Global polarization of $\Lambda$ and $\bar{\Lambda}$ hyperons in Au+Au collisions at $\sqrt{s_{\rm NN}}=19.6$ and $27$ GeV

The STAR collaboration Abdulhamid, M.I. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Rev.C 108 (2023) 014910, 2023.
Inspire Record 2659670 DOI 10.17182/hepdata.140936

In relativistic heavy-ion collisions, a global spin polarization, $P_\mathrm{H}$, of $\Lambda$ and $\bar{\Lambda}$ hyperons along the direction of the system angular momentum was discovered and measured across a broad range of collision energies and demonstrated a trend of increasing $P_\mathrm{H}$ with decreasing $\sqrt{s_{NN}}$. A splitting between $\Lambda$ and $\bar{\Lambda}$ polarization may be possible due to their different magnetic moments in a late-stage magnetic field sustained by the quark-gluon plasma which is formed in the collision. The results presented in this study find no significant splitting at the collision energies of $\sqrt{s_{NN}}=19.6$ and $27$ GeV in the RHIC Beam Energy Scan Phase II using the STAR detector, with an upper limit of $P_{\bar{\Lambda}}-P_{\Lambda}<0.24$% and $P_{\bar{\Lambda}}-P_{\Lambda}<0.35$%, respectively, at a 95% confidence level. We derive an upper limit on the na\"ive extraction of the late-stage magnetic field of $B<9.4\cdot10^{12}$ T and $B<1.4\cdot10^{13}$ T at $\sqrt{s_{NN}}=19.6$ and $27$ GeV, respectively, although more thorough derivations are needed. Differential measurements of $P_\mathrm{H}$ were performed with respect to collision centrality, transverse momentum, and rapidity. With our current acceptance of $|y|<1$ and uncertainties, we observe no dependence on transverse momentum and rapidity in this analysis. These results challenge multiple existing model calculations following a variety of different assumptions which have each predicted a strong dependence on rapidity in this collision-energy range.

5 data tables

The first-order event-plane resolution determined by the STAR EPD as a function of collision centrality is roughly doubled in comparison to previous analyses using the STAR BBC. We see $R_{\rm EP}^{(1)}$ peak for mid-central collisions.

The mid-central $P_{\rm H}$ measurements reported in this work are shown alongside previous measurements in the upper panel, and are consistent with previous measurements at the energies studied here. The difference between integrated $P_{\bar{\Lambda}}$ and $P_{\Lambda}$ is shown at $\sqrt{s_{\rm{NN}}}$=19.6 and 27 GeV alongside previous measurements in the lower panel. The splittings observed with these high-statistics data sets are consistent with zero. Statistical uncertainties are represented as lines while systematic uncertainties are represented as boxes. The previous $P_{\bar{\Lambda}}-P_{\Lambda}$ result at $\sqrt{s_{\rm NN}}=7.7$ GeV is outside the axis range, but is consistent with zero within $2\sigma$.

$P_{\rm H}$ measurements are shown as a function of collision centrality at $\sqrt{s_{\rm NN}}$=19.6 and 27 GeV. Statistical uncertainties are represented as lines while systematic uncertainties are represented as boxes. $P_{\rm H}$ increases with collision centrality at $\sqrt{s_{\rm NN}}$=19.6 and 27 GeV, as expected from an angular-momentum-driven phenomenon.

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Global $\Lambda$-hyperon polarization in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV

The STAR collaboration Abdallah, M.S. ; Aboona, B.E. ; Adam, J. ; et al.
Phys.Rev.C 104 (2021) L061901, 2021.
Inspire Record 1897216 DOI 10.17182/hepdata.110658

Global hyperon polarization, $\overline{P}_\mathrm{H}$, in Au+Au collisions over a large range of collision energy, $\sqrt{s_\mathrm{NN}}$, was recently measured and successfully reproduced by hydrodynamic and transport models with intense fluid vorticity of the quark-gluon plasma. While naïve extrapolation of data trends suggests a large $\overline{P}_\mathrm{H}$ as the collision energy is reduced, the behavior of $\overline{P}_\mathrm{H}$ at small $\sqrt{s_\mathrm{NN}}<7.7$ GeV is unknown. Operating the STAR experiment in fixed-target mode, we measured the polarization of $\Lambda$ hyperons along the direction of global angular momentum in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV. The observation of substantial polarization of $4.91\pm0.81(\rm stat.)\pm0.15(\rm syst.)$% in these collisions may require a reexamination of the viscosity of any fluid created in the collision, of the thermalization timescale of rotational modes, and of hadronic mechanisms to produce global polarization.

6 data tables

The measured invariant-mass distributions of two classes of $\Lambda$-hyperon decays. The decay classes are defined using the scalar triple product $\left(\vec{p}_\Lambda\times\vec{p}_p^*\right)\cdot \vec{B}_{\rm STAR}$, which is positive for right decays and negative for left decays. The right decay class has a notably sharper invariant-mass distribution than the left decay class, and this is due to the effects of daughter tracks crossing in the STAR TPC with the STAR magnetic field anti-parallel to the lab frame's z direction. The opposite pattern is obtained by flipping the sign of the STAR magnetic field or by reconstructing $\bar{\Lambda}$ hyperons.

The signal polarizations extracted according to the restricted invariant-mass method as a function of $\phi_\Lambda - \phi_p^*$, for positive-rapidity $\Lambda$ hyperons. The sinusoidal behavior is driven by non-zero net $v_1$. The vertical shift corresponds to the vorticity-driven polarization; in collider mode, where the net $v_1$ is zero, this dependence on $\phi_\Lambda - \phi_p^*$ does not exist.

The integrated Global $\Lambda$-hyperon Polarization in mid-central collisions at $\sqrt{s_{\rm NN}}=3$ GeV. The trend of increasing $\overline{P}_{\rm H}$ with decreasing $\sqrt{s_{\rm NN}}$ is maintained at this low collision energy. Previous experimental results are scaled by the updated $\Lambda$-hyperon decay parameter $\alpha_\Lambda=0.732$ for comparison with this result. Recent model calculations extended to low collision energy show disagreement between our data and AMPT and rough agreement with the 3-Fluid Dynamics (3FD) model. Previous measurements shown alongside our data can be found at: https://www.hepdata.net/record/ins750410?version=2; https://www.hepdata.net/record/ins1510474?version=1; https://www.hepdata.net/record/ins1672785?version=2; https://www.hepdata.net/record/ins1752507?version=2.

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Version 2
Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid

The STAR collaboration Adamczyk, L. ; Adkins, J.K. ; Agakishiev, G. ; et al.
Nature 548 (2017) 62-65, 2017.
Inspire Record 1510474 DOI 10.17182/hepdata.77494

The extreme temperatures and energy densities generated by ultra-relativistic collisions between heavy nuclei produce a state of matter with surprising fluid properties. Non-central collisions have angular momentum on the order of 1000$\hbar$, and the resulting fluid may have a strong vortical structure that must be understood to properly describe the fluid. It is also of particular interest because the restoration of fundamental symmetries of quantum chromodynamics is expected to produce novel physical effects in the presence of strong vorticity. However, no experimental indications of fluid vorticity in heavy ion collisions have so far been found. Here we present the first measurement of an alignment between the angular momentum of a non-central collision and the spin of emitted particles, revealing that the fluid produced in heavy ion collisions is by far the most vortical system ever observed. We find that $\Lambda$ and $\overline{\Lambda}$ hyperons show a positive polarization of the order of a few percent, consistent with some hydrodynamic predictions. A previous measurement that reported a null result at higher collision energies is seen to be consistent with the trend of our new observations, though with larger statistical uncertainties. These data provide the first experimental access to the vortical structure of the "perfect fluid" created in a heavy ion collision. They should prove valuable in the development of hydrodynamic models that quantitatively connect observations to the theory of the Strong Force. Our results extend the recent discovery of hydrodynamic spin alignment to the subatomic realm.

2 data tables

Lambda and AntiLambda polarization as a function of collision energy. A 0.8% error on the alpha value used in the paper is corrected in this table. Systematic error bars include those associated with particle identification (negligible), uncertainty in the value of the hyperon decay parameter (2%) and reaction plane resolution (2%) and detector efficiency corrections (4%). The dominant systematic error comes from statistical fluctuations of the estimated combinatoric background under the (anti-)$\Lambda$ mass peak.

Lambda and AntiLambda polarization as a function of collision energy calculated using the new $\alpha_\Lambda=0.732$ updated on PDG2020. Systematic error bars include those associated with particle identification (negligible), uncertainty in the value of the hyperon decay parameter (2%) and reaction plane resolution (2%) and detector efficiency corrections (4%). The dominant systematic error comes from statistical fluctuations of the estimated combinatoric background under the (anti-)$\Lambda$ mass peak.


Differential cross sections and recoil polarizations for the reaction gamma p -> K+ Sigma0

The CLAS collaboration Dey, B. ; Meyer, C.A. ; Bellis, M. ; et al.
Phys.Rev.C 82 (2010) 025202, 2010.
Inspire Record 857728 DOI 10.17182/hepdata.55696

High-statistics measurements of differential cross sections and recoil polarizations for the reaction $\gamma p \rightarrow K^+ \Sigma^0$ have been obtained using the CLAS detector at Jefferson Lab. We cover center-of-mass energies ($\sqrt{s}$) from 1.69 to 2.84 GeV, with an extensive coverage in the $K^+$ production angle. Independent measurements were made using the $K^{+}p\pi^{-}$($\gamma$) and $K^{+}p$($\pi^-, \gamma$) final-state topologies, and were found to exhibit good agreement. Our differential cross sections show good agreement with earlier CLAS, SAPHIR and LEPS results, while offering better statistical precision and a 300-MeV increase in $\sqrt{s}$ coverage. Above $\sqrt{s} \approx 2.5$ GeV, $t$- and $u$-channel Regge scaling behavior can be seen at forward- and backward-angles, respectively. Our recoil polarization ($P_\Sigma$) measurements represent a substantial increase in kinematic coverage and enhanced precision over previous world data. At forward angles we find that $P_\Sigma$ is of the same magnitude but opposite sign as $P_\Lambda$, in agreement with the static SU(6) quark model prediction of $P_\Sigma \approx -P_\Lambda$. This expectation is violated in some mid- and backward-angle kinematic regimes, where $P_\Sigma$ and $P_\Lambda$ are of similar magnitudes but also have the same signs. In conjunction with several other meson photoproduction results recently published by CLAS, the present data will help constrain the partial wave analyses being performed to search for missing baryon resonances.

149 data tables

Differential cross section as a function of COS(THETA(K+,CM)) for the centre-of mass range 1.69 to 1.7 GeV.

Differential cross section as a function of COS(THETA(K+,CM)) for the centre-of mass range 1.7 to 1.71 GeV.

Differential cross section as a function of COS(THETA(K+,CM)) for the centre-of mass range 1.71 to 1.72 GeV.

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Differential cross section and recoil polarization measurements for the gamma p to K+ Lambda reaction using CLAS at Jefferson Lab

The CLAS collaboration McCracken, M.E. ; Bellis, M. ; Meyer, C.A. ; et al.
Phys.Rev.C 81 (2010) 025201, 2010.
Inspire Record 840934 DOI 10.17182/hepdata.54967

We present measurements of the differential cross section and Lambda recoil polarization for the gamma p to K+ Lambda reaction made using the CLAS detector at Jefferson Lab. These measurements cover the center-of-mass energy range from 1.62 to 2.84 GeV and a wide range of center-of-mass K+ production angles. Independent analyses were performed using the K+ p pi- and K+ p (missing pi -) final-state topologies/ results from these analyses were found to exhibit good agreement. These differential cross section measurements show excellent agreement with previous CLAS and LEPS results and offer increased precision and a 300 MeV increase in energy coverage. The recoil polarization data agree well with previous results and offer a large increase in precision and a 500 MeV extension in energy range. The increased center-of-mass energy range that these data represent will allow for independent study of non-resonant K+ Lambda photoproduction mechanisms at all production angles.

241 data tables

Differential cross section as a function of COS(THETA(K)) for the centre-of-mass range 1.62-1.63 GeV.

Differential cross section as a function of COS(THETA(K)) for the centre-of-mass range 1.63-1.64 GeV.

Differential cross section as a function of COS(THETA(K)) for the centre-of-mass range 1.64-1.65 GeV.

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Electroproduction of $\phi(1020)$ mesons at $1.4\leq Q^2\leq$ 3.8 GeV$^2$ measured with the CLAS spectrometer

The CLAS collaboration Santoro, J.P. ; Smith, E.S. ; Garc con, M. ; et al.
Phys.Rev.C 78 (2008) 025210, 2008.
Inspire Record 781974 DOI 10.17182/hepdata.50913

Electroproduction of exclusive $\phi$ vector mesons has been studied with the CLAS detector in the kinematical range $1.6\leq Q^2\leq 3.8$ GeV$^{2}$, $0.0\leq t^{\prime}\leq 3.6$ GeV$^{2}$, and $2.0\leq W\leq 3.0$ GeV. The scaling exponent for the total cross section as $1/(Q^2+M_{\phi}^2)^n$ was determined to be $n=2.49\pm 0.33$. The slope of the four-momentum transfer $t'$ distribution is $b_{\phi}=0.98 \pm 0.17$ GeV$^{-2}$. The data are consistent with the assumption of s-channel helicity conservation (SCHC). Under this assumption, we determine the ratio of longitudinal to transverse cross sections to be $R=0.86 \pm 0.24$. A 2-gluon exchange model is able to reproduce the main features of the data.

5 data tables

Axis error includes +- 18.6/18.6 contribution.

Axis error includes +- 18.6/18.6 contribution.

Axis error includes +- 18.6/18.6 contribution.

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First measurement of beam-recoil observables C(x) and C(z) in hyperon photoproduction.

The CLAS collaboration Bradford, R.K. ; Schumacher, R.A. ; Adams, G. ; et al.
Phys.Rev.C 75 (2007) 035205, 2007.
Inspire Record 732402 DOI 10.17182/hepdata.31496

Spin transfer from circularly polarized real photons to recoiling hyperons has been measured for the reactions $\vec\gamma + p \to K^+ + \vec\Lambda$ and $\vec\gamma + p \to K^+ + \vec\Sigma^0$. The data were obtained using the CLAS detector at Jefferson Lab for center-of-mass energies $W$ between 1.6 and 2.53 GeV, and for $-0.85<\cos\theta_{K^+}^{c.m.}< +0.95$. For the $\Lambda$, the polarization transfer coefficient along the photon momentum axis, $C_z$, was found to be near unity for a wide range of energy and kaon production angles. The associated transverse polarization coefficient, $C_x$, is smaller than $C_z$ by a roughly constant difference of unity. Most significantly, the {\it total} $\Lambda$ polarization vector, including the induced polarization $P$, has magnitude consistent with unity at all measured energies and production angles when the beam is fully polarized. For the $\Sigma^0$ this simple phenomenology does not hold. All existing hadrodynamic models are in poor agreement with these results.

34 data tables

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.032 GeV and W = 1.679 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.132 GeV and W = 1.734 GeV.

Coefficients Cx and Cz for the reaction GAMMA P --> K+ LAMBDA for incident energy = 1.232 GeV and W = 1.787 GeV.

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Measurement of tensor polarization elastic electron deuteron scattering at large momentum transfer.

The JLAB t(20) collaboration Abbott, D. ; Ahmidouch, A. ; Anklin, H. ; et al.
Phys.Rev.Lett. 84 (2000) 5053-5057, 2000.
Inspire Record 523086 DOI 10.17182/hepdata.40433

Tensor polarization observables (t20, t21 and t22) have been measured in elastic electron-deuteron scattering for six values of momentum transfer between 0.66 and 1.7 (GeV/c)^2. The experiment was performed at the Jefferson Laboratory in Hall C using the electron HMS Spectrometer, a specially designed deuteron magnetic channel and the recoil deuteron polarimeter POLDER. The new data determine to much larger Q^2 the deuteron charge form factors G_C and G_Q. They are in good agreement with relativistic calculations and disagree with pQCD predictions.

5 data tables

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Angular dependence of the p p elastic scattering spin correlation parameter A(00nn) between 0.8 and 2.8 GeV: Results for 1.80-GeV to 2.24-GeV

Allgower, C.E. ; Ball, J. ; Barabash, L.S. ; et al.
Phys.Rev.C 62 (2000) 064001, 2000.
Inspire Record 539075 DOI 10.17182/hepdata.25464

Measurements at 19 beam kinetic energies between 1795 and 2235 MeV are reported for the pp elastic scattering spin correlation parameter A00nn=ANN=CNN. The c.m. angular range is typically 60–100°. The measurements were performed at Saturne II with a vertically polarized beam and target (transverse to the beam direction and scattering plane), a magnetic spectrometer and a recoil detector, both instrumented with multiwire proportional chambers, and beam polarimeters. These results are compared to previous data from Saturne II and elsewhere.

21 data tables

Measured values of CNN at EKIN 1795 Mev.. Fractional systematic uncertainty in the absolute beam and target polarization is +-0.110.

Measured values of CNN at EKIN 1845 Mev.. Fractional systematic uncertainty in the absolute beam and target polarization is +-0.073.

Measured values of CNN at EKIN 1935 Mev.. Fractional systematic uncertainty in the absolute beam and target polarization is +-0.095.

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The p p elastic scattering analyzing power measured with the polarized beam and the unpolarized target between 1.98-GeV and 2.80-GeV.

Allgower, C.E. ; Ball, J. ; Beddo, M. ; et al.
Nucl.Phys.A 637 (1998) 231-242, 1998.
Inspire Record 478006 DOI 10.17182/hepdata.36350

A polarized proton beam extracted from SATURNE II was scattered on an unpolarized CH 2 target. The angular distribution of the beam analyzing power A oono was measured at large angles from 1.98 to 2.8 GeV and at 0.80 GeV nominal beam kinetic energy. The same observable was determined at the fixed mean laboratory angle of 13.9° in the same energy range. Both measurements are by-products of an experiment measuring the spin correlation parameter A oon .

19 data tables

Analysing power measurements at a fixed laboratory angle of 13.9 degrees.

No description provided.

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