QCD Instanton Vacuum Research Articles

Photoproduction of ηc,b near threshold

We analyze the photoproduction of ηc,b off a proton in the threshold region, in terms of C-odd gluonic correlations in the off-forward proton matrix element. Near threshold, the skewness is large, leading to a production amplitude that is dominated by four C-odd twist-3 gluon GPDs. We use the QCD instanton vacuum to estimate these C-odd contributions in the proton. The results are used to estimate the differential cross sections for coherent photoproduction of ηc,b in the threshold region, at current electron facilities. Published by the American Physical Society 2024

Pion gravitational form factors in the QCD instanton vacuum. II

We revisit the hard QCD contributions to the pion gravitational form factors, in terms of the twist-2,3 pion distribution amplitudes (DAs), including novel semihard contributions from the instantons. The pion DAs are evaluated in the QCD instanton vacuum and then properly evolved to higher resolution. The results are compared to our recent results from the QCD instanton vacuum, as well as Bethe-Salpeter calculations and recent lattice data. The interpolated hard and soft contributions to the pion D form factor are used to derive the (gravitational) pressure and shear within the pion, with a clear delineation of their range. Published by the American Physical Society 2024

Pion gravitational form factors in the QCD instanton vacuum. I

The pion form factors of the QCD energy-momentum tensor (EMT) are studied in the instanton liquid model (ILM) of the QCD vacuum. In this approach, the breaking of conformal symmetry is encoded in the form of stronger-than-Poisson fluctuations in the number of instantons. For the trace of the EMT, it is shown that the gluonic trace anomaly term contributes half the pion mass, with the other half coming from the quark-mass-dependent σ term. The Q2 dependence of the form factors is governed by glueball and scalar meson exchanges. For the EMT, the spin-0 (trace) and spin-2 (traceless rank-2 tensor) form factors are computed at next-to-leading order in the instanton density using effective quark operators. Relations between the gluon and quark contributions to the EMT form factors are derived. The form factors are also expressed in terms of the pion light-front wave functions in the ILM. The results at the low resolution scale of the inverse instanton size are evolved to higher scales using the renormalization group equation. The ILM results compare well with those of recent lattice QCD calculations. Published by the American Physical Society 2024

Glue in hadrons at medium resolution and the QCD instanton vacuum

We discuss a general framework for the evaluation of the gluonic form factors in light hadrons at low momentum transfer, in the QCD instanton vacuum. At medium resolution of the order of the inverse mean instanton size, the glue is mostly localized in single or pairs of pseudoparticles and globally constrained by the fluctuations of their topological charges. These pseudoparticles trap light quarks, giving rise to emerging multiflavor ’t Hooft interactions. We explicitly evaluate the gluonic scalar, pseudoscalar, energy-momentum tensor (EMT), and the leading C-odd and C-even three-gluon hadronic form factors, at next to leading order in the instanton density, including molecular clusters of like and unlike instantons. We use the results for the EMT to address the contribution of the gluons in Ji’s mass and spin sum rules, at low resolution. When evolved, our results for the mass and spin composition of the nucleon are shown to be in good agreement with the recently reported lattice results at higher resolution. Published by the American Physical Society 2024

Hadronic structure on the light front. VIII. Light scalar and vector mesons

We use the QCD instanton vacuum model to discuss the emergence of the light scalar and vector mesons on the light front. We take into account both the instanton and anti-instanton single and molecular interactions on the light quarks, in the form of nonlocal effective interactions. Although the molecular induced interactions are suppressed by a power of the packing fraction, they are still sufficient to bind the vector mesons, while keeping most of the scalar spectrum relatively unchanged. We explicitly derive the light front distribution amplitudes and partonic functions for the scalar and vector mesons, and compare them after pertinent QCD evolution, to the available empirical and lattice measured counterparts. The Dirac electric form factors for both the pion and ρ meson are derived, and shown to compare well with current data. Published by the American Physical Society 2024

Hadronic structure on the light front. VII. Pions and kaons and their partonic distributions

This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front, motivated by the QCD vacuum structure and lattice results. The spontaneous breaking of chiral symmetry on the light front, is shown to parallel that in the rest frame, where the non-local instanton induced $^\prime$t Hooft interaction plays a central role. By rewriting this interaction solely in terms of the good component of the fermionic field, a scalar chiral condensate emerges in the mean-field approximation, which is identical to the one obtained in the rest frame. The pions and kaons emerge as deeply bound Goldstone modes in the chiral limit, with the scalar-isoscalar sigma meson mode as a threshold state with zero binding. We explicitly derive the light front distribution amplitudes (DAs) and partonic functions (PDFs) for these mesons. The DAs and PDFs are in good agreement with those extracted from the QCD instanton vacuum in the rest frame, using the large momentum effective theory (LaMET). The QCD evolved DAs and PDFs compare well with available measurements, as well as recent lattice results.

Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum

We briefly review some essential aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry, the spontaneous breaking of chiral symmetry, and the axial U(1) anomaly. The anomaly causes the intrinsic nucleon spin to transmute to the vacuum topological charge by quantum tunneling. We use Ji′s invariant spin decomposition to discuss the spin budget of the nucleon as a quark–diquark state in the QCD instanton vacuum. A measure of the intrinsic quark spin of the nucleon is a measure of the quenched topological susceptibility of the QCD instanton vacuum.

Pion and kaon distribution amplitudes up to twist-3 in the QCD instanton vacuum

We discuss the pion and kaon distribution amplitudes up to twist-3 in the context of the random instanton vacuum (RIV). We construct explicitly the pertinent quasipion and quasikaon distributions in the RIV, and analyze them in leading order in the diluteness factor, at a resolution fixed by the inverse instanton size. The distribution amplitudes (DA) follow from the large momentum limit. The results at higher resolution are discussed using QCD evolution, and compared to their asymptotic limits and some lattice results.

Mass sum rule of hadrons in the QCD instanton vacuum

We briefly review the key aspect of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry and the trace anomaly. We use Ji$^\prime s$ invariant mass decomposition of the energy momentum tensor together with the trace anomaly, to discuss the mass budget of the nucleon and pion in the QCD instanton vacuum. A measure of the gluon condensate in the nucleon, is a measure of the compressibility of the QCD instanton vacuum as a dilute topological liquid.

Pion and kaon parton distributions in the QCD instanton vacuum

We discuss a general diagrammatic description of n-point functions in the QCD instanton vacuum that resums planar diagrams, enforces gauge invariance and spontaneously broken chiral symmetry. We use these diagrammatic rules to derive the pion and kaon quasi-parton amplitude and distribution functions at leading order in the instanton packing fraction for large but finite momentum. The instanton and anti-instanton zero modes and non-zero modes are found to contribute to the quasi-distributions, but the latter are shown to drop out in the large momentum limit. The pertinent pion and kaon parton distribution amplitudes and functions are made explicit at the low renormalization scale fixed by the inverse instanton size. Assuming that factorization holds, the pion parton distributions are evolved to higher renormalization scales with one-loop DGLAP and compared to existing data.

Erratum: Probing Wilson loops in the QCD instanton vacuum [Phys. Rev. D91, 034023 (2015)

Erratum: Probing Wilson loops in the QCD instanton vacuum [Phys. Rev. D<b>91</b>, 034023 (2015)

Probing Wilson loops in the QCD instanton vacuum

We discuss the quark and gluon condensates in the presence of a rectangular Wilson loop using the QCD instanton vacuum with three light dynamical quarks. The scalar quark condensate is found to decrease while the gluon condensate increases. We also derive the static potential between two QCD dipoles and show that it is attractive but short ranged at large distances. Its relevance to static QCD string interactions is discussed.

Leading-twist pion and kaon distribution amplitudes from the QCD instanton vacuum

We investigate the leading-twist light-cone distribution amplitudes for the pion and kaon, based on the nonlocal chiral quark model from the instanton vacuum. Effects of explicit flavor SU(3)-symmetry breaking are taken into account. The Gegenbauer moments are computed, analyzed and compared with those of other models. The one-loop QCD evolution of the moments is briefly discussed. The transverse momentum distributions are also discussed for the pion and kaon light-cone wave functions.

Off-shell photon light-cone wave functions of odd chirality in the effective low-energy theory

The Lorentz decomposition of the light-cone distribution amplitudes is carried out up to twist four. The Wandzura-Wilczek-like relations associated with the transverse photon wave function are derived in the same way as for the rho meson. The on-shell and off-shell photon wave functions with odd chirality at the leading twist in the effective low-energy theory derived from the instanton vacuum of QCD are calculated. The explicit expression of the transverse photon wave function, ${\ensuremath{\phi}}_{\ensuremath{\gamma}\ensuremath{\perp}}(u,{P}^{2})$, is worked out, and the twist-two parts of the other two photon wave functions, ${h}_{\ensuremath{\gamma}\ensuremath{\parallel}}^{(s),\mathrm{twist}\text{ }\mathrm{two}}(u,{P}^{2})$ and ${h}_{\ensuremath{\gamma}\ensuremath{\parallel}}^{(t),\mathrm{twist}\text{ }\mathrm{two}}(u,{P}^{2})$, are calculated based on the Wandzura-Wilczek-like relations. The dependence of the coupling ${f}_{\ensuremath{\gamma}}^{\ensuremath{\perp}}({P}^{2})$ and the light-cone photon wave functions with respect to the virtuality, ${P}^{2}$, are analyzed, and the end-point behavior as well as the middle-point behavior of the photon wave functions is discussed.

Off-Shell Photon Light-Cone Transverse Wavefunction atLeading Twist

The explicit expression of the transverse photon wavefunctionϕγ⊥(u,P2) at the leading twist with theon-shell and the off-shell momenta are calculated in theeffective low-energy theory derived from the instanton vacuum ofQCD, where both the space-like region as well as the time-like one ofthe momenta for the virtual photons are investigated. Inaddition, the problem about the consistency between the twodifferent definitions of the transverse photon wavefunction withchiral-odd Dirac structure, σμν, has beenconsidered, and proven to be true at the leading order by means ofthe sum rule method. A brief discussion of the dependence of thetransverse light-cone photon wavefunction ϕγ⊥(u,P2)and its coupling, Fγ⊥(u,P2) to the correspondingquark–antiquark current with respect to P2, and that about theend-point behaviour of the transverse photon wavefunction is given.

Current mass dependence of the quark condensate in instanton vacuum

We discuss the current mass dependence of the basic quantities of the quark models -- constituent quark mass M and quark condensate i<psi^dagger psi >. The framework of the consideration is QCD instanton vacuum model.

Twist-3 contribution tohLin the instanton vacuum

We show that the instanton model of the QCD vacuum indicates the parametric smallness of the twist-3 contributions to the polarized structure function ${h}_{L}.$ This smallness is related to the diluteness of the QCD instanton vacuum.

Instanton-induced soft-pion wave function and hard-pion form factor

An instanton-induced pion wave function is constructed. It provides an intrinsick⊥-dependence which suppresses soft virtual one-gluon exchanges and thus legitimates the perturbative QCD (pQCD) calculations of the pion electromagnetic form factor in the region of momentum transfers above the scaleQc>(√3/(2√f))(1/ϱc)∼1 GeV, wheref=(2nc)(π2πc4/2) is a packing fraction parameter, ϱc is an effective instanton size andnc is an effective density of instantons in the instanton vacuum of QCD.

Foundations of the constitutent quark model

‘Constituent quarks’ means massive quarks, in contrast to the nearly massless u, d, s quarks of the QCD lagrangian. The dynamical or constituent masses appear owing to the spontaneous chiral symmetry breaking in QCD. A realistic mechanism of the chiral symmetry breaking is provided by instantons. Therefore, I review the present status of the QCD instanton vacuum, emphasizing the mechanism of chiral symmetry breaking and of the generation of the constituent quark mass. I end up with the Nambu-Jona-Lasinio-type effective theory to which QCD is reduced at low momenta.

INSTANTONS AND EMC-EFFECT FOR SPIN-DEPENDENT FUNCTION

It is shown that the polarization contribution of the instanton vacuum of QCD gives 70% contribution to the nucleon helicity. However, it is cancelled by the contribution of sea quarks which are polarized against the nucleon spin.