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.     

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.     

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.     

The pion form factor from lattice QCD with two dynamical flavours

We compute the electromagnetic form factor of the pion, using non-perturbatively O(a) improved Wilson fermions. The calculations are done for a wide range of pion masses and lattice spacings. We check for finite size effects by repeating some of the measurements on smaller lattices. The large number of lattice parameters we use allows us to extrapolate to the physical point. For the square of the charge radius we find fm², in good agreement with experiment. PACS 12.38.Gc; 13.40.Gp; 14.40.-n     

Hadron spectra and pion form factor in dynamical holographic QCD model with anomalous 5D mass of scalar field

The simplest version of the dynamical holographic QCD model is described by adding the KKSS model action on a dilaton-graviton coupled background, in which the AdS5 metric is deformed by the gluon condensation and further deformed by the chiral condensation. In this framework, both the chiral symmetry breaking and linear confinement can be realized. The light-flavor hadron spectra and the pion form factor were investigated, but it was difficult to reconcile the light-flavor hadron spectra and pi...     

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.     

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.     

The applicability of perturbative QCD to the pion form factor and the pionic wavefunction

We reanalyse the pionic form factor by using perturbative QCD theory and contributions from endpoint regions. We find that the perturbative QCD can be applied to the pionic form factor asQ ²>4 GeV² and they become unreliable asQ ²≦4 GeV². Therefore the applicability of perturbative QCD to the form factor is questionable only asQ ²≦4 GeV².     

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.     

N-to-Delta axial transition form factors from lattice QCD

We evaluate the N to Delta axial transition form factors in lattice QCD with no dynamical sea quarks, with two degenerate flavors of dynamical Wilson quarks, and using domain wall valence fermions with three flavors of staggered sea quarks. We predict the ratio C(5)(A)(q(2))/C(3)(V)(q(2)) relevant for parity violating asymmetry experiments and verify the off-diagonal Goldberger-Treiman relation.     

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.     

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.     

Twist-3 distribution amplitudes of the pion and kaon from the QCD sum rules

Twist-3 distribution amplitudes of the pion and kaon are studied in this paper. We calculate the first several moments for the twist-3 distribution amplitudes ( and ) of the pion and kaon by applying the QCD sum rules. Our results show that (i) the first three moments of and the first two moments of and of the pion and kaon can be obtained with 30 uncertainty; (ii) the fourth moment of the and the second moment of the can be obtained when the uncertainty are relaxed to 35 ; (iii) the fourth moment of the can be obtained only when the uncertainty are relaxed to 40 ; (iv) we have and after including the -corrections to the perturbative part. These moments will be helpful for constructing the twist-3 wave functions of the pion and kaon.Received: 6 January 2005, Revised: 29 March 2005, Published online: 22 June 2005PACS: 13.20.He, 11.55.Hx     

Measurement of the pion axial form factor from radiative decay

The decay π⁺→e⁺νγ has been measured by detecting the positron with a magnetic spectrometer and the photon with an array of NaI scintillators. Using CVC to compute the vector form factor from the π⁰ lifetime we use our data to determine the ratio γ of the axial-vector form factor to the vector form factor. With the best present value for the π⁰ lifetime (0.897±0.022±0.017)×10⁻¹⁶ s and F_V=(2.55 ±0.05)×10⁻² we obtain two solutions: γ=0.52 ±0.06, favored by a likelihood ratio greater than 8.5 against γ=−2.48±0.06.