Differential HBT Method to Analyze Rotation. L.P. Csernai, S. Velle , D.J. Wang University of Bergen, Norway. #395 QM’2014. Peripheral Collisions (A+A). Global Symmetries Symmetry axes in the global CM-frame: ( y -y) ( x,z -x,-z) Azimuthal symmetry: φ- even ( cos n φ)
L.P. Csernai, S. Velle, D.J. Wang
University of Bergen, Norway
Global Collective flow and fluctuations canbe separated using symmetries:[Csernai & Stöcker, J. Phys. G (2014) to be p.]for this the participant c.m. and the symmetryaxes should be determined as described in:[ Csernai, Eyyubova & Magas, PRC 86(12)024912, & PRC 88 (13) 019902]
Relativistic, 1D Riemann expansion is added to each stopped streak
Initial state by V. Magas, L.P. Csernai and D. Strottman Phys. Rev. C 64 (2001) 014901 & Nucl. Phys. A 712 (2002) 167.
[See Poster # 608 V.K. Magas & L.P. Csernai]
Pb+Pb 1.38+1.38 A TeV, b= 70 % of b_max
Lagrangian fluid cells, moving, ~ 5 mill.
MIT Bag m. EoS
FO at T ~ 200 MeV, but calculated much longer, until pressure is zero for 90% of the cells.
Structure and asymmetries of init. state are maintained in nearly perfect expansion.
[ Csernai L P, Magas V K, Stoecker H, Strottman D D, Phys. Rev. C 84 (2011) 024914 ]
PICR method !!!
From Rotation and Kelvin-Helmholtz Instabilitywe get high angular momentum and vorticity:
[See Poster # 424 D.J. Wang & L.P. Csernai]
[ F. Becattini, L.P. Csernai, D.J. Wang, Phys. Rev. C 88, 034905]
[See Poster # 394 L.P. Csernai, F. Becattini & D.J. Wang]
The method uses two particle correlations:
with k= (p1+p2)/2 and q=p1-p2 :
and S(k,q) is the space-time source or emission function, while R(k,q) can be calculated
the help of a function J(k,q):
which leads to:
This is one of the standard method used for many years. The crucial is the function S(k,q).
Thus the weight factor is:
and for the mirror image source:
The correlation function depends on the direction and size of k , and on rotation. we introduce two vectors k+ , k- symmetrically and define the Differential c.f. (DCF):
The DCF would vanish for symmetric sources (e.g. spherical and non-rotation sources)
We can rotate the frame of reference:
For lower, RHIC energy:
One can evaluate the DCF in these tilted reference frames where (without rotation) the
DCF is minimal.
 M.A. Lisa, et al.,
Phys. Lett. B 496, 1 (2000);
Phys. Lett. B 489, 287 (2000);
Phys. Rev. C 84, 014908 (2011);
Phys. Rev. C 89, 014903 (2014).
 L.P. Csernai, G. Eyyubova
& V.K. Magas, Phys. Rev. C 86,