AND/OR - Are MC and Data (in)consistent? - further analysis and new measurements to do - Effects on inefficiency evaluation 1 G. Martellotti 21/05/2015 INFN Roma + Alessia

AND/O R MC and DATA seem to be inconsistent. But… Two different definitions: MC : % of penetrating tracks Data : AND/OR for reconstructed hits (crossings) We cannot assume that all the particles not giving the AND are ‘’single gap’’ tracks They can be ‘’large angle’’ penetrating tracks hitting non projective pads  large difference on efficiency evaluation 2

EFFECTS ON INEFFICIENCY We have the OR of two layers. Both must be inefficient to have inefficiency.  For uncorrelated hits the OR inefficiency is ~ (ineff 1L ) 2 while for the fraction of correlated hits of penetrating tracks is ~ (ineff 1L ) If R OR is the rate on the OR of two layers, the rate on one layer is R 1L =R OR (1+fc)/2 where fc is the fraction of correlated hits. This is for wire and cathode channels. Layer inefficiency is Ineff 1L ~ δ eff *R 1L where δ eff is the effective dead time The inefficiency of the OR of 2 layers is ~ fc* Ineff 1L Than, to build up the logical pad, we perform the AND of X, Y stripes  the inefficiency of logical pad = ineff X + ineff Y + ineff X *ineff Y The ‘’hit correlation’’ measured from the AND/OR ratio for logical pads cannot be assumed as correalation for logical channels X and Y which is larger. In M23R12 the small correlation measured for logical pads is due to the small wire strip size. Large angle tracks don’t giving AND because they are hitting a different physical channel X, will easily have correlated hits in the large logical channel Y (if correlation is larger, the rate R 1L is larger  # the dead time of each layer is larger and the inefficiency of the OR is, further on, larger) 3

 The inefficiency has been significantly underevaluated in the regions where logical pads are crossings of X,Y channels (M23R12) Correlations (AND/OR ratio) should be evaluated on data separately for X and Y channels and not for logical pads. But the analysis is complicated by the presence of the many misterious ‘’single strip hits’’ When beam is on, we can measure Rates and AND/OR ratio switching off one or more gaps in the chamber…  Let’s see if we can make a working MODEL … 4

Penetrating tracks cross 4 gaps. After crossing the first gap, they can hit next gap in the same pad (small angle-pad centered tracks) or not (large angle-peripheral tracks). - Here pad can be either the logical pad or the logical channel (X,Y) in M23R12 Let’s call: S = fraction of hit pads due to single-gap tracks in a gap (assumed the be the same in all gaps) P = fraction of hit pads due to penetrating tracks crossing 4 gaps (tracks penetrating 2-3 gaps are rare and are neglected) S+P = 1 FP = fraction of new (non projective) pads generated by a penetrating track in the next gap The hit rate on the first gap is R 1 = K(P + S) (K = R 1 ) By definition, the contiguous gap will have FP hits in a different pad  The OR rate of 2 contiguous gaps is R 12 = K(P(1-F)+2FP+2S) = K(P+FP+2S) When going from gap 2 to gap 3, by definition of F, again a fraction F of P (not necessarily due to the same tracks previously jumping pad) gives a new hit in the third gap  The OR rate of 3 contiguous gaps is R 123 = K(P(1-F)+3FP+3S) = K(P+2FP+3S)  The rate of the OR of 4 gaps is R 1234 = K(P(1-F)+4FP+4S) = K(P+3FP+4S) R And =K(1-F)P 5

Summing the rate of pads covering the same area we have the same particle rate seen by wires and cathodes. Wires count 23% more than cathodes The hit number (and the rate we would measure) is higher for wires presumably due to the higher cross-talk for wires # The fractions S and P are expected to be about the same (independent of the detector segmentation). # F is instead expected to be much higher for wires. M2R1 - Sum of rates measured on FE counters for all the channels of the same chamber or half chamber 6 The Rate (K) is different for wires and cathodes

Let’s make a (reasonable?) assumption on S, P, F for M2R1 Suppose the MC is right  40% penetrating tracks, 60% single gap tracks (15% on each gap)  on each gap P= 40/(40+15)=73%  P= 73%, S= 27%. Tentatively let’s assume F ~.6 for wires (large F value required trying to reproduce And/OR measurements) In the following table I also assume F=.1 (or.2) for cathodes. R 1 = K(P + S) = K, P+S=1, R And =K(1-F)P ORwirORcatANDwirANDcat R 12 = K(P+2S+FP) 1.71xR 1w (xR 1c ).29(xR 1w ) (xR 1c ) R 123 = K(P+3S+2FP) R 1234 = K(P+4S+3FP) ANDw/ORw = 9.3% ANDc/ORc = 33% - 26% This picture is more or less consistent with the AND/OR for logical pads = 7% measured by Giacomo (the AND/OR for logical pads must be < ANDw/Orw) 7 Large correlation for Y

Here a different assumption on S, P, F for M2R1: Suppose the MC overestimates by a factor 2 the % of penetrating tracks  20% penetrating tracks, 80% single gap tracks (20% on each gap)  P= 50%, S= 50%. In the following table I assume F=.4 for wires and F=.1-.2 for cathodes OR WirOR catANDwirANDcat R 12 = K(P+2S+FP) 1.7xR 1w xR 1c.30xR 1w xR 1c R 123 = K(P+3S+2FP) R 1234 = K(P+4S+3FP) – ANDw/ORw = 9.7% ANDc/ORc = 17% - 14% Also this picture is roughly consistent with the AND/OR for logical pads = 7%  We don’t have a unique possible solution In both pictures correlations for (wires and) cathodes are larger than for logical pads  Inefficiency was underevaluated 8

Can we estimate separately S and FP ? YES The AND measures the projective hits of penetrating tracks: R And = K(1 - F)P (neglecting accidentals, S and FP are eliminated)  S+FP =(1 - R And /R 1 ) is known, but we don’t know S (uncorrelated) and FP (correlated) A reasonable estimate of S can be done measuring R 123, R 13 (OR of gap1 gap3) R 1 = K(P + S), R 12 = R 23 = K(P+2S+FP) R 123 = K(P+3S+2FP) R 13 = K(P+2S+F 13 P) F 13 (≤) ~ 2F ( * ) S ~ (R R 13 )/R 1 This can be done for wires, cathodes and logical pads. For cathodes the condition F 13 ~ 2F (or (2F-F 13 )P <<S) is certainly very well satisfied but we have the problem of how to manage the ‘’single strip hits’’. For logical pads the approximation is less straightforward but the ‘’single strip hits’’ are eliminated and I’m pretty sure the approximation is good enough. ( * ) F 13 (≤ 2F) ≠ 2F only when a track fires in gap1 the pad N and in gap3 the pad N+2 but not the pad N+1 (assuming that tracks are straight tracks) 9

We should also measure Cluster Size for the OR of 1,2,3,4 gaps The hit pads in one gap are K(P+S) = KCS 1 (P part +S part ) where P part and S part are the particles and CS 1 the average cluster size in one gap (if we can assume CS 1 to be the same for P part and S part ). In the OR of 2 gaps, the hits are K(P+2S+FP) and the particles K(P part +2S part ) = K(P+2S)/CS 1. CS 12 =CS 1 [1+FP/(P+2S)] CS 123 =CS 1 [1+2FP/(P+3S)] CS 1234 =CS 1 [1+3FP/(P+4S)] Given P and S we have a redundant measurement of F (…check of the hypotheses) In the case of M2R1 we have CSw 1234 =2, CSc 1234 =1.3 we also know that CSw 12 =1.23xCSc Assuming the first case (MC like) P=.73, S=.27, Fw=.6 -.5, Fc= we get a reasonable picture WIRESCATHODES CS CS 12 =CS 1 (1+0.57F) (*) CS 123 =CS 1 (1+0.95F) CS 1234 =CS 1 (1+1.21F)2.00 – (*) (about consistent with CSw 2 /CSc 2 =1.23 measured) With the Cluster Size we can estimate correlations for X and Y separately

11 Evaluate the effects of different correlations on INEFFICIENCY Rates at luminosity = 2x10 33 These should be ~ rates of reconstructed hits comprising ghosts (see the linear increase of hits with nPV shown by Alessia) The ghost fraction is not well known

Inefficiency (from CARIOCA dead time) assuming the large ghost fraction of the left plot (if less ghosts  higher inefficiency) Correlation measured for logical pads was assumed for X and Y (wrong assumption) Hits/TS Rate of reconstructed hits in kHz/cm 2 Inefficiency Particle hits Reco hits Rate of reconstructed hits in kHz/cm 2 12

13 – correlations of a reasonable case MC like were assumed (P=.73, S=.27, Fw=.6, Fc=.15) – Inefficiency is ~ 2 times higher. Hits/TS Rate of reconstructed hits in kHz/cm 2 Particle hits Reco hits Inefficiency Rate of reconstructed hits in kHz/cm 2

– correlations of the most favourable case considered were assumed (P=.5, S=.5, Fw=.4, Fc=.2) – correlations of a reasonable case MC like were assumed (P=.73, S=.27, Fw=.6, Fc=.15) Rate of reconstructed hits in kHz/cm 2 14 Inefficiency Inefficiency reduced but still much higher than the one wrongly assumed

15 IN SUMMARY We have underestimated inefficiency by a large factor. We don’t know yet, but this factor could be of the order of 2 (even higher) - On top of this if single strips are, as it seems, signals generated in the FE, the inefficiency due to dead time is further underestimated

Summary Rates foreseen at 2x10 33 were extrapolated from the rates of reco hits (logical pads) measured on 2012 data  Rates of real particles at 2x10 33 were overevaluated when we assumed no ghosts in 2012 conditions (this is good for dead time inefficiency which is only affected by the real particles rate. Rate were probably underevaluated neglecting the ‘’single strip’’ rate Inefficiency was strongly underevaluated when we assumed for Y strips the too small hit correlation measured for logical pads - How much ? We should be able to estimate the correct correlations (  correct inefficiency) analysing special runs switching off gaps 16

Mesurements to do (at least for M23R12) # rates R 1, R 12, R 123, R 13 for logical pads and possibly for X, Y channels # cluster sizes CS 1, CS 12, CS 123, CS 1234 for X and Y Only estimating P, S, F we can evaluate correlations and correctly compare different chamber configurations # R 1, R 12 can be also measured, for X and Y channels, from the FE counters and compared with the rates obtained from the analysis (and hopefully have further indications to explain the misterious ‘’single strip hits’’ and understand how to treat their contribution to R 123, R 13 ). Any way I think we should adopt new chamber configurations 17

SPARES 18

19 Comparison of different chamber configurations – assuming correlations of a case MC like (P=.73, S=.27, Fw=.6, Fc=.15) Next step

Hits/TS Rate of reconstructed hits in kHz/cm 2 Particle hits Reco hits Hits (logical pads) /TS as a function of the Rate of reconstructed hits 20 Rate of particle hits in kHz/cm 2 Hits/TS Particle hits Reco hits Typical occupancy of M2R1 TS for standard configuration (2 gaps ON per Layer) IDEM as a function of the Rate of Particle hits

21 Hits/TS Rate of particle hits in kHz/cm 2 Particle hits Reco hits 2 gaps per Layer Standard configuration (left) Only 1 gap per layer ON (right) Hits/TS Rate of particle hits in kHz/cm 2 Large reduction of hits/TS (and consequently ghost reduction) due to the small correlation for logical pads Typical occupancies in the TS of M2R1

22 2 gaps per Layer Inefficiency Rate of particle hits in kHz/cm 2 1 gap per Layer Inefficiency Rate of particle hits in kHz/cm 2 Significant gain in efficiency. But << of what estimated when we wrongly assumed (in particular for cathodes) the small correlation measured for logical pads. What about EFFICIENCY