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Perspective for the measurement of D + elliptic flow. F. Prino 1 , E. Bruna 2 , M. Masera 2 1 INFN – Sezione di Torino 2 Dip. Fisica Sperimentale, Università di Torino. Elliptic flow. y. Y RP. x. Elliptic flow.
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Perspective for the measurement of D+ elliptic flow F. Prino1, E. Bruna2, M. Masera2 1 INFN – Sezione di Torino 2 Dip. Fisica Sperimentale, Università di Torino Alice Physics Week, December 5-9 2005
Elliptic flow y YRP x Elliptic flow • Anisotropy in particle azimuthal distribution due to collective motion (flow) of particles • Driven by anisotropic pressure gradients originating from the almond-shaped overlap zone of the colliding nuclei in non-central collisions • Fourier expansion of particle azimuthal distribution relative to the reaction plane • Reaction plane (YRP) defined by beam direction and impact parameter Alice Physics Week, December 5-9 2005
Flow and anisotopy • Elliptic Flow not the only source of correlations between D± azimuthal angles and the reaction plane • D± azimuthal anisotropy may also originate from: • Parton energy loss • Smaller in-medium length L in-plane (parallel to reaction plane) than out-of-plane (perpendicular to the reaction plane) • Drees, Feng, Jia, Phys. Rev. C71, 034909 • Dainese, Loizides, Paic, EPJ C38, 461 • Scattering on pions • Due to elliptic flow, azimuthal distribution of pions is anisotropic • more pions in-plane than out-of-plane • What is measured is v2 (which is not only due to flow) Alice Physics Week, December 5-9 2005
Unknown reaction plane Event plane resolution Measurement of v2 • Calculate the 2nd order coefficient of Fourier expansion of particle azimuthal distribution relative to the reaction plane • The reaction plane is unknown. • Estimate the reaction plane from particle azimuthal anisotropy: • Yn = Event plane (nth harmonic) = estimator of the unknown reaction plane • Calculate particle distribution relative to the event plane • Correct for event plane resolution • Resolution contains the unknown YRP • Can be extracted from sub-events Alice Physics Week, December 5-9 2005
Motivation and method • GOAL: Evaluate the statistical error bars for measurements of v2 for D± mesons decaying in Kpp • v2 vs. centrality (pT integrated) • v2 vs. pT in different centrality bins • TOOL: fast simulation (ROOT + 3 classes + 1 macro) • Assume to have only signal • Generate ND±(Db, DpT) events with 1 D± per event • For each event • Generate a random reaction plane (fixed YRP=0) • Get an event plane (with correct event plane resolution) • Generate the D+ azimuthal angle (φD) according to the probability distribution p(φ) 1 + 2v2 cos [2(φ-YRP)] • Smear φDwith the experimental resolution on D± azimuthal angle • Calculate v′2(D+), event plane resolution and v2(D+) Alice Physics Week, December 5-9 2005
PPR chap 6.4 Our simulation Event plane simulation • Simple generation of particle azimuthal angles () according to a probability distribution • Faster than complete AliRoot generation and reconstruction • Results compatible with the ones in PPR chapter 6.4 Alice Physics Week, December 5-9 2005
Ntrack = number of p, K and p in AliESDs of Hijing events with b = <b> Hadron integrated v2 input values (chosen ≈ 2 RHIC v2) Event plane resolution scenario • Event plane resolution depends on v2 and multiplicity Alice Physics Week, December 5-9 2005
D± azimuthal angle resolution • From 63364 recontructed D+ • 200 events made of 9100 D+ generated with PYTHIA in -2<y<2 • Average resolution = 8 mrad = 0.47 degrees Alice Physics Week, December 5-9 2005
D± statistics • Nevents for 2·107 MB triggers • Ncc = number of c-cbar pairs • Includes shadowing • Shadowing centrality dependence from Emelyakov et al., PRC 61, 044904 • D± yield calculated from Ncc • Fraction ND±/Ncc (≈0.38) from tab. 6.7 in chapt. 6.5 of PPR • Geometrical acceptance and reconstruction efficiency • Extracted from 1 event with 20000 D± in full phase space • B. R. D± Kpp = 9.2 % • Selection efficiency • No final analysis yet • Assume e=1.5% (same as D0) Alice Physics Week, December 5-9 2005
Results: v2 vs. centrality 2·107 MB events • Error bars quite large • Would be larger in a scenario with worse event plane resolution • May prevent to draw conclusions in case of small anisotropy of D mesons Alice Physics Week, December 5-9 2005
Results: v2 vs. pT 2·107 MB events Alice Physics Week, December 5-9 2005
Combinatorial background • Huge number (≈1010) of combinatorial Kpp triplets in a central event • ≈108 triplets in invariant mass range 1.84<M<1.90 GeV/c2 (D± peak ± 3s ) • Final selection cuts not yet ready • Signal almost free from background only for pT>5-6 GeV/c • Need to separate signal from background in v2 calculation • FIRST IDEA: sample candidate Kpp triplets in bins of azimuthal angle relative to the event plane (Dφ= φ-Y2) • Build invariant mass spectra in bins of Dφ and centrality / pT Alice Physics Week, December 5-9 2005
Analysis in bins of Dφ (I) • Extract number of D± in 90º “cones”: • in-plane (-45<Dφ<45 U 135<Dφ<225) • out-of-plane (45<Dφ<135 U 225<Dφ<315) Alice Physics Week, December 5-9 2005
0<b<3 3<b<6 6<b<9 v2 values and error bars compatible with the ones obtained from <cos(2Dφ)> Analysis in bins of Dφ (II) • Fit number of D± vs. Dφ with A[1 + 2v2cos(2Dφ) ] Alice Physics Week, December 5-9 2005
Other ideas for background Different analysis methods to provide: • Cross checks • Evaluation of systematics • Apply the analysis method devised for Ls by Borghini and Ollitrault [ PRC 70 (2004) 064905 ] • To be extended from pairs (2 decay products) to triplets (3 decay products) • Extract the cos[2(φ-YRP)] distribution of combinatorial Kpp triplets from: • Invariant mass side-bands • Different sign combinations (e.g. K+p+p+ and K-p-p-) Alice Physics Week, December 5-9 2005
Conclusions • Large stat. errors on v2 of D± → Kpp in 2·107 MB events • How to increase the statistics? • Sum D0→Kp and D±→Kpp • Number of events roughly 2 → error bars on v2 roughly /√2 • Sufficient for v2 vs. centrality (pT integrated) • Semi-peripheral trigger • v2 vs. pT that would be obtained from 2·107 semi-peripheral events ( 6<b<9 ) Alice Physics Week, December 5-9 2005
BACKUP SLIDES Alice Physics Week, December 5-9 2005
Worse resolution scenario • Low multiplicity and low v2 Large contribution to error bar on v2 from event plane resolution Alice Physics Week, December 5-9 2005
Glauber calculations (I) • N-N c.s.: • scc from HVQMNR • + shadowing • Pb Woods-Saxon Alice Physics Week, December 5-9 2005
Glauber calculations (II) • N-N c.s.: • scc from HVQMNR • + shadowing • Pb Woods-Saxon Alice Physics Week, December 5-9 2005
Shadowing parametrization • Eskola et al., Eur. Phys. J C 9 (1999) 61. • Emel’yanov et al., Phys. Rev. C 61 (2000) 044904. Rg(x~10-4,Q2=5 GeV2) = 65% from EKS98 Alice Physics Week, December 5-9 2005
More details on v2 error bars High resolution scenario Low resolution scenario Alice Physics Week, December 5-9 2005