Title: Global polarization of Lambda hyperons in Au+Au Collisions at RHIC BES

PA's: Isaac Upsal, Mike Lisa and Sergei Voloshin

Target Journal: PRL (with a followup PRC)

Abstract:
Non-central collisions between nuclei at ultra-relativistic energies are characterized by angular momentum of $10^5-10^6~\hbar$.  QCD spin-orbit coupling or early-stage hydrodynamic viscosity might transfer some of this angular momentum to the hot plasma created at mid-rapidity, but the degree to which this occurs is completely unknown.  The quark-gluon plasma generated in heavy ion collisions is usually modeled via nearly ideal hydrodynamics, and finite angular momentum would lead to vorticity in the fluid field at the femtoscopic scale, the physical implications of which are largely unexplored.  Experimentally, this vorticity would lead to global polarization-- i.e. alignment of spin with the collision's angular momentum-- of hadrons that are ultimately emitted from the plasma.  Using data measured by the STAR Collaboration at RHIC, we present the first observation of global polarization in relativistic nuclear collisions by correlating the self-analyzing decay of ($\Lambda$ ($\overline{\Lambda}$) baryons (antibaryons) with the first-order event plane of the collision.  This observation opens the door to further experimental and theoretical exploration of the role of vorticity and angular momentum in the quark gluon plasma.

Figure 1: Schematic cartoon of a non-central heavy ion collision.  Forward-going fragments are measured in the STAR Beam-Beam Counters (BBCs) and provide an estimate of the direction of the angular momentum $\hat{L}$ of the system at mid-rapidity.  $\Lambda$s and $\overline{\Lambda}$s emitted from the collision have their spins partially aligned with $\hat{L}$ if the fluid has finite vorticity.  (Note: this cartoon conveys the general idea but is not final.  We would, however, like to have a "cool" schematic to show the effect, including vortices in the QGP.  Let us discuss the idea of the figure, and then the PAs can figure out how to implement.)

Figure 2: The average polarization for Lambdas and AntiLambdas from 20\%-50\% central collisions.  The data have been corrected for event plane resolution effects.  This figure has been updated by Mike on 5 March 2016.  An additional update from Isaac with systematic error bands is forthcoming.

Conclusions:
We have reported the first observation of a global polarization in heavy ion collisions.  The fact that $\Lambda$ baryons and $\overbar{\Lambda}$ antibaryons show the same polarization rules out a QED-based magnetic alignment of dipole moments.  In a hydrodynamic scenario, our results imply vorticity in the fluid, a feature lacking in many models currently used to extract transport properties of the plasma.  Theoretical work is required to quantify the vorticity of the fluid implied by our results and to explore the consequences of this vorticity on the dynamics of the system.

 
Comments:
This is a discovery paper.  We will follow up with a much longer paper discussing systematic error details, other ways of quantifying the effect, null tests (rotated background, etc), and possibly theoretical calculations (depending on theorists).  Probably the 14.5 GeV will also appear only in the longer PRC, as that data is rather different than the previous energies as regards Lambdas, due to HFT.  Finally, in that paper, we will present the minimum-bias results as well.  These results are less signficant (fewer Nsigma away from 0) than the centrality-selected data, due to broadening of the underlying distribution, however, they may be compared to the previously-published 62.4 GeV data and are consistent with it (once a sign error in that previous analysis is corrected).

The quantity plotted is

where alpha = 0.642 is the "analyzing power" of the Lambda decay, known from other measurements.  pstar-hat is the direction of the daughter proton momentum in the Lambda frame.  Lhat^est is the direction of the QGP angular momentum, as estimated from the first-order event plane measured in the BBCs.
Another way to express the effect is to quantify the "Polarization" which is twice the quantity shown above.

To be done:
Systematic errors due to cuts, etc.  Early estimates are that these will be small compared to the large statistical errors.
Removing effect of combinatoric background.  This is basically an overall factor (Area under Lambda peak)/(Area under Lambda peak - combinatoric background) ~ 1.1.
Finallly, feed down from Sigmas.

Supporting Material:
From Isaac:
https://drupal.star.bnl.gov/STAR/blog/iupsal/lambda-polarization-bulkcorr-oct-14-2015

https://drupal.star.bnl.gov/STAR/blog/iupsal/lambda-spin-fugacity-measurement-systematics

https://drupal.star.bnl.gov/STAR/blog/iupsal/dnp-meeting-october-28-31-2015

From Mike:
Mike's presentation at WPCF 2015 drupal.star.bnl.gov/STAR/presentations/wpcf-2015/mike-lisa