Muon g-2, rare decays P \to l^+l^- and transition form factors P \to \gamma\gamma^*

Measuring the muon anomalous magnetic moment g-2 and the rare decays of light pseudoscalar mesons into lepton pair P \to 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. We comment on the (in)consistency of these data with perturbative QCD expectation.Comment: 4 pages, 3 figures, invited talk at the 3rd Joint International Hadron Structure'09 Conference, Tatranska Strba (Slovak Republic), Aug. 30--Sept. 3, 2009; v2 - some typos are correcte

Off-diagonal quark distribution functions of the pion within an effective single instanton approximation

We develop a relativistic quark model for pion structure, which incorporates the non-trivial structure of the vacuum of Quantum Chromodynamics as modelled by instantons. Pions are boundstates of quarks and the strong quark-pion vertex is determined from an instanton induced effective lagrangian. The interaction of the constituents of the pion with the external electromagnetic field is introduced in gauge invariant form. The parameters of the model, i.e., effective instanton radius and constituent quark masses, are obtained from the vacuum expectation values of the lowest dimensional quark and gluon operators and the low-energy observables of the pion. We apply the formalism to the calculation of the pion form factor by means of the isovector nonforward parton distributions and find agreement with the experimental data.Comment: LaTeX; altered version; references and figures added. Published: paper has been accepted for publication in Nucl. Phys.

On high Q2Q^{2} behavior of the pion form factor for transitions γ∗γ→π0\gamma^{\ast} \gamma \to \pi^{0} and γ∗γ∗→π0\gamma ^{\ast} \gamma^{\ast} \to \pi^{0} within the nonlocal quark-pion model

The behavior of the transition pion form factor for processes \gamma^*\gamma -> \pi^0 and \gamma^* \gamma^* -> \pi^0 at large values of space-like photon momenta is estimated within the nonlocal covariant quark-pion model. It is shown that, in general, the coefficient of the leading asymptotic term depends dynamically on the ratio of the constituent quark mass and the average virtuality of quarks in the vacuum and kinematically on the ratio of photon virtualities. The kinematic dependence of the transition form factor allows us to obtain the relation between the pion light-cone distribution amplitude and the quark-pion vertex function. The dynamic dependence indicates that the transition form factor \gamma^* \gamma -> \pi^0 at high momentum transfers is very sensitive to the nonlocality size of nonperturbative fluctuations in the QCD vacuum.Comment: LaTex file with 3 ps-figure

Instanton effects in quark form factor and quark-quark scattering at high energy

The nonperturbative effects in the high-energy processes involving strongly interacting particles are studied within the instanton liquid model of the QCD vacuum (ILM) by using the Wilson integral framework. The detailed analysis of nonperturbative contributions to the electromagnetic quark form factor is presented considering the structure of the instanton induced effects in the evolution equation describing the high energy behaviour of the form factor. It is shown that the instantons yield in high energy limit the logarithmic corrections to the amplitudes which are exponentiated in small instanton density parameter. By using the Gaussian interpolation of the constrained instanton solution, we show that the all-order multi-instanton contribution is well approximated by the weak field limit result. The role of the instantons in high energy diffractive quark-quark scattering, in particular, in formation of the soft Pomeron, is also considered. We show that within the ILM the C-odd diffractive amplitude is suppressed as 1/s compared to the C-even one. The further applications of the developed approach in studying the nonperturbative effects in high energy hadronic processes are briefly discussed.Comment: 37 pages + 9 figures; JHEP styl

Model analysis of the world data on the pion transition form factor

We discuss the impact of recent Belle data on our description of the pion transition form factor based on the assumption that a perturbative formalism and a nonperturbative one can be matched in a physically acceptable manner at a certain hadronic scale $Q_{0}$. We discuss the implications of the different parameters of the model in comparing with world data and conclude that within experimental errors our description remains valid. Thus we can assert that the low $Q^2$ nonperturbative description together with an additional $1/Q^2$ term at the matching scale have a strong influence on the $Q^2$ behavior up to very high values of $Q^2$ .Comment: 6 pages and 3 figures. Contains a comparison with other models and additional reference

QED radiative corrections to the decay pi^0 to e^+e^-

We reconsider QED radiative corrections (RC) to the $\pi^{0}\to e^{+}e^{-}$ decay width. One kind of RC investigated earlier has a renormalization group origin and can be associated with the final state interaction of electron and positron. It determines the distribution of lepton pair invariant masses in the whole kinematic region. The other type of RC has a double-logarithmic character and is related to almost on-mass-shell behavior of the lepton form factors. The total effect of RC for the $\pi^{0}\to e^{+}e^{-}$ decay is estimated to be 3.2% and for the decay $\eta \to e^{+}e^{-}$ is 4.3%.Comment: 12 pages, 3 figure

Instanton Corrections to Quark Form Factor at Large Momentum Transfer

Within the Wilson integral formalism, we discuss the structure of nonperturbative corrections to the quark form factor at large momentum transfer analyzing the infrared renormalon and instanton effects. We show that the nonperturbative effects determine the initial value for the perturbative evolution of the quark form factor and attribute their general structure to the renormalon ambiguities of the perturbative series. It is demonstrated that the instanton contributions result in the finite renormalization of the next-to-leading perturbative result and numerically are characterized by a small factor reflecting the diluteness of the QCD vacuum within the instanton liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe

Extended nonlocal chiral-quark model for the heavy-light quark systems

In this talk, we report the recent progress on constructing a phenomenological effective model for the heavy-light quark systems, which consist of (u,d,s,c,b) quarks, i.e. extended nonlocal chiral-quark model (ExNLChQM). We compute the heavy-meson weak-decay constants to verify the validity of the model. From the numerical results, it turns out that (f_D, f_B, f_{D_s}, f_{B_s})=(207.54,208.13,262.56,262.39) MeV. These values are in relatively good agreement with experimental data and various theoretical estimations.Comment: 3 pages, 4 figures, Talk given at the 20th International IUPAP Conference on Few-Body Problems in Physics (FB20), 20~25 August 2012, Fukuoka, Japa

Instanton Contribution to the Quark Form Factor

The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism. The properties of the Wilson loops with cusp singularities are studied taking into account the perturbative and nonperturbative contributions, where the latter are considered within the framework of the instanton liquid model. For the integration path corresponding to this form factor -- the angle with infinite sides -- the explicit expression for the vacuum expectation value of the Wilson operator is found to leading order. The calculations are performed in the weak-field limit for the instanton vacuum contribution and compared with the one- and two-loop order results for the perturbative part. It is shown that the instantons produce the powerlike corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.Comment: Version coincident with the journal publication. LaTeX, 15 pages, 1 figur

Pseudoscalar meson form factors and decays

In this communication we discuss few topics related with modern experimental data on the physics of light pseudoscalar mesons. It includes the contribution of the pseudoscalar mesons to the muon anomalous magnetic moment (AMM), $g-2$, the rare decays of light pseudoscalar mesons to lepton pair, the transition form factors of pseudoscalar mesons at large momentum transfer, the pion transversity form factor. Measuring the muon anomalous magnetic moment $g-2$ and the rare decays of light pseudoscalar mesons into lepton pair $P\rightarrow l^{+}l^{-}$ 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 shown how to describe these data and how the meson distribution amplitude evolves as a function of the dynamical quark masses and meson masses.Comment: 14 pages, 7 figures, based on the talks given at Hadron Structure 11 (Slovakia, Tatransk\'a \v{S}trba, June 27th - July 1st, 2011), The Actual Problems of Microworld Physics (Gomel, Belarus, August 1 - 12, 2011), International Workshop on e+e- collisions from Phi to Psi (Novosibirsk, Russia, September 19-22, 2011