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.     

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.     

Pion form factor in QCD: How to calculate?

The calculation of the pion form factor F _π(Q ²) in QCD is discussed. The main points of the nonlocal condensate QDC sum rule approach are considered and its results for the pion form factor are shown compared with the predictions of the perturbative and lattice QCD. The local duality (LD) approach for the pion FF in QCD is studied. It is shown that the main parameter of the approach for Q ² ≥ 2 GeV², namely, s ₀^LD(Q ²) should grow with an increase in Q ², rather than remain constant.     

Beyond leading order QCD perturbative corrections to the pion form factor

The order α_s²(Q²) corrections to the pion form factor, F_π(Q²), are calculated using perturbative quantum chromodynamics and dimensional regularization. In the $\text{MS}$ renormalization scheme these corrections are large. This means that reliable perturbative predictions cannot be made until momentum transfers, Q, of about 300–400 GeV are reached or unless one can sum the large perturbative terms to all orders. Attempts to reorganize the perturbation series so that the first term gives a better approximation of the complete sum indicate that at Q = 10 GeV the pion form factor may be about a factor of two larger than the leading order result.     

Extraction of the neutron charge form factor G<Superscript>n</Superscript><Subscript>E</Subscript>(Q<Superscript>2</Superscript>) from the charge form factor of deuteron G<Superscript>d</Superscript><Subscript>C</Subscript>(Q<Superscript>2</Superscript>)

We extract the neutron charge form factor G ⁿ _E(Q ²) from the charge form factor of deuteron G ^d _C(Q ²) obtained from T ₂₀(Q ²) data at 0≤Q ²≤ 1.717 (GeV/c)². The extraction is based on the relativistic impulse approximation in the instant form of the relativistic Hamiltonian dynamics. Our results (12 new points) are compatible with existing values of the neutron charge form factor of other authors. We propose a fit for the whole set (36 points) taking into account the data for the slope of the form factor at Q ² = 0. Received: 26 July 2002 / Accepted: 18 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: krutov@ssu.samara.ru RID="b" ID="b"e-mail: troitsky@theory.sinp.msu.ru Communicated by V.V. Anisovich     

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.     

Form factors,threshold relations,and large angle elastic scattering of pions

The form factor F(q²) of the pion in a simple core model is investigated, together with the deep inelastic electroproduction structure function, F₂(ω). A relation between these two, analagous to the Drell-Yan-West relation for nucleons, is derived and it is found that F₂ is related to either the form factor or the square of the form factor depending on how rapidly F(q²) ultimately falls with momentum transfer. The unitarity equation and its implications for this kind of threshold relation are discussed. The simple core model is also applied to elastic large angle ππ scattering.     

The longitudinal structure function F L(x, Q 2) and the gluon distribution G(x, Q 2) at low x

We obtain a relation between the longitudinal structure function F _L(x, Q ²), F ₂(x, Q ²) and G(x, Q ²) at small x, using the formalism recently reported by one of the authors [2]. We also obtain a relation between F _L(x, Q ²), F ₂(x, Q ²) and its slope (dF ₂(x, Q ²))/(dlnQ ²). This provides us with the determination of the longitudinal structure function F _L(x, Q ²) from F ₂(x, Q ²) data and hence extract the gluon distribution G(x, Q ²).     

Event-by-event search for charged-neutral fluctuations in Pb-Pb collisions at 158 A⋅GeV

We analyse the proton electromagnetic form factor ratioR(Q ² ) =QF ₂ (Q ² )/F ₁ (Q ² ) as a function of momentum transferQ ² within perturbative QCD. We find that the prediction for (R(Q ² ) at large momentum transferQ depends on the exclusive quark wave functions, which are unknown. For a wide range of wave functions we find thatQF ₂ F ₁ ～ const. at large momentum transfer, which is in agreement with recent JLAB data.     

The BFKL-Regge phenomenology of deep inelastic scattering

We calculate the Regge trajectories of the subleading BFKL singularities and eigenfunctions for the running BFKL pomeron in the color dipole representation. We obtain a viable BFKL-Regge expansion of the proton structure function F _2p (x,Q ²) in terms of several rightmost BFKL singularities. We find large subleading contributions to F _2p (x,Q ²) in the HERA kinematical region which explain the lack of predictive power of GLDAP extrapolations of F _2p (x,Q ²) to the region of small x. We point out the relation of our early finding of precocious BFKL asymptotic behavior to the nodal structure of subleading BFKL eigenfunctions. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 134–138 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit     

Regge behavior of DIS structure functions in scalar theories

The Bethe-Salpeter formalism is used to incorporate the valence Regge behavior into the total DIS amplitude. For a special case of scalar quarks with massless scalar exchange, the model is solved both analytically and numerically and exact scaling is found for the valence quark contribution F ₂(x) ∼ (1/x) ^l(0)−1 which mimicks the ρ-trajectory term. The solution solves a long-standing problem by showing that the coefficient in the Regge pole expansion is indeed fine-tuned to give the expected scaling. The method allows for generalization to the region of nonzero momentum transfer and calculation of the DVCS amplitude. The text was submitted by the authors in English.     

On the perturbative stability of the QCD predictions for the ratio R=FL/FT in heavy-quark leptoproduction

We analyze the perturbative and parametric stability of the QCD predictions for the Callan–Gross ratio, R(x,Q ²)=F _L /F _T , in heavy-quark leptoproduction. We consider the radiative corrections to the dominant photon–gluon fusion mechanism. In various kinematic regions, the following contributions are investigated: exact NLO results at low and moderate Q ²≲m ², asymptotic NLO predictions at high Q ²≫m ², and both NLO and NNLO soft-gluon (or threshold) corrections at large Bjorken variable x. Our analysis shows that large radiative corrections to the structure functions F _T (x,Q ²) and F _L (x,Q ²) cancel each other in their ratio R(x,Q ²) with good accuracy. As a result, the NLO contributions to the Callan–Gross ratio are less than 10% in a wide region of the variables x and Q ². We provide compact LO predictions for R(x,Q ²) in the case of low x ≪1. A simple formula connecting the high-energy behavior of the Callan–Gross ratio and low-x asymptotics of the gluon density is derived. It is shown that the obtained hadron-level predictions for R(x→0,Q ²) are stable under the DGLAP evolution of the gluon distribution function. Our analytic results simplify the extraction of the structure functions F ₂ ^c (x,Q ²) and F ₂ ^b (x,Q ²) from measurements of the corresponding reduced cross sections, in particular at DESY HERA.     

Sum rules and the pion form factor in QCD

We propose a new approach to the investigation of the pion electromagnetic form factor in QCD based on the systematic use of the QCD sum rule technique. The theoretical curve obtained for F_π(Q²) is in good agreement with existing experimental data.     

Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

We revisit F _π(Q ²) and F _Pγ(Q ²), P = π, η, η′, making use of the local-duality (LD) version of QCD sum rules. We give arguments that the LD sum rule provides reliable predictions for these form factors at Q ² ≥ 5–6 GeV², the accuracy of the method increasing with Q ² in this region. For the pion elastic form factor, the well-measured data at small Q ² give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q ² ≈ 4–8 GeV²; we therefore conclude that large deviations from LD in the region Q ² = 20–50 GeV² seem very unlikely. The data on the (η, η′) → γγ* form factors meet the expectations from the LD model. However, the BaBar results for the π ⁰ → γγ* form factor imply a violation of LD growing with Q ² even at Q ² ≈ 40 GeV², at odds with the η, η′ case and with the general properties expected for the LD sum rule.     

Optimal bounds for the pion form factor from analyticity and experimental data

Optimal bounds for the pion electromagnetic form factor F(t) below threshold and on the pion mean-square charge radius 〈r_π²〉 = 6F'(0) are derived. Use is made of analyticity arguments and of experimental data on F(t) from e⁺e^? → π⁺π^? as well as e^?p → e^?nπ⁺. The method accounts in an approximate way for the statistical errors of the experimental information. Numerical results for F(t) are calculated for the CEA as well as the DESY electroproduction data.     

DSE Perspective on QCD Modeling,Distribution Amplitudes,and Form Factors

We describe results for the pion distribution amplitude (PDA) at the non-perturbative scale μ = 2 GeV by projecting the Poincaré-covariant Bethe–Salpeter wave-function onto the light-front and use it to investigate the ultraviolet behavior of the electromagnetic form factor, F _π (Q ²), on the entire domain of spacelike Q ². The significant dilation of this PDA compared to the known asymptotic PDA is a signature of dynamical chiral symmetry breaking on the light front. We investigate the transition region of Q ² where non-perturbative behavior of constituent-like quarks gives way to the partonic-like behavior of quantum chromodynamics (QCD). The non-perturbative approach is based on the Dyson–Schwinger equation (DSE) framework for continuum investigations in QCD. The leading-order, leading-twist perturbative QCD result for Q ² F _π (Q ²) underestimates the new DSE computation by just 15 % on \({Q^2\gtrsim 8\,}\) GeV², in stark contrast with the result obtained using the asymptotic PDA.     

Scaling violation in the pion structure function

TheQ ²-dependence of the pion structure function extracted from high transverse momentum π⁰ production cross sections is examined. We find, in thex→1 region, that this dependence can be parametrized by a power of (1?x) increasing as ln lnQ ². This is in agreement with the expectations of asymptotic freedom and also seen in the structure function extracted from dilepton production. It is not possible to fit all of theQ ²-dependence with a simple power law term.     

Scaling and non-scaling in a rest frame quark-parton model of the proton

Electron-proton deep inelastic scattering is treated as the incoherent scattering of electrons by bound Dirac partons in the proton rest frame. An approximate bound state wave function is used for the initial parton, while the final parton is considered free. A good fit is obtained to the structure function F₁(x,Q²) in the range x > 0.15, Q² > 2 GeV. The subsequent prediction for F₂(x,Q²) is not as good, indicating a small additional contribution by longitudinal photons for W < 2.5 GeV. The parton momentum distribution is found to contain transverse momentum of 400–600 MeV, increasing with x.     

The ratio of the magnetic to the electric proton form factors in Quantum Chromodynamics

We propose a two parameter expression for the high momentum transfer behaviour of the ratio of proton form factors G_M(Q²)/Q_E(Q²) based on perturbation theory calculations in Quantum Chromodynamics. A fit to the present experimental data and its consistency with a previous fit to the high Q² behaviour of the Dirac form factor [1] is also discussed.