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 H(e,e'pi+)n cross section was measured at four-momentum transfers of Q2=1.60 and 2.45 GeV2 at an invariant mass of the photon nucleon system of W=2.22 GeV. The charged pion form factor (F_pi) was extracted from the data by comparing the separated longitudinal pion electroproduction cross section to a Regge model prediction in which F_pi is a free parameter. The results indicate that the pion form factor deviates from the charge-radius constrained monopole form at these values of Q2 by one sigma, but is still far from its perturbative Quantum Chromo-Dynamics prediction.
Separated cross sections at mean Q**2 of 1.60 GeV**2.
Separated cross sections at mean Q**2 of 2.45 GeV**2.
Extracted values of the charged pion form-factor. Errors are the statistical and experimental systematics combined in quadrature.
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 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.
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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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%.
Quasielastic e-d cross sections have been measured at forward and backward angles. Rosenbluth separations were done to obtain RL and RT at Q2=1.75, 2.50, 3.25, and 4.00 (GeV/c)2. The neutron form factors GEn and GMn have been extracted using a nonrelativistic model. The sensitivity to deuteron wave function, relativistic corrections, and models of the inelastic background are reported. The results for GMn are consistent with the dipole form, while GEn is consistent with zero. Comparisons are made to theoretical models based on vector meson dominance, perturbative QCD, and QCD sum rules, as well as constituent quarks.
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 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.
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.
No description provided.
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Results of one-parameter fit. |Ge|=|Gm| assumed.
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