Offline meeting 25.09.2009 Azimuthally sensitive Hanbury-Brown-Twiss (HBT) Interferometry Lukasz Graczykowski Warsaw University of Technology Johanna Gramling Heidelberg University SUPERVISORS: Adam Kisiel, Yiota Foka

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

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

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

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

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

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/

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

Correlation function – 1D projections 1 kT bin (0. 1-0 Correlation function – 1D projections 1 kT bin (0.1-0.6 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

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: 0.1-0.159 GeV/c 1st kT bin: 0.1-0.183 GeV/c 2nd kT bin: 0.159-0.249 GeV/c 2nd kT bin: 0.183-0.267 GeV/c 3rd kT bin: 0.249-0.345 GeV/c 3rd kT bin: 0.267-0.357 GeV/c 4th kT bin: 0.345-0.6 GeV/c 4th kT bin: 0.357-0.6 GeV/c

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

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

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

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

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

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

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

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

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

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

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

References [1] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. 93, 012301 (2004). [2] A. Kisiel et al., Phys. Rev. C79, 014902 (2009)

Additional slides

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.

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

Correlation function – 2D projections THERMINATOR

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