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.
We report measurements of the proton form factors GEp and GMp extracted from elastic scattering in the range 1≤Q2≤3 (GeV/c)2 with total uncertainties < 15% in GEp and < 3% in GMp. Comparisons are made to theoretical models, including those based on perturbative QCD, vector-meson dominance, QCD sum rules, and diquark constituents in the proton. The results for GEp are somewhat larger than indicated by most theoretical parametrizations, and the ratios of the Pauli and Dirac form factors Q2(F2pF1p) are lower in value and demonstrate a weaker Q2 dependence than those predictions. A global extraction of the elastic form factors from several experiments in the range 0.1 0.1<Q2<10 (GeV/c)2 is also presented.
Point-to-point systematic uncertainty is 0.5%, overall normailzation uncertainty is 1.9%.
Point-to-point systematic uncertainty is 0.5%, overall normailzation uncertainty is 1.9%.
Point-to-point systematic uncertainty is 0.5%, overall normailzation uncertainty is 1.9%.
The proton elastic electric and magnetic form factors, GEp(Q2) and GMp(Q2), have been separately measured in the range Q2=1.75 to 8.83 (GeV/c)2, more than doubling the Q2 range of previous data. Scaled by the dipole fit, GD(Q2), the results for GMp(Q2)/μpGD(Q2) decrease smoothly from 1.05 to 0.91, while GEp(Q2)/GD(Q2) is consistent with unity. Comparisons are made to QCD sum rule, diquark, constitutent quark, and vector meson dominance models, none of which agree with all of the new data. The ratio Q2F2/F1 approaches a constant value for Q2>3 (GeV/c)2.
Magnetic form factors.
Electric form factors.
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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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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