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.
We analyze the instanton transitions in the framework of the gauge invariant variational calculation in the pure Yang-Mills theory. Instantons are identified with the saddle points in the integration over the gauge group which projects the Gaussian wave functional onto the gauge invariant physical Hilbert space. We show that the dynamical mass present in the best variational state provides an infrared cutoff for the instanton sizes. The instantons of the size $ρ<1/M$ are suppressed and the large size instanton problem arising in the standard WKB calculation is completely avoided in the present…
We review several aspects of Yang-Mills theory (YMT) in two dimensions, related to its perturbative and topological properties. Consistency between light-front and equal-time formulations is thoroughly discussed.
The influence of nonperturbative fields on instantons in quantum chromodynamics is studied. Nonperturbative vacuum is described in terms of nonlocal gauge invariant vacuum averages of gluon field strength. Effective action for instanton is derived in bilocal approximation and it is demonstrated that stochastic background gluon fields are responsible for infra-red (IR) stabilization of instantons. Dependence of characteristic instanton size on gluon condensate and correlation length in nonperturbative vacuum is found. It is shown that instanton size in QCD is of order of 0.25 fm. Comparison of …
The influence of nonperturbative fields on instantons in quantum chromodynamics is studied. Nonperturbative vacuum is described in terms of nonlocal gauge invariant vacuum averages of gluon field strength.Effective action for instanton is derived in bilocal approximation and it is demonstrated that stochastic background gluon fields are responsible for infra-red (IR) stabilization of instantons. Dependence of characteristic instanton size on gluon condensate and correlation length in nonperturbative vacuum is found. Comparison of obtained instanton size distribution with lattice data is made.
We calculate the values of non-factorizable dimension-7 vacuum condensates in the instanton vacuum. We comment on a method, recently proposed by Oganesian, to estimate the dimension-7 condensates by factorization of dimension-10 condensates in various inequivalent ways. The instanton estimates could be used to analyze the stability of QCD sum rules with increasing dimensions.
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.
The instanton--anti-instanton pair induced asymptotics of perturbation theory expansion for the cross section of electron--positron pair annihilation to hadrons and hadronic width of $τ$-lepton was found. For $N_f = N_c$ the nonperturbative instanton contribution is finite and may be calculated without phenomenological input. The instanton induced peturbative asymptotics was shown to be enhanced as $(n+10)!$ and in the intermediate region $n<15$ may exceed the renormalon contribution. Unfortunately, the analysis of $\sim 1/n$ corrections shows that for $n \sim 10$ the obtained asymptotic expre…
The pion wave function is computed in the low energy effective theory inspired by the instanton vacuum model. The resultat is numerically rather close to the asymptotical wave function.
A large body of evidence from lattice calculations indicates that instantons play a major role in the physics of light hadrons. This evidence is summarized, and recent results concerning the instanton content of the SU(3) vacuum, instanton contributions to the static potential, and a new class of instanton solutions at finite temperature are reviewed.
Roles of instantons in strangeness hadron physics are discussed. After introducing general features of instantons, hadron spectroscopy under the influence of instanton-quark effective interactions is discussed. Emphases are on the H dibaryon, spin-orbit splittings of P-wave baryons and baryon-baryon interactions and spectrum of the pentaquarks.
In $N+1$ dimensions, false vacuum decay at zero temperature is dominated by the $O(N+1)$ symmetric instanton, a sphere of radius $R_0$, whereas at temperatures $T>>R_0^{-1}$, the decay is dominated by a `cylindrical' (static) $O(N)$ symmetric instanton. We study the transition between these two regimes in the thin wall approximation. Taking an $O(N)$ symmetric ansatz for the instantons, we show that for $N=2$ and $N=3$ new periodic solutions exist in a finite temperature range in the neighborhood of $T\sim R_0^{-1}$. However, these solutions have higher action than the spherical or the cylindr…
The influence of nonperturbative fields on instantons in quantum chromodynamics is studied. Nonperturbative vacuum is described in terms of nonlocal gauge invariant vacuum averages of gluon field strength. Effective action for instanton is derived in bilocal approximation and it is demonstrated that stochastic background gluon fields are responsible for infra-red (IR)stabilization of instantons. Comparison of obtained instanton size distribution with lattice data is made.
We describe quenched spectroscopy in SU(2) gauge theory using smoothed gauge field configurations. We investigate the properties of quarks moving in instanton background field configurations, where the sizes and locations of the instantons are taken from simulations of the full gauge theory. By themselves, these multi-instanton configurations do not confine quarks, but they induce chiral symmetry breaking.
It is a common belief that the last missing piece of the Standard Model of particles physics was found with the discovery of the Higgs boson at the Large Hadron Collider. However, there remains a major prediction of quantum tunnelling processes mediated by instanton solutions in the Yang-Mills theory, that is still untested in the Standard Model. The direct experimental observation of instanton-induced processes, which are a consequence of the non-trivial vacuum structure of the Standard Model and of quantum tunnelling in QFT, would be a major breakthrough in modern particle physics. In this p…
We formulate a toy model for the $θ$ vacuum that embodies the n-point moments of the even and odd topological charge densities. The partition function is $2π$ periodic only after resumming over all winding modes. We apply the same analysis to the quenched instanton vacuum at finite $θ$ and derive saddle-point results for the vacuum energy density that are manifestly $2π$ periodic whatever $θ$. We briefly discuss the consequences of unquenching the fermions on our results.
In the framework of the instanton vacuum model we evaluate the Chiral Perturbation Theory (ChPT) low-energy constants h_3,l_7. We found that in the instanton vacuum model the constant l_7 is very sensitive to the shape of the instanton and the instanton vacuum parameters. We evaluated the constant l_7 for two different zero-mode profiles and as a function of the average instanton size ρand inter-instanton distance R. Our result agrees with an old "order of magnitude" estimate of this constant from [1]. The obtained value of l_7 implies that the pure QCD contribution to the pion mass difference…
We extend the use of Configurational Information Measures (CIMSs) to instantons and vacuum decay in arbitrary spatial dimensions. We find that both the complexity and the information content in the shape of instanton solutions have distinct regions of behavior in parameter space, discriminating between qualitative thin and thick wall profiles. For Euclidean spaces of dimension $D$, we show that for $D \gt 6$ instantons undergo a qualitative change of behavior from their lower- dimensional counterparts, indicating that $D=6$ is a critical dimension. We also find a scaling law relating the diffe…
The influence of nonperturbative fields on instantons in quantum chromodynamics is studied. Effective action for instanton is derived in bilocal approximation and it is demonstrated that stochastic background gluon fields are responsible for IR stabilization of instantons. It is shown that instanton size in QCD is of order of 0.25 fm. Comparison of obtained instanton size distribution with lattice data is made.
We suggest a constrained instanton (CI) solution in the physical QCD vacuum which is described by large-scale vacuum field fluctuations. This solution decays exponentially at large distances. It is stable only if the interaction of the instanton with the background vacuum field is small and additional constraints are introduced. The CI solution is explicitly constructed in the ansatz form, and the two-point vacuum correlator of gluon field strengths is calculated in the framework of the effective instanton vacuum model. At small distances the results are qualitatively similar to the single ins…
We study the contribution of instantons to the binding and the mass of the lightest scalar glueball, in gluondynamics. We show that the short-range correlations introduced by such non-perturbative vacuum fluctuations are sufficient to give raise to a scalar glueball bound-state, with mass in good agreement with the results of recent lattice calculations.
This is the first of a series of papers devoted to a systematic study of QCD correlation functions in a framework of 'instanton vacuum' models. The topic of this paper is to work out approximate formulae for quark propagators in a multi-instanton environment. As an application, and also as a necessary step toward understanding the correlation functions, we study the propagators of scalar and spinor quarks, using the simplest possible model, the so called 'random instanton vacuum' (RIV). Results related to heavy-light mesons, are found to be very consistent with phenomenology.
The thermal and quark/baryon chemical potential dependences of quark condensate and masses of $π$- and $σ$-mesons are studied in the instanton model of the QCD vacuum in precritical region. The impact of phonon-like excitations of instanton liquid on the characteristics of $σ$-meson in such an environment is also examined.
A new approach to effective theory of quarks in the instanton vacuum is presented. Exact equations for the quark propagator and Lagrangian are derived which contain contributions of all quark modes with known coefficients. The resulting effective Lagrangian resembles that of the Nambu--Jona--Lasinio model. The commonly used zero--mode approximation is shown to be invalid in the chiral limit.
By means of the functional integral method we show that in the case of the quark-antiquark pairing at zero temperature and zero chemical potential (in the vacuum) the singlet pairing is more preferable than that with the color-flavor locking (CFL)
We have calculated the 3-point correlation function for the electromagnetic interaction of the pion in an ensembles of instantons and anti-instantons, modelling the QCD vacuum. The results are well described by a pion pole and the pion formfactor is extracted, nicely following a standard monopole fit. The experimental data on the formfactor are well reproduced, provided an average instanton size is fixed at ${\barρ}=0.35\pm 0.03\fm$, the same as found for a variety of other correlation functions and was found on the lattice.
For a scalar theory whose classical scale invariance is broken by quantum effects, we compute self-consistent bounce solutions and Green's functions. Deriving analytic expressions, we find that the latter are similar to the Green's functions in the archetypal thin-wall model for tunneling between quasi-degenerate vacua. The eigenmodes and eigenspectra are, however, very different. Large infrared effects from the modes of low angular momentum $j=0$ and $j=1$, which include the approximate dilatational modes for $j=0$, are dealt with by a resummation of one-loop effects. For a parametric example…
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 quasi-pion and quasi-kaon 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.
We calculate the lowest-dimensional nonlocal quark and gluon condensates within the single instanton approximation of the instanton liquid model. As a result, we determine the values of average virtualities of quarks $λ_q^2$ and gluons $λ_g^2$ in the QCD vacuum and obtain parameterless predictions for the ratio $λ_g^2/λ_q^2 = 12/5$, and for some ratios of different vacuum condensates of higher dimensions. The nonlocal properties of quark and gluon condensates are analyzed, and insufficiency of the single instanton approximation is discussed.
We are considering the modifications of gluon properties in Instanton Liquid Model (ILM) for the QCD vacuum. Re-scattering of a gluons on an instantons leads to the dynamical momentum-dependent gluon mass $M_g(q).$ First, we considered scalar "gluon", since there are no zero-modes problem and found its dynamical mass $M_s(q)$. At the typical phenomenological values of the average instanton size $ρ=1/3\,\,fm$ and average inter-instanton distance $R=1\,\, fm$ we got $M_s(0)=256\,\,MeV$. Further, we extended this approach to the real vector gluon with careful consideration of zero-modes and got $…
We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the instantons of large and small sizes. The former are described in terms of the local scalar condensate, while the latter can be interpreted as the nonlocal scalar condensate. We solve the corresponding QCD sum rules equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small size instantons w_s \approx 2/3.
A low energy theorem concerning a matrix element of the QCD axial anomaly between vacuum and two-photons states is tested against different instanton models. In the chiral limit the theorem is fulfilled by the Diakonov&Petrov model, whereas it is violated by single-instanton approximations. Beyond the chiral limit the theorem, and two relations established for other matrix elements of the QCD axial anomaly between vacuum and meson states, result to be violated also by the Diakonov&Petrov model.
A new approach to effective theory of quarks in the instanton vacuum is presented. Exact equations for the quark propagator and Lagrangian are derived which contain contributions of all quark modes with known coefficients. The resulting effective Lagrangian differs from the standard one and resembles that of the Nambu-Jona-Lasinio model.
Assuming the gluon field is well approximated by instanton configurations we derive a partition function and calculate the specific correlators. Namely, the heavy quark propagator and heavy quark-aniquark correlator with the account of the light quark determinant and QCD instanton vacuum properties. With these knowledge we calculate the light quark contribution to the interaction between heavy quarks, which might be essential for the properties of a few heavy quarks systems like oniums and double-heavy baryons.
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 to increase. 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.
Heavy hadrons are analyzed in a random and dilute gas of instantons. We derive the instanton-induced interactions between heavy and light quarks at next to leading order in the heavy quark mass and in the planar approximation, and discuss their effects on the hadronic spectrum. The role of these interactions in the formation of exotic hadrons is also discussed.
We give a brief status report on our on-going investigation of the prospects to discover QCD instantons in deep inelastic scattering (DIS) at HERA. A recent high-quality lattice study of the topological structure of the QCD vacuum is exploited to provide crucial support of our predictions for DIS, based on instanton perturbation theory.
We review our recent study of the role played by the chiral interactions induced by instantons, in the lowest-lying sector of the light hadron spectrum. We discuss how the ordering of the lowest meson and baryon excitations is explained by the structure of the instanton-induced quark-quark and gluon-gluon interaction. We focus on the pion, nucleon, vector- and axial-vector mesons, and on the scalar glueball. We find that all these hadrons are bound in this model and have realistic masses.
We calculate the nucleon matrix element of Weinberg's dimension-6 CP-odd gluon operator $f^{abc} (\tilde F_{μν})^a (F^{μρ})^b (F^ν_{\;\;ρ})^c$ in the instanton vacuum. In leading order of the instanton packing fraction, the dimension-6 operator is effectively proportional to the topological charge density $(\tilde F_{μν})^a (F^{μν})^a$, whose nucleon matrix element is given by the flavor-singlet axial charge and constrained by the $U(1)_A$ anomaly. The nucleon matrix element of the dimension-6 operator is obtained substantially larger than in other estimates, because of the strong localization…
The leading-twist wave functions of the pion and the photon at a low normalization point are calculated in the effective low--energy theory derived from the instanton vacuum. The pion wave function is found to be close to the asymptotic one, consistent with the recent CLEO measurements. The photon wave function is non-zero at the endpoints. This different behavior is a consequence of the momentum dependence of the dynamical quark mass suggested by the instanton vacuum. We comment on the relation of meson wave functions and off-forward parton distributions in this model.
The current status of the muon anomalous magnetic moment problem is briefly presented. The corrections to muon anomaly coming from the effects of hadronic vacuum polarization, Z*γγ* effective vertex and light-by-light scattering are estimated within the instanton model of QCD vacuum.
We study the tunneling of virtual matter-antimatter pairs from the quantum vacuum in the presence of a spatially uniform, time-dependent electric background composed of a strong, slow field superimposed with a weak, rapid field. After analytic continuation to Euclidean spacetime, we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production…
We calculate the two-pion light-cone distribution amplitudes in the effective low-energy theory based on the instanton vacuum. These generalized distribution amplitudes describe the soft (non-perturbative) part of the process $γ^*γ\to ππ$ in the region where the c.m. energy is much smaller than the photon virtuality. They can also be used in the analysis of exclusive processes such as $γ^* p \to p + 2π, 3π$ etc.
We discuss two dimensional $QCD (N_c\to\infty)$ with fermions in the fundamental as well as adjoint representation. We find factorial growth $\sim (g^2N_cπ)^{2k}\frac{(2k)!(-1)^{k-1}}{(2 π)^{2k}}$ in the coefficients of the large order perturbative expansion. We argue that this behavior is related to classical solutions of the theory, instantons, thus it has nonperturbative origin. Phenomenologically such a growth is related to highly excited states in the spectrum. We also analyze the heavy-light quark system $Q\bar{q}$ within operator product expansion (which it turns out to be an asymptotic…
In this talk, we report our present work on the chiral magnetic effect (CME) under a strong magnetic field at low temperature. To this end, we use the instanton vacuum with the finite instanton-number fluctuation Delta, which relates to the nontrivial topological charge Q_t. We compute the vacuum expectation values of the local chiral density <rho_chi>, chiral charge density <n_chi> and induced electromagnetic current <j_mu>. We observed that the longitudinal EM current is much larger than the transverse one, |j_perp/j_parallel| ~ Q_t, and the <n_chi> equals to the |<j_(3,4)>|. It also turns o…
The instanton interaction in QCD generates an effective potential for scalar quark-antiquark condensates in the color singlet and octet channels. For three light quark flavors the cubic term in this potential induces an octet condensate and ``spontaneous breaking'' of color in the vacuum. Realistic masses of the rho- and eta'-mesons are compatible with renormalization-group-improved instanton perturbation theory.
We revisit the QCD+QED axial anomaly low-energy theorems which give an exact relation between the matrix elements of the gluon and photon parts of the axial anomaly operator equation within the framework of the {\em effective action} derived from the instanton vacuum. The matrix elements between the vacuum and two photon states and between the vacuum and two gluon states are investigated for arbitrary $N_f $ in the chiral limit. Having gauged the effective action properly, we show that the model does exactly satisfy the low-energy theorems.
The singlet coupling to the topological charge density in the instanton vacuum, causes the instantons and antiinstantons to be screened over distances of the order of 1/2 fm. Dilute instanton systems behave as a free gas, while dense instanton systems behave as a plasma. The free gas behaviour is favored by a density of 1 fm$^{-4}$. Owing to the Higgs mechanism, the $η$' mass is heavy (1100 MeV). The vacuum topological susceptibility is small (0.07 fm$^{-4}$) and consistent with the QCD Ward identity. In the chiral limit, the singlet screening vanishes, leading to a four dimensional plasma sta…
In the framework of the Instanton Liquid Model we evaluate the heavy quark $\bar{Q}Q$ potential at nonzero temperature $T$. The potential has two components: contribution due to direct interaction with instantons, and the modification of the one-gluon exchange contribution via instanton-generated dynamical \char`\"{}electric\char`\"{} gluon mass $M_{el}(q,T)$. We conclude that the nonperturbative ILM contributions to the $Q\bar{Q}$ potential have pronounced temperature dependence, which might be tested in phenomenological analyses of charmonia production data.
The QCD vacuum is populated by instantons that correspond to the tunneling processes in the vacuum. This mechanism creates the strong vacuum gluon fields. As result, the QCD vacuum instantons induce very strong interactions between light quarks, initially almost massless. Such a strong interactions bring a large dynamical mass M of the light quarks and bound them to produce almost massless pions in accordance with the spontaneous breaking of the chiral symmetry (SBCS). On the other hand, the QCD vacuum instantons also interact with heavy quarks and responsible for the generation of the heavy-h…
The correlator of vector and nonsinglet axial-vector currents in the external electromagnetic field is calculated within the instanton liquid model of QCD vacuum. In general the correlator has two Lorentz structures: longitudinal w_L and transversal w_T with respect to axial-vector index. Within the instanton model the saturation of the anomalous w_L structure is demonstrated. It is known that in the chiral limit the transversal structure w_T is free from perturbative corrections. In this limit within the instanton model we calculate the transversal invariant function w_T at arbitrary momentum…
We discuss the role of instantons in the spectroscopy of ordinary and exotic hadrons as well as in high energy reactions. We argue that the instanton induced flavor- and spin-dependent quark-quark and quark-gluon interactions can explain many features of the hadron spectrum. The observed anomalous spin and flavor effects in various reactions with hadrons can also be understood within the instanton model for QCD vacuum.
The correlator of singlet axial-vector and vector currents in the external electromagnetic field is studied within the instanton liquid model of QCD vacuum. In the chiral limit we calculate the longitudinal w_L^0 and transversal w_T^0 with respect to axial-vector index invariant amplitudes at arbitrary momentum transfer q. It is demonstrated how the anomalous longitudinal part of the correlator is renormalized at low momenta due to the presence of the U_A(1) anomaly.
The pion electric polarizability, α^E_π^\pm, the leading order hadronic contribution to the muon anomalous magnetic moment, $a_μ^{hvp 1} $, and the ratio of the difference to the sum of vector and axial-vector correlators, (V-A)/(V+A), are found within the instanton model of QCD vacuum. The results are compared with phenomenological estimates of these quantities following from the ALEPH and OPAL data on vector and axial-vector spectral densities.
We study baryon and diquark correlation functions in the framework of an instanton model for the QCD vacuum. The model naturally accomodates a light scalar diquark. As a consequence, the correlation functions for the nucleon and delta are found to be qualitatively different. Using a complete set of all available correlation functions we determine masses and coupling constants for these particles. We compare our results with predictions from QCD sum rules and recent lattice measurement of point-to-point correlators.
QCD instantons are arguably the best motivated yet unobserved nonperturbative effects predicted by the Standard Model. A discovery and detailed study of instanton-generated processes at colliders would provide a new window into the phenomenological exploration of QCD and a vastly improved fundamental understanding of its non-perturbative dynamics. Building on the optical theorem, we numerically calculate the total instanton cross-section from the elastic scattering amplitude, also including quantum effects arising from resummed perturbative exchanges between hard gluons in the initial state, t…
In the framework of the instanton vacuum model we make expansion over the current mass $m$ and number of colors $N_c$ and evaluate ${\cal O}(1/N_c, m, m/N_c, m \ln m/N_c)$-corrections to the dynamical quark mass $M$, the quark condensate $<\bar qq>$, the pion mass $M_π$ and decay constant $F_π$. We found the SU(2) $χ$PT low-energy constants $\bar l_3, \bar l_4$ in a good correspondence with the phenomenology and lattice calculations.
We investigate the leading-twist light-cone distribution amplitudes for the pion and kaon based on the gauge-invariant nonlocal chiral quark model from the instanton vacuum in the presence of external axial-vector currents. We find that the nonlocal contribution from the gauge invariance has much effects on the pion distribution amplitudes, while it changes mildly the kaon ones. We also study the Gegenbauer moments of the distribution amplitudes and compare them with the empirical analysis of the CLEO data.
