V2 measurement with CMS Tracker

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CMS Analysis Note 2007/004
Azimuthal Anisotropy in Heavy Ions Collisions
with CMS Tracker
Status of Note
G. Eyyubova , V.L. Korotkikh, I.P. Lokhtin,
S.V.Petrushanko, L.I. Sarycheva, A.M. Snigirev,
Moscow State University D. Krofcheck (University
of Auckland)
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• The first approval step the Note was reported on
  CMS Physics Days, March 29, 2007
• http//indico.cern.ch/conferenceDisplay.py?confId
  14022
• It was not approved, the referees still have some
  remarks.
• The version 4 of Note AN-2007/004
• https//twiki.cern.ch/twiki/bin/view/CMS/HiDocumen
  tsInProgress
• http//lav01.sinp.msu.ru/vlk/v2_tracker/Note100k_
  2.pdf

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• Committee Requests for approval of
• CMS AN 2007/004
• General Remarks and author responds
• The Analysis should be based on the full
  available statistics.
• ? It is done, we used MIT base, 100K events
• All measured quantities should be quoted with
  statistical errors.
• ? All values are quoted with statistical errors
• A detailed discussion of systematic errors of the
  measurement is required.
• ? Discussion on the level of factors R and C is
  presented . We need a new sim and rec database
  with different input generator parameters. It
  will be done in future.
• The tracking efficiency and fake rates for the
  track sample need to be shown and discussed.
• ? It is done by the same way as C. Roland in
  14, but at small bin size for low pT.
• Properties of the Generator input need to be
  discussed and documented very clearly.
• ? Detail properties of the generator are
  presented on Fig. 5-9
• The note addresses the observed v2 based on
  SimTracks in the tracker acceptance compared to
  reconstructed tracks. No attempt is made to
  extract the true v2. I.e no corrections for event
  plane resolutions, non-flow effects etc are
  applied. This needs to be stated more clearly
• ? It is done.

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The aim elliptic flow with Tracker
The statistic was increased. Now, 100K events
Our analysis is based on CMS HI Group MIT
data-base (HYDJET 1.0, jet quenching off) ORCA
8_13_3 PbPb , b9fm pT gt0.9 GeV/c Track
selection nhitgt12, clgt0.01
Simulated ? Reconstructed

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Efficiency and fake rate for the sample, PbPb,
b9 fm
100K events
The global track finding efficiency in
nucleus-nucleus collisions is 80 . A falling
efficiency at pTlt1.5 GeV gives some problems in
rec events and need study in future.
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Generator input
The impact parameter b dependence of v2
for charged particles in PbPb collisions with
HYDJET.
The charged particle multiplicity at central
rapidity region as a function of impact
parameter b in PbPb collisions with HYDJET.
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Generator input
Event plane resolution ? is mainly sensitive to
two factor the strength of elliptic flow and
the event multiplicity.
?R reaction plane angle ?2 event plane angle
?? ?2 ?R
Event plane resolution ?(??) as a function of b
(impact parameter) in PbPb events with HYDJET.
Event plane resolution ?(??) as a function
of v2 in PbPb events with HYDJET.
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Generator input
Variance s(v2) for charged particles as a
function of impact parameter b in PbPb
collisions with HYDJET. s(v2) is defined as a
width of Gaussian distribution of v2 values over
events.
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Calculation of event plane angle
The event plane angle, ?n, can be determined
from the measured n-th harmonics via the
standard method (19S. A. Voloshin and Y.
Zhang, Z. Phys. C 70, 665 (1996). 20A. M.
Poskanzer and S. A. Voloshin, Phys. Rev. C 58,
1671 (1998).)
(3)
n 2 ?
It is generally true that better accuracy for the
determination of vn is achieved by using the
event plane angle determined from the same
harmonic
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?2 determination, PbPb b 9fm
The distribution of ?? ?2 ?R can be
analytically investigated
sim
rec
?? ?2 ?R

• Solid line denotes the fit by exact formula,
  dashed line is 1s Gaussian fit.
• ?sim 0.283 0.004 , ?rec 0.327 0.004
  from Gaussian fit. The difference between
  simulated and reconstructed angle resolution is
  15.
• The parameter ? from fit by exact formula is
  connected with reaction plane correction factor R
  . We calculate R1sim according formulae in 20
• ?sim 1.4850.005 ? R1sim0.7300.002.
  (compare below R2sim ltCos2(?2-?R)gt )

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The reaction plane correction factor R
Standard technique is
R ltCos2(?2-?R)gt and with no unflow corrections
v2truev2obs/R

• To understand uncertainties biased to v2obs one
  can present it in the following way

The correction factor R2sim ltcos2(?2-?R)gt is
calculated and it is equal to R2sim
0.7310.002 (in good agreement with
R1sim0.7300.002) If we take v2obs0.1067
(Method 1) and v2truev2gen0.0851, then
C0.044 The additional term C is 41 with
respect to v2obs in the simulated events. R and C
content large unflow and autocorrelation
corrections
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v2 calculation
We use three methods to calculate v2
(1) Method 1
?2 - event plane angle.
(2) Method 2
v2fit from a fit of dN/df distribution in each
event by dN/d? N0/2? 12
v2fitcos2(? - ?R ) with three parameters N0 ,
v2fit, ?R .
(3) Method 3
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v2 calculated with event plane angle
sim
rec
Table 1
results
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Differential pT and ? dependences of v2
- reconstructed ? - simulated values
Our estimate of overall systematic error, 8, is
based on the 8 difference between simulated and
reconstructed integral v2obs (See Table 1).
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Summary

• The azimuthal flow was calculated by three
  methods. The results of V2 calculation are close.
• The analysis, based on a full CMS detector
  simulation of HYDJET PbPb events with b9 fm,
  shows that the reaction plane resolution achieved
  by using the CMS Tracker is only by 15 worse
  than the resolution obtained on the generator
  level.
• The pT and ? dependences of v2 can be
  reconstructed using the CMS Tracker with high
  accuracy. The difference between v2 , calculated
  with sim and rec events, is not more then 8 in
  overall.
• Some of the areas for future studies
• The detailed analysis of systematic biases to the
  measure v2true
• a) use sub-event method to exclude
  autocorrelation,
• b) use without and with unflow correlations
  (HYDRO and HYDJET).
• 2) To compare 4-particle and 2-particle cumulant
  methods.
• 3) To calculate non-second coefficients of
  Fourier expansion.
• 4) To measure elliptic flow at low pT (down to a
  few hundred MeV/c) and calculate
• v2 of identified protons, pions and kaons

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Author request

• Welcome CMS HI collaborator comments
• Updated Note needs to be present to referee for
  new approving

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Acknowledgments

• The authors thank David dEnterria, Olga
  Kodolova, Christof Roland, Stephen Sanders, Irina
  Vardanyan, Gabor Veres, Constantin Loizides,
  Wolfgang Adam, Paolo Bartalini and Boleslaw
  Wyslouch
• for fruitful discussions.

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Backside slides
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Importance The azimuthal anisotropy of charged
particles in heavy ion collisions is a very
sensitive signature of quark-gluon plasma
evolution at early stages.
The elliptic flow was measured at low and high
energies. A ratio of elliptic flow to spatial
eccentricity as a function of the rapidity
density normalized by the reaction overlap area
achieves the value of 0.2 at RHIC energies, which
is consistent with the hydrodynamical limit.
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• The HYDJET Generator
• Developed within the CMS HI Group
• (I.P. Lokhtin and A.M. Snigirev, Eur. Phys. J.
  C16 527 )
• Soft particle production using Hydrodynamic
  model,
• includes bulk properties, flow etc
• Jets produced using PYQUEN

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HYDRO HYDJET
I. Lokhtin http//cern.ch/lokhtin/hydro/hydjet.htm
l
All region of ?
All region of pT
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In real data one can use for instance sub-event
technique to determine a correction factor.
Having sub-events A, B, C in three different
rapidity windows, the reaction plane correction
factor RA for sub-event A is found as
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Elliptic coefficient v2

• The true reaction plane angle ?0 is not known.
• It must be evaluated in each event. The
  estimation of the reaction plane angle
  event plane angle.
• v2true v2obs

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• ????????, ???????? ???????? ??? ???????? ? ??????
  ??? an unnatural trend to decrease around 0.9
  GeV (?? ?????????? ?????)
• ?? ?????? Wolfgang
• Dear Gyulnara,
• it's true that using the same cut for simulated
  and reconstruc-ted tracks is not stable.
  Reconstructed tracks will migrate (due to
  standard pt resolution some effect of fake hits
  etc.). Since you have a strongly falling spectrum
  it is indeed probable that you have a net
  increase of reconst-ructed tracks close to the
  pt-limit.
• Best regards,
• Wolfgang

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