A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.     

The pion radius

The pion radius has been measured by direct scattering of 50 GeV negative pions from stationary electrons in a hydrogen target. We find the square of the radius to be 〈r_π²〉 = (0.61 ± 0.15)fm².     

Drawing insights from pion parton distributions

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence,glue and sea distributions within the pion;unifying them with,inter alia,electromagnetic pion elastic and transition form factors.The analysis reveals the following momentum fractions at the scale ζ2:=2GeV:〈xvalence〉=0.48(3),〈xglue〉=0.41(2),〈xsea〉=0.11(2);and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking,the valence-quark distribution function,q^π(x),exhibits the x≈1 behaviour predicted by quantum chromodynamics(QCD).After evolution to ζ=5.2 GeV,the prediction for q^π(x)matches that obtained using lattice-regularised QCD.This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.     

Heavy particle content in QCD jets

We calculate the multiplicity of heavy quark pairs in gluon jets in lowest order QCD, along with the non-perturbative correction related to the gluon condensate 〈(α/π)F²〉. The value of the non-perturbative correction is

where M is the mass of the heavy quark, N is the number of colors, and C_F and C_A are the values of the Casimir operators in the fundamental and adjoint representation respectively. α(M) is the running coupling constant at the scale of the heavy quark, and 〈F²〉 is the gluon condensate, usually determined to be 〈α/πF²〉 ∼ 0.012 GeV⁴. The non-perturbative correction is extremely small.     

Pion form factor from 480 MeV to 1100 MeV

The pion form factor is measured in the reaction e⁺e^? → π⁺π^? for center of mass energies in the range 480–1100 MeV. Our results are first analysed in terms of the conventional Vector Meson Dominance formalism, and then taking into account the ωπ inelastic channel. The result of this later formalism is a pion form factor (F_π) which fits quite well all the existing data on F_π both in the timelike and spacelike regions, and pion mean square radius of 〈r_π²〉 = 0.460 ± 0.011 fm² or $\text{〈r}{}_{\mathrm{\pi }}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.678 ± 0.008}\text{fm}$.     

Dynamical properties of the vacuum in non-abelian field theories with and without supersymmetry

In QCD with massless quarks, the effective potential for the color singlet operator (F_μν^a)² can be constructed by the use of the trace anomaly equation and tells us that magnetic gluon condensation, 〈0|(F_μν^a)²|0〉 > 0, occurs. When the method is applied to supersymmetric QCD, however, it gives us a puzzle; the gluons condense with negative energy density, and supersymmetry is broken in a pathological manner with the appearance of a negatively normed Nambu-Goldstone fermion. Spurred on by this observation, we examine in detail the properties of the vacuum for the super (and ordinary) O(N) non-linear σ model in two dimensions for which a similar puzzling situation occurs with regard to the lagrangian condensate. We find, in particular, that (i) the chiral condensate plays a crucial role in resolving the puzzle and that (ii) it is the nature of the response of the lagrangian condensate to the test charge, not the sign or the magnitude of the condensate itself, that determines the phase of the system. Implications of these results for (super) QCD, including an unconventional possibility of “electric” gluon condensation, are discussed.     

On the formation of a random color magnetic quantum liquid in QCD

It is shown that a quantum state consisting of a condensate of color magnetic flux tubes is formed in QCD for a rather weak coupling g²/4π = 0.37. This result is obtained in a systematic search for energy minimizing forms of the QCD unstable magnetic mode. The magnetic field is argued to be of a “random” type with 〈H〉 = 0 and 〈H²〉 ≠ 0 at any point.     

QCD sum rules in exclusive kinematics and pion wave function

We suggest a modification of the QCD sum rules for three-point correlation functions that relates hadron expectation values of an operator of interest to properties of the QCD vacuum in alternating external fields. A new sum rule is obtained for the nucleon magnetic moments. Relations are found between the couplings g_πNN , g_ρωπ and the value of the pion wave function at the point with equal momentum carried by the quark and the antiquark. Our results seem to exclude the possibility of having a pronounced dip in the pion wave function in the middle point, as has been assumed on the evidence of a large value of the second moment.     

Sum rules and the pion form factor in QCD

We propose a new approach to the investigation of the pion electromagnetic form factor in QCD based on the systematic use of the QCD sum rule technique. The theoretical curve obtained for F_π(Q²) is in good agreement with existing experimental data.     

Neutral-pion correlations. Test of production models

The observed increase of the average number of neutral pions, 〈n_o〉_n?, as a function of the number of charged pions produced in high-energy experiments, can be accounted for by several theoretical models. We analyze the basic trends of the models and find that in the region where 〈n_o〉_n? increases, the π⁰ multiplicity distribution is mainly determined by the isospin properties of the pion clusters and is insensitive to the overall multiplicity distribution. We calculate the values of f_2,n?⁰, the correlation parameter of two π⁰ for a given number of π^?, and show how its measurement can provide a clear test of the different production models.     

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.     

High-pT pion production in ππ interactions

Charged pion production in high energy π^-π^- interactions is studied in the p_T region of 1–2 GeV/c. The characteristics of pion production in π^-π^- interactions are compared with those in π^-p and pp interactions. The p_T dependence of pion production in these reactions follows a systematic trend which indicates that high-p_T pion production for ππ interactions as well as for πp and pp interactions proceeds via quark-quark scattering as predicted by QCD.     

Optimal bounds for the pion form factor from analyticity and experimental data

Optimal bounds for the pion electromagnetic form factor F(t) below threshold and on the pion mean-square charge radius 〈r_π²〉 = 6F'(0) are derived. Use is made of analyticity arguments and of experimental data on F(t) from e⁺e^? → π⁺π^? as well as e^?p → e^?nπ⁺. The method accounts in an approximate way for the statistical errors of the experimental information. Numerical results for F(t) are calculated for the CEA as well as the DESY electroproduction data.     

QCD with Chiral Chemical Vector: Models Versus Lattices

A formation of Local Parity Breaking (LPB) in central heavy-ion collisions (HIC) at high energies is discussed. LPB in the fireball can be produced by a difference between the number densities of right- and left-handed chiral fermions (Chiral Imbalance) which is implemented by a chiral (axial) chemical potential. Based on the effective meson Lagrangian motivated by QCD in the chiral medium the properties of light scalar and pseudoscalar mesons (π, a₀) are analyzed. It is found that exotic decays of scalar mesons arise as a result of mixing of π and a₀ vacuum states in the presence of chiral imbalance. The pion electromagnetic formfactor obtains a parity-odd supplement which generates a photon polarization asymmetry in pion polarizability. We believe that the above-mentioned properties of LPB can be revealed in experiments on LHC, RHIC, CBM FAIR and NICA accelerators.     

Determination of quark and gluon vacuum condensates from τ-lepton decay data

The values of the gluon and four-quark vacuum condensates are estimated using recent experimental data on the semileptonic τ-lepton decays τ→v_τ+nπ, which determine the vector and axialvector hadronic spectral functions. An optimal estimate is achieved through a systematic combined use Finite Energy, Laplace and Gaussian transform QCD sum rules. As a byproduct, the values of the dimensiond=8 vacuum condensates in the vector and axial-vector channels are also estimated.     

Electromagnetic corrections to the s-wave scattering lengths in pionic hydrogen

Motivated by the recently performed X-ray precision experiments on pionic hydrogen (preceding paper), we reconsider the problem of electromagnetic corrections to the π - N scattering lengths. Based on a relativistic two-channel approach, we find corrections to the π⁻p elastic and single-charge-exchange (SCE) scatering lengths due to the point-Coulomb interaction, the finite-size Coulomb interaction (including the pion size), the first-order vacuum polarization (Uehling potential) and the (π⁻p) - (π⁰n) mass difference (mass difference effect). We also estimate the contribution due to the (γ,n) decay channel. The total corrections to the elastic and the SCE scattering lengths are found to be δ_ε = −(2.1 ± 0.5) × 10⁻² and δ_Γ = −(1.3 ± 0.5) × 10⁻². Previously published values for the corrections are critically compared with our results.     

Non-perturbative QCD effects explain the ΔI = 12 rule in the chiral limit

It is shown that in the chiral limit, the enhancement of the $\text{ΔI=}\text{1}\text{2}$ transitions for mesons is explained by the large size of non-perturbative QCD matrix elements. For $\text{〈}\text{s}\text{s〉 = 〈}\text{u}\text{u〉}$ we obtain ∣M(K_S⁰ → 2π⁰) ∣ =(5.2±0.6) × 10^?7m_K in excellent agreement with experiment.     

Isovector kaon form factor in the dispersion theory and S-wave π K-scattering lengths

A one-dimensional integral representation for isovector kaon form factor is constructed within the dispersion theory in terms of the pion form factor and the backwardπK-scattering amplitude. The normalization condition for isovector kaon form factor at zero momentum transfer gives a sum rule for theπK-scattering amplitude, with the use of which difference between thes-waveπK-scattering lengths in triplet and singlet isospin states is estimated to bea ₀ ^3/2 - a ₀ ^1/2 ≈μ ^{? 1} whereμ is the pion mass. In agreement with the vector-meson-dominance model, deviations of the isovector kaon form factor from half of the pion form factor are found to be small.