1. Study of Bose-Einstein correlations for pions at √s = 7 TeV
Marcin Kucharczyk, Tadeusz Lesiak, Bartosz Małecki, Mariusz Witek
Institute of Nuclear Physics PAN, Kraków, Poland

2. Outline Introduction Analysis method Data selection Results Summary
Alice, Atlas and CMS already published Bose-Einstein correlation papers at central rapidities.
LHCb can add measurements in the forwad region.
Twiki analysis page

3. HBT interferometry In 1950s Robert Hanbury Brown an Richard Q. Twiss
(radio astronomy engineers) found
correlations between photons from different sources
Initially this observation was not accepted.
Opponents were quoting Dirac: “Interference between two different photons can never occur.”
Laboratory experiments quoted conclusion:”…in agreement with quantum theory, the photons of two coherent light beams are independent from each other .”
It turned out that the observed effect does not contradicts Quantum Mechanics but oppositely, it is its consequence related to Bose-Einstein statistics.
Intensity interference (second order interference) to measure the
diameters of radio sources.
By changing the distance between detectors, one can measure the diameter of emitting source.

4. From interferometry to particle physics
Goldhaber, Goldhaber, Lee and Pais.
Experiment at the Bevalac/LBL, in Berkeley to look at the resonances by comparing Q distribution of unlike-sign pairs π+π- to like sign π+π+ or π-π-.
No resonance was discovered (not enough statistics) but unexpected angular correlation among identical pions was observed.
Counterpart of the HBT effect in particle physics
Quantum interference effect between indistinguishable particles emitted by a finite source.
Useful tool to probe the spatial and temporal structure of the hadron emission volume.

5. Correlation function Used in this analysis Goldhaber parametrization
Q distribution for like-sign pair in data – includes qunatum correlations
Q distribution for reference sample – no quantum correlations
Goldhaber parametrization
+ for bosons
- for fermions
R - radius of the spherical source
λ - chaoticity parameter
λ=0 fully coherent source
λ=1 completely chaotic source
Alternative, Levi parametrization to include shape of long range correlations
Used in this analysis

6. Choice of reference sample
The reference sample should be free from Bose-Einstein Correlations (BEC) while possessing other correlations related to e. g. charge, energy-momentum conservation, particle decays, event topology etc.
Three reference samples considered
Used in this analysis
1. Event-mix – pairs of identical charged pions each originating from different events
Reference samples derived from data but
random choice of pairs eliminates BEC and all other non trivial correlation.
2. PV-mix – pairs of identical charged pions each originating from different PVs in the same event
Reference sample derived from data and preserves other correlations but
unlike-sign pairs may originate from resonances
effects of electric attraction present
3. Unlike-sign – pairs of unlike sign pions from same event

7. Double Ratio (DR) Double Ratio - an improved correlation function.
Features of DR
Insensitive to single particle efficiency effects (true also for C2)
spatial acceptance
selection cuts
PID ( contamination of other particles without BEC)
Insensitive to two-track efficiency effects if properly simulated.
Reduces imperfections of reference sample.
MC correlation function contains similar pattern of distortions as correlation function for data.
By dividing them, one can eliminated second order effects to large extend and imperfections of the reference sample.

8. Datasets MC - 20 M events DATA - 40 M events MC 10 M events
NoBias. Pythia8, Sim08, Reco14, 2011
Bose-Einstein correlations switched off.
MC 10 M events
Pythia 6.4, Perugia0 tuning 2011
For systematics due to model
DATA - 40 M events
MinBias, Stripping 20r1, Reco 14
To study BEC we are interested in proton-proton interactions i.e. single PV.
Data MINIBIAS.DST contains NoBias and MinimumBias with multiple PVs
MinimumBias introduces a certain PT(ET) cut which biases PV
PV unbiasing procedure (DATA only)
Yes
NoBias event? No
Select all PVs with tracks fired the L0 MinBias trigger.
Accept all PVs
Remove randomly one of the PVs that fired the MinBias trigger.
Accept all remaining PVs

9. Track selection Relatively loose cuts for tracks IP cut Long track
MC resampling method was chosen for correcting simulated PID
Standard binning
Λ0→pπ calibration sample added for protons.
Corrected ProbNNs are drown according to true MCID.

10. Three multiplicity bins
R, radius of the source depends on total multiplicity Ntot of the event
Nch – VELO multiplicity of charged tracks is good probe of the Ntot
To check the R(Nch) dependence the data were split into 3 multiplicity bins
Bin
VELO Nch
Activity class 1
0-10
(52-100)% 2
11-20
(15-52)% 3
20-60
(0-15)%
Nch bins were chosen to have similar number of pairs in each beam.
Activity classes were calculated according to Nch bins
They are useful to compare between experiments.
For example: activity class (0-15)% corresponds to 15 % of all events with highest VELO multiplicity.
On next slides pictures of correlation function or double ratio will be shown for bin 2.
Full set of plot is available in the note on the analysis Twiki page

11. Correlation functions and double ratio: like-sign
like-sign π+π+ or π-π-
DATA
Double Ratio = MC

12. Correlation functions and double ratio: unlike-sign
Not used as reference sample.
Only to control the effects at Q range of BEC signal and asymptotic behavior at large Q
DATA
Double Ratio = MC
Coulomb effect
Not perfect simulation of resonances

13. Coulomb effect correction
Final state interactions:
Strong – independent of charge combination
Electromagnetic (Coulomb effect)
like-sign – repulsive, BEC effect decreased
unlike-sign – attractive, BEC effect increased
Coulomb effect has been calculated.
It can be removed using Gamov penetration factor.
Residual acceptance effects included in systematics.

14. Clones and ghosts
Clones and ghosts are expected to appear in the low Q region thus can affect the BEC signal.

15. Stability cross-checks
Variation of single track reconstruction efficiency/acceptance
Fitting procedure (ToyMC fits)
Variation of IP cut
Magnet polarity
Data taking period (before/after technical stop)
Contamination from beam-gas interactions
ToyMC fits – pull distributions
Slightly overestimated errors σpull = 0.95
Artificial introduction of additional inefficiency for single track reconstruction. Linear decrease of efficiency from
100% at η=2 down to 80% at η=5.
Strong prove of insensitivity to single track inefficiency and detector acceptance
Data taking period (before/after technical stop)

16. Systematic uncertainties
Sources of systematics (dominant ones in red):
Differences between data and simulation:
Dependence on generation model (different tunings of Pythia).
Two particle efficiencies at very low Q (ghosts and clones).
Residual acceptance effects
Reconstruction
Number of PVs in an event ( 1, 2, 3-4 )
Particle identification (ProbNNpi cut)
Particle identification (MC recalibration)
PV reconstruction efficiency
Resolution of Q variable
Technical:
Lower limit of Q distribution in a fit
Upper limit of Q distribution in a fit
Q distribution binning

17. Systematic uncertainties – generation model
Dependence on generation model (different tunings of Pythia).
Pythia 8 default LHCb tuning
Pythia 6.4 Perugia0 tuning
ΔR/R ~ (6-9)%
Δλ/λ ~ (2-4)%
Systematics

18. Systematic uncertainties – number of PVs
Number of PVs in an event ( 1, 2, 3-4 )
Distributions almost identical but some systematic differencies affect the fit results
ΔR/R ~ (4-6)%
Δλ/λ ~ (4-6)%

19. Systematic uncertainties - summary
Summary of systematic uncertainties for the 3 bins of PV VELO track multiplicities
Bin 1 - low
Bin 2 - medium
Bin 3 - high

20. Results Bin 1 - low Bin 2 - medium Bin 3 - high
Some systematic patterns can be observed in pulls. Phenomenological Levi parametrization is only approximation derived with certain assumptions.

21. Results

22. Summary
Bose-Einstein correlations for pions produced in p-p collisions at √sNN = 7 TeV have been measured in the forward region.
The analysis showed that LHCb is able to perform BEC measurements. It opens the possibility for other studies.
different collisions: pp, pPb, PbPb(?)
3D analysis for pions (LCMS system)
3-body correlations for pions
extend analysis for: KK, ΛΛ and charm (?)
different beam energies: e.g. pp 7,8,13 TeV; pPb 5TeV

23. Backup slides