Hyperon form factors and diquark correlations

Using $e^{+}{e}^{-}$ annihilation data taken at the CESR collider with the CLEO-c detector, measurements of hyperon pair production cross sections and elastic and transition electromagnetic form factors have been made at the charmonium resonances: $\psi (2S)$, $\sqrt{s}=3.69\mathrm{GeV}$, $|Q^2|=13.6{\mathrm{GeV}}^2$, $\mathcal{L}=48{\mathrm{pb}}^{-1}$; $\psi (3770)$, $\sqrt{s}=3.77\mathrm{GeV}$, $|Q^2|=14.2{\mathrm{GeV}}^2$, $\mathcal{L}=805{\mathrm{pb}}^{-1}$; and $\psi (4170)$, $\sqrt{s}=4.17\mathrm{GeV}$, $|Q^2|=17.4{\mathrm{GeV}}^2$, $\mathcal{L}=586{\mathrm{pb}}^{-1}$. Results with good statistical precision are obtained with high efficiency particle identification. Systematics of pair production cross sections, and form factors with respect to the number of strange quarks in the hyperons are studied, and evidence is presented for the effects of diquark correlations in comparative results for ${\mathrm{\Lambda }}^0$ and ${\mathrm{\Sigma }}^0$, both of which have the same $uds$ quark content but different isospin.

Figure 1

Invariant mass distributions for $\psi (2S)$ data. The solid red curves show the results of the fits to these spectra, while the dashed red line shows the background component of the fit. Clear peaks corresponding to each hyperon are seen, and their fitted yields are displayed in each panel. The dashed vertical lines correspond to the “signal” region used for the momentum plots in Fig. 2.

Figure 2

Momentum distributions for hyperon candidates in the “signal” mass regions defined in Fig. 1 for $\psi (2S)$ data. The clear peaks at high momentum are due to pair production of hyperons. The yields at lower momenta are due to hyperons produced in association with other hadrons and the combinatorial backgrounds underneath the hyperon peaks seen in Fig. 1.

Figure 3

Invariant mass distributions for hyperon candidates in $\psi (2S)$ data in the pair-production region given by $E(B)/E(\mathrm{beam})=0.99–1.01$. The solid red curves show the result of the fit to this spectrum described in the text, while the dashed red line shows the background component of the fit.

Figure 4

Invariant mass distributions for hyperon candidates in $\psi (3770)$ data in the pair-production region given by $E(B)/E(\mathrm{beam})=0.99–1.01$. The solid red curves show the result of the fit to this spectrum described in the text, while the dashed red line shows the background component of the fit.

Figure 5

Invariant mass distributions for hyperon candidates in $\psi (4170)$ data in the pair-production region given by $E(B)/E(\mathrm{beam})=0.99–1.01$. The solid red curves show the result of the fit to this spectrum described in the text, while the dashed red line shows the background component of the fit.

Figure 6

${\mathrm{\Lambda }}^0{\mathrm{\Sigma }}^0$ yield distributions as function of $\mathrm{X}\equiv [E({\mathrm{\Lambda }}^0)+E({\mathrm{\Sigma }}^0)]/\sqrt{s}$.

Figure 7

Summary of cross section results. The theoretical prediction for the ratios in panel (c) is $1/s^5=2.74$. The data show systematics with clear differences between baryons containing 0, 1, or 2 strange quarks.

Figure 8

Summary of form factor results. The ratios of $G_M$ at $\psi (3770)$ and $\psi (4170)$ in panel (c) are predicted to be equal to $1/s^2=1.5$. As noted for the cross section ratios in Fig. 7, the data above show different values for baryons containing 0, 1, and 2 strange quarks.

Figure 9

Illustration of the $|Q^2|$ dependence of form factors. Results from the present analysis are shown by the filled circles (“NU”). Results from previous measurements by the DM2 [3] and BABAR [4] Collaborations are also shown with closed triangles and open circles, respectively. The first panel shows measurements of proton timelike form factors for comparison from BABAR [15], Fermilab E760/E835 [16], BES [17], and analyses of CLEO data (NU) [18].