NA49 and NA61 Collaboration Meeting CERN, 14 October 2010 Azimuthal angle fluctuations Katarzyna Grebieszkow NA49 and NA61 Collaboration Meeting CERN, 14 October 2010

Motivation: f measure: Search for plasma instabilities (Mrówczyński, Phys. Lett. B314, 118 (1993)) Critical point and onset of deconfinement Flow fluctuations (Mrówczyński, Shuryak, Acta Phys. Polon. B34, 4241 (2003), Miller, Snellings arXiv:nucl-ex/0312008 ) f measure: Measures azimuthal fluctuations on event-by-event basis Strongly intensive variable(!) Used by NA49 for pT and q fluctuations single−particle variable 𝑧 φ =φ− φ ˉ φ ˉ − average over single−particle inclusive distribution event variable 𝑍 φ = 𝑖=1 𝑁 φ 𝑖 − φ ˉ where summation runs over particles in a given event Finally Φ φ = 𝑍 φ 2 𝑁 − 𝑧 φ 2 ˉ ... − averaging over events if A+A is a superposition of independent N+N  f (A+A) = f (N+N) For a system of independently emitted particles (no inter-particle correlations)  f = 0

Background effects: Note: f measures “magnitude” of fluctuations but there is no information about their origin. Apart from the most interesting effects (see previous page) we catch: Resonance decays Momentum conservation Flow (Di-)jets Quantum Statistics These various physics effects were studied in: 1. S. Mrówczyński, Acta Phys. Polon. B31, 2065 (2000) 2. T. Cetner and K. Grebieszkow, Hot Quarks 2010 proceedings, arXiv:1008.3412 3. T. Cetner, K. Grebieszkow, and S. Mrówczyński – paper about Ff properties; nearly submitted Two examples of simulations

NA49 first results NA49 azimuthal acceptance is limited Detector is left-right symmetric Acceptance for positive and negative particles is the same, provided the azimuthal angle for one charge is reflected => to allow quantitative comparison of Ff for positively and negatively charged particles we rotate particles of one charge

BEFORE: Example for STD+ How to redefine azimuthal angle Warning: when applying such a redefinition we will be able to show separately neg. and pos. charged particles but a combination “all charged” is completely without sense AFTER: For a complete list of event and track cuts see PRC70, 034902 (2004) and PRC79, 044904 (2009). In principle, forward rapidity region was used (4.0 < yp < 5.5 for system size dependence and 1.1 < y*p < 2.6 for energy scan; for “full” rapidity range f was not stable )

Raw data, not corrected for TTR Pomysl: policzyc te poprawki dla 29 I 31 podprobek (nie wiem czy jest sens bo wartosci zostana a tylko moga sie zmienic bledy) I pewnie uznac ze poprawki sa male czyli < -5 MeV I dla sys size I dla energii wiec nic nie poprawic tylko pokazac surowe dane I zrobic blad systematyczny 5 MeV od punktu w gore (do dolu nie) Uwaga: roznice w wartosciach dltaPhi dla 158 GeV z sys size I energy scan; sprawdzic czy to ma sens, popatrzec na krotnosci, etc. czy dobrze sie wszystko policzylo Statistics increased since Hot Quarks 2010 Now, we have maximal possible statistics for both system size dependence and energy scan

TTR corrections -A sqrt(N)+B TTR additive correction = Ff (after Geant + reconstruction) – Ff (mixed) Important: verified that for mixed events Ff is consistent with zero! -A sqrt(N)+B Pomysl: policzyc te poprawki dla 29 I 31 podprobek (nie wiem czy jest sens bo wartosci zostana a tylko moga sie zmienic bledy) I pewnie uznac ze poprawki sa male czyli < -5 MeV I dla sys size I dla energii wiec nic nie poprawic tylko pokazac surowe dane I zrobic blad systematyczny 5 MeV od punktu w gore (do dolu nie) Uwaga: roznice w wartosciach dltaPhi dla 158 GeV z sys size I energy scan; sprawdzic czy to ma sens, popatrzec na krotnosci, etc. czy dobrze sie wszystko policzylo Formula -A sqrt(N)+B better describes data than -A sqrt(N). But for (only!) p+p data TTR correction (resulting from the fit) is slightly above zero mradians (all corrections should be negative!). Therefore we keep raw Ff value for p+p data and increase systematic error instead.

Final results (Hot Quarks 2010, CPOD 2010) Pomysl: policzyc te poprawki dla 29 I 31 podprobek (nie wiem czy jest sens bo wartosci zostana a tylko moga sie zmienic bledy) I pewnie uznac ze poprawki sa male czyli < -5 MeV I dla sys size I dla energii wiec nic nie poprawic tylko pokazac surowe dane I zrobic blad systematyczny 5 MeV od punktu w gore (do dolu nie) Uwaga: roznice w wartosciach dltaPhi dla 158 GeV z sys size I energy scan; sprawdzic czy to ma sens, popatrzec na krotnosci, etc. czy dobrze sie wszystko policzylo Ff > 0, maximum for peripheral Pb+Pb; qualitatively similar structure for pT and N fluctuations in NA49; effect still not understood Ff (negative) > 0; different than in UrQMD (1.3) Ff (positive) consistent with zero

What can be done next: … only (semi-)central samples: 1. Systematic errors of Ff (varying event and track cuts) 2. Comparison with models (for system size dependence)

Impact parameter distribution UrQMD 3.3, minimum bias Pb+Pb, top SPS energy (158A GeV) Events with No._of_collisions=0 rejected All generated events sample used for analysis Only events with No._of_collisions=0 (peripheral mainly) na gorze po prawej - tylko eventy z a1!=0 na dole po lewej – eventy odrzucone (a1==0) na dole po prawej – eventy po wszystkich cieciach (a1. a3, npart) a1 – liczba zderzeń w evencie a3 – liczba zderzeń nieelastycznych w evencie trzeba stosować cięcia a1!=0 && a3!=0 && npart!=416 (2A) Rejected events with No._of_collisions=0 and No._of_inelastic_coll.=0 and No._of_particles=2A (416) Fig. Bartosz Maksiak

Impact parameter 1 2 3 4 5 6 Fig. Bartosz Maksiak 1 2 3 4 5 6 Used only events with No._of_collisions ≠ 0 and No._of_inelastic_coll. ≠ 0 and No._of_final_state particles ≠ 2A (here 416) Fig. Bartosz Maksiak

Not uniform !!? Inclusive azimuthal angle distribution in UrQMD 3.3 Minimum bias Pb+Pb collisions at 158A GeV beam energy Not uniform !!? Centrality 1 (5% most central) Centrality 2 Centrality 2 Centrality 3 Centrality 4 Centrality 5 Centrality 6 (peripheral) Fig. Bartosz Maksiak

Inclusive azimuthal angle distribution in UrQMD 3 Inclusive azimuthal angle distribution in UrQMD 3.3 (separately for all charged, negatively charged and positively charged) Centrality 3; Pb+Pb collisions at 158A GeV beam energy all neg. pos. Fig. Bartosz Maksiak

Shape of azimuthal angle distribution confirmed by 4 people in independent UrQMD simulations Pb+Pb NA49 Centrality 2 top SPS Au+Au STAR b > 5 fm close to top SPS energy Pb+Pb NA49 20% most central top SPS

1. Redefinition of azimuthal angle for neg 1. Redefinition of azimuthal angle for neg. charged used (angle3, see also back-up slides), although the angle distribution was complete 2. All produced charged hadrons Compare it with energy scan in UrQMD

Energy scan (7.2% most central Pb+Pb), UrQMD 1.3 Hot Quarks 2010 Warning: in this simulation we did not know that azimuthal angle was not perfectly flat so “NA49 acceptance” (curves in pT versus angle) was normally used. Anyhow, as this is a central sample the azimuthal angle is not distorted too much...

Back-up slides

forward rapidity Original definition of azimuthal angle: Events and track cuts: vertex cuts -> included (vertex_x,y,z positions, ntf/nto cut, etc.) track.iflag&0xFF000000 ==0, nmp>30, np/nmp > 0.5, zfirst< 200, |bx|<2.0 |by|<1.0 0.005 < pT < 1.5 GeV/c forward rapidity (4.0 < yp < 5.5 for system size dependence and 1.1 < y*p < 2.6 for energy scan) y*p < y*beam – 0.5 (additional cut for the energy scan) azimuthal angle restrictions – the same as used for pT fluctuations analysis: common (very narrow) for energy scan and wider for system size dependence at 158A GeV (see both pT fluctuations papers or plots at the end of back-ups) Original definition of azimuthal angle: angle=(atan2(track->GetPy(), track->GetPx())); //in radians (-p, p)

angle STD+ positive STD+ negative STD+ negative Note: I do not use wrong side tracks at all STD+ positive STD+ negative STD+ negative -3.14 radians 3.14 radians -3.14 radians 3.14 radians angle STD- negative STD- positive STD- positive -3.14 radians 3.14 radians -3.14 radians 3.14 radians

Original definition of azimuthal angle: angle=(atan2(track->GetPy(), track->GetPx())); //in radians (-p, p) But one can also use redefined angle3 instead of angle: double angle3=(atan2(track->GetPy(), track->GetPx())); if(track->GetCharge()<0) //STD+ (for STD would be >0) { if(angle3<0) angle3=angle3+2*TMath::Pi(); angle3=angle3-TMath::Pi(); } The result: new angle3 for all particles (both negative and positive) and both STD+ and STD- has values concentrated around zero radians 2nd step Shift of whole histogram 1st step Shift of one part only original STD+ negative STD+ negative STD+ negative STD+ negative -3.14 radians 3.14 radians -3.14 radians 3.14 radians -3.14 radians 3.14 radians

(all particles for both STD+ and STD- are around zero)  angle3 (all particles for both STD+ and STD- are around zero) all But we will have completely different Ff values if we use angle4 instead of angle3 -3.14 radians 3.14 radians  angle4 (all particles for both STD+ and STD- are around +- p) 1. Mean inclusive angle (bar_f) is close to 0 radians for all cases 2. Distribution of M(f) (event average) is wider when using angle4 (particles around +- p) when compared to angle3 => higher e-by-e fluctuations 3. All the problems appear because our azimuthal acceptance if not flat all all

40A GeV in energy scan 158A GeV in sys. size dep. 00C production (STD- normal intensity) 7.2% most central Pb+Pb: Ff (all, negative, positive) [mradians]: -2.2 ± 1.1 <N>=44.2 5.2 ± 0.9 <N>=16.9 -6.7 ± 0.8 <N>=27.3 ↕ 00W production (STD+ normal intensity) -2.5 ± 0.7 <N>=44.4 3.7 ± 1.0 <N>=17.2 -6.5 ± 0.6 <N>=27.1 Acceptance (pT, angle, rapidity) as in our both PRCs; not corrected for TTR Acceptance (pT, angle, rapidity) as in our both PRCs; not corrected for TTR 158A GeV in sys. size dep. 00O production (STD- normal intensity) 5% most central Pb+Pb: Ff (all, negative, positive) [mradians]: -82.9 ± 3.1 <N>=237.0 -42.4 ± 3.7 <N>=110.6 -52.0 ± 2.8 <N>=126.4 ↕ 00B production (STD+ normal intensity) -83.6 ± 2.7 <N>=238.5 -42.7 ± 3.1 <N>=111.8 -52.5 ± 2.0 <N>=126.7 Ff is THE SAME !! for STD+ and STD- if we use angle3

40A GeV in energy scan 158A GeV in sys. size dep. 00C production (STD- normal intensity) 7.2% most central Pb+Pb: Ff (all, negative, positive) [mradians]: -15.8 ± 4.7 <N>=44.2 15.5 ± 4.4 <N>=16.9 -36.5 ± 4.4 <N>=27.3 ↕ 00W production (STD+ normal intensity) -18.2 ± 2.8 <N>=44.4 11.5 ± 3.2 <N>=17.2 -37.3 ± 2.3 <N>=27.1 Acceptance (pT, angle, rapidity) as in our both PRCs; not corrected for TTR Acceptance (pT, angle, rapidity) as in our both PRCs; not corrected for TTR 158A GeV in sys. size dep. 00O production (STD- normal intensity) 5% most central Pb+Pb: Ff (all, negative, positive) [mradians]: -122.0 ± 3.0 <N>=237.0 -68.1 ± 3.1 <N>=110.6 -103.5 ± 2.3 <N>=126.4 ↕ 00B production (STD+ normal intensity) -113.3 ± 3.0 <N>=238.5 -54.9 ± 2.8 <N>=111.8 -105.2 ± 4.0 <N>=126.7 Ff is THE SAME !! for STD+ and STD- if we use angle4

STD+ Regions of good acceptance in NA49 redefinition Pos. charged Pb+Pb 158A GeV/c Forward rapidity (4.0 < yp < 5.5) redefinition STD+ Pos. charged Neg. charged Redefinition = something similar to defining angle3 but instead of +- p we use +- 180 degrees (due to historical reason; good acceptance regions were already defined in some of our fluctuations papers) See acceptance curves used in analysis:

System size dependence acceptance Both pos. and neg. charged included in plots but azimuthal angle of neg. (for STD+!!) redefined (see previous page) See our PRC70, 034902 (2004) and PRC79, 044904 (2009) for detailed parametrizations of acceptance regions (particles inside black lines) in each rapidity bin Energy scan acceptance; here for 2.0 < y*p < 2.2