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

The evolution of neck for the asymmetric system ⁵⁸Fe + ²⁴⁴Pu at E _c.m. = 260 MeV has been studied with the coupled Langevin equations in two-dimensional collective space and the results compared to those obtained with a one-dimensional approach under the frozen assumption. It is found that the coupling between the radial and neck degrees of freedom reduces the drift velocity of neck growth and delays the transition from dinucleus to mononucleus. Besides, the coupling brings the system into a somehow elongated shape when the injection into the asymmetric fission valley takes place, hence, the fusion probability and the relevant evaporation residue (ER) cross-sections decrease. For the system ⁵⁸Fe + ²⁴⁴Pu , the ER cross-sections decrease by about 30% as compared to those obtained under the frozen approximation. Therefore, we may arrive at the conclusion that for the heavy asymmetric systems such as ⁵⁸Fe + ²⁴⁴Pu the coupling between different degrees of freedom has important effects on the evolution from dinucleus to mononucleus and the frozen approximation is basically not satisfied as far as the neck dynamics is concerned. However, as compared to the symmetric reactions, the influence of the neck dynamics on the fusion hindrance factor of heavy systems is much weaker for the asymmetric reactions.     

Compatibility of higher rho-resonances with the pion form factor data

A realistic pion form factor model respecting the usual fundamental principles supplemented by reasonable assumptions is constructed by means of conformai mapping having some specific uniformization properties. The model includes the contributions of higher rho-resonances without any conflict with analyticity, provides a certain flexibility for the asymptotic behaviour and depends just on the physical parameters. The best fit of all existing data is achieved with(770),'(1600) and the asymptoticst ^–3/2. The predicted values of the pion charge radius, P-wave isovector scattering length, as well as theI=J = 1 scattering amplitude at the experimental measurable region coincide with the world averaged data.Dedicated to the 30th anniversary of the Joint Institute of Nuclear Research.The authors are indebted to Prof. V. A. Meshcheryakov, Dr. S. B. Gerasimov and Dr. D. Krupa for many stimulating and illuminating discussions.     

Constraining the low-energy pion electromagnetic form factor with spacelike data

The pionic contribution to the g-2 of the muon involves a certain integral over the modulus squared of F_π(t), the electromagnetic form factor of the pion. We extend techniques that use cut-plane analyticity properties of F_π(t) in order to account for present day estimates of the pionic contribution and experimental information at a finite number of points in the spacelike region. Using data from several experiments over a large kinematic range for |t|, we find bounds on the expansion coefficients of F_π(t), sub-leading to the charge radius. The value of one of these coefficients in chiral perturbation theory respects these bounds. Furthermore, we present a sensitivity analysis to the inputs. A brief comparison with results in the literature that use observables other than the g-2 and timelike data is presented.     

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.     

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.     

Measurement of the charged pion electromagnetic form factor

Separated longitudinal and transverse structure functions for the reaction 1H(e,e(')pi(+))n were measured in the momentum transfer region Q2 = 0.6--1.6 (GeV/c)(2) at a value of the invariant mass W = 1.95 GeV. New values for the pion charge form factor were extracted from the longitudinal cross section by using a recently developed Regge model. The results indicate that the pion form factor in this region is larger than previously assumed and is consistent with a monopole parametrization fitted to very low Q2 elastic data.     

Lattice QCD and the timelike pion form factor

We present a formula that allows one to calculate the pion form factor in the timelike region 2m(π) ≤ √(s) ≤ 4m(π) in lattice QCD. The form factor quantifies the contribution of two-pion states to the vacuum polarization. It must be known very accurately in order to reduce the theoretical uncertainty on the anomalous magnetic moment of the muon. At the same time, the formula constitutes a rare example where, in a restricted kinematic regime, the spectral function of a conserved current can be determined from Euclidean observables without an explicit analytic continuation.     

Non-locality effects on the pion nucleon form factor

We investigate effects of the non-locality in the elementary pion quark coupling on theπNN form factor in the framework of the chiral bag model. We show that this nonlocality leads to shorter ranged form factors thereby reducing the discrepancy between large bag-model confinement radii and empirically found small-ranged cut-off parameters.     

Generalized vector dominance and the pion form factor

We have calculated the pion form factor using the bound state Bethe-Salpeter amplitudes and the quark form factor of a relativistic quark model. We obtain a generalized vector dominance structure and an asymptotic behaviour in the space-like region F_π(Q)² −0.33 GeV²/Q².     

Quark mass dependence of the pion vector form factor

We examine the quark mass dependence of the pion vector form factor, particularly the curvature (mean quartic radius). We focus our study on the consequences of assuming that the coupling constant of the ρ   to pions, g_ρππ$g_{\rho \pi \pi }$, is largely independent of the quark mass while the quark mass dependence of the ρ mass is given by recent lattice data. By employing the Omnès representation we can provide a very clean estimate for a certain combination of the curvature and the square radius, whose quark mass dependence could be determined from lattice computations. This study provides an independent access to the quark mass dependence of the ρππ   coupling and in this way a non-trivial check of the systematics of chiral extrapolations. We also provide an improved value for the curvature for physical values for the quark masses, namely 〈r⁴〉=0.73±0.09 fm⁴$〈r^4〉=0.73\pm 0.09{\text{fm}}^4$ or equivalently cV=4.00±0.50 GeV−4$c_V=4.00\pm 0.50{\text{GeV}}^{-4}$.     

Twist-3 contribution to the pion electromagnetic form factor

Non-leading contribution to the pion electromagnetic form factor which comes from the pion twist-3 wave function is analyzed in the modified hard scattering approach (MHSA) proposed by Li and Sterman. This contribution is enhanced significantly due to bound state effect (the twist-3 wave function is independent of the fractional momentum carried by the parton and has a large factor with being the pion meson mass and being the mean u- and d-quark masses). Consequently, although it is suppressed by the factor , the twist-3 contribution is comparable with and even larger than the leading twist (twist-2) contribution at intermediate energy region of being . Received: 23 March 1998 / Published online: 3 November 1999     

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.     

QCD constraints for the electromagnetic form factor of the pion

Using the modulus representation, we derive constraints for the behaviour of the electromagnetic form factor of the pion in the time like region [1 GeV², +∞], from information given by perturbative QCD in the space like region [?μ ², ?∞]. A phenomenological μ dependent upper bound for the exponent of the first non leading logarithmic correction is deduced. Restrictions and problems of the method are discussed.