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| 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 | ||
| Phys. Rev. Lett. 135 (2025) 132301 | ||
| 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 $ \text{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 | |
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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. The mass spectrum is fitted by a double Gaussian together with an additional term that is needed to account for the combinatorial background, $ A_{1}q^{1/2} + A_{2}q^{3/2} $, where $ q = m_{\text{inv}} - (m_{\pi}+m_{\mathrm{p}}) $. The vertical bars show the statistical uncertainties. |
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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. The mass spectrum is fitted by a double Gaussian together with an additional term that is needed to account for the combinatorial background, $ A_{1}q^{1/2} + A_{2}q^{3/2} $, where $ q = m_{\text{inv}} - (m_{\pi}+m_{\mathrm{p}}) $. The 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. The mass spectrum is fitted by a double Gaussian together with an additional term that is needed to account for the combinatorial background, $ A_{1}q^{1/2} + A_{2}q^{3/2} $, where $ q = m_{\text{inv}} - (m_{\pi}+m_{\mathrm{p}}) $. The 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 [66] 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 [66] 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 [66] 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. |
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Figure A1:
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 A2:
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 A3:
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 A4:
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 | |
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Table 1:
For each $ N_\text{trk}^\text{offline} $ range where at least one reconstructed $ \Lambda $ or $ \overline{\Lambda} $ candidate is found, the fraction of MB triggered events found in this range, the average $ N_\text{trk}^\text{offline} $ value for this range $ \langle N_\text{trk}^\text{offline}\rangle $, and the average number of tracks after correcting for track reconstruction inefficiencies and misidentification rates $ \langle N_\text{trk}^\text{corrected} \rangle $ are reported. |
| 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 that 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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