Strong <Emphasis Type="Italic">CP</Emphasis> violation and the neutron electric dipole form factor

We calculate the neutron electric dipole form factor induced by the CP-violating θ term of QCD within a perturbative chiral quark model which includes pion and kaon clouds. On this basis, we derive the neutron electric dipole moment and the electron—neutron Schiff moment. From the existing experimental upper limits on the neutron electric dipole moment, we extract constraints on the θ parameter and compare our results with other approaches. The text was submitted by the authors in English.     

Measurement of the e+e? → π+π? cross section with the CMD-2 detector in the 370–520-MeV energy range

The results of the experiment on the measurement of the e ⁺ e ⁻ → π⁺π⁻ cross section in a cm energy range of 370–520 MeV are presented. The systematic measurement error is equal to 0.7%. In the vector dominance model, the pion electromagnetic radius is calculated using all the CMD-2 data on the pion form factor. The cross section for the production of a muon pair is measured in the energy range of the experiment. Original Russian Text ? V.M. Aul’chenko, R.R. Akhmetshin, V.Sh. Banzarov, L.M. Barkov, N.S. Bashtovoĭ, D.V. Bondarev, A.E. Bondar’, A.V. Bragin, N.I. Gabyshev, D.A. Gorbachev, A.A. Grebenyuk, D.N. Grigor’ev, S.K. Dhawan, D.A. Epifanov, A.S. Zaĭtsev, S.G. Zverev, F.V. Ignatov, V.F. Kazanin, S.V. Karpov, I.A. Koop, P.P. Krokovny, A.S. Kuz’min, I.B. Logashenko, P.A. Lukin, A.P. Lysenko, A.I. Mil’shteĭn, K.Yu. Mikhaĭlov, I.N. Nesterenko, M.A. Nikulin, A.V. Otboev, V.S. Okhapkin, E.A. Perevedentsev, A.S. Popov, S.I. Redin, B.L. Roberts, N.I. Root, A.A. Ruban, N.M. Ryskulov, A.L. Sibidanov, V.A. Sidorov, A.N. Skrinsky, V.P. Smakhtin, I.G. Snopkov, E.P. Solodov, J.A. Thompson, G.V. Fedotovich, B.I. Khazin, V.W. Hughes, A.G. Shamov, Yu.M. Shatunov, B.A. Shvarts, S.I. éĭdel’man, Yu.V. Yudin, 2006, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 84, No. 8, pp. 491–495.     

Nucleon form factors in a relativistic quark model

Electromagnetic form factors of protons and neutrons are investigated based on a relativistic quark model with the inclusion of a pion cloud. Pseudo-scalar π-quark interaction is employed to study the coupling between the nucleon and the π. The results show the important role of the pion cloud for the neutron charge form factor. Moreover, our numerical analysis indicates a difference between the relativistic and the nonrelativistic treatments. Received: 10 March 1999 / Revised version: 14 June 1999     

Quark-hadron duality in electron-pion scattering

We explore the relationship between exclusive and inclusive electromagnetic scattering from the pion, focusing on the transition region at intermediate Q². Combining Drell-Yan data on the leading twist quark distribution in the pion with a model for the resonance region at large x, we calculate QCD moments of the pion structure function over a range of Q², and quantify the role of higher twist corrections. Using a parameterization of the pion elastic form factor and phenomenological models for the π↦ρ transition form factor, we further test the extent to which local duality may be valid for the pion. Received: 10 February 2003 / Accepted: 12 March 2003 / Published online: 27 May 2003     

A coherent interpretation of the form factors of the nucleon in terms of a pion cloud and constituent quarks

The recent measurements of the electric form factor of the neutron suggest that its shape may be interpreted as a smooth broad distribution with a bump at 0.3 (GeV/c)² superimposed. As a consequence the corresponding charge distribution in the Breit frame shows a negative charge extending as far out as 2 fm. It is natural to identify this charge with the pion cloud. This realisation is then used to reanalyse all old and new data of the electric and magnetic from factors of the proton and the neutron by a phenomenological fit and by a fit based on the constituent quark model. It is shown that it is possible to fit all form factors coherently with both ansaetzen and that they all show the signal of the pion cloud.Received: 6 March 2003, Published online: 17 June 2003PACS: 14.20.Dh Protons and neutrons - 13.40.Gp Electromagnetic form factors - 21.10.Ft Charge distribution     

Relativistic constituent quark model and experiments at JLab

Within the relativistic-quantum-mechanics version developed by the present authors in their previous studies, the pion electromagnetic form factor is calculated in the region of high momentum transfers reached and planned to be reached in experiments at the Thomas Jefferson Laboratory (JLab). An asymptotic expansion was obtained for the pion form factor for Q ² → ∞. This expansion describes well existing experimental values and the results of a QCD simulation of future experiments at JLab. It is shown that the region of experiments at JLab is an asymptotic region for the relativistic constituent quark model and that the behavior of the pion form factor, F _π (Q ²)Q ² = const, can be obtained within this model.     

New spins for ground states and isomers in 115Pd and 117Pd

Considering the nucleon as a system of confined valence quarks surrounded by pions we derive a Galster-like parameterization of the neutron electric form factor G_Eⁿ. Furthermore, we show that the proposed parameterization can be linked to properties of the pion cloud. By this, the high-quality data for the pion form factor can be used in predictions of G_Eⁿ in the low-Q² region, where the direct double-polarization measurements are not available.Received: 11 August 2003, Revised: 16 October 2003, Published online: 5 January 2004PACS: 13.40.Gp Electromagnetic form factors - 12.39.Jh Nonrelativistic quark model     

On the pion distribution amplitude shape

We argue that the recent BaBar data on γ → π e.m. transition form factor at large photon virtuality supports the idea that pion distribution amplitude (DA) is close to unity with ϕ_π^′(0)/6 ≫ 1 at a normalization point of μ = 0.6–0.8 GeV. Such pion DA can be obtained in the effective chiral quark model. The possible flat shape of the pion DA implies that the standard expansion of the DA in Gegenbauer polynomials can be divergent. On basis of chiral models we predict that the two-pion DA should exhibit anomalous endpoint behaviour for pions in the S-wave and that such feature is absent for higher partial waves. The latter implies that the ρ, f ₂, etc. meson DAs have no anomalous endpoint behaviour. Possible implications of such pion DA for other hard exclusive processes are shortly discussed.     

Signatures of chiral dynamics in the nucleon to Delta transition⋆

Utilizing the methods of chiral effective field theory we present an analysis of the electromagnetic NΔ-transition current in the framework of the non-relativistic “small scale expansion” (SSE) to leading-one-loop order. We discuss the momentum dependence of the magnetic dipole, electric quadrupole and Coulomb quadrupole transition form factors up to a momentum transfer of Q² < 0.3GeV^2. Particular emphasis is put on the identification of the role of chiral dynamics in this transition. Our analysis indicates that there is indeed non-trivial momentum dependence in the two quadrupole form factors at small Q² < 0.15GeV^2 arising from long-distance pion physics, leading, for example, to negative radii in the (real part of the) quadrupole transition form factors. We compare our results with the EMR(Q²) and CMR(Q²) multipole ratios from pion-electroproduction experiments and find a remarkable agreement up to four-momentum transfer of Q² ≈ 0.3GeV^2. Finally, we discuss the chiral extrapolation of the three transition form factors at Q² = 0, identifying rapid changes in the (real part of the) quark mass dependence of the quadrupole transition moments for pion masses below 200MeV, which arise again from long-distance pion dynamics. Our findings indicate that dipole extrapolation methods currently used in lattice QCD analyses of baryon form factors are not applicable for the chiral extrapolation of NΔ quadrupole transition form factors.     

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 F _πγγ*(Q ²), 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 F _πγ*γ(Q ²) ∼ 1/Q ² corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as F _πγ*γ(Q ²) ∼ ln(Q ²)/Q ². 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.     

Novel insights into the γγ?→π0 transition form factor

BaBar’s observation of significant deviations of the pion transition form factor (TFF) from the asymptotic expectation with Q ²>9 GeV² has brought about a serious crisis to the fundamental picture established for such a simple q[`(q)]q\bar{q} system by perturbative QCD, i.e. the dominance of collinear factorization at high momentum transfers for the pion TFF. We show that non-factorizable contributions due to open flavors in γγ ^∗→π ⁰ could be an important source that contaminates the pQCD asymptotic limit and causes such deviations with Q ²>9 GeV². Within an effective Lagrangian approach, the non-factorizable amplitudes can be related to intermediate hadron loops, i.e. K ^(∗) and D ^(∗) etc., and their corrections to the π ⁰ and η TFFs can be estimated.     

Partially conserved axial-vector current inS-matrix theory

Mandelstam’s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm _π andm _ϱ as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionmϱ²−mπ²=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.     

How the recent BABAR data for P → γγ* affect the Standard Model predictions for the rare decays P → l+l?

Measuring the lepton anomalous magnetic moments (g − 2) and the rare decays of light pseudoscalar mesons into lepton pairs P → l ⁺ l ⁻, serve as important tests of the Standard Model. To reduce the theoretical uncertainty in the standard model predictions, the data on the charge and transition form factors of the light pseudoscalar mesons play a significant role. Recently, new data on the behavior of the transition form factors P → γγ* at large momentum transfer were supplied by the BABAR collaboration. There are several problems with the theoretical interpretation of these data: (1) An unexpectedly slow decrease of the pion transition form factor at high momenta, (2) the qualitative difference in the behavior of the pion form factor and the η and η′ form factors at high momenta, (3) the inconsistency of the measured ratio of the η and η′ form factors with the predicted one. We comment on the influence of the new BABAR data on the rare decay branchings.     

OPE and sum rules for correlators of pseudoscalar and axial currents

We study the operator product expansion (OPE) and quark-hadron duality for two-and three-point correlators of the axial (A) and pseudoscalar (P) currents of the light quarks. In the chiral limit, these correlators are often dominated by nonperturbative power corrections leading to subtleties of quark-hadron duality relations and of the extraction of properties of light pseudoscalars. For the two-point correlators, we show the sum rule for 〈PP〉 to be sensitive to the excited light pseudoscalar. For the three-point correlators, we derive the Ward identities which provide the normalization of the pion electromagnetic form factor at zero momentum transfer. For large momentum transfer, we demonstrate the way the correct behavior of the pion form factor in agreement with perturbative QCD emerges from condensate terms in the OPE for the 〈PV P〉 and 〈AV P〉 correlators. The local-duality sum rule for 〈AV A〉 is shown to lead to the pion form factor with the required properties for all values of the momentum transfer. The text was submitted by the authors in English. On leave from Institute of Nuclear Physics, Moscow State University, Moscow, Russia.     

Measurement of the pion form factor in the range 1.04–1.38 GeV with the CMD-2 detector

The cross section for the process e ⁺ e ⁻ → π⁺π⁻ is measured in the c.m. energy range 1.04—1.38 GeV by analyzing 995 000 selected collinear events including 860000 e ⁺ e ⁻ events, 82000 μ⁺μ⁻ events, and 33000 π⁺π⁻ events. The systematic and statistical errors of measuring the pion form factor are equal to 1.2–4.2 and 5–13%, respectively. __________ Translated from Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, Vol. 82, No. 12, 2005, pp. 841–845. Original Russian Text Copyright ? 2005 by Aul’chenko, Akhmetshin, Banzarov, Barkov, Bashtovoĭ, Bondarev, Bondar’, Bragin, Valishev, Gabyshev, Gorbachev, Grebenyuk, Grigor’ev, Dhawan, Epifanov, Zaĭtsev, Zverev, Ignatov, Kazanin, Karpov, Koop, Krokovny, Kuz’min, Logashenko, Lukin, Lysenko, Mil’shteĭn, Mikhaĭlov, Nesterenko, Nikulin, Otboev, Okhapkin, Perevedentsev, Polunin, Popov, Redin, Roberts, Root, Ruban, Ryskulov, Sibidanov, Sidorov, Skrinsky, Smakhtin, Snopkov, Solodov, Thompson, Fedotovich, Khazin, Hughes, Shamov, Shatunov, Shwartz, éĭdel’man, Yudin. Deceased.     

Asymptotic bounds on pion form factor

A technique recently developed for inelastic electron proton scattering is applied for inelastic electron pion scattering. It is found that all the derivatives of off-shell form factor of pion nears=m _π ² and for largeQ ² are bounded from above, provided that the dispersion relation for the form factor requires no more than one subtraction. The elastic pion form factor is bounded by [lnQ ²] ^c /Q ², wherec is any positive constant.     

Sigma Terms of Light-Quark Hadrons

A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature’s fundamental parameters. A hadron’s σ-term is a measure of this dependence. The connection between a hadron’s σ-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit σ_π = m_π/2. This truncation also provides a decent estimate of σ_ρ because the two dominant self-energy corrections to the ρ-meson’s mass largely cancel in their contribution to σ_ρ. The truncation is less accurate for the ω, however, because there is little to compete with an ω → ρπ self-energy contribution that magnifies the value of σ_ω by ≲25%. A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Δ, and thereby σ_N and σ_Δ. This “quark-core” piece is augmented by the “pion cloud” contribution, which is positive. The analysis yields σ_N ≃ 60 MeV and σ_Δ ≃ 50 MeV.     

Rare decay π<Superscript>0</Superscript> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> as a test of standard model

Experimental and theoretical progress concerning the rare decay π⁰ → e ⁺ e ⁻ is briefly reviewed. It includes the latest data from KTeV and a new model-independent estimate of the decay branching which show the deviation between experiment and theory at the level of 3.3σ. The predictions for η and η′ decays into lepton pair are presented. We also comment on the impact on the pion rare decay estimate of the data of BABAR collaboration on the pion transition form factor at large momentum transfer.