1. 1 Azimuthal angle fluctuations (draft of NA49 publication) NA61/SHINE and NA49 Software/Analysis meeting February 15 th – 18 th, WUT Katarzyna Grebieszkow

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3. 3 I. Introduction and Motivation II.  measure of fluctuations III. Experimental setup IV. Data selection and analysis A) Data sets B) Event and particle selection C) Corrections and error estimate V. Results and discussion A) Results B) Comparison with the UrQMD model C) Effect of flow VI. Summary and outlook “Event-by-event average azimuthal angle fluctuations in nucleus+nucleus collisions at the CERN Super Proton Synchrotron”

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6. NA49 acceptance 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   for positively and negatively charged particles we rotate particles of one charge See our PRC70, 034902 (2004) and PRC79, 044904 (2009) for detailed parametrizations of acceptance regions (particles inside black lines) in each rapidity bin 2.0 <y *  <2.2 System size dependence Energy scan

7. 7 y * p < y * beam – 0.5 (additional cut for the energy scan)

8. 8 Raw data, not corrected for TTR

9. 9 TTR corrections TTR additive correction =   (after Geant + reconstruction) –   (mixed) Important: verified that for mixed events   is consistent with zero! 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   value for p+p data and increase statistical error instead. -A sqrt(N)+B

10. 10 Data corrected for TTR    > 0, maximum for peripheral Pb+Pb; qualitatively similar structure for p T and N fluctuations in NA49    (negative) > 0; different than in UrQMD (1.3)    (positive) consistent with zero

11. 11 negatively charged positively charged all values in miliradians ntf – number of tracks used to fit main vertex nto – number of tracks registered in TPCs np – number of measured points for a track nmp – maximal number of points (from geometry of the track) Components of systematic errors Values of several cuts were varied in reasonable ranges. The “partial” systematic errors was taken as a half of difference between the lowest and the highest value. Final error is a maximum from partial error (measurements are correlated)

12. 12 negatively charged positively charged all values in miliradians for centrality bins 5, 4, and 2 – linear fit taken from bins 6, 3, and 1 ntf – number of tracks used to fit main vertex nto – number of tracks registered in TPCs np – number of measured points for a track nmp – maximal number of points (from geometry of the track)

13. 13 Data corrected for TTR systematic errors shown

14. 14 Comparison with UrQMD

15. 15 NA49 Collab. PRC68, 034903 (2003) Pion elliptic flow v 2 (upper, left, green) All 6 centralities available But v 2 data obtained at midrapidity; our   was measured at forward rapidity 1.1 < y *   < 2.6 T. Cetner, KG, S. Mrówczyński, arXiv:1011.1631 (accepted by PRC) The effect of flow (here v 2 only) Poissonian multiplicity distribution assumed (formula below); mean multiplicities (pos. and neg.) taken from this analysis Non-uniform azimuthal acceptance of NA49 not taken into account Effect of flow (v 2 )

16. 16 NA49 Collab. PRC68, 034903 (2003) Pion elliptic flow v 2 (upper, left) Only 3 centralities available v 2 data obtained at different rapidities; here values read out for y *   = 1.85 T. Cetner, KG, S. Mrówczyński, arXiv:1011.1631 (accepted by PRC) The effect of flow (here v 2 only) Poissonian multiplicity distribution assumed; mean multiplicities (pos. and neg.) taken from this analysis (averaged for bins 1-2, 3-4, and 5-6) Effect of flow (v 2 )

17. 17 NA49 Collab. PRC68, 034903 (2003) Pion elliptic flow v 2 (Fig. 6, upper, left) and pion directed flow v 1 (Fig. 12, upper, left) Only 3 centralities available v 2 and v 1 data obtained at different rapidities; here values read out for y *   = 1.85 T. Cetner, KG, S. Mrówczyński, arXiv:1011.1631 (accepted by PRC) The effect of flow (v 2 and v 1 ) Poissonian multiplicity distribution assumed; mean multiplicities (pos. and neg.) taken from this analysis (averaged for bins 1-2, 3-4, and 5-6) Effect of flow (v 2 & v 1 )

18. 18 Fast generator of v 1 and v 2 v 1 and v 2 values taken from PRC68, 034903 (2003) at forward-rapidity mean multiplicities from this analysis exponential m T distribution with T slope = inclusive average p T taken from PRC70, 034902 (2004) Gaussian shape of rapidity with y cms =2.9 and  y = 1.7 NA49 acceptance (PRC70, 034902 (2004)) taken into account (solid curves only) but multiplicities reproduced Conclusion: the magnitude of   reproduced by the effect of v 1 and v 2

19. 19 Back-up slides

20. 20 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 < p T < 1.5 GeV/c forward rapidity (4.0 < y  < 5.5 for system size dependence and 1.1 < y *  < 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 p T fluctuations analysis: common (very narrow) for energy scan and wider for system size dependence at 158A GeV (see both p T fluctuations papers) Original definition of azimuthal angle: angle=(atan2(track->GetPy(), track->GetPx())); //in radians (- ,  )

21. 21 Example for STD+ How to redefine azimuthal angle BEFORE: 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 < y  < 5.5 for system size dependence and 1.1 < y *  < 2.6 for energy scan ; for “full” rapidity range   was not stable ) Warning: when applying such a redefinition we will be able to show separately neg. and pos. charged particles but a combination “all charged” cannot be shown Note: I do not use wrong side tracks at all

22. 22 Original definition of azimuthal angle: angle=(atan2(track->GetPy(), track->GetPx())); //in radians (- ,  ) But one can also use redefined angle3 instead of angle: double angle3=(atan2(track->GetPy(), track->GetPx())); if(track->GetCharge() 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 STD+ negative -3.14 radians 3.14 radians STD+ negative STD+ negative -3.14 radians 3.14 radians STD+ negative -3.14 radians 3.14 radians origina l 1 st step Shift of one part only 2 nd step Shift of whole histogram

23. 23 Very narrow bins in N part proj but N part target not measured in NA49. Significant increase of  for peripheral Pb+Pb; a large effect can still originate from fluctuations of the number of target participants (see V.P. Konchakovski et al., Phys. Rev C73, 034902 (2006) ) Average p T and multiplicity fluctuations for central interactions as well as for different centralities of minimum bias Pb+Pb collisions at 158A GeV maximum p T and N of fluctuations in peripheral Pb+Pb data

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