NA60 Group meeting, 31 March 2005, Markus Keil1 Update on the pixel efficiencies in the Indium run 2003

NA60 Group meeting, 31 March 2005, Markus Keil2 Same behaviour for all planes, but more pronounced for the planes close to the target Pixel efficiency seems to depend on the instantaneous occupancy in the analysed event (expressed by the number of VT tracks) Reminder: status collaboration meeting Fake tracks? Use matched muons to get best possible tracks

NA60 Group meeting, 31 March 2005, Markus Keil3 Matched muon tracks Use only matched muon tracks for efficiency measurement Problem: low statistics –Average over whole plane –Don’t exclude any pixel Same result as for all tracks: –Stable up to ~100 VT tracks –Then decrease of efficiency by several %

NA60 Group meeting, 31 March 2005, Markus Keil4 How is the efficiency calculated? (very schematic!) 1. Extrapolate track 2. Define surrounding (GetChi2Distance()) 3. Count all hits (clusters) (i.e. the real hit and fakes) 4. To determine number of fakes, do the same for mixed event

NA60 Group meeting, 31 March 2005, Markus Keil5 Fake subtraction (very schematic) → (3 – 2) / 1 = 100% Of course these values have to be considered as averages The real values are rather 1.2 and 0.3 than 3 and 2…

NA60 Group meeting, 31 March 2005, Markus Keil6 At high occupancy? Possibility of the following case: Two tracks close to each other → merged cluster Fake subtraction: (4 – 4) / 1 = 0 Question: How close are the tracks to each other? Question: How close do they have to be to cause trouble?

NA60 Group meeting, 31 March 2005, Markus Keil7 How close do the tracks have to be? Depends on orientation w.r.t. to the pixel orientation: (consider only 1-pixel clusters) Case 1: Distance ~60  m, 2 clusters Case 2: Distance ~850  m, 1 cluster → Below ~60  m always merged, up to 850  m possibly merged

NA60 Group meeting, 31 March 2005, Markus Keil8 How close are the tracks? Distance to closest track, integrated in percent → Non-negligible effect in the critical range

NA60 Group meeting, 31 March 2005, Markus Keil9 Calculating efficiencies I – Binomial Binomial distribution: Distribution for events with two possible outcomes (flipping a coin, detector does (not) detect a given track…) If the probability for a positive result is p, then in N tries one expects pN positive results ± sqrt(Np(1-p)) For the efficiency  and N Tracks tracks: =  N Tracks With a measured number of hits (counting only 1 hit!):  measured = N Hits / N Tracks However: Only 2 allowed result: Hit(s) / No Hits

NA60 Group meeting, 31 March 2005, Markus Keil10 Calculating efficiencies II – Fake subtraction If allowing (and counting) more than 1 hit per track, one cannot use the binomial distribution Instead we sum up all the hits (fake + real) and all the fakes, and subtract them, applying a poissonian error to both numbers Then we divide them by the total number of tracks Obviously the subtraction is the problem. Is there another possibility?

NA60 Group meeting, 31 March 2005, Markus Keil11 Calculating efficiencies III – Binomial with fakes Consider the binomial case of success/no success: –Is there a (1,2,3…) hit in the surrounding of the track? If the efficiency is , in how many cases will the answer be “yes”? –A) no fakes: N Yes =  N Tracks –B) with fakes: N Yes =  N Tracks + p Fake (1-  )N Tracks Instead of solving A for , we solve B: –  = (N Yes - p Fake N Tracks ) / (1-p Fake ) This method does avoid subtraction N Hits - N Fakes N.B.: Here p Fake is the probability to have ANY number of fakes in the surrounding

NA60 Group meeting, 31 March 2005, Markus Keil12 Summary Lower efficiency at high occupancy: –Obviously no problem of fake tracks –Most likely a problem of merged clusters and the way fakes are subtracted Change the efficiency calculation method to check…