We used an
exact, rotating and self-similarly expanding
hydrodynamics model for
peripheral HICs by T. Csörgö and M.I. Nagy. The theoretical framework associated
with the lambda polarization was deduced by F. Becattini et al. in their paper on
relativistic distribution function for particles with spin at local thermodynamical
equilibrium with which the authors deduce an expected value for the polarization of
We chose a direction of initial momentum, in the z-direction
in a custom HIC
coordinate system, in which the reaction plane is defined by the xz-plane, and took
the dot product with the vorticiously flowing inverse temperature field to integrate
over space to then arrive at an expression for the expected polarization. The results
were analytic including some Whittaker functions. We conclude that the
polarization of lambda particles at the previous 2.76 TeV per nucleon energy of the
Large Hadron Collider in Geneva, Switzerland, will be as large as 16% in the
negative y-direction at large center-of-mass momenta (pluss or minus 4 GeV/c,
increasing most quickly in the x-direction).
Here, I will probe the current results as they emanate from
models. Although I would ideally use real data, this option is not available to
me until the announcement of OpenAlice through CERN's OpenData initiative.
Until that time, I will use the excellent theoretical power of the Standard Model of
Electroweak Theory as coded in the powerful FLUKA code. With this I will
simulate proton-proton (pp) collisions, and measure the angular distribution of
protons in the lambda rest frame to assess the magnitude of the polarization.
To be clear: Becattini et al.'s results
have already been experimentally confirmed
by the observation of the polarization of lambdas and anti-lambdas at LHC;
in conference proceedings, using small datasets produced by RHIC and ALICE,
Mike Liza has shown that the direction of polarization is the same for both particle
type, thus establishing the fact that this interaction is real, and it is definitely not an
electromagnetic phenomenon, but a phenomenon of spin-orbital angular momentum
coupling at thermodynamical equilibirum in an inverse temperature field.