Effect of the cross-term hnb nc i to the CMC φ2 (PbPb)
N. G. Antoniou, N. Davis, F. K. Diakonos
University of Athens,
Department of Physics,
Sector of Nuclear and Elementary Particle Physics
November 26, 2013
N. Davis (U.o.A.)
CMC cross-term effect
November 26, 2013
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Partitioning of ∆F2 (M )
∆F2 (M ) can be broken up as:
hnc (nc − 1)i
hn (n − 1)i
hn nc i
(d )
= F2 ( M ) − b b 2
−2 b 2
2
h ni i
hni i
h ni i
|
|
| {z }
{z
}
{z
}
∆F2 (M )
cross −term
(b )
λ 2 ( M ) F2 ( M )
(m )
where λ(M ) ≡ hnb i/hni i and F2
moments).
(b )
(M ) ' F2 (M ) (scaled
(d )
(m )
For CMC, noise level λ = 95.6% ⇒ F2 (M ) − F2
closely equal to the first two terms.
(M ) is very
∆F2 (M ) with all terms gives the same φ2 = 0.37 as the pure CMC.
Therefore, to estimate the effect of omitting the cross-term, we
compare the φ2 of pure CMC and CMC with noise.
N. Davis (U.o.A.)
CMC cross-term effect
November 26, 2013
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Noisy CMC samples (PbPb)
Pure CMC: φ2,CMC ' 0.37 for M 2 > 6000. Mean event multiplicity
and RMS selected to match Pb+Pb system, hn i = 10.9 ± 3.3.
We convert each critical track to noise with probability λ = 0.956
(lower than Si+A CMC, selected so that moments match
experimental dataset). Noise follows Pb+Pb px,y distribution.
(m )
3 sets of 1,5M events each were produced. F2 (M ) for each set was
estimated using the analytical calculation. ∆F2 (M ) and φ2 were then
calculated in the usual way for each set, giving 1000 × 3 = 3, 000
bootstrap estimates of φ2 .
The resulting bootstrap distribution of φ2 can then be compared to
the pure CMC.
N. Davis (U.o.A.)
CMC cross-term effect
November 26, 2013
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Results
0.04
Bootstrap of φ2 gives φ2 = 0.38+
−0.03
φ2 median value is very close to the theoretically expected. The
confidence interval is similar to what we get with the Pb+Pb data set.
67% Φ2 : 80.35, 0.38, 0.42<
400
Counts
300
200
100
0
0.30
0.35
0.40
0.45
Φ2
N. Davis (U.o.A.)
CMC cross-term effect
November 26, 2013
4/4
Back Up Slides
N. Davis (U.o.A.)
CMC cross-term effect
November 26, 2013
5/4