Instanton Vacuum Research Articles

Heavy and light quarks in the instanton vacuum

Assuming the gluon field is well approximated by instanton configurations we derive a light quarks determinant and calculate its contribution to the specific heavy quarks correlators -- namely, the heavy quark propagator and heavy quark-aniquark correlator, receiving the instanton generated light-heavy quarks interaction terms contributions. 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.

Neutrino production of single pions: Dipole description

The light-cone distribution amplitudes for the axial current are derived within the instanton vacuum model (IVM), which incorporates nonperturbative effects including spontaneous chiral symmetry breaking. This allows to extend applicability of the dipole approach, usually used in the perturbative domain, down to $Q^{2}\to0$, where partially conserved axial current (PCAC) imposes a relation between the neutrino-production cross section and the one induced by pions. A dramatic breakdown of the Adler relation (AR) for diffractive neutrino-production of pions, caused by absorptive corrections, was revealed recently in arXiv:1105.1711. Indeed, comparing with the cross section predicted by the dipole phenomenology at $Q^{2}\to0$ on a proton target we confirmed the sizable deviation from the value given by the AR, as was estimated in arXiv:1105.1711 within a simplified two-channel model. The dipole approach also confirms that in the black-disc limit, where the absorptive corrections maximize, the diffractive cross section ceases, on the contrary to the expectation based on PCAC.

Pion Electromagnetic Form Factor and ??-meson Mass Shift at Finite Density

We investigate the pion electromagnetic charge radii and mass dropping of themeson at finite density. We first calculate the pion charge radii within the framework of the nonlocal chiral quark model from the instanton vacuum both at zero and finite densities. In order to relate the change of the pion charge radius to that of the �-meson mass at finite density, we employ the vector-meson dominance for the pion electromagnetic form factor. It turns out that the pion charge radius is getting larger as the quark chemical potential increases. As a result, the �-meson mass falls off as the quark chemical potential grows and is found to be dropped by about 10% at normal nuclear matter density: m � /m� ≈ 1 − 0.12µB/µ0, which is compatible to the results of the measurement

Spin structure of the pion from the instanton vacuum

We investigate the spin structure of the pion within the framework of the nonlocal chiral quark model from the instanton vacuum. We first evaluate the tensor form factors of the pion for the first and second moment (n=1,2) and compare it with the lattice data. Combining the tensor form factor of the pion with the electromagnetic one, we determine the impact-parameter dependent probability density of transversely polarized quarks inside the pion. It turns out that the present numerical results for the tensor form factor as well as those for the probability density are in good agreement with the lattice data. We also discuss the distortion of the spatial distribution of the quarks in the transverse plane inside the pion.

Shadowing in Compton scattering on nuclei

We evaluate the shadowing effect in deeply virtual and real Compton scattering on nuclei in the framework of the color dipole model. We rely on the soft photon wave function derived in the instanton vacuum model, and employ the impact parameter dependent phenomenological elastic dipole amplitude. Both the effects of quark and the gluon shadowing are taken into account.

Publisher’s Note: QCD isospin breakingχPTlow-energy constants from the instanton vacuum [Phys. Rev. D81, 054029 (2010)

Publisher’s Note: QCD isospin breaking<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>χ</mml:mi><mml:mi>PT</mml:mi></mml:math>low-energy constants from the instanton vacuum [Phys. Rev. D<b>81</b>, 054029 (2010)

QCD isospin breakingχPT low-energy constants from the instanton vacuum

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 \rho and 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 is small, ~1% of the observed experimental value.

Chiral magnetic effect at low temperature

We investigate the chiral magnetic effect (CME) under a strong magnetic field B = B_0 x_3 at low temperature T < T^chi_c. For this purpose, we employ the instanton vacuum configuration 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>, which signal the CME, as functions of T and B_0. 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 out that the CME becomes insensitive to the magnetic field as T increases, according to the decreasing instanton, i.e. tunneling effect. Within our framework, the instanton contribution to the CME becomes almost negligible beyond T~300 MeV.

OFF-SHELL TWIST-FOUR PHOTON LIGHT-CONE WAVEFUNCTION FOR THE CHIRALITY-CONSERVING QUARK–ANTIQUARK VECTOR CURRENT IN THE LOW-ENERGY EFFECTIVE THEORY OF QCD

Within the framework of the low-energy effective theory arising from the instanton vacuum model of QCD, the twist-four virtual photon wavefunction, gγ3(u, P2), corresponding to the nonlocal quark–antiquark vector current is calculated at the low-energy scale. The coupling constant, fγ(P2), of the quark–antiquark vector current to the virtual photon state is also obtained. The behavior of the coupling as well as the obtained photon wave function especially at the end points is discussed.

The scalar glueball in the instanton vacuum

We study the contribution of instantons to the binding and the mass of the lightest scalar glueball, in gluon dynamics. We show that the short-range correlations introduced by such non-perturbative vacuum fluctuations are sufficient to give rise to a scalar glueball bound state, with a mass in good agreement with the results of recent lattice calculations.

Modified action for light quarks in the instanton vacuum

The procedure of averaging in an instanton medium in quarks with any number of flavors is discussed. It is shown that the effect of the instanton medium is equivalent to an interaction of light quarks with dynamically generated mass (four-quark interaction Nf = 2) and massless bosonic spinor fields (ghosts). The fact that the instanton liquid is dilute makes it possible to use perturbation theory.

PION AND KAON STRUCTURES FROM THE INSTANTON VACUUM

In this presentation, we briefly review recent investigations on pion and kaon structures from the instanton vacuum. Starting from the low-energy QCD partition function, we have computed the Gasser-Leutwyler low-energy constants, electromagnetic form factors of the pion and kaon, and semileptonic decay form factors of the kaon. The results are in good agreement with the experimental and empirical data.

Deeply virtual Compton scattering via color dipoles: Nonperturbative effects

We study the deeply virtual Compton scattering amplitude within the color dipole approach. The light-cone wave function of a real photon is evaluated in the instanton vacuum model. Our parameter-free calculations are able to describe H1 data, both the absolute values and the $t$ dependences, at medium-high values of ${Q}^{2}$. The ${Q}^{2}$ dependence is found to be sensitive to the choice of the phenomenological cross section fitted to deep-inelastic scattering data.

Scalar susceptibility from the instanton vacuum with meson-loop corrections

The scalar susceptibility (${\ensuremath{\chi}}_{s}$) of QCD, which represents the response of the chiral condensate to a small perturbation of explicit chiral-symmetry breaking ($m\ensuremath{\ne}0$), is investigated within the nonlocal chiral quark model ($\mathrm{NL}\ensuremath{\chi}\mathrm{QM}$) based on the instanton vacuum configuration for ${N}_{f}=2$. We also take into account $1/{N}_{c}$ meson-loop (ML) corrections including scalar and pseudoscalar mesons. It turns out that the chiral condensate is modified to a large extend by the ML corrections in the vicinity of $m=0$, whereas its effect becomes weak beyond $m\ensuremath{\approx}100\text{ }\text{ }\mathrm{MeV}$. As numerical results, we find that ${\ensuremath{\chi}}_{s}=\ensuremath{-}0.34\text{ }{\mathrm{GeV}}^{2}$ with the ML corrections and $0.18\text{ }\text{ }{\mathrm{GeV}}^{2}$ without it. From these observations, we conclude that the ML corrections play an important role in the presence of finite current-quark mass.

MAGNETIC SUSCEPTIBILITY OF THE QCD VACUUM AT FINITE DENSITY

We present in this talk a recent investigation on the magnetic susceptibility (χ) of the QCD vacuum at finite density, utilizing the nonlocal chiral quark model from the instanton vacuum. We take into account the nonzero current-quark mass (mq) explicitly to consider the effect of explicit flavor SU(3) symmetry breaking. It turns out that, when we turn on the current-quark mass (mq ≠ 0), χ becomes smaller, indicating less response to the externally induced electromagnetic field, in comparison to that for mq = 0.

Pion weak decay constant at finite density from the instanton vacuum

We investigate the pion weak decay constant (Fπ) and pion mass (mπ) at finite density within the framework of the nonlocal chiral quark model from the instanton vacuum with the finite quark-number chemical potential (μ) taken into account. We mainly focus on the Nambu–Goldstone phase below the critical value of the chemical potential μc≈320 MeV, which is determined consistently within the present framework. The breakdown of Lorentz invariance at finite density being considered, the time (Fπt) and space (Fπs) components are computed separately, and the corresponding results turn out to be: Fπt=82.96 MeV and Fπs=80.29 MeV at μc, respectively. Using the in-medium Gell-Mann–Oakes–Renner (GOR) relation, we show that the pion mass increases by about 15% at μc.

Electromagnetic form factors of the pion and kaon from the instanton vacuum

We investigate the pion and kaon (${\ensuremath{\pi}}^{+}$, ${K}^{+}$, ${K}^{0}$) electromagnetic form factors in the spacelike region: ${Q}^{2}\ensuremath{\lesssim}1\text{ }\text{ }\mathrm{GeV}$, based on the gauged low-energy effective chiral action from the instanton vacuum in the large ${N}_{c}$ limit. Explicit flavor SU(3) symmetry breaking is taken into account. The nonlocal contributions turn out to be crucial to reproduce the experimental data. While the pion electromagnetic form factor is in good agreement with the data, the kaon one seems underestimated. We also calculate the electromagnetic charge radii for the pion and kaon: $⟨{r}^{2}{⟩}_{{\ensuremath{\pi}}^{+}}=0.455\text{ }\text{ }{\mathrm{fm}}^{2}$, $⟨{r}^{2}{⟩}_{{K}^{+}}=0.534\text{ }\text{ }{\mathrm{fm}}^{2}$, and $⟨{r}^{2}{⟩}_{{K}^{0}}=\ensuremath{-}0.060\text{ }\text{ }{\mathrm{fm}}^{2}$ without any adjustable free parameter except for the average instanton size and interinstanton distance, and they are compatible with the experimental data. The low-energy constant ${L}_{9}$ in the large ${N}_{c}$ limit is estimated to be $8.42\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ from the pion charge radius.

Magnetic Susceptibility of the QCD Vacuumat a Finite Quark-chemical Potential

We investigate the magnetic susceptibility (chi) of the QCD vacuum at finite density (the quark chemical potential mu_q > 0) and at zero temperature in the chiral limit, within the framework of the medium-modified nonlocal chiral quark model from the instanton vacuum. The model is characterized by the average inter-instanton distance R ~ 1 fm and average instanton size rho ~ 1/3 fm. It is found that the magnetic susceptibility chi decreases smoothly with respect to mu_q and turns out to be about a half of its vacuum value at the critical density (mu_q ~ mu_c).

Sigma meson and phonon-like excitations of the instanton vacuum

The possible nature of two experimentally observed scalar mesons that are widely spaced in mass and whose special features may be caused by the excitations of the instanton liquid considered as a model of the QCD vacuum. It is shown that mass changes in the scalar sector may prove to be unexpectably large, even though the scale of such corrections to the dynamical quark mass is relatively small.

1/Nccorrections to the magnetic susceptibility of the QCD vacuum

We investigate the magnetic susceptibility of the QCD vacuum with the $1/{N}_{c}$ corrections taken into account, based on the instanton vacuum. Starting from the instanton liquid model, we derive the gauged light-quark partition function in the presence of the current quark mass as well as of external Abelian vector and tensor fields. We consider the $1/{N}_{c}$ meson-loop corrections which are shown to contribute to the magnetic susceptibility by around 15% for the up (and down) quarks. We also take into account the tensor terms of the quark-quark interaction from the instanton vacuum as well as the finite-width effects, both of which are of order $\mathcal{O}(1/{N}_{c})$. The effects of the tensor terms and finite width turn out to be negligibly small. The final results for the up-quarks are given as: $\ensuremath{\chi}⟨i{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\psi}{⟩}_{0}\ensuremath{\simeq}35--40\text{ }\text{ }\mathrm{MeV}$ with the quark condensate $⟨i{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}\ensuremath{\psi}{⟩}_{0}$. We also discuss the pion mass dependence of the magnetic susceptibility in order to give a qualitative guideline for the chiral extrapolation of lattice data.