1. Offline meeting
Azimuthally sensitive Hanbury-Brown-Twiss (HBT) Interferometry Lukasz Graczykowski Warsaw University of Technology Johanna Gramling Heidelberg University SUPERVISORS: Adam Kisiel, Yiota Foka

2. Outline HBT – comparison with the elliptic flow
Azimuthally sensitive HBT – what it is
What was done – short summary of code development
Correlation functions in different kT bins (R vs kT plot)
Reaction Plane calculated in flow code
Azimuthally sensitive HBT dependence on RP angle

3. Comparison of HBT with elliptic flow
Spatial anisotropy
Coordinate space
Elliptic flow
Momentum anisotropy
Momentum space
Reaction plane
Reaction plane
Time

4. Azimuthally sensitive HBT
We look at the HBT radii versus the difference between Reaction Plane and pair emission angle Ф
[1]

5. What was done (1) Run Femto analysis code with kT binning:
EPOS: pp, real freeze-out coordinates
THERMINATOR (centrality 20-30%): heavy ions, „natural” elliptic flow, Reaction Plane
Pythia: no freeze-out coordinates => limited usuefulness (omitted in this presentation)
Create macros to fit 3D correlation functions (and plot 1D and 2D projections), plot R vs q range to estimate systematic errors
Create macro to plot R vs kT
Create new pair cut: on angle between Reaction Plane and pair emission angle Ф

6. What was done (2)
Run Femto analysis with Ф cut and RP value from Monte Carlo
Create macros to fit the correlation functions for different Ф bins and plot R2 vs Ф
Run Flow code to calculate RP and store it in the AOD header (code by Dennis Diederix with further modifications)
Create new task to read both RP's (from MC and reconstructed) and compare them (distribution plots, difference plot and correlation plot)
Use reconstructed RP in azimuthally sensitive HBT analysis
Do kT and Ф binning together and fit the correlation functions
Create macro to plot R2 vs Ф with kT and Ф binning done together

7. Analyzed data EPOS ~90 000 (900 GeV) and ~105 000 (7 TeV) pp events
/alice/cern.ch/user/a/akisiel/PDC09/ EPOSPDC09/
THERMINATOR
~ 1500 PbPb events
Centrality: 20-30%
/alice/cern.ch/user/a/akisiel/PDC09/Th erminatorPDC09/

8. Correlation function – 1D projections 1 kT bin (0.1-0.6 GeV/c), (1)
THERMINATOR EPOS (7 TeV)

9. Correlation function – 1D projections 1 kT bin (0. 1-0
Correlation function – 1D projections 1 kT bin ( GeV/c), EPOS (2)
2-gaussian fit works well
Offset seen before now disappears
Since 1-gaussian fit doesn't work very well, the HBT radii which are got from it should be treated very carefully

10. kT distribution (1) THERMINATOR, EPOS - Pi+
THERMINATOR EPOS (7 TeV)
To make kT binning for R vs kT plots, kT=0.5*|p1+p2|
4 kT bins
The same number of pairs in each kT bin:
THERMINATOR EPOS
1st kT bin: GeV/c st kT bin: GeV/c
2nd kT bin: GeV/c nd kT bin: GeV/c
3rd kT bin: GeV/c rd kT bin: GeV/c
4th kT bin: GeV/c th kT bin: GeV/c

11. Rout vs kT (1) THERMINATOR
kT bins as shown before
x error bars → kT bin range
Decrease of R value as expected
Fit crashes in 1st kT bin → plots only for three kT bins

12. Rout vs kT (1) EPOS (7 TeV) kT bins as shown before
x error bars → kT bin range

13. Rout vs kT (1) EPOS (900 GeV)
kT bins as shown before (done as for EPOS 7 TeV)
Fitted with 1-gaussian
x axis error bars → kT bin range
We can see different dependence on kT than for THERMINATOR

14. Azimuthally sensitive HBT
4 bins in Ф angle
Each „Ф bin” has the same kT range (0.1 – 0.55 GeV/c)
RP calculated using code implemented in Flow analysis part of AliRoot by Dennis Diederix, then read from AODs

15. Comparison of RP's THERMINATOR (1)
Calculated Reaction Plane
Reaction Plane from Monte Carlo

16. Comparison of RP's THERMINATOR (2)
Peak at 0 as expected
Well-fitted with gaussian
But distributions seen on slide before are not similar as they should be...
Correlation → not exactly straight line

17. R2 versus Ф: Source function fit (1) THERMINATOR: Out, Side, Long
Model input
Oscillations seen in mostly in Rout and Rside

18. R2 versus Phi: RP from Monte Carlo THERMINATOR
Correlation function fit
Reaction Plane used from Monte Carlo
Oscillations: as expected
But large error bars

19. R2 versus Phi: RP from AOD (1) THERMINATOR: Out, Side, Long, 1 kT bin
We see some oscillations as expected, but statistics is too low to make any conclusions

20. R2 versus Phi: RP from AOD (2) THERMINATOR: Out, Side, Long, 4 kT bins
Decrease of R in kT bins seen as expected
We see some oscillations (as expected), but error bars are too large
Larger statistics is required

21. Conclusion
Azimuthally sensitive HBT is used at RHIC, interesting at LHC
Experimental tools are now ready: all cuts and macros are ready and tested:
macros to fit both EPOS and Therminator corr. f. with cross terms and with 2-gaussian
macros to estimate systematic errors
macros to plot R vs kT
macros to get RP from AODs and to fit and plot R vs Ф
Now larger statistics for EPOS and THERMINATOR is required to make more detailed study with higher statistics

22. References
[1] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. 93, (2004).
[2] A. Kisiel et al., Phys. Rev. C79, (2009)

23. Additional slides

24. How do we do HBT?
We have two identical particles which are emitted from the points x1 and x2 of the source with different momenta p1 and p2. In general, if we have many such pairs we can create a correlation function.
The correlation function depends on the q vector (which is the difference between p1 and p2). Studying it gives us information about sizes of the source in spatial coordinates.

25. Predictions for the LHC
[2]
The hydrodynamical model worked well for RHIC: so the predictions were made for the LHC
Different freeze-out characteristics in dependence of the source lifetime: Initial anisotropy can be even switched around for long lifetimes

26. Correlation function – 2D projections THERMINATOR

27. Source function fit THERMINATOR
To get sizes (R values) from the model
Well-fitted with
𝑓 𝑥 =𝑁⋅exp − 𝑥 2 4⋅ 𝑅 2