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].     

QCD sum rules and the Skyrme model at large Nc

We study the large-N_c behaviour of the baryon spectrum using QCD duality sum rules. A comparison of our results with the ones of the Skyrme model gives a determination of the Skyrme parameter e and a relation between the pion decay constant f_π and the quark condensate. As a consequence, we show that f_π is the only scale which controls the hadron dynamics. An extrapolation of our large-N_c results into the real world N_c = 3 yields a good agreement with phenomenological estimates.     

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.     

Comments on a Minimal Quasiparticle Approach for the QGP and Its Large-N c Limits

A minimal quasiparticle approach for describing QGP at temperatures much higher than the critical one is discussed. It involves an ideal-gas framework in which quark and gluon masses depend on temperature. This model is able to reproduce the recent equations of state computed in lattice QCD for temperatures typically higher than 2 T _c , in a range in which it is reasonable to neglect interactions between quasiparticles. In addition, the equations of state for a generic gauge theory with gauge groups SU(N _c ) and quarks in an arbitrary representation are studied. The gauge independence in the pure glue sector and the large-N _c equivalence between the gauge groups SU(N _c ) and SO(2N _c ) in a full plasma is finally shown for normalized thermodynamic quantities.     

Effects of explicit SUf(3) breaking on the quark condensates

Effects of the explicit breaking of flavour symmetry on the quark condensates in the large-N_c limit are examined with the use of a QCD-motivated effective lagrangian. It is shown that, as the current mass increases, the non-perturbative quark condensate decreases in the absolute values, which agrees well with that obtained from QCD sum rules, not only qualitatively but also quantitatively. The condensatesat finite temperature are also investigated in relation to the chiral transition.     

Gauge invariant quark Green’s functions with polygonal Wilson lines

Properties of gauge invariant two-point quark Green’s functions, defined with polygonal Wilson lines, are studied. The Green’s functions can be classified according to the number of straight line segments their polygonal lines contain. Functional relations are established between the Green’s functions with different numbers of segments on the polygonal lines. An integrodifferential equation is obtained for the Green’s function with one straight line segment, in which the kernels are represented by a series of Wilson loop vacuum averages along polygonal contours with an increasing number of segments and functional derivatives on them. The equation is exactly solved in the case of two-dimensional QCD in the large-N _c limit. The spectral properties of the Green’s function are displayed.     

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).     

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.     

Structure of the Gauge Invariant Quark Green’s Function in QCD2

We study, in two-dimensional QCD and in the large-N _c limit, the properties of the gauge invariant quark Green’s function, defined with a path-ordered phase factor along a straight line. The analysis is done by means of an exact integrodifferential equation. The Green’s function is found to be infrared finite, with singularities represented by an infinite number of threshold type branch points with a power ?3/2, starting at positive mass squared values. Its expression is analytically determined.     

Large corrections to high-pT hadron-hadron scattering in QCD

We have computed the first non-trivial QCD corrections to the quark-quark scattering process which contributes to the production of hadrons at large p_T in hadron-hadron collisions. Using quark distribution functions defined in deep inelastic scattering and fragmentation functions defined in one particle inclusive e⁺e^? annihilation, we find that the corrections are large. This implies that QCD perturbation theory may not be reliable for large-p_T haron physics.     

The large-N deconfinement phase transition in a partially reduced Eguchi-Kawal model

We construct generalized twisted Eguchi-Kawai models which for large-N reduce space-time to a lattice of arbitrary size. Large-N lattice gauge theory at finite temperature is investigated in a model on a lattice with L₀ time slices and two lattice points in very time slice. We observe the large-N deconfinement phase transition in the weak coupling region. Assuming asymptotic scaling we find a transition temperature T_c = (101±4)Λ_L.     

O(mq/N) effects in the Ward identities approach to the pseudoscalar nonet

Anomalous Ward identities are investigated in the combined chiral and large-N limit of QCD, up to non-leading O(m_q/N) terms, taking into account chiral symmetry breaking effects in the η′ axial vector couplings. The bound θ > 16° for the η - η′ mixing angle is obtaned. Gasser and Leutwyler results on the O(m_q²) corrections to the η mass are used to determine the size of the O(m_q/N) terms, which are found to be reasonably small. Problems with the anomaly predictions for η, η′ → γγ are pointed out. Some aspects of the non-smoothness of the large-N expansion in presence of SU₃ breaking effects are clarified.     

Photoproduction of μ pairs and large-pT particles in QCD

We calculate cross sections for $\text{γ}\text{N}\text{→ μ}\text{μ}\text{X}\text{, γ}\text{N}\text{→ (}\text{jet)X and}\text{γ}\text{N}\text{→ π}{}^{\mathrm{+}}\text{X}$ using the distribution functions for quarks in the photon predicted by QCD. The Drell-Yan contribution to the μ-pair cross section is masked by the Bethe-Heitler process in the region where it is interesting. However, the characteristic cross section for photoproduction of large-p_T particles, which is predicted by QCD, is measurable.     

QCD Chiral Restoration at Finite T Under the Magnetic Field

We investigate the chiral restoration at finite temperature (T) under the strong external magnetic field ${{\bf B}=B_{0}\hat{z}}$ of the SU(2) light-flavor QCD matter. We employ the instanton-liquid QCD vacuum configuration accompanied with the linear Schwinger method for inducing the magnetic field. The Harrington–Shepard caloron solution is used to modify the instanton parameters, i.e. the average instanton size ${(\bar{\rho})}$ and inter-instanton distance ${(\bar{R})}$ , as functions of T. In addition, we include the meson-loop corrections as the large-N _c corrections because they are critical for reproducing the universal chiral restoration pattern. We present the numerical results for the constituent-quark mass as well as chiral condensate which signal the spontaneous breakdown of chiral-symmetry (SBχS), as functions of T and B. Besides we find that the changes for the F _π and m _π due to the magnetic field is relatively small, in comparison to those caused by the finite T effect.     

Bound-state approach to strangeness in the Skyrme model

We show that baryons carrying heavy flavors, such as strangeness and charm, can be described by bound states of the corresponding heavy mesons in the background field of the basic SU(2) skyrmion. This method is quantitatively successful to O(N_c⁰), in the sense of the large-N_c expansion, but at O(1/N_c) it experiences problems associated with our lack of knowledge of higher-derivative terms in the Skyrme action. We derive a model-independent mass relation for strange baryons which is in excellent agreement with experiment.     

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.     

On the structure of the QCD vacuum in the large-N limit

We present an approximate QCD vacuum for SU(N → ∞). It is a generalization of the ferromagnetic vacuum first obtained by Savvidy for SU(2) and generalized by one of us to SU(3) and SU(4). Problems occuring for N ? 5 are handled in the large-Nlimit by a contnious formalism, and the vacuum obtained is characterized by N ? 1 constant, commuting, color magnetic fields with an isotropic distribution of spatial directions. The energy density of this vacuum is lower than of the perturbative vacuum by a number proportional to N², as expected from general large-N arguments. Like the Savvidy vacuum the large-N vacuum may decay into a variant of the domained Copenhagen vacuum. We give a lower limit on the domain size.     

Scattering amplitudes of QCD string in the worldline formalism

I review the derivation of large-N QCD meson scattering amplitudes in the Regge regime, where the effective theory of long strings applies in d = 4. A special attention is payed to the reparametrization path integral which plays a crucial role in the consistency of off-shell amplitudes. I show how the linear Reggeon trajectory is obtained for QCD string in the mean-field approximation, which turns out to be exact for the Nambu-Goto string, and discuss the interrelation with perturbative QCD.     

The Quantum N-Body Problem and the Auxiliary Field Method

Approximate analytical energy formulas for N-body semirelativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. We first review the method in the case of nonrelativistic two-body problems. A general procedure is then given for N-body systems and applied to the case of baryons in the large-N _c limit.