Tilted Pion Sources from Azimuthally Sensitive HBT Interferometry

1
Tilted Pion Sources from Azimuthally Sensitive
HBT Interferometry Ulrich Heinz1, Mike Lisa1, Urs
Wiedemann2 1 The Ohio State University, 2 CERN

HBT probes freeze-out space-time structure
What is the space-time structure of the pion
freeze-out distribution in heavy ion collisions?
S(x,K) is the phase-space distribution at
freeze-out
View from above

• Coordinate space tilt...
• vs. momentum-space tilt reveals nature of p
  directed flow RQMD predicts opposite tilts,
  contrary to hydro scenario
• p from D-decays reflect coordinate-space
  structure of proton directed flow

• Transverse deformation...
• initial vs. final shape sensitive to history of
  elliptic flow
• coordinate space vs. momentum space deformation
  sensitve to nature of elliptic flow
• exotica (nutcrackers)

RQMD Au(2 AGeV)Au
Example analysis of toy model
2D projections of 3D correlation functions for 8
cuts in f (generated with Pratts CRAB)
Analysis of midrapidity pions from semicentral Au
(4 AGeV) Au collisions in E895

• Freezeout distribution
• tilted Gaussian in space-time
• thermal in momentum

fpair
This relates HBT radii to source in natural
coordinates
s3 7 fm
(1)
1D projections of the correlation function for
f45? ? 22.5? (stars), and of the Gaussian fit
(lines)
Below, the stars are results of Gaussian fits to
the 3D correlation functions
where the spatial correlation tensor is given by
Experimental Reality - finite reaction plane
resolution
Measured reaction plane differs statistically
from true one by some angle Df, resulting in
reduced oscillations. Similar to flow studies,
first-order oscillations (here quantified by
S13 ) must be corrected by 1/?cos(Df)? Second-orde
r oscillations (here quantified by (S22-S11 ))
must be corrected by 1/?cos(2Df)? S00, S33, and
(S22S11 ) are unaffected Generally small effect
on homogeneity lengths (0.3 fm) and tilt angle
(3)

• Symmetry considerations
• 1) Mirror reflection in reaction plane f?-f
• 2) For AB collisions Point reflection about
  origin
• y0 corresponds to f?fp

and the lines are simultaneous fits to the HBT
radii with Eq. (1), yielding the Extracted
spatial correlation tensor
S13 and diagonal components nonzero Eq. (2) ? qs
24.6 ? 0.6
colored contours 2D projections of measured 3D
correlation functions black contours projection
of Gaussian fits to correlation function
necessary vanishing points
necessary vanishing points
Extra constraints at midrapidity
General constraints
Extract tilt angle qs , and homogeneity lengths
in natural frame from diagonal elements of
R(qs)Smn R(qs)
Rotated spatial correlation tensor

• diagonal matrix
• eigenvalues are squaredhomogeneity lengths

x2 x2
qs 37o s0 3.7 fm/c s1 4.0 fm s2 5.2
fm s3 5.2 fm
x3
?
to scale
x1
x1

• At low pT (transverse space-momentum correlations
  small ? Smn f-independent)
• 5 nonvanishing components Smn encode all
  spacetime structure
• Smm lengths of homogeneity
• S13 correlation between x1 x3 ? spatial
  tilt angle

(2)

• No radii vanish, even at ycm and pT0 ? always 6
  relevant radii
• first harmonic oscillations _at_ ycm!!!

• Clearly observable new HBT effect!
• Spatial tilt of source in reaction plane - the
  last static component
• Measures geometrical aspects of anisotropic flow
• N.B. for studies at RHIC need first-order
  reaction plane for tilt

Phys. Lett. B489, 287 (2000) nucl-th/0003022