1. Hit rate at high luminosity logical channels - ghosts – efficiency Toy Monte Carlo : # I have assumed a uniform particle distribution inside the TS # I have assumed a fraction of BC/orbit = 0.7 # Given a particle rate/cm 2 # Given the geometry of the Trigger Sectors (in M2 and M2R1)  Number of logical pads hit in the TS (per BC)  Inefficiency due to CARIOCA dead time  Number of logical pads reconstructed (X & Y crossing)  Accidental ‘’triggers’’ Thanks to Alessia and Roberta for useful discussions

2. Rates at 2x10 33 with shielding (kHz/cm 2 ) PROCEDURE: A = Trigger Sector area. Average number of hits/BC on TS = N = RxA/(0.7x40) with R= rate/cm 2 (in MHz) # Poisson distribution with average N is used to find the average number of X Y crossings. X Y strips are sent to the TRIGGER and DAQ to reconstruct logical channels (XY crossings) Strips are composed by only one (as in M2M3R1) or more physical channels Ored. INPUT: rates reported by Giacomo as particle rate. I evaluated the ghost rate starting from this. This assumption is reasonable if the extrapolation done by Giacomo starts from low rate data.

3. We should carefully check who really are the ‘’uncorrelated’’ hits # Understand the apparent disagreement with Monte Carlo. Notice that there are 2 different definitions: In Data the AND of projectively aligned pads is required to have correlated hits In MC the fraction of tracks crossing all the 4 gaps is shown To calculate the rates on the FE channels and inefficiencies, I assumed the percentage of correlated and uncorrelated hits measured in the past at 2.76 TeV and used by Giacomo

4. LOGICAL PAD HITS/BC In TRIGGER SECTOR (‘’PARTICLES’’) NUMBER OF LOGICAL PADS RECONSTRUCTED FROM X Y CROSSINGS Rate/cm 2 kHz Trigger Sector: 48 logical pads obtained by crossing 6x8 X and Y channels Area=95 cm 2 M2R1 Min chamb Average Max chamb dead time inefficiency is not yet considered. Average rates/cm 2 for the chambers with minimal, average, maximal population. The rates on Trigger Sectors are spread from ~ 100 to 800 kHz/cm 2. The ghost number on the chambers is underevaluated due to non linear effects. N hits on the TS GHOSTS

5. Now the effect of inefficiency due to CARIOCA dead time PARTICLES M2R1 Inefficiency due to dead time is applied to each FE physical channel (1) Carioca dead time =75ns is assumed for both wires and cathodes. The two bi-gap layers are Ored. The AND of XY is required Fortunately Ghosts don’t contribute to dead time. The effect of inefficiency increases dramatically at a relatively high rate.  important to reduce the rate # improve the shielding # feed each FE with only one gap Particle HITS not in dead time Rate/cm 2 (kHz) N hits on the TS (1) Efficiency = (1 - δeff R/0.7) Where R is the rate (in GHz) measured on the FE channels δeff = δcar -12.5 ns GHOSTS

6. The inefficiency could be recovered if in the region M2R1 the OR of wires and cathodes is accepted but the rate of accidental combination would enormously increase (see next) Particles X Y OR X Y AND If the inefficiency is still too high we must reduce the pad size Most of the hits are uncorrelated  Feeding the FE by only 1 gap, the rates can be reduced by ‘’almost’’ a factor 2 (red lines  blue lines) PRESENT DETECTOR PAD DETECTOR Pad=logical pad Two curves ~ superimposed: no inefficiency N hits on the TS

7. Accidental associations/Triggers opening a random FOI (1Y, 5 X) Requiring the OR of X and Y strips. ( The FOI is all contained in the TS) Accidental probability is too high  MUID should work with AND.  Check how the evaluation of MisID is presently performed Not considering inefficiency Rate/cm 2 (kHz) M2R1 probability The probability of accidentals in M2 is relevant for trigger/filter on muon Pt. Given a low Pt muon detected in M3- M4-M5, it will result accidentally a high Pt muon with this probability. Considering inefficiency

8. Accidental associations/Triggers opening a random FOI (1Y, 5 X) Requiring the AND of X and Y strips If the accidental trigger probability is too high also with the AND (to be studied), to reduce accidentals we can only reduce the rate # feed the Front End with 1 gap only # improve the shielding M2R1 probability Rate/cm 2 (kHz) Present strip detector

9. For comparison the case of the pad detector with pads = logical pads is reported. Almost no difference in the accidental ‘’trigger’’ probability To reduce the accidental probability only drastic actions are possible: # One could reduce the Y pad size by a factor 2 (Y pad is larger than Mult. Scatt.) and eventually require in M3 M2 a coincidence in Y/2 pads)  a factor 2 reduction # One could built a detector with 4 independent gaps with their front end (1 AND 2) OR (3 AND 4)  very strong reduction probability Rate/cm 2 (kHz) For a pad detector Accidental associations/Triggers opening a random FOI (1Y, 5 X) M2R1 Inefficiency recovered Accidentals still high

10. Trigger Sector: 48 logical pads X Y = 6 x 8 Area=110 cm 2 M3R1 ‘’EFFICIENCY’’ N hits on the TS Rate/cm 2 (kHz) INEFFICIENCY EFFECT particle s ghosts hits not in dead time INEFFICIENCY NOT INCLUDED The effect of inefficiency seems much less dramatic than for M2R1 (I will further comment on it)

11. Accidental associations/Triggers opening a random FOI (1Y, 5 X) Requiring the AND of X and Y strips M3R1 probability Rate/cm 2 (kHz) The probability of accidental associations is > 2 times smaller w.r.t. the M2R1 case

12. Trigger Sector: 48 logical pads 12 x 4 X Y Area=380 cm 2 M2R2 N hits on the TS Rate/cm 2 (kHz) INEFFICIENCY EFFECT Apparently we don’t have significant inefficiency from CARIOCA. In M2R2, logical pads are obtained crossing wires with a cathode pad being the OR of 4 pyisical channels having an area 4 times smaller (~ 4 times smaller dead time) particles N particles on the TS ghosts NO INEFFICIENCY hits not in dead time

13. The Trigger Sectors of M2R2can be reduced (presently 12 x 4 logical pads are obtained crossing wire strips with a cathode pad obtained by the OR of 2x2 phys. chann.) this pad has Y = Y of the logical pad, but X = 2X of the logical pad) The vertical size of the TS is fixed, but it can be divided in two TS of 24 logical pads 6 x 4.  The efficiency does not change. The number of ghosts is strongly reduced. N hits on the TS particles ghosts

14. M2R1 M2R2 Inefficiencies reported by Giacomo M3R1 Apparent disagreement with inefficiencies reported by Giacomo

15. WHAT TO DO # Investigate how to reduce the size of trigger sectors in M2 R2,R3,R4 (IB – ODE … I would benefit from information/discussion about) # Investigate the problem (the nature) of ‘’uncorreleted’’ hits, understanding the apparent discrepancy between MC and measurement. (as soon as we can, make a new measurement with only one layer, two layers in OR – AND and switching off one of the two gaps of the FE) # I would like to better understand the MuID and MisID algorithms in use # Investigate the apparent disagreement with the inefficiencies reported by Giacomo # I think that to cope with the large CARIOCA dead time, at least in M2 R1 we have to design a new Pad detector (a working group..)