CMS-HIN-24-002

CMS-HIN-24-002 ; CERN-EP-2024-328
Observation of $\Lambda$ hyperon local polarization in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV
CMS Collaboration
11 February 2025
Submitted to Phys. Rev. Lett.
Abstract: The polarization of the $\Lambda$ and $\overline{\Lambda}$ hyperons along the beam direction has been measured in proton-lead (pPb) collisions at a center-of-mass energy per nucleon pair of 8.16 TeV. The data were obtained with the CMS detector at the LHC and correspond to an integrated luminosity of 186.0 $\pm$ 6.5 nb $^{-1}$ . A significant azimuthal dependence of the hyperon polarization, characterized by the second-order Fourier sine coefficient $P_{z,\mathrm{s}2}$ , is observed. The $P_{z,\mathrm{s}2}$ values decrease as a function of charged particle multiplicity, but increase with transverse momentum. A hydrodynamic model that describes the observed $P_{z,\mathrm{s}2}$ values in nucleus-nucleus collisions by introducing vorticity effects does not reproduce either the sign or the magnitude of the pPb results. These observations pose a challenge to the current theoretical implementation of spin polarization in heavy ion collisions and offer new insights into the origin of spin polarization in hadronic collisions at LHC energies.
Links: e-print arXiv:2502.07898 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Example of a simultaneous fit to the mass spectrum (left) and $\langle \cos\theta^{*}\sin[2(\phi-\Psi_{2})] \rangle^{S+B}$ (right) for the multiplicity range 185 $\leq N_\text{trk}^\text{offline} <$ 250. Vertical bars show the statistical uncertainties.
png pdf	Figure 1-a: Example of a simultaneous fit to the mass spectrum (left) and $\langle \cos\theta^{*}\sin[2(\phi-\Psi_{2})] \rangle^{S+B}$ (right) for the multiplicity range 185 $\leq N_\text{trk}^\text{offline} <$ 250. Vertical bars show the statistical uncertainties.
png pdf	Figure 1-b: Example of a simultaneous fit to the mass spectrum (left) and $\langle \cos\theta^{*}\sin[2(\phi-\Psi_{2})] \rangle^{S+B}$ (right) for the multiplicity range 185 $\leq N_\text{trk}^\text{offline} <$ 250. Vertical bars show the statistical uncertainties.
png pdf	Figure 2: left: The second-order Fourier sine coefficients of $\Lambda$ , $\overline{\Lambda}$ and $\Lambda$ + $\overline{\Lambda}$ polarizations along the beam direction as functions of $N_\text{trk}^\text{offline}$ in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV. Results from hydrodynamic calculations [57] are shown as solid and dashed lines. The $N_\text{trk}^\text{offline}$ values of $\Lambda$ + $\overline{\Lambda}$ results are shifted horizontally for better visibility. right: The second-order Fourier sine coefficients $\Lambda$ + $\overline{\Lambda}$ polarization along the beam direction as functions of $p_{\mathrm{T}}$ for 3 $\leq N_\text{trk}^\text{offline} <$ 60, 60 $\leq N_\text{trk}^\text{offline} <$ 120, and 185 $\leq N_\text{trk}^\text{offline} <$ 250 in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV. Vertical bars represent statistical uncertainties, while shaded areas show systematic uncertainties.
png pdf	Figure 2-a: left: The second-order Fourier sine coefficients of $\Lambda$ , $\overline{\Lambda}$ and $\Lambda$ + $\overline{\Lambda}$ polarizations along the beam direction as functions of $N_\text{trk}^\text{offline}$ in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV. Results from hydrodynamic calculations [57] are shown as solid and dashed lines. The $N_\text{trk}^\text{offline}$ values of $\Lambda$ + $\overline{\Lambda}$ results are shifted horizontally for better visibility. right: The second-order Fourier sine coefficients $\Lambda$ + $\overline{\Lambda}$ polarization along the beam direction as functions of $p_{\mathrm{T}}$ for 3 $\leq N_\text{trk}^\text{offline} <$ 60, 60 $\leq N_\text{trk}^\text{offline} <$ 120, and 185 $\leq N_\text{trk}^\text{offline} <$ 250 in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV. Vertical bars represent statistical uncertainties, while shaded areas show systematic uncertainties.
png pdf	Figure 2-b: left: The second-order Fourier sine coefficients of $\Lambda$ , $\overline{\Lambda}$ and $\Lambda$ + $\overline{\Lambda}$ polarizations along the beam direction as functions of $N_\text{trk}^\text{offline}$ in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV. Results from hydrodynamic calculations [57] are shown as solid and dashed lines. The $N_\text{trk}^\text{offline}$ values of $\Lambda$ + $\overline{\Lambda}$ results are shifted horizontally for better visibility. right: The second-order Fourier sine coefficients $\Lambda$ + $\overline{\Lambda}$ polarization along the beam direction as functions of $p_{\mathrm{T}}$ for 3 $\leq N_\text{trk}^\text{offline} <$ 60, 60 $\leq N_\text{trk}^\text{offline} <$ 120, and 185 $\leq N_\text{trk}^\text{offline} <$ 250 in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV. Vertical bars represent statistical uncertainties, while shaded areas show systematic uncertainties.
png pdf	Figure 3: The second-order Fourier sine coefficients of $\mathrm{K^0_S}$ with $\cos\theta^{*}$ calculated from the higher $p_{\mathrm{T}} \pi$ from $\mathrm{K^0_S}$ decay, $\Lambda$ , $\overline{\Lambda}$ and $\Lambda$ + $\overline{\Lambda}$ polarization along the beam direction as functions of $N_\text{trk}^\text{offline}$ in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV. Vertical bars show statistical uncertainties. Shaded areas show systematic uncertainties. The $N_\text{trk}^\text{offline}$ values of $\Lambda$ + $\overline{\Lambda}$ results are shifted for better visibility.
png pdf	Figure 4: The second-order Fourier sine coefficients of $\Lambda$ polarization along the beam direction as functions of $N_\text{trk}^\text{offline}$ in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV extracted with tracker and HF based event planes. Vertical bars show statistical uncertainties. Shaded areas show systematic uncertainties.
png pdf	Figure 5: The second-order Fourier sine coefficients of $\overline{\Lambda}$ polarization along the beam direction as functions of $N_\text{trk}^\text{offline}$ in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV extracted with tracker and HF based event planes. Vertical bars show statistical uncertainties. Shaded areas show systematic uncertainties.
png pdf	Figure 6: The second-order Fourier sine coefficients of $\Lambda$ + $\overline{\Lambda}$ polarization along the beam direction as functions of $N_\text{trk}^\text{offline}$ in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}} =$ 8.16 TeV extracted with tracker and HF based event planes. Vertical bars show statistical uncertainties. Shaded areas show systematic uncertainties.

Tables

png pdf

Table 1:
The average multiplicity before (and after) corrections,

$\langle N_\text{trk}^\text{offline}\rangle$ (

$\langle N_\text{trk}^\text{corrected} \rangle$ ) with track

$p_{\mathrm{T}} > 0.4{\,\text{Ge\hspace{-.08em}V\hspace{-0.16em}/\hspace{-0.08em}}c}$ and

$|\eta| <$ 2.4 in each multiplicity interval of pPb collisions containing at least one reconstructed

$\Lambda$ or

$\overline{\Lambda}$ candidate. The uncertainties reported for

$\langle N_\text{trk}^\text{corrected} \rangle$ are systematic uncertainties, as the statistical uncertainties are negligible.

Summary

In summary, the first measurement of the second-order sine Fourier coefficients

$P_{z,\mathrm{s}2}$ of hyperon polarization along the beam direction in proton-lead collisions is presented. The data were obtained using the CMS detector at a nucleon-nucleon center of mass energy of 8.16 TeV. Significant positive

$P_{z,\mathrm{s}2}$ values are observed for

$\Lambda$ and

$\overline{\Lambda}$ particles as a function of charged particle multiplicity and transverse momentum. The observed signal exhibits behavior similar to those seen in nucleus-nucleus collisions, with

$P_{z,\mathrm{s}2}$ values increasing with rising transverse momentum and decreasing charged particle multiplicity. Hydrodynamic calculations with various polarization scenarios, which describe the results in nucleus-nucleus collisions, fail to describe the positive sign of the proton-lead results. These results pose a challenge to the current theoretical interpretation of spin polarization in heavy ion collisions.

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