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 s dependence of the proton form factor in the time-like region has been determined up to s =4.2 GeV 2 , assuming the validity of the | G e | = | G m | = | G | hypothesis. Data were taken in a dedicated experiment performed at the LEAR antiproton ring at CERN, increasing by one order of magnitude the available statistics on the proton form factor near threshold in the time-like region. Our result consist of cross section measurements of the p p → e + e − reaction for different beam momenta in the kinematical r 3.6⩽ s ⩽4.2 GeV 2 . The observed s dependence of the form factor close to threshold differs appreciably from the one suggested by previous experiments.
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Results of one-parameter fit. |Ge|=|Gm| assumed.
The s dependence of the electromagnetic proton form factors in the time-like region has been determined from the threshold ( s = 4 M p 2 ) up to s = 4.2 GeV 2 . Data were collected in a dedicated experiment performed at the LEAR antiproton ring at CERN, increasing by one order of magnitude the available statistics. Total and differential cross section of the p p → e − e + reaction have been measured. The electric and magnetic form factors are found to have comparable value. The observed form factor shows a clear steep s dependence close to the threshold.
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The cross section for the process e + e − → p p has been measured in the s range 3.6–5.9 GeV 2 by the FENICE experiment at the e + e − Adone storage ring and the proton electromagnetic form factor has been extracted.
Cross section measurement.
Proton form-factor measurement.
Cross sections for the reaction pp¯→e+e− have been measured at s=8.9,12.4, and 13.0 GeV2. The cross sections have been analyzed to obtain the proton electromagnetic form factors in the timelike region. We find that GM(q2)∝q−4αs2(q2) for q2≥5 (GeV/c)2.
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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.
Thee+e−→K+K− cross section has been measured from about 750 events in the energy interval\(1350 \leqq \sqrt s\leqq 2400 MeV\) with the DM2 detector at DCI. TheK± form factor |FF±| cannot be explained by the ρ, ω, ϕ and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.
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We report measurements of the two-photon processes e+e−→e+e−π+π− and e+e−→e+e−K+K−, at an e+e− center-of-mass energy of 29 GeV. In the π+π− data a high-statistics analysis of the f(1270) results in a γγ width Γ(γγ→f)=3.2±0.4 keV. The π+π− continuum below the f mass is well described by a QED Born approximation, whereas above the f mass it is consistent with a QCD-model calculation if a large contribution from the f is assumed. For the K+K− data we find agreement of the high-mass continuum with the QCD prediction; limits on f′(1520) and θ(1720) formation are presented.
Data read from graph. Additional overall systematic error 20% not included.
Data read from graph.. Additional overall systematic error 20% not included.
Data read from graph.. Additional overall systematic error 20% not included.. The Q**2 dependence is normalized to unity for the bin centred on Q**2 = 0.
The e + e − → p p cross section has been measured in the energy interval (1975 ⩽ 2 E ⩽ 2250) MeV for |cos θ | < 0.7. The measurement is based on ∼ 100 events, thus improving by a factor 3 on the previous existing statistics in this energy interval. The form factor | G | 2 is given as a function of energy under the assumption | G E | = | G M |. We also give the first measurement of the differential cross section, averaged over the energy interval, and estimate the ratio G M |/| G E | from it.
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