Instanton-induced Interactions Research Articles

Baryons and tetraquarks using instanton-induced interactions

We analyze some aspects of the perturbative and nonperturbative interactions in the composition of heavy quarkonia, heavy and light baryons (ccc and uuu ones), as well as all charm tetraquarks (ccc¯c¯). Using the hyperspherical approximation and effective radial potentials (in six and nine dimensions, respectively) we derive their spectra and wave functions. In all of the cases, we focus on the splittings between the S-shell levels, which are remarkably insensitive to the quark masses, but proportional to the effective interaction potentials. We use the traditional Cornell-like potentials, and the nonperturbative instanton-induced static potentials, from correlators of two, three, and four Wilson lines, and find rather satisfactory description of spectra in all cases. Published by the American Physical Society 2024

Hadronic structure on the light front. II. QCD strings, Wilson lines, and potentials

This is the second paper on hadronic wave functions in the light-front formulation. We first consider only confinement effects, using the classical Nambu-Gotto string with massive end points in the light-cone gauge. We derive the light-front Hamiltonian and show how to solve it, using an expansion in suitable basis functions. We next discuss the correlators of Wilson lines on the light front, leading to an effective Hamiltonian that includes spin effects. At the end, we consider a separate problem of instanton-induced interactions, at the origin of the pion as a massless Goldstone mode on the light front.

Charmonium spectrum and the color-octet heavy-quark potential from the instanton vacuum


 The properties of quarkonia are discussed in the framework of the nonrelativistic potential approach based on the instanton-induced interactions from the instanton vacuum. we have obtained the spectrum of charmonia and discuss the results. We also examine the instanton effects on the color-octet heavy-quark potential.

Asymmetric magnetized QCD matter realized by scalar and instanton-induced interactions

In a strong magnetic field utilizing a two-flavor NJL model, the isospin symmetry and asymmetry can be realized by altering the fraction parameter [Formula: see text] of the two kinds of interactions, i.e. the scalar coupling and instanton-induced coupling. As [Formula: see text] increases, the [Formula: see text] quark mass decreases while [Formula: see text] quark mass increases monotonously. The two mass lines cross at [Formula: see text] with an isospin symmetry mass [Formula: see text]. Even in the flavor-decoupled state, i.e. the strong isospin asymmetry, the [Formula: see text] and [Formula: see text] mass lines can have a common mass at a critical temperature [Formula: see text]. As the magnetic field becomes stronger, the [Formula: see text] will move towards the chiral restoration phase. The strong isospin asymmetry will lead to a split of the pseudocritical temperatures for [Formula: see text] and [Formula: see text] quarks, which can be reflected by the two peaks of the specific heat and sound velocity.

Nucleon-nucleon interaction with one-pion exchange and instanton-induced interactions

Singlet $(^{1}S_{0})$ and triplet $(^{3}S_{1})$ nucleon-nucleon potentials are obtained in the framework of the SU(2) nonrelativistic quark model using the resonating-group method in the Born-Oppenheimer approximation. The full Hamiltonian used in the investigation includes the kinetic energy, two-body confinement potential, one-gluon-exchange potential (OGEP), one-pion exchange potential (OPEP), and instanton induced interaction (III), which includes the effect of quark exchange between the nucleons. The contribution of the OGEP, III, and OPEP to the nucleon-nucleon adiabatic potential is discussed.

Implementation of the Nambu Jona-Lasinio model in hybrid stars

The model of Nambu and Jona-Lasinio has been extensively used to model the possible occurrence of quark matter in the core of compact stars. While based entirely on similar physical assumptions, previous studies have been performed using a variety of model versions, differing in both the number of active quark flavors and the structure of the quark-quark interaction. We discuss the results of our systematic analysis, designed to clarify the role of the vector and instanton-induced interactions in determining the properties of hybrid stars. The results of our calculations, carried out using a state-of-the-art description of the hadronic phase, show that the instanton-induced interaction does not affect the stiffness of the quark matter equation of state, whereas the effect of the repulsive vector interaction is sizable. However, no values of the corresponding coupling constants allow for the formation of a stable core of quark matter.

Gluelump model with transverse constituent gluons

We show that C -odd gluelumps can be successfully described as bound states of a single transverse constituent gluon evolving in the flux-tube-like potential generated by a static color-octet source. The use of a helicity degree of freedom rather than a spin one for the constituent gluon forbids the states that are not observed in lattice QCD. Our model leads to a gluelump mass spectrum in remarkable agreement with the available lattice data provided that an additional parity splitting mass term is introduced. We argue that such a term is due to instanton-induced interactions in gluelumps.

Gluons in glueballs: Spin or helicity?

In the past decade, lattice QCD has been able to compute the low-lying glueball spectrum with accuracy. Like other effective approaches of QCD, potential models still have difficulties to cope with gluonic hadrons. Assuming that glueballs are bound states of valence gluons with zero current mass, it is readily understood that the use of a potential model, intrinsically noncovariant, could be problematic in this case. The main challenge for this kind of model is actually to find a way to introduce properly the more relevant degree of freedom of the gluon: spin or helicity. In this work, we use the so-called helicity formalism of Jacob and Wick to describe two-gluon glueballs. We show, in particular, that this helicity formalism exactly reproduces the ${J}^{PC}$ numbers which are observed in lattice QCD when the constituent gluons have a helicity-1, without introducing extra states as is the case in most of the potential models. These extra states appear when gluons are seen as spin-1 particles. Using a simple spinless Salpeter model with Cornell potential within the helicity formalism, we obtain a glueball mass spectrum which is in good agreement with lattice QCD predictions for helicity-1 gluons provided instanton-induced interactions are taken into account.

Meson and glueball spectra with the relativistic flux tube model

The mass spectra of heavy and light mesons is computed within the framework of the relativistic flux tube model. A good agreement with the experimental data is obtained provided that the flux tube contributions, including retardation and spin-orbit effects, are supplemented by a one-gluon-exchange potential, a quark self-energy term, and instanton-induced interactions. No arbitrary constant is needed to fit the absolute scale of the mass spectra, and the different parameters are fitted on lattice QCD to strongly restrict the arbitrariness of our model. The relevance of the present approach is discussed in the case of glueballs, and the glueball spectrum we compute is compared to the lattice QCD one. Finally, we make connections between the results of our model and the nature of some newly discovered experimental states such as the ${f}_{0}(1810),X(3940)$, and $Y(3940)$.

Light hadron spectra in the constituent quark model with the Kobayashi–Kondo–Maskawa-’t Hooft effective UA (1) symmetry breaking interaction

We make a critical comparison of several versions of instanton-induced interactions present in the literature, all based on ITEP group’s extension to three colours and flavours of ’t Hooft’s effective lagrangian, with the predictions of the phenomenological Kobayashi–Kondo–Maskawa (KKM) chiral quark lagrangian. We analyze the effects of all versions of the effective U A (1) symmetry breaking interactions on light hadron spectra in the non-relativistic constituent quark model. We show that the KKMT force, when used as a residual hyperfine interaction reproduces the correct ordering of pseudoscalar and vector mesons even without explicitly taking chiral symmetry into account. Moreover, the nucleon spectra are also correctly reproduced, only the Roper resonance remains too high, albeit lower than usual, at 1660 MeV. The latter’s lower than expected mass is not due to a small excitation energy, as in the Glozman–Riska (GR) model, but to a combination of colour, flavour, and spatial wave function properties that enhance the relevant matrix elements. The KKMT interaction explicitly depends on flavour and spin of the quarks, but unlike the GR flavour–spin one it has a firm footing in QCD. In the process we provide several technical advances, in particular we show the first explicit derivation of the three-body Fierz transformation and apply it to the KKM interaction. We also discuss the ambiguities associated with the colour degree of freedom.

Effects of instanton induced interactions on pentaquarks

Roles of instanton induced interactions (III) in the masses of pentaquark baryons, ${\ensuremath{\Theta}}^{+}$ ($J=1/2$ and $3/2$) and ${\ensuremath{\Xi}}^{--}$, and a dibaryon, $H$, are discussed using the MIT bag model. It is shown that the two-body terms in III give a strong attraction mainly due to the increase of the number of flavor antisymmetric quark pairs in multiquark systems. In contrast, the three-body $u$-$d$-$s$ interaction is repulsive. It is found that III lowers the mass of negative-parity ${\ensuremath{\Theta}}^{+}$ as much as 100 MeV from the mass predicted by the bag model without III. We also consider possible quark model configurations for positive-parity ${\ensuremath{\Theta}}^{+}$ under III.

QCD instantons and the soft pomeron

We study the rôle of semiclassical QCD vacuum solutions in high-energy scattering by considering the instanton contribution to hadronic cross sections. We propose a new type of instanton-induced interactions (“instanton ladder”) that leads to the rising with energy cross section σ∼s Δ of Regge type (the pomeron). We argue that this interaction may be responsible for the structure of the soft pomeron. The intercept Δ>0 is calculated. It has a nonanalytic dependence on the strong coupling constant, allowing a nonsingular continuation into the nonperturbative region. We derive the pomeron trajectory, which appears to be approximately linear in some range of (negative) momentum transfer t, but exhibits a curvature at small t. Possible rôle of instantons in multiparticle production is also discussed.

Soft Pomeron in QCD

This talk is a brief presentation of our view on the Pomeron, as a nonperturbative QCD phenomenon but from sufficiently short distances. Our approach is based on the scale anomaly of QCD and emphasizes the rôle of semi-classical QCD vacuum fields. We show that both the intercept and the slope of Pomeron trajectory appear to be determined by the energy density of nonperturbative QCD vacuum. The particular example of semi-classical QCD vacuum fields is discussed based on a new type of instanton-induced interactions (“instanton ladder”) that leads to the rising with energy cross section σ ∼ s Δ P of Regge type (the Pomeron).

Masses of the Goldstone modes in the CFL phase of QCD at finite density

We construct the U L (3)× U R (3) effective lagrangian which encodes the dynamics of the low energy pseudoscalar excitations in the Color-Flavor-Locking superconducting phase of QCD at finite quark density. We include the effects of instanton-induced interactions and study the mass pattern of the pseudoscalar mesons. A tentative comparison with the analytical estimate for the gap suggests that some of these low energy momentum modes are not stable for moderate values of the quark chemical potential μ.

Instanton-induced interactions in finite density QCD

We consider the finite density, zero-temperature behaviour of quark matter in the instanton picture. Since the instanton-induced interactions are attractive in both $\bar{q}q$ and $qq$ channels, a competition ensues between phases of matter with condensation in either or both. It results in chiral symmetry restoration due to the onset of diquark condensation, a `colour superconductor', at finite density.

Instanton-induced interactions in finite density QCD: from chiral symmetry breaking to colour superconductivity

We consider the finite density, zero-temperature behaviour of quark matter in the instanton picture. Since the instanton-induced interactions are attractive in both qq and qq channels, a competition ensues between phases of matter with condensation in either or both. It results in chiral symmetry restoration due to the onset of diquark condensation, a ‘colour superconductor’, at finite density.

Instanton-Induced Interactions in Finite Density QCD: from Chiral Symmetry Breaking to Colour Superconductivity

Instanton-Induced Interactions in Finite Density QCD: from Chiral Symmetry Breaking to Colour Superconductivity

Light quarks in the instanton vacuum at finite baryon density

We consider the finite density, zero-temperature behaviour of quark matter in the instanton picture. Since the instanton-induced interactions are attractive in both $\bar{q}q$ and $qq$ channels, a competition ensues between phases of matter with condensation in either or both. It results in chiral symmetry restoration due to the onset of diquark condensation, a `colour supercondutor', at finite density. Also present is a state with both manners of condensation, however this phase is found to be thermodynamically disfavoured for equilibrium matter. Properties of quark matter in each phase are discussed, with emphasis on the microscopic effects of the effective mass and superconducting energy gap.

Color-flavor locking and chiral symmetry breaking in high density QCD

We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3) color × SU(3) L × SU(3) R symmetries are broken down to the diagonal subgroup SU(3) color+ L+ R by the formation of a condensate of quark Cooper pairs. We discuss general properties that follow from this hypothesis, including the existence of gaps for quark and gluon excitations, the existence of Nambu-Goldstone bosons which are excitations of the diquark condensate, and the existence of a modified electromagnetic gauge interaction which is unbroken and which assigns integral charge to the elementary excitations. We present mean-field results for a Hamiltonian in which the interaction between quarks is modeled by that induced by single-gluon exchange. We find gaps of order 10–100 MeV for plausible values of the coupling. We discuss the effects of non-zero temperature, non-zero quark masses and instanton-induced interactions on our results.

Three-flavor QCD at high density: Color-flavor locking and chiral symmetry breaking

We propose a symmetry breaking scheme for QCD with three massless quarks at high baryon density wherein the color and flavor SU(3) color × SU(3) L × SU(3) R symmetries are broken down to the diagonal subgroup SU(3) color+ L+ R by the formation of a condensate of quark Cooper pairs. We discuss general properties that follow from this hypothesis, including the existence of gaps for quark and gluon excitations, the existence of Nambu-Goldstone bosons which are excitations of the diquark condensate, and the existence of a modified electromagnetic gauge interaction which is unbroken and which assigns integral charge to the elementary excitations. We present mean-field results for a Hamiltonian in which the interaction between quarks is modelled by that induced by single-gluon exchange. We find gaps of order 10–100 MeV for plausible values of the coupling. We discuss the effects of nonzero temperature, nonzero quark masses and instanton-induced interactions on our results.