Nonlocal Chiral Quark Model Research Articles

Fragmentation and quark distribution functions for the pion and kaon with explicit flavor-SU(3)-symmetry breaking

We investigate the unpolarized pion and kaon fragmentation functions, employing the nonlocal chiral-quark model, which manifests the nonlocal interactions between the quarks and pseudoscalar mesons, considering the explicit flavor-SU(3)-symmetry breaking in terms of the current-quark masses. Moreover, we study the quark-distribution functions, derived from the fragmentation ones with the Drell-Yan-Levi relation. Numerical results are evaluated to higher Q^2 by the DGLAP evolution and compared with the empirical data. The ratios between the relevant valance quark-distribution functions are also discussed. It turns out that the present results are in relatively good agreement with available data and other theoretical estimations.

The muon anomaly and [formula omitted] light-by-light contribution. Estimation of the value and error band in nonlocal chiral quark model.

The contribution into the anomalous magnetic moment of muon ( g − 2 ) μ from the light-by-light processes with neutral pion is calculated in the nonlocal chiral quark model. The full kinematic dependence of the meson-two-photon vertices is taken into account in this process. Estimation for an error band of the pion contribution in nonlocal chiral quark model is given.

The light-by-light contribution to the [formula omitted] of muon from lightest pseudoscalar and scalar mesons within nonlocal chiral quark model.

The light-by-light contribution from the lightest neutral pseudoscalar and scalar mesons to the anomalous magnetic moment of muon is calculated in the framework nonlocal S U ( 3 ) × S U ( 3 ) quark model. The model is based on a four-quark interaction of the Nambu–Jona-Lasinio type and tʼHooft six-quark interaction. Full kinematic dependencies of vertices with off-shell mesons in the light-by-light scattering amplitude is taken into account.

Pseudoscalar meson transition form factors in nonperturbative QCD approach

In this communication we discuss a few topics related to modern experimental data on physics of light pseudoscalar mesons. It includes the contribution of the pseudoscalar mesons to the muon anomalous magnetic moment (AMM), g − 2 , rare decays of light pseudoscalar mesons to a lepton pair, transition form factors of pseudoscalar mesons at large momentum transfer, the pion transversity form factor. Measuring the muon anomalous magnetic moment g − 2 and rare decays of light pseudoscalar mesons into a lepton pair P → l + l − serve as important test of the standard model. To reduce the theoretical uncertainty in the standard model predictions, the data on the transition form factors of light pseudoscalar mesons play significant role. Recently new data on behavior of these form factors at large momentum transfer was supplied by the BABAR collaboration. Within the nonlocal chiral quark model it is shown how to describe these data and how the meson distribution amplitude evolves as a function of the dynamical quark masses and meson masses.

Unpolarized Fragmentation Function for the Pion and Kaon via the Nonlocal Chiral-Quark Model

In this talk we present our recent studies for the unpolarized fragmentation functions for the pion and kaon, employing the nonlocal chiral quark model, which manifests the nonlocal interaction between the quarks and pseudoscalar mesons, in the light-cone frame. It turns out that the nonlocal interaction produces considerable differences in comparison to typical local-interaction models.

Fragmentation functions and parton distribution functions for the pion with the nonlocal interactions

We study the unpolarized fragmentation functions and the parton distribution functions of the pion employing the nonlocal chiral quark model. This model manifests the nonlocal interactions between the quarks and pseudoscalar mesons in the light-cone coordinate. We find that the nonlocal interactions result in substantial differences in comparison to the result of typical models with only local couplings. We also perform the high ${Q}^{2}$-evolution for our results which is calculated at a relatively low-renormalization scale ${Q}^{2}\ensuremath{\approx}0.36\text{ }\text{ }{\mathrm{GeV}}^{2}$ and compare them with the experimental data. It has shown that our results after evolution are in qualitatively good agreement with those experimental data.

Extended nonlocal chiral-quark model for theD- andB-meson weak-decay constants

In this work, we construct a phenomenological effective model for the heavy-light quark systems, which consist of (u,d,c,b) quarks, i.e. extended nonlocal chiral-quark model (ExNLChQM) to compute the heavy-meson weak-decay constants f_D and f_B. ExNLChQM is based on the heavy-quark effective field theory as well as the dilute instanton-vacuum configuration. In ExNLChQM, a certain portion of the heavy-meson mass is considered to be generated from the nontrivial QCD vacuum contribution, being similar to that for the light quarks in usual instanton approaches. Hence, the effective heavy- and light-quark masses become momentum-dependent and play the role of a smooth UV regulator. Employing a generic external-field method applied to the effective action from ExNLChQM, we obtain f_D = (169.28 ~ 234.57) MeV and f_B = (165.41 ~ 229.21) MeV from the numerical results, depending on different model parameters. These values are in relatively good agreement with experimental data and various theoretical estimations. We also discuss the heavy-quark effects on the QCD vacuum, and the decay constants f_D^* and f_B^* in terms of the heavy-quark spin symmetry.

Generalized form factors and spin structures of the kaon

We investigate the spin structure of the kaon, based on the nonlocal chiral quark model from the instanton vacuum. We first revisit the electromagnetic form factors of the pion and kaon, improving the results for the kaon. We evaluate the generalized tensor form factors of the kaon in order to determine the probability density of transversely polarized quarks inside the kaon. We consider the effects of flavor SU(3) symmetry breaking, so that the probability density of the up and strange quarks are examined in detail. It is found that the strange quark behaves differently inside the kaon in comparison with the up quark.

Pion-to-photon transition distribution amplitudes and related form factors in the non-local chiral quark model

Transition distribution amplitudes (TDAs) are non-perturbative quantities appearing in the description of certain exclusive processes, for instance hadron-anti-hadron annihilation HH -> gamma*gamma or backward virtual Compton scattering. They are similar to generalized parton distributions (GPDs), except that the non-diagonality concerns not only the momenta, but also the physical states (they are defined in terms of hadron-photon matrix element of a non-local operator). For the case of hadronic states such as pions, there are two TDAs of interest: the vector and the axial one. They are straightforwardly related to the axial and vector form factors controlling weak pion decays pi^+- -> e^+-nugamma. The value at zero momentum transfer of the vector form factor is fixed by the axial anomaly, while this is not the case for the axial one. Moreover, the vector form factor is related to the pion-photon transition form factor which was recently measured by Belle and BaBar giving contradictory results at high momentum transfers. We have studied pion-to-photon TDAs within the non-local chiral quark model using modified non-local currents satisfying Ward-Takahashi identities. We found that the value of the axial form factor at zero momentum transfer is shifted towards the experimental value due to the non-locality of the model (in the local quark models the values of both vector and axial form factors at zero momentum transfer are the same, what is not consistent with the data). We also calculate the pion-photon transition form factor and compare it with the data.

Calculation of hadronic contribution to the anomalous magnetic momentum of muon (g − 2)μ from light by light scattering diagram in nonlocal chiral quark model

The correction to anomalous magnetic momentum muon from the light by light scattering diagram with intermediate pion is calculated in framework nonlocal chiral quark model. To fix the model parameters it is suggested to use the values of mass and two photon width of the neutral pion. The value of the correction is in region \(a_\mu ^{\pi ^0 , LbL} = (5.05 \pm 0.03) \times 10^{ - 10}\) for different set of model parameters.

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

The pseudoscalar hadronic channel contribution of the light-by-light process to the muon (g−2) μ within the nonlocal chiral quark model

The light-by-light contribution to the anomalous magnetic moment of muon (g-2)_{\mu} from the hadronic exchanges in the neutral pseudoscalar meson channel is calculated in the nonlocal chiral quark model. The full kinematic dependence of the meson-two-photon vertices on the virtualities of the mesons and photons is taken into account. The status of various phenomenological and QCD short-distance constraints is discussed and the comparison with the predictions of other models is performed. It is demonstrated that the effect of the full kinematic dependence in the meson-photon vertices is to reduce the contribution of pseudoscalar exchages to a_\mu ^{PS,LbL} by approximately factor 1.5 in comparison with the most of previous estimates.

Nonlocal Polyakov–Nambu–Jona-Lasinio model beyond mean field and the QCD phase transition

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted so that the physical values of the pion mass and the weak pion decay constant are obtained. The size of the 1/Nc correction to the quark condensate is carefully studied and compared with the usual local Nambu-Jona-Lasinio model. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. The model is also applied to finite temperature. We find that the 1/Nc corrections dominate the melting of the chiral condensate at low temperatures, T<100 MeV, in agreement with chiral perturbation theory. On the other hand, the relative importance of the 1/Nc corrections in the cross-over regime depends on the parameter T0 of the Polyakov loop potential. For T0=270 MeV, corresponding to a fit of lattice data for pure gluodynamics, the correction terms are large and lead to a lowering of the chiral phase transition temperature in comparison with the mean-field result. Near the phase transition the 1/Nc expansion breaks down and a non-perturbative scheme is needed to include mesonic correlations in that regime. Lowering T0 leads to a more rapid cross-over even at the mean-field level and the unstable region for the 1/Nc corrections shrinks. For T0< 220 MeV the temperatures of deconfinement and chiral restoration are practically synchronized.

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.

Pion radiative weak decays in nonlocal chiral quark models

We analyze the radiative pion decay π+→e+νeγ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV and FA at q2=0 — where q2 is the e+νe squared invariant mass — and the slope a of FV(q2) at q2→0. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable agreement with the corresponding experimental data. The comparison of our results with those obtained in the (local) NJL model and the relation of FV and a with the form factor in π0→γ⁎γ decays are discussed.

Photon-pion transition form factor at high photon virtualities within the nonlocal chiral quark model

Recently, the BABAR collaboration reported the measurements of the photon-pion transition form factor Fπγγ*(Q2), which are in strong contradiction to the predictions of the standard factorization approach to perturbative QCD. In the present work, based on a nonperturbative approach to the QCD vacuum and on rather universal assumptions, we show that there exist two asymptotic regimes for the pion transition form factor. One regime with the asymptotic behavior Fπγ*γ(Q2) ∼ 1/Q2 corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as Fπγ*γ(Q2) ∼ ln(Q2)/Q2. Furthermore, considering specific nonlocal chiral quark models, we find the region of parameters, where the existing CELLO, CLEO and BABAR data for the pion transition form factor are successfully described.

Calculation of the hadron contribution from light-by-light scattering to the anomalous (g-2)μ muon magnetic moment for a nonlocal quark model

The muon contribution to the anomalous magnetic moment from light-by-light scattering diagrams with pion participation is calculated for a nonlocal chiral quark model. For various nonlocal model parameterizations, the contribution makes a μ Had,LbL = 5.1(0.2) 10−10. Later on, we plan to calculate contributions from diagrams with an intermediate scalar meson and quark boxing.

Nonlocal quark model beyond mean field

The nonlocal chiral quark model is extended beyond mean field using a strict 1/Nc expansion scheme. The nonlocal interaction has the advantage that all diagrams are finite and leads to unique evaluation of the 1/Nc corrections. Parameters of the nonlocal model are refitted making use of the physical values of the pion mass and the weak pion decay constant. The size of the 1/Nc correction to the quark condensate is carefully studied in nonlocal and local Nambu-Jona-Lasinio models. It is found that even the sign of the corrections can be different.

NON-LOCAL CHIRAL QUARK MODELS WITH POLYAKOV LOOP AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL

We analyze the chiral restoration and deconfinement transitions in the framework of a non-local chiral quark model which includes terms leading to the quark wave function renormalization, and takes care of the effect of gauge interactions by coupling the quarks with the Polyakov loop. Non-local interactions are described by considering both a set of exponential form factors, and a set of form factors obtained from a fit to the mass and renormalization functions obtained in lattice calculations.

MESON MASSES AT FINITE TEMPERATURE IN A NONLOCAL SU(3) CHIRAL QUARK MODEL

We study the temperature behavior of light scalar and pseudoscalar meson masses within a three-flavor nonlocal chiral quark model that includes the coupling of quarks to the Polyakov loop. Chiral restoration and deconfinement transitions are described.