one parameter set in the 1/N _c-expansion scheme, whereas we did not succeed in obtaining such a fit in the nonperturbative scheme. We also investigate the temperature dependence of the quark condensate. Here, we find consistency with the chiral perturbation theory to the lowest order. Similarities and differences of both schemes are discussed.