Transcript Combinatorial Background

Combinatorial Background
• PHENIX
– EWG Electron Working Group (A.Toia)
September 6, 2005
1
Data Selection
•
•
•
•
•
ZVertex ±30 cm
pT cuts 150 MeV/c – 20 GeV/c
Matching
Dch quality
RICH ring quality
September 6, 2005
2
“systematics are of much bigger
concern than statistics“
• Out of ~ 9000 files 3000 files have been
cut away, due to
– Wrong field
– Bad quality from certain detectors
– Momentum average
– Readout trouble
• Event selection:
– Minimum bias as only criterion
September 6, 2005
3
Cuts
• Single Cuts
– RICH ring properties
– EMC matching
– Energy-Momentum matching
– pT cuts
• Pair Cuts, battling
– “geometrical ghosts“ (no sharing of detector
hits)
– “optical ghosts“ (e.g. RICH ring sharing)
September 6, 2005
4
Background Calculation
• A priori assumption:
– Positive and negative particles have unequal
acceptances
– To be proved (cornerstone):
• “despite initial thoughts to the contrary, we shall
prove, even in the presence of wildly differing
acceptances, that the
integral number of like-sign measured pairs
can be directly related to the
integral of the combinatorial background“
September 6, 2005
5
Like Sign Method (I)
• Starting from a single event generated into 4p:
– Np positrons, Ne electrons, Possibility to be measured: ep/e
– Probability to measure np/e out of Np/e (Binomial distribution)
B n p e , e p e  
Np e
n p e! N p e  n p e
 e  1  e 
np
p e
N p e n p
e
e
p e
n p e  e p e N p e , n p e   e p e 1  n p e N p e  e p2 e N p2 e
2
September 6, 2005
6
Like Sign Method (II)
• Having np positrongs and ne electrons in the acceptance
n p e n p e  1
like sign and nen p unlike sign pairs
2
can be built.
• For a single event under consideration (Np,Ne)
n p 1  n p 
B n p , e p 
2
n p 0
Np
n pp   pp 
Np
 Np

1
2

  pp  n p  B n p , e p    n p B n p , e p 
 n 0

2
n

0
p
p




1
1
2
  pp n p   n p   ppe p2 N p N p  1
2
2
September 6, 2005
7
Like Sign Method (III)
• equivalent:
1
nee   eee e2 N e N e  1
2
nep   epe pe e N p N e
• Pair survival probability:
– where “ep is the probability that a single positron survives everything in
the event that was present to itself …“
– “pp is the probability that once each of the two positrons survived the
environment of the rest of surrounding event, that they additionally
survive each other!“
– PHENIX: large acceptance and segmentation, granularity pp is nearly
identical to 1.0.
September 6, 2005
8
Like Sign Method (VI)
• To get the mean npp averaged over all events <npp>, properly weighted
sum over all possible intitial events, (Np, Ne), weighted by the
probability of each of the two primary multiplicities, (P(Np), P(Ne)):

n pp
1
   ppe p2 N p N p  1Pp N p 
N p 0 2
1
  ppe p2
2
 N 
2
p

 Np
• Assumption: P(Np) follows Poisson statistics:
n pp
September 6, 2005
1
  ppe p2 N p
2
N 
2
p
 Np
2
 Np
2
9
Like Sign Method (V)
• Unlike sign combinatorial background :
– (w/o any assumption about underlying statistics)
nep   ep


  n n P N  P N 
N p 0 N e 0
p e
p
p
p
p
  epe pe e N p N e
– Assuming and by inspection:
nep  2
n pp nee
N ep  2
N pp N ee
September 6, 2005
 pe   pp ep
N ep  N evt  nep
10
N ep  2
N pp N ee
• “We make no assumptions about the apertures or efficiences of the
spectrometer. Despite this generality we have a result that states
that the mean number of combinatorial ep per event is identically
related to the mean number of measured like-sign pairs per event“
• Having measured Nevt events „we can find that the total integral of
combinatorial pairs is fixed by the integrals of the measured likesign pairs“
• To summarize: “The like-sign method instructs the experimentalist
to measure the shape of the combinatorial background using the
event mixing technique. The normalization of the resulting shape is
then defined by the measured like-sign yield“
September 6, 2005
11
Poisson statistics ?
September 6, 2005
12
Event Mixing - Event Buffering
• Mixing the present event
with all buffered events
Nevt
Nevt-1
Npool size
buffered
events
Nevt-Npool size
September 6, 2005
 Npool size are generated by
the positrons and
 Npool size are generated by
mixing the electrons from
the present event with the
Npool size sets of
positrons/electrons
 2 x Npool size mixed events
• Also possible for like-sign
pairs
13
Comparison of Like-Sign (same event)
and Event mixing Buffering
• For like-sign pairs:
– The buffering techique has the advantage that it is sensitive to a
signal in the like sign pairs either physical or detector response
generated.
• Tool to ensure that detector effects are properly removed
– The buffering technique does suffer one drawback:
• Relies upon a mixed events internal Poisson statistic.
• Not true for a real event, but sub samples in centrality may be
Poisson
September 6, 2005
14
Event characterization (centrality, vertex, (event plane))
Nevt
Nevt-1
Npool size
buffered
events
Nevt-Npool size
September 6, 2005
15