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

Alice Physics Week, December 5-9 2005 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 Elliptic flow x y YRP Alice Physics Week, December 5-9 2005

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

Alice Physics Week, December 5-9 2005 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 (n th 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 Unknown reaction plane Event plane resolution Alice Physics Week, December 5-9 2005

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 φD with the experimental resolution on D± azimuthal angle Calculate v′2(D+), event plane resolution and v2(D+) Alice Physics Week, December 5-9 2005

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 Our simulation PPR chap 6.4 Alice Physics Week, December 5-9 2005

Event plane resolution scenario Event plane resolution depends on v2 and multiplicity Ntrack = number of p, K and p in AliESDs of Hijing events with b = <b> bmin-bmax <b> Ntrack v2 0-3 1.9 7000 0.02 3-6 4.7 5400 0.04 6-9 7.6 3200 0.06 9-12 10.6 1300 0.08 12-18 14.1 100 0.10 Hadron integrated v2 input values (chosen ≈ 2  RHIC v2) 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

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) bmin-bmax (fm) s (%) Nevents (106) Ncc / ev. D± yield/ev. 0-3 3.6 0.72 118 45.8 3-6 11 2.2 82 31.8 6-9 18 42 16.3 9-12 25.4 5.1 12.5 4.85 12-18 8.4 1.2 0.47 Alice Physics Week, December 5-9 2005

Results: v2 vs. centrality 2·107 MB events bmin-bmax N(D±)selected s(v2) 0-3 1070 0.024 3-6 2270 0.015 6-9 1900 0.016 9-12 800 0.026 12-18 125 0.09 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

Alice Physics Week, December 5-9 2005 Results: v2 vs. pT 2·107 MB events pT limits N(D±)sel s(v2) 0-0.5 140 0.06 0.5-1 280 0.04 1-1.5 390 1.5-2 360 2-3 535 0.03 3-4 250 0.05 4-8 265 8-15 50 0.11 pT limits N(D±)sel s(v2) 0-0.5 120 0.06 0.5-1 230 0.05 1-1.5 330 0.04 1.5-2 300 2-3 450 0.03 3-4 210 4-8 220 8-15 40 0.11 pT limits N(D±)sel s(v2) 0-0.5 50 0.10 0.5-1 100 0.07 1-1.5 140 0.06 1.5-2 125 2-3 190 0.05 3-4 90 4-8 95 8-15 20 0.15 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

Analysis in bins of Dφ (II) Fit number of D± vs. Dφ with A[1 + 2v2cos(2Dφ) ] 0<b<3 3<b<6 6<b<9 v2 values and error bars compatible with the ones obtained from <cos(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

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 ) pT limits N(D±)sel s(v2) 0-0.5 645 0.03 0.5-1 1290 0.02 1-1.5 1800 0.017 1.5-2 1650 0.018 2-3 2470 0.015 3-4 1160 4-8 1225 8-15 220 0.05 Alice Physics Week, December 5-9 2005

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 Rg(x~10-4,Q2=5 GeV2) = 65% from EKS98 Eskola et al., Eur. Phys. J C 9 (1999) 61. Emel’yanov et al., Phys. Rev. C 61 (2000) 044904. Alice Physics Week, December 5-9 2005

More details on v2 error bars High resolution scenario bmin-bmax N(D±)selected s(v2’) RCF s(RCF) s(v2) (from v2’ + from RCF) 0-3 1070 0.0213 0.896 0.006 0.024 (= √ (0.0242+ 0.00022) 3-6 2270 0.0148 0.9708 0.0009 0.015 (= √ (0.0152+ 0.000012) 6-9 1900 0.0159 0.9771 0.0007 0.016 (= √ (0.0162+ 0.000032) 9-12 800 0.025 0.971 0.001 0.026 (= √ (0.0262+ 0.000062) 12-18 125 0.061 0.65 0.06 0.09 (= √ (0.092+ 0.0022) Low resolution scenario bmin-bmax N(D±)selected s(v2’) RCF s(RCF) s(v2) (from v2’ + from RCF) 0-3 1070 0.022 0.76 0.014 0.029 (= √ (0.0292+ 0.00022) 3-6 2270 0.015 0.934 0.002 0.016 (= √ (0.0162+ 0.000072) 6-9 1900 0.016 0.953 0.017 (= √ (0.0172+ 0.000062) 9-12 800 0.025 0.004 0.027 (= √ (0.0272+ 0.00022) 12-18 125 0.061 0.57 0.08 0.11 (= √ (0.1072+ 0.022) Alice Physics Week, December 5-9 2005