1. Dividing the J/y / DY result by the normal nuclear absorption curve ⇒ 0.84  0.05
preliminary
regions that will be exploited by the centrality study in Indium-Indium collisions
Theoretical predictions for the pattern as a function of centrality are welcome!

2. How to compare J/ψ / DY between NA50 and NA60
The original problem
We determine the ratio J/ψ /DY in 20 centrality bins for Pb-Pb
We determine the ratio J/ψ /DY integrated on centrality for In-In
We want to see if the results are compatible or not
A simpler problem
In the first case above, you want to compare the 2 “analysis”:
a/ 20 bins in centrality
b/ just ignoring the centrality information (1 single centrality bin)

3. Centrality Let b be the impact parameter of the collision
Let φ(b) the probability to have a collision with impact parameter b
We consider either 20 bins in b with limits:
b0 b1 b2 b3 b4 b5 … b19 b Analysis F (like fine)
Or one single large bin [b0 , b20 ] when ignoring centrality Analysis L (like large)

4. J/ψ, DY and their ratio We want to compute the ratio:
In analysis F, for a given Bi bin, with N(Bi) total number of collisions this ratio, is:
with N(Bi) =

5. namely , the ratio:
or, approximately, given that is almost constant
within the Bi bin :
NJ/ψ(Bi) / NDY (Bi)

6. In analysis L , we ignore the information we have on centrality.
We have, altogether,
a given number of J/ψ events Nψ
a given number of DY events NDY
and a given total number of collisions N
with impact parameter between b0 and b20.
Nψ =
NDY =
N =

7. The ratio Nψ / NDY taken in a single large bin is now :
( i.e. the ratio of the averages in the large bin [b0 , b20 ] )
the average value of the impact parameter b is:

8. The question What is the relation between the fine bin determination
determined from analysis F
and the value
determined from analysis L ??

9. Homework Take NJ/ψ(b) like 1 / b3 Take NDY (b) like 1 / b
Take φ(b) like b
Take b between 1 and 2 (1 or 20 bins)
Compute the 20 ratios NJ/ψ(b)/ NDY (b)
Compute the single ratio NJ/ψ / NDY
Compute <b>
Conclude

10. 10 bins vs. 1 bin to start with
b J/ψ DY Ratio
whereas
J/ψ = 0.5, DY= 1
leading to a ratio 0.5
while <b> = 1.54
so that
1.5 – J/ψ / DY for <b> is
1.6 – for 10 bins
1.7 – for 20 bins
1.8 – and a ratio of 0.5
1.9 – is reached for b=1.4

11. 20 bins vs. 1 bin J/ψ DY Ratio J/ψ DY Ratio¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦ ¦