An analysis of the new pion form factor data

A form factor F(t) for the pion is constructed which is compatible with analyticity and the data in the space-like and time-like region. For the mean square pion radius 〈r²〉 = (0.46_?0.08^+0.06) fm² is obtained. Typical errors of the extrapolated F(t) are given (e.g. F(t =?8 GeV²/c²) = 0.07_?0.10^+0.04). Assuming F(t) ≈ β/(?t)^α at the end of the space-like data region we obtain β = 0.31, α = 0.81 for t in GeV²/c² together with the error contours of (α, β). No conclusive answer on the existence of zeroes of F(t) can be given.     

Information on the pion distribution amplitude from the pion-photon transition form factor with the Belle and BABAR data

We perform an analysis of all existing experimental data on the pion-photon transition form factor (TFF). In the calculation, we include the next-to-leading order correction to the valence-quark contribution and estimate the non-valence-quark contribution by a phenomenological model based on the TFF's limiting behavior at both Q²→0 and Q²→∞. At present, the pion distribution amplitude (DA) is not de nitely determined, it is helpful to have a pion DA model that can mimic all the behaviors suggested in the literature. For the purpose, we adopt the conventional model for pion wavefunction/DA whose broadness is dominantly controlled by a single parameter B. We fix the DA parameters by using the CELLO, CLEO, BABAR and Belle data within small Q² region (Q²≤15 GeV²), where all the data are consistent with each other. The pion-photon TFF is then extrapolated into a larger Q² region. It is found that we still need more data at a large Q² region in order to determine the precise value of B, and we hope that the de nite behavior of pion DA can be concluded nally by the consistent data in the coming future.     

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.     

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.     

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.     

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.     

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.     

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.