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The update of the e^+e^-topi^+pi^- process cross section, measured in the energy region sqrt{s}<1 GeV with SND detector at VEPP-2M collider is presented.
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The NA62 experiment at CERN collected a large sample of charged kaon decays with a highly efficient trigger for decays into electrons in 2007. The kaon beam represents a source of tagged neutral pion decays in vacuum. A measurement of the electromagnetic transition form factor slope of the neutral pion in the time-like region from $1.05times10^6$ fully reconstructed $pi^0$ Dalitz decay is presented. The limits on dark photon production in $pi^0$ decays from the earlier kaon experiment at CERN, NA48/2, are also reported.
A new limit of pion form factor at very large $Q^2$ is obtained by using a pion wave function determined from an effective chiral field theory of mesons. It shows that when $Q^2>>(1.8GeV)^2$ the pion form factor reaches the asymptotic limit ${alpha_s(Q^2)over Q^2}$.
The electromagnetic form factor of the pion in the space-like region, and at finite temperature, $F_{pi}(Q^{2},T)$, is obtained from a QCD Finite Energy Sum Rule. The form factor decreases with increasing T, and vanishes at some critical temperature, where the pion radius diverges. This divergence may be interpreted as a signal for quark deconfinement.
The pion electromagnetic form factor and two-pion production in electron-positron collisions are simultaneously fitted by a vector dominance model evolving to perturbative QCD at large momentum transfer. This model was previously successful in simultaneously fitting the nucleon electromagnetic form factors (spacelike region) and the electromagnetic production of nucleon-antinucleon pairs (timelike region). For this pion case dispersion relations are used to produce the analytic connection of the spacelike and timelike regions. The fit to all the data is good, especially for the newer sets of time-like data. The description of high-$q^2$ data, in the time-like region, requires one more meson with $rho$ quantum numbers than listed in the 2014 Particle Data Group review.
A novel method is employed to compute the pion electromagnetic form factor, F_pi(Q^2), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in quantum chromodynamics (QCD). The DSE architecture unifies this prediction with that of the pions valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q^2 F_pi(Q^2) underestimates the full computation by just 15% on Q^2>~8GeV^2, in stark contrast with the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q^2>~8GeV^2 but, even so, the magnitude of Q^2 F_pi(Q^2) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the Standard Model.
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