Experimental determination of the complete spin structure for $\overline{p}p\to \overline{\Lambda }\Lambda$ at $p_{\overline{p}}=1.637\mathrm{GeV}/c$

The reaction $\overline{p}p\to \overline{\Lambda }\Lambda \to \overline{p}{\pi }^{+}p{\pi }^{-}$ has been measured with high statistics at a beam momentum of $p_{\overline{p}}=1.637\mathrm{GeV}/c$. The use of a transversely polarized frozen-spin target combined with the self-analyzing property of $\Lambda /\overline{\Lambda }$ decay allows access to unprecedented information on the spin structure of the interaction. The most general spin-scattering matrix can be written in terms of 11 real parameters for each bin of scattering angle; each of these parameters is determined with reasonable precision. From these results, all conceivable spin correlations are determined with inherent self-consistency. Good agreement is found with the few previously existing measurements of spin observables in $\overline{p}p\to \overline{\Lambda }\Lambda$ near this energy. Existing theoretical models do not give good predictions for those spin observables that had not been previously measured.

Figure 1

Coordinate axes used to decompose each individual particle's spin directions. The $\hat{n}$ direction is common. The target polarization direction, which is perpendicular to ${\hat{l}}_p$, is also shown for a typical event in which the normal to the scattering plane is at angle Φ relative to the polarization direction.

Figure 2

(a) A schematic plan view of the detectors, magnet, and target. The solenoid field, shown in the positive $y$ direction, could be reversed to reduce systematic uncertainties. Tracks from a typical event are superimposed. (b) An expanded view of the target region shows the beam-defining scintillators and the veto scintillators used to select events in which only neutral particles exit the target. The hodoscope planes completed the trigger by requiring charged particles downstream of the decay region.

Figure 3

Schematic cross-sectional view through the cryostat system (four concentric vertical cylinders) holding the frozen spin target (a horizontal cylinder). Coordinates are indicated relative to the center of the target. The antiproton beam entered through the four thin windows on the left and interacted in the frozen butanol target. Hyperons escaped with relatively little interaction through the large exit windows shown on the right. Dashed lines represent 20 μm titanium windows while dash-dot lines represent 40 μm aluminum windows. Coils which provide the holding field are shown shaded. The trigger selected only those events in which the hyperons survived long enough to escape the cryostat and pass the veto detectors before decaying.

Figure 4

Distribution of fit quality $\mathcal{Q}$ found by treating liklihood as if it were distributed with a ${\chi }^2$ statistic. Dotted line is the Monte Carlo prediction normalized to the data over the interval $0.1\le \mathcal{Q}\le 1$.

Figure 5

Comparison of hyperon decay vertex $z$-coordinate distributions between data (solid line) and simulated data set (shaded).

Figure 6

Results for the ϕ-averaged differential cross section (solid). The previous measurement [2] at $1.642\mathrm{GeV}/c$, scaled by a factor of 1.26 to match present integrated cross section, is superimposed (open diamonds).

Figure 7

Fit results for spin-matrix parameters $a,b$, and $c$. Arbitrary phase is chosen by constraining parameter $a$ to be real and nonnegative. Statistical errors are shown on each data point, with $2\sigma$ error bars superimposed (dashed). Estimated systematic error width is shown at the bottom of each plot (dark-shaded region).

Figure 8

Fit results for spin-matrix parameters $d,e$, and $g$. Statistical errors are shown on each data point, with $2\sigma$ error bars superimposed (dashed). Estimated systematic error width is shown at the bottom of each plot (dark-shaded region).

Figure 9

Current results for polarization, $Q[n_{\Lambda }]=Q[n_{\overline{\Lambda }}]$ (filled circles). The previous measurement [2] at $1.642\text{GeV}/c$ is superimposed (open squares). Statistical errors are shown on each current data point, with $2\sigma$ error bars superimposed (dashed). The estimated systematic error width is shown at the bottom of each plot (dark-shaded region).

Figure 10

Current results for previously measured spin correlations between $\overline{\Lambda }$ and Λ (filled circles). Previous measurements [2] are superimposed (open squares). Statistical errors are shown on each current data point, with $2\sigma$ error bars superimposed (dashed). Estimated systematic error width is shown at the bottom of each plot (dark-shaded region). Spin correlations are (a) $Q[m_{\overline{\Lambda }},m_{\Lambda }]$, (b) $Q[m_{\overline{\Lambda }},l_{\Lambda }]$, (c) $Q[n_{\overline{\Lambda }},n_{\Lambda }]$, and (d) $Q[l_{\overline{\Lambda }},l_{\Lambda }]$.

Figure 11

Current results for singlet fraction $S_F$ (filled circles). Previous measurement [2] is superimposed (open squares). Statistical errors are shown on each current data point, with $2\sigma$ error bars superimposed (dashed). Estimated systematic error width is shown at the bottom of each plot (dark-shaded region).

Figure 12

Results for spin transfer observables $Q[n_p,n_{\Lambda }]$ (often called depolarization, $D_{\mathit{nn}}$) and $Q[n_p,n_{\overline{\Lambda }}]$ (often called spin transfer, $K_{\mathit{nn}}$) at $1.637\mathrm{GeV}/c$, compared to MEX [7] and QG [9] model predictions at $1.642\mathrm{GeV}/c$. Statistical and systematic errors are shown as in previous figures.

Figure 13

Results for the 12 additional spin observables which appear directly in the measured angular distribution. Statistical and systematic error estimates are displayed as before. The spin observables displayed are (a) $Q[n_p]$, (b) $Q[m_p,m_{\Lambda }]$, (c) $Q[m_p,l_{\Lambda }]$, (d) $Q[m_p,m_{\overline{\Lambda }}]$, (e) $Q[m_p,l_{\overline{\Lambda }}]$, (f) $Q[m_p,m_{\overline{\Lambda }},n_{\Lambda }]$, (g) $Q[m_p,n_{\overline{\Lambda }},m_{\Lambda }]$, (h) $Q[m_p,n_{\overline{\Lambda }},l_{\Lambda }]$, (i) $Q[m_p,l_{\overline{\Lambda }},n_{\Lambda }]$, (j) $Q[n_p,m_{\overline{\Lambda }},m_{\Lambda }]$, (k) $Q[n_p,m_{\overline{\Lambda }},l_{\Lambda }].$, and (l) $Q[n_p,l_{\overline{\Lambda }},m_{\Lambda }]$.

Figure 14

Results for eight spin observables which do not appear directly in the measured angular distribution. Direct measurement of an individual one of these observables would require a longitudinally polarized target proton but would not require beam polarization. Statistical and systematic error estimates are displayed as before. The spin observables displayed are (a) $Q[l_p,m_{\Lambda }]$, (b) $Q[l_p,l_{\Lambda }]$, (c) $Q[l_p,m_{\overline{\Lambda }}]$, (d) $Q[l_p,m_{\overline{\Lambda }},n_{\Lambda }]$, (e) $Q[l_p,n_{\overline{\Lambda }},m_{\Lambda }]$, (f) $Q[l_p,n_{\overline{\Lambda }},l_{\Lambda }]$, (g) $Q[l_p,l_{\overline{\Lambda }}]$, and (h) $Q[l_p,l_{\overline{\Lambda }},n_{\Lambda }]$.

Figure 15

Results for the final 12 spin observables which do not appear directly in the measured angular distribution. Direct measurement of an individual one of these observables would require a polarized antiproton beam. Statistical and systematic error estimates are displayed as before. For one angular bin in each of figures (a) and (l), double minima resulted in disjoint regions falling within the 1σ limit. The spin observables displayed are (a) $Q[m_{\overline{p}},m_p]$, (b) $Q[m_{\overline{p}},m_p,n_{\Lambda }]$, (c) $Q[m_{\overline{p}},m_p,m_{\overline{\Lambda }},m_{\Lambda }]$, (d) $Q[m_{\overline{p}},m_p,m_{\overline{\Lambda }},l_{\Lambda }]$, (e) $Q[m_{\overline{p}},m_p,l_{\overline{\Lambda }},l_{\Lambda }]$, (f) $Q[m_{\overline{p}},l_p]$, (g) $Q[m_{\overline{p}},l_p,n_{\Lambda }]$, (h) $Q[m_{\overline{p}},l_p,m_{\overline{\Lambda }},m_{\Lambda }]$, (i) $Q[m_{\overline{p}},l_p,m_{\overline{\Lambda }},l_{\Lambda }]$, (j) $Q[m_{\overline{p}},l_p,n_{\overline{\Lambda }}]$, (k) $Q[m_{\overline{p}},l_p,l_{\overline{\Lambda }},m_{\Lambda }]$, and (l) $Q[l_{\overline{p}},l_p]$.

Figure 16

Comparison of quark-gluon predictions [25] to measured spin-transfer and depolarization observables. Measured results presented in Figs. 13 and 14 are repeated here for comparison with the predictions. Statistical and systematic error estimates are displayed as before. The spin observables displayed are (a) $Q[m_p,m_{\Lambda }]$, (b) $Q[m_p,m_{\overline{\Lambda }}]$, (c) $Q[m_p,l_{\Lambda }]$, (d) $Q[m_p,l_{\overline{\Lambda }}]$, (e) $Q[l_p,m_{\Lambda }]$, (f) $Q[l_p,m_{\overline{\Lambda }}]$, (g) $Q[l_p,l_{\Lambda }]$, and (h) $Q[l_p,l_{\overline{\Lambda }}]$.