Comments on mesonic correlators in the worldline formalism

We elaborate on how to incorporate mesonic correlators into the worldline formalism. We consider possible applications to QCD-like theories in various dimensions. We focus on large-Nc two-dimensional QCD (the ?t Hooft model) and relate it to a single harmonic oscillator. We also discuss the dependence of the Peskin S-parameter on the number of massless flavors and their representation and compare our expression to the corresponding expression obtained at weak coupling. Finally, we use the worldline formalism to discuss how the Veneziano limit of QCD is realized in holography in the limit of small Nf/Nc.     

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.     

Baryons in chiral SU(N)—QCD on the light-cone in 1 + 1-dimensions

We demonstrate that using bosonization techniques in 1+1-dimensional QCD in the chiral limit a unique definition of baryons is possible for finiteN _c despite the fact that mesons, baryons and anti-baryons are massless. The definition which is based on the construction of an SU(2)-algebra provides the basis for a new approach to investigate hadronic properties in the strong coupling limit. It is used to study the Fock-state decomposition and structure functions of baryons for various finite values ofN _c . The results are discussed in comparison to similar calculations based on discretized lightcone quantization.     

Hadron scattering in two-dimensional QCD: (I). Formalism and leading order calculations

Two-dimensional quantum chromodynamics in the 1/N_c expansion is explored as a model for hadronic interactions. In meson-meson scattering, order 1/N_c terms exhibit embryonic “Regge” behaviour, with the crossed channel factorization, signature and exchange degeneracy properties found in dual Regge models. “Regge” intercepts are additive in the quark quantum numbers exchanged, and have a lower limit for large quark masses. Residues also factorize in the direct channel. An analogue for fixed angle scattering is presented which has deviations from dimensional counting rules related to form factors and Regge intercepts.     

Analysis of the hadronic light-by-light contributions to the muon g − 2

We calculate the hadronic light-by-light contributions to the muon g − 2. We use both 1/N_c and chiral counting to organize the calculation. Then we calculate the leading and next-to-leading order in the 1/N_c expansion low energy contributions using the Extended Nambu-Jona-Lasinio model as hadronic model. We do that to all orders in the external momenta and quark masses expansion. Although the hadronic light-by-light contributions to muon g − 2 are not saturated by these low energy contributions we estimate them conservatively. A detailed analysis of the different hadronic light-by-light contributions to muon g − 2 is done. The dominant contribution is the twice anomalous pseudoscalar exchange diagram. The final result we get is a_μ^{light-by-light} = (−9.2 ± 3.2) × 10⁻¹. This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon g − 2 experiment.     

Is the number of light flavors in QCD great?

At a qualitative level, it is well known that QCD featuring a large number of quark flavors must differ drastically from actual QCD. However, it is possible to consider the large-N_f limit (where N_f is the number of light flavors in QCD) such that the basic dynamics of the system remains unchanged. This is the region of chiral perturbation theory, where the limit N_f → ∞ is simultaneously the limit of a large number of colors, N_c. Features are indicated that make it possible, in such a situation, to compare analytically the same quantity in a simplified model of actual QCD and in the large-N_f limit, and methods are proposed for calculating these features. Calculations in the limit N_f → ∞ are of no use in assessing quantities of the theory at small N f.     

What QCD sum rules tell about the rho meson — A new answer to an old question

First, a historical overview is presented concerning the use of QCD sum rules to learn about the p-meson properties at finite nuclear densities. Second, it is shown that the combination of the sum rule technique with the large-N _c expansion provides new insight. Especially it is possible to determine from the in-medium sum rules a vacuum(!) quantity which is an important ingredient for hadronic in-medium calculations of the p-meson spectral function. This quantity is the coupling strength of the p-nucleon system to the baryonic resonance N^*(1520).     

Glueball singularity,flavour loops and the Harari-Freund picture

We discuss several points concerning the structure of the cylinder term in the dual topological expansion. Using dual field theory as a guide, we concentrate on the possibility of a two-singularity scheme à la Harari-Freund. We start from results obtained previously at the lowest order in ?=N _f /N _c and study what can be the role of flavour-loop corrections in the real world where ?～1. It is argued that, in spite of the actual value of ?, precise mechanisms exist which can weaken the role of the flavour-loop corrections in the kinematical region where “soft” dynamics dominates. We also claim that theS-matrix at largeN _c (?≈-0) incorporates already many realistic features, and we refute some objections recently raised against the Harari-Freund picture.     

Determination of the hadronic width of the ground state in pionic hydrogen

In a new high-precision experiment at the Paul Scherrer Institut (PSI), the hadronic shift (ε _1s) and width (Γ_1s) of the ground state of pionic hydrogen, which are directly connected to the pion-nucleon isospin scattering lengths, were remeasured (PSI-Experiment R-98-01 Gotta et al. 1998). The results can be confronted with recent work of effective field theories defined in the low-energy limit of quantum chromodynamics (QCD), such as, e. g., chiral perturbation theory (ChPT). In addition, Γ_1s is connected to the pion-nucleon coupling constant f _πN. A precisely known value for f _πN allows an accurate determination of the Goldberger-Treiman discrepancy, which constitutes a measure of chiral symmetry breaking. This contribution is mainly devoted to describe a method for an accurate extraction of the hadronic width from the π ^??H data.     

Decays of excited baryons in the large- N<Subscript>c</Subscript> expansion of QCD

We present the analysis of the decay widths of excited baryons in the framework of the 1/N _c expansion of QCD. These studies are performed up to order 1/N _c and include both positive- and negative-parity excited baryons.     

Color,flavor, duality,and the pomeron

AtN _c /N _f =∞ such that quark loops are absent the Harari-Freund (HF)P+f model of diffraction can be motivated through the identification Pomeron ≈ glueball,f≈leading planar trajectory. AtN _c =3, the presence of confinement-related mass scales introduced by quark loops is a basic complication that can easily change this situation to, e.g., a dominantP?f identity structure. Aurenche and Gonzales Mestres (AGM) have argued that diffraction is essentially identical atN _c /N _f =∞ and atN _c =3. They further claim to have generated the HF scheme directly atN _c =3 through the novel mechanism of a multiperipheral iteration of daughters that becomes theP. We respond to these arguments. We give a general qualitative discussion of changes expected in theN _c /N _f =∞ toN _c =3 transition. Important hadron scattering quantities like particle multiplicities are very different in dynamics dominated by glue and atN _c =3, unlike other quantities like resonance width to mass ratios. We argue that the weak coupling dual model is not a reliable guide toN _c =3 dynamics. We criticize AGM's “daughter generated Pomeron”, and we close with a brief summary of other attempts to generate theP+f model.     

Hard-thermal-loop QCD trace anomaly

In this proceedings I summarize results of QCD trace anomaly from recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculations. I focus on the trace anomaly scaled by T ² for pure-glue and N _f = 3 QCD. The comparison to available lattice data suggests that for pure-glue QCD agreement between HTLpt results and lattice data for the trace anomaly begins at temperatures above 8 T _c while when including quarks (N _f = 3) agreement begins already at temperatures above 2 T _c . The results in both cases indicate that at very high temperatures the T ²-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.     

One-loop corrections to the baryon axial vector current

The symmetry breaking corrections to the pion?Cbaryon couplings vanish to first order in 1/N _c, where N _c is the number of colours. Loop graphs with octet and decuplet intermediate states cancel to various orders in N _c as a consequence of the large-N _c spin-flavour symmetry of QCD baryons. The baryon axial vector current is computed at one-loop order in heavy baryon chiral perturbation theory in the large N _c limit. 1/N _c corrections in the case of g _A in QCD are presented here.     

How large is “large N c ” for nuclear matter?

We argue that a so far neglected dimensionless scale, the number of neighbors in a closely packed system, is relevant for the convergence of the large-N _c expansion at high chemical potential. It is only when the number of colors is large w.r.t. this new scale $( \sim \mathcal{O}(10))$ that a convergent large-N _c limit is reached. This provides an explanation as to why the large-N _c expansion, qualitatively successful in vacuum QCD, fails to describe high baryo-chemical potential systems, such as nuclear matter. It also means that phenomenological claims about high-density matter based on large-N _c extrapolations should be treated with caution. This work is based on [1].     

Long-distant contribution and χ c1 radiative decays to light vector meson

The discrepancy between the PQCD calculation and the CLEO data for χ _c1→γ V (V=ρ ⁰,?ω,?φ) stimulates our interest in exploring other mechanisms of χ _c1 decay. In this work, we apply an important non-perturbative QCD effect, i.e., the hadronic loop mechanism, to study χ _c1→γ V radiative decay. Our numerical result shows that the theoretical results including the hadronic loop contribution and the PQCD calculation of χ _c1→γ V are consistent with the corresponding CLEO data of χ _c1→γ V. We expect further experimental measurement of χ _c1→γ V, which will be helpful to test the hadronic loop effect on χ _c1 decay.     

Transversal and Longitudinal Gluon Spectral Functions from Twisted Mass Lattice QCD with <Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">f</Emphasis></Subscript> = 2 + 1 + 1 Flavors

I report on the first application of a novel, generalized Bayesian reconstruction (BR) method for spectral functions to the characterization of QCD constituents. These spectral functions find applications in off-shell kinetics of the quark-gluon plasma and in calculations of transport coefficients. The new BR method is applied to Euclidean propagator data, obtained in Landau gauge on lattices with N_f = 2 + 1 + 1 dynamical flavors by the “twisted mass at finite temperature” (tmfT) collaboration. The deployed reconstruction method is designed for spectral functions that can exhibit positivity violation (opposed to that of hadronic bound states). The transversal and longitudinal gluon spectral functions show a robust structure composed of quasiparticle peak and a negative trough. Characteristic differences between the hadronic and the plasma phase and between the two channels become visible. We obtain the temperature dependence of the transversal and longitudinal gluon masses.     

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.