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.

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Presentation transcript:

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!

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)

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 b20 Analysis F (like fine) Or one single large bin [b0 , b20 ] when ignoring centrality Analysis L (like large)

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) =

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

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 =

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:

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

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 bins vs. 1 bin to start with b J/ψ DY Ratio 1.0 - 1.1 0.0909 0.1 0.909 whereas 1.1 - 1.2 0.0757 0.1 0.757 J/ψ = 0.5, DY= 1 1.2 - 1.3 0.0641 0.1 0.641 leading to a ratio 0.5 1.3 - 1.4 0.0549 0.1 0.549 while <b> = 1.54 1.4 - 1.5 0.0476 0.1 0.476 so that 1.5 – 1.6 0.0417 0.1 0.417 J/ψ / DY for <b> is 1.6 – 1.7 0.0368 0.1 0.368 0.417 for 10 bins 1.7 – 1.8 0.0327 0.1 0.327 0.415 for 20 bins 1.8 – 1.9 0.0292 0.1 0.292 and a ratio of 0.5 1.9 – 2.0 0.0263 0.1 0.263 is reached for b=1.4

20 bins vs. 1 bin J/ψ DY Ratio J/ψ DY Ratio 0.0476 0.05 0.952 ¦ 0.0215 0.05 0.43 0.0433 0.05 0.866 ¦ 0.020 0.05 0.40 0.0395 0.05 0.790 ¦ 0.019 0.05 0.38 0.0362 0.05 0.724 ¦ 0.018 0.05 0.36 0.0333 0.05 0.666 ¦ 0.017 0.05 0.34 0.0308 0.05 0.615 ¦ 0.016 0.05 0.32 0.0285 0.05 0.57 ¦ 0.015 0.05 0.30 0.0265 0.05 0.53 ¦ 0.014 0.05 0.28 0.0246 0.05 0.49 ¦ 0.0135 0.05 0.27 0.0230 0.05 0.46 ¦ 0.013 0.05 0.26