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| CMS-PAS-HIN-26-002 | ||
| Measurements of $ \Lambda $ hyperon spin correlations in proton-proton and proton-lead collisions | ||
| CMS Collaboration | ||
| 2026-05-17 | ||
| Abstract: The spin correlations of $ \Lambda\Lambda $, $ \Lambda\overline{\Lambda} $, and $ \overline{\Lambda}\overline{\Lambda} $ hyperon pairs are measured in proton-proton (pp) collisions at $ \sqrt{s}= $ 13 TeV and proton-lead (pPb) collisions at $ \sqrt {\smash [b]{s_{_{\mathrm {NN}}}}} = $ 8.16 TeV at the LHC. The data were collected with the CMS detector, corresponding to integrated luminosities of 28.6 $ \mathrm{pb}^{-1} $ and 186 $ \mathrm{nb}^{-1} $ for pp and pPb collisions, respectively. The analysis is performed for hyperons with the transverse momentum 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and pseudorapidity $ |\eta| < $ 2.4. The spin correlations are studied as functions of the hyperon pair separation, defined as $ \Delta R = \sqrt{(\Delta \eta)^2 + (\Delta \phi)^2} $. Negative values of the spin correlation are observed at small $ \Delta R $ for the $ \Lambda\Lambda $ and $ \overline{\Lambda}\overline{\Lambda} $ pairs, while the $ \Lambda\overline{\Lambda} $ results do not show a significant deviation from zero within the uncertainties. The magnitude of the correlation shows a decreasing trend with the $ \Delta R $ increase, becoming consistent with zero at large $ \Delta R $. The correlation values integrated over the full $ \Delta R $ range have negative central values for all hyperon pair combinations, and tend to have larger magnitudes for the $ \Lambda\Lambda $ and $ \overline{\Lambda}\overline{\Lambda} $ pairs than for the $ \Lambda\overline{\Lambda} $ pairs. Larger correlation values are observed in pp compared to pPb collisions, particularly at small $ \Delta R $. A comparison with the measurement by the STAR Collaboration in pp collisions at $ \sqrt{s}= $ 200 GeV shows a different behavior of the $ \Lambda\overline{\Lambda} $ correlation at small $ \Delta R $. These results extend the study of hyperon pair spin correlations to the LHC energies and provide new information on the energy dependence of their behavior at small $ \Delta R $. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
The two-dimensional invariant mass distributions of the reconstructed $ \Lambda\Lambda $ candidate pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in 8.16 TeV pPb collisions. |
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Figure 2:
Left: One-dimensional invariant mass distribution of $ \Lambda\overline{\Lambda} $ candidate pairs, obtained by projecting the two-dimensional invariant mass distribution onto the $ \Lambda $ axis. The fit result, including the signal and combinatorial background components, is shown by the red line. Right: The acceptance-corrected $ dN/d\cos(\theta^{*}) $ distribution for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in pPb collisions with the results of the fit to a linear function (red line). The vertical bars, representing the statistical uncertainties, are typically smaller than the marker size. |
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Figure 3:
Spin correlation $ P_{\Lambda_{1},\Lambda_{2}} $ distributions as functions of $ \Delta R $ for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in $ \text{pp} $ and pPb collisions. The right panel shows the corresponding results integrated over the full $ \Delta R $ range. The STAR results with $ |y| < $ 1 in $ \text{pp} $ collisions at $ \sqrt{s}= $ 200 GeV [19] are shown for comparison, with the definition of \dR shown in parentheses in the $ x $ axis title. The STAR short- (long-) range result is extracted from $ \Lambda\overline{\Lambda} $ pairs with $ |y| < $ 0.5 and $ |\phi| < \pi/ $ 3 (0.5 $ < |y| < $ 2 and/or $ \pi/3 < |\phi| < \pi $). The vertical bars represent the statistical uncertainties, while the shaded areas show the systematic ones. |
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Figure 4:
The $ P_{\Lambda_{1},\Lambda_{2}} $ values as functions of $ \Delta R $ for $ \Lambda\Lambda $ (left) and $ \overline{\Lambda}\overline{\Lambda} $ (right) pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in $ \text{pp} $ and pPb collisions. The right panel shows the corresponding results integrated over the full $ \Delta R $ range. The results for pPb collisions with an additional requirement of $ q_{\text{inv}} > $ 0.4 GeV are also shown. The corresponding EPOS results are included for comparison. The vertical bars represent statistical uncertainties, and shaded bands represent systematic uncertainties. |
png pdf |
Figure 5:
Left: Same-event $ dN/d\cos(\theta^{*}) $ distribution for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in pPb collisions. Right: Mixed-event $ dN/d\cos(\theta^{*}) $ distribution for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in pPb collisions. The vertical bars, representing the statistical uncertainties, are typically smaller than the marker size. |
png pdf |
Figure 5-a:
Left: Same-event $ dN/d\cos(\theta^{*}) $ distribution for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in pPb collisions. Right: Mixed-event $ dN/d\cos(\theta^{*}) $ distribution for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in pPb collisions. The vertical bars, representing the statistical uncertainties, are typically smaller than the marker size. |
png pdf |
Figure 5-b:
Left: Same-event $ dN/d\cos(\theta^{*}) $ distribution for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in pPb collisions. Right: Mixed-event $ dN/d\cos(\theta^{*}) $ distribution for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in pPb collisions. The vertical bars, representing the statistical uncertainties, are typically smaller than the marker size. |
png pdf |
Figure 6:
Spin correlation $ P_{\Lambda_{1},\Lambda_{2}} $ distributions as functions of $ \Delta R $ for $ \Lambda\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |y| < $ 1.0 in $ \text{pp} $ collisions. The right panel shows the corresponding results integrated over the full $ \Delta R $ range. The results are not corrected for $ \Lambda $/$ \overline{\Lambda} $ reconstruction efficiency. The STAR results in $ \text{pp} $ collisions at $ \sqrt{s}= $ 200 GeV [19] are shown for comparison. The STAR short- (long-) range result is extracted from $ \Lambda\overline{\Lambda} $ pairs with $ |y| < $ 0.5 and $ |\phi| < \pi/ $ 3 (0.5 $ < |y| < $ 2 and/or $ \pi/3 < |\phi| < \pi $). Vertical bars show statistical uncertainties. Shaded areas show systematic uncertainties. |
png pdf |
Figure 7:
The $ P_{\Lambda_{1},\Lambda_{2}} $ values as functions of $ \Delta R $ for $ \Lambda\overline{\Lambda} $ (left), $ \Lambda\Lambda $(middle) and $ \overline{\Lambda}\overline{\Lambda} $ (right) pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in $ \text{pp} $ and pPb collisions. The right panel shows the corresponding results integrated over the full $ \Delta R $ range. The corresponding EPOS results are included for comparison. The vertical bars represent statistical uncertainties, and shaded bands represent systematic uncertainties |
png pdf |
Figure 8:
The $ P_{\Lambda_{1},\Lambda_{2}} $ values as functions of $ \Delta R $ for $ \Lambda\Lambda $ (left) and $ \overline{\Lambda}\overline{\Lambda} $ (right) pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 in $ \text{pp} $ and pPb collisions. The right panel shows the corresponding results integrated over the full $ \Delta R $ range. The STAR results in $ \text{pp} $ collisions at $ \sqrt{s}= $ 200 GeV [19] are shown for comparison. The STAR short- (long-) range result is extracted from $ \Lambda\Lambda $ and $ \overline{\Lambda}\overline{\Lambda} $ pairs with $ |y| < $ 0.5 and $ |\phi| < \pi/ $ 3 (0.5 $ < |y| < $ 2 and/or $ \pi/3 < |\phi| < \pi $). The vertical bars represent statistical uncertainties, and shaded bands represent systematic uncertainties. |
| Tables | |
png pdf |
Table 1:
Summary of systematic uncertainties in the $ P_{\Lambda_{1},\Lambda_{2}} $ values are shown for the integrated results and for results binned in $ \Delta R $ in pPb ($ \text{pp} $) collisions. |
| Summary |
| In summary, the spin correlations of $ \Lambda\overline{\Lambda} $, $ \Lambda\Lambda $, and $ \overline{\Lambda}\overline{\Lambda} $ pairs with 0.8 $ < p_{\mathrm{T}} < $ 6.0 GeV and $ |\eta| < $ 2.4 have been measured in proton-proton collisions at $ \sqrt{s}= $ 13 TeV and proton-lead collisions at $ \sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}= $ 8.16 TeV collected with the CMS detector in 2018 and 2016, respectively. The dependence on the hyperon pair separation, defined as $ \Delta R = \sqrt{(\Delta \eta)^2 + (\Delta \phi)^2} $, is studied. Negative $ P_{\Lambda_{1},\Lambda_{2}} $ values are observed at small $ \Delta R $ for $ \Lambda\Lambda $ and $ \overline{\Lambda}\overline{\Lambda} $ pairs, while the $ \Lambda\overline{\Lambda} $ results do not show a statistically significant deviation from zero within the uncertainties. The magnitude of $ P_{\Lambda_{1},\Lambda_{2}} $ shows a decreasing trend with the $ \Delta R $ increase, becoming consistent with zero at large $ \Delta R $. The $ P_{\Lambda_{1},\Lambda_{2}} $ values integrated over the full $ \Delta R $ range for all types of pairs are found to be negative, and tend to have larger magnitudes for $ \Lambda\Lambda $ and $ \overline{\Lambda}\overline{\Lambda} $ than for $ \Lambda\overline{\Lambda} $ pairs. A trend of larger $ P_{\Lambda_{1},\Lambda_{2}} $ values is seen in proton-proton than in proton-lead collisions, particularly at small $ \Delta R $. Results obtained with an additional requirement of excluding pairs with small relative four-momentum are consistent with those without this requirement, suggesting that the observed behavior is not dominated by Hanbury--Brown--Twiss correlations. A comparison with the corresponding measurement by the STAR Collaboration in proton-proton collisions at $ \sqrt{s}= $ 200 GeV shows a different behavior for the $ \Lambda\overline{\Lambda} $ pair correlations at small $ \Delta R $. These results extend the study of $ \Lambda $ hyperon spin correlations to the LHC energies and suggest a collision energy dependence in the small-$ \Delta R $ region, with the underlying mechanisms remaining an open question. |
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