Measurement of Bose-Einstein correlations in the first LHC-CMS data

1. Measurement of Bose-Einstein correlations in the first LHC-CMS data Ezio Torassa INFN Padova on behalf of the CMS Collaboration Physics at the LHC 2010, 7-12 June, DESY, Hamburg

2. L >> d Introduction Optics rA1 P1 A Plane wave rB1 d Monochromatic Source B The interference pattern is related to the “source geometry” (d) Particles The two particle wave function must be symmetric for bosons : p1 p2 When bosons have identical quantum numbers (1=2) the global wave function reaches the maximum value: A B Physics at the LHC 2010, 7-12 June, DESY, Hamburg

3. Introduction The correlation function is defined as the ratio: joint prob. for identical boson emission independent prob. for identical boson emission for incoherent sources the joint mean time probability gives the following correlation function: For four-momenta small differences, enhancement of the correlation function should be observed The proximity in phase space can be quantified by the Lorentz-inv. • Wis the Fourier transform of the spatial distribution of the emission region • lis the strength of the emission source • ris the radius of the emission source • daccounts for long range Q correlations For the static spherical emission region hypothesis: Physics at the LHC 2010, 7-12 June, DESY, Hamburg

4. Introduction The Bose-Einstein correlation was observed for the fist time by Goldhaber (1960) in proton-antiproton interactions at √s = 2.1 GeV Several measurements have been reported by different experiments The most appropriate (Q) function, the value of the correlation source radius r and the their dependences (i.e. from √s or from the charged-particle multiplicity) are some open questions. For the first time we measured the Bose-Einstein correlation in proton-proton collisions at √s = 900 GeV and √s = 2.36 TeV (December 2009 LHC-CMS data) √s Min. Bias sel. events # tracks # sel. tracks # sel. pairs 900 GeV~ 280 k ~ 5500 k ~ 2900 k ~ 11 M 2.36 TeV~ 14 k ~ 360 k ~ 190 k ~ 1 M Physics at the LHC 2010, 7-12 June, DESY, Hamburg

5. Reference samples the distribution of pairs of the same charge a similar distribution with non interfering track pairs R(Q) is measured by dividing: • We considered pairs from 7 reference samples: • opposite charge (natural choice but contains resonances) • opposite hemisphere same charge ( p → -p for one track) • opposite hemisphere opposite charge • rotated ( [px , py , pz] → [-px , -py , pz] for one track ) • mixed events(random) • mixed events (similar multiplicity) • mixed events (similar invariant mass of all charged particles) Physics at the LHC 2010, 7-12 June, DESY, Hamburg

6. Reference samples • As an example the ratio R(Q) obtained with: • opposite-hemisphere same charge • shows a significant excess at small Q values • (in the default MC the Bose-Einstein correlation is not simulated) dN/dQ R (Q) arXiv:1005.3294v1 CMS AN QCD-10-003 - Approved by Phys. Coord. Physics at the LHC 2010, 7-12 June, DESY, Hamburg

7. Coulomb interactions Coulomb interactions modify the relative momentum pair distribution following the Gamow factors (not simulated in the Monte Carlo): same charge: Ws= (e2 -1) / 2 different charge: WD= (1-e2) / 2 different charge before Gamow correction after Gamow correction (WD) CMS AN QCD-10-003 - Approved by Phys. Coord. The Gamow factor correction is tested with the different charge distribution and applied to the same charge and different charge distributions Physics at the LHC 2010, 7-12 June, DESY, Hamburg

8. Double ratio In order to reduce the bias due to the construction of the reference samples a double ratio R is defined: R (double ratio) R (single ratio) CMS PAS QCD-10-003 CMS PAS QCD-10-003 Physics at the LHC 2010, 7-12 June, DESY, Hamburg

9. Check 1: reconstruction bias Pythia includes the functionality to simulate the Bose-Einstein correlation. To check against possible biases due to the reconstruction we compared the fitted parameters in the generated tracks and reconstructed tracks Dedicated Monte Carlo: MSTJ(51)=1 PARJ(92)=0.9 PARJ(93)=0.125 Generated Reconstructed CMS AN QCD-10-003 - Approved by Phys. Coord. Physics at the LHC 2010, 7-12 June, DESY, Hamburg

10. Check 2: particle identification • The signal sample is a pair combination between tracks with same charge. • As a cross check the dE/dx measurements are used to select • enriched  sample • another sample with  and non- candidates dE/dx R (using dE/dx) CMS PAS TRK-10-001 arXiv:1005.3294v1 p K p Physics at the LHC 2010, 7-12 June, DESY, Hamburg

11. Parametrization Different (Q) functions where tested (Exponential, Gaussian, Levy, Kozlov Gaussian, Kozlov exponential) Gaussian form (Q) = exp (-Q2r2) Exponential form (Q) = exp (-Qr) CMS PAS QCD-10-003 CMS PAS QCD-10-003 Physics at the LHC 2010, 7-12 June, DESY, Hamburg

12. Combined reference sample The parameters of the correlation function were obtained using a “combined “ reference sample r.m.s. from each individual fit provides the systematic error contribution arXiv:1005.3294v1 900 GeV Combined reference sample Gaussian and exponential fit 2.36 TeV Physics at the LHC 2010, 7-12 June, DESY, Hamburg

13. Results Systematics: ± 7% for λ± 12% for r Several reference samples none is perfect ± 2.8% for λ± 0.8% for r The Coulomb interactions were considered with the Gamow factor corrections. The estimated uncertainty for WS is ±15% Measurement @ 2.36 TeV Measurement @ 900 GeV λ = 0.625 ± 0.021stat ± 0.046sys r = 1.59 ± 0.05stat ± 0.19sys λ = 0.662 ± 0.073stat ± 0.048sys r = 1.99 ± 0.18stat ± 0.24sys Physics at the LHC 2010, 7-12 June, DESY, Hamburg

14. Results Comparison with previous measurements Most of the previous experiments provided r measurement with a “traditional” Gaussian fit. The comparison can be done between first momentum with a scale factor √ : Physics at the LHC 2010, 7-12 June, DESY, Hamburg

15. Dependencies Charged track multiplicity dependence arXiv:1005.3294v1 Small dependence of λ from NCH Significant increase of the size of the emission region r as the charged track multiplicity increases Physics at the LHC 2010, 7-12 June, DESY, Hamburg

16. Conclusions • The signal of the Bose-Einstein correlation has been observed for • the first time in proton-proton collisions at √s of 900 GeV and 2.36 TeV • the exponential form(Q) = exp (-Qr) fits the data significantly better • with respect to the Gaussian form • the radius of the emission source measured from the fit is • r = 1.59 ± 0.2 (900 GeV) r = 1.99 ± 0.3 (2.36 TeV) • an increase of the parameterrwith charged-particle multiplicity in the • event is observed Physics at the LHC 2010, 7-12 June, DESY, Hamburg

17. Backup Event selection The events were selected by requiring activity in both CMS beam scintillator counters Track selection • Charged particles are selected to increase their purity, ensure good two-track separation and remove pathologies: • Ndof > 5 • “track high purity” selection • pt > 200 MeV/c • fit χ2 < 5 • |ηtrack| < 2.4 • |dxy| BS < 0.15 cm (transverse impact parameter w.r.t. the collision point) • Rxy < 20 cm (first measured hit w.r.t. the primary vertex) Physics at the LHC 2010, 7-12 June, DESY, Hamburg