The e + e − → π + π − cross section has been measured from about 280 events (an order of magnitude more than the previous world statistics) in the energy interval 1.35 ⩽ s ⩽ 2.4 GeV with the DM2 detector at DCI. The pion squared form factor | F π | 2 shows a deep minimum around 1.6 GeV/ c 2 and is better fit under the hypothesis of two ϱ-like resonance ⋍0.25 GeV/ c 2 wide with 1.42 and 1.77 GeV/ c 2 masses.
Statistical errors only.
Using 20.7 pb^-1 of e+e- annihilation data taken at sqrt{s} = 3.671 GeV with the CLEO-c detector, precision measurements of the electromagnetic form factors of the charged pion, charged kaon, and proton have been made for timelike momentum transfer of |Q^2| = 13.48 GeV^2 by the reaction e+e- to h+h-. The measurements are the first ever with identified pions and kaons of |Q^2| > 4 GeV^2, with the results F_pi(13.48 GeV^2) = 0.075+-0.008(stat)+-0.005(syst) and F_K(13.48 GeV^2) = 0.063+-0.004(stat)+-0.001(syst). The result for the proton, assuming G^p_E = G^p_M, is G^p_M(13.48 GeV^2) = 0.014+-0.002(stat)+-0.001(syst), which is in agreement with earlier results.
Born cross section of $e^+e^-\rightarrow h^+h^-$
Timelike form factor
High precision measurements of the form factors of proton, pion, and kaon for timelike momentum transfers of |Q^2|=s=14.2 and 17.4 GeV^2 have been made. Data taken with the CLEO-c detector at sqrt(s)=3.772 GeV and 4.170 GeV, with integrated luminosities of 805 pb^-1 and 586 pb^-1, respectively, have been used to study $e^+e^-$ annihilations into pi+pi-, K+K^-, and ppbar. The perturbative QCD prediction that at large Q^2 the quantity Q^2F(Q^2) for vector mesons is nearly constant, and varies only weakly as the strong coupling constant alpha_S(Q^2) is confirmed for both pions and kaons. In contrast, a significant difference is observed between the values of the corresponding pQCD suggested near-constant quantity, |Q^4|G_M(|Q^2|)/mu_p for protons at |Q^2|=14.2 GeV^2 and 17.4 GeV^2. The results suggest the constancy of |Q^2|G_M(|Q^2|)/mu_p, instead.
Born cross section of $e^+e^-\rightarrow h^+h^-$
Timelike form factor
The EM form factor of the pion has been studied in the time-like region by measuring σ (e + e − → π + π − ) normalized to σ (e + e − → μ + μ − ). Results have been obtained for q 2 down to the physical threshold.
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The pion form factor is measured in the reaction e + e − → π + π − for center of mass energies in the range 480–1100 MeV. Our results are first analysed in terms of the conventional Vector Meson Dominance formalism, and then taking into account the ωπ inelastic channel. The result of this later formalism is a pion form factor ( F π ) which fits quite well all the existing data on F π both in the timelike and spacelike regions, and pion mean square radius of 〈 r π 2 〉 = 0.460 ± 0.011 fm 2 or 〈r π 2 〉 1 2 = 0.678 ± 0.008 fm .
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