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
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
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.
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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We present results for the total cross section of e + e − annihilation into two hadrons at 1.6 GeV: σ ππ = σ KK = (1.8 ± 1.1) × 10 -33 cm 2 .From these values we obtain the time-like electromagnetic form factors these mesons: | F π | 2 = 0.24 ± 0.14 and | F K | 2 = 0.46 ± 0.26.
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The possible existence of new vector mesons above the ρ is investigated. The conclusion is that our data are compatible with the existence of the ρ′-meson only if we assume as a firm theoretical prediction the Gounaris-Sakurai tail of the standard ρ-meson. Furthermore our data are compatible with the existence of the ρ″-meson if we assume the validity of the\(\bar p\)p model for the calculation of the multihadron cross-section.
THESE MEASUREMENTS OF THE PION FORM FACTOR ARE GIVEN IN D. BOLLINI ET AL., NCL 14, 418 (1975).
THESE MEASUREMENTS OF THE FOUR CHARGED PION CROSS SECTION ARE GIVEN IN M. BERNARDINI ET AL., PL 53B, 384 (1974).
THESE MEASUREMENTS OF THE TOTAL HADRONIC CROSS SECTION ARE GIVEN IN M. BERNARDINI ET AL., PL 51B, 200 (1974).
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The study of 620 hadron pairs produced in the s -range (1.44−9.0) GeV 2 , has yielded 110 collinear hadronic events. Their identification in terms of π and K mesons allows the determination of the time-like electromagnetic from factors of these pseudoscalar mesons in the above time-like range. The total number of (e + e − ) events observed in the same experimental conditions is 18 048.
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