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L1 Quadrant Matching Calorimeter & CTT/PS

L1 Quadrant Matching Calorimeter & CTT/PS. Why?. Need for quadrant matching arose for low E T multi-electron triggers where the dijet trigger rates are typically large. J/ Y e e ( e.g. B d J/ Y K S ) J/ Y and U calibrations of EM calorimeters gaugino pairs to trileptons

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L1 Quadrant Matching Calorimeter & CTT/PS

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  1. L1 Quadrant MatchingCalorimeter & CTT/PS Why? Need for quadrant matching arose for low ET multi-electron triggers where the dijet trigger rates are typically large. • J/Y e e ( e.g. Bd J/Y KS ) • J/Y and U calibrations of EM calorimeters • gaugino pairs to trileptons • Any single e trigger that uses preshower confirmation may as well use CAL/PS quadrant matching if available, as will be required offline. • Tau triggers (match isolated track and narrow • jet?) Gain: Application of quadrant match at Level 1 improves the dijet rate reduction by factors of 2 - 5 depending on algorithm, for J/Y efficiency loss of 10 - 15%

  2. Triggers • Quadrant match triggers built from ORs of coincidence ANDs of Calorimeter and Track/Preshower terms: • e.g. TERM = Sa (Ca * Ta) • where Ca is some calorimeter term for quadrant a and Ta is some CTT or Preshower term for quadrant a . (a = 1, … 4 for quadrants) i.e.TERM =C1 * T1 + C2*T2 +C3*T3 +C4*T4 (* == AND; + == OR) • Quadrant matching requires use of ORing capability in L1 Framework • Pair triggers require more ORs -- e.g. 2 electron candidates in same or adjacent quadrants of CC : • { Sq(CEQ(2,q)*TPQ(2,q)) } + • { [CEQ(1,1)*TPQ(1,1) + CEQ(1,3)*TPQ(1,3)] * • CEQ(1,1)*TPQ(1,2) + CEQ(1,4)*TPQ(1,4) ] } • * (OTHER possible terms ) ( 6 ORs ) • CEQ(n,q) for n CCEM objects, quadrant q • TPQ(n,q) for n CFT/CPS matched tracks, quad q

  3. Trigger Algorithms Earlier trigger studies used n Trigger Towers (TT) in Quadrant for matching; but Level 1 Calorimeter trigger does not presently support use of quadrants for trigger towers -- must use Large Tile Areas = LTAs LTAs defined for Dh = 0.8, Df = 2p/4 Two possible hardware algorithms for summing LTAs in Adder Trees considered: 1)TILE Algorithm: Sum EM ET for TTs within LTA . Sum hadronic ET for TTs within LTA . Do these sums for two thresholds (Lo and Hi) for EM and HAD. Define objects: 1e = EMLTA(Lo,q) and NOT [ HADLTA(Lo,q) ] 2e = EMLTA(Hi,q) and NOT [ HADLTA(Hi,q) ] Require one LTA quadrant with 2e, or two adjacentquadrants with 1e . Also require 1 or 2 CTT/CPS matches in the same quadrant, as appropriate. (A possible modification could give more direct indication of 1 or 2 trigger towers per LTA) Typical tile threshold values: EMLo = 1.5 or 2.0 GeV ; (EMHi = 2 x EMLo ) ; HADLo (veto) = 2.0, 2.5 GeV or ; (HADHi = 2 x HADLo)

  4. Trigger Algorithm, cont’d 2) TOWER Algorithm: For every TT in the LTA, contribute 1.0 to the EM LTA sum if ETEM (TT) > TTEM threshold. For every TT in the LTA, contribute 1.0 to the HAD LTA sum if ETHAD (TT) > TTHD threshold. Form the quantity (EM LTA) - (HAD LTA) = TOT LTA for all Trigger Towers in the LTA; this is equivalent to summing the trigger towers in the LTA with EM TT above EM threshold TTEM and below HAD threshold TTHD. The trigger algorithm is then the requirement that TOT LTA 2 in some quadrant, or that two adjacent quadrants have TOT LTA 1. Typical thresholds: TTEM = 2.0, 2.5 GeV TTHD = 2.0 GeV The thresholds may be different for different tiles (e.g. for CC (h < 1.6) ; EC (h > 1.6) ) Either algorithm 1 or algorithm 2 gives the AND/OR term : CEQ(n,q) for n=1,2 calorimeter objects and q=1,2,3,4 quadrants for matching with CTT/CPS/FPS info in the Level 1 Framework.

  5. Comments • BothTILE and TOWER Algorithms use reference sets that are distinct from those used for trigger towers (e.g. the AND/OR terms like CEM, JCR, CJT, etc.) Thus there is no penalty for devoting the LTA reference sets to the quadrant matching. • Summing the Trigger Tower EM and HAD ET’s into the LTAs for the TILE Algorithmscan be done with no additional penalty in time in the present L1 CAL trigger. • Summing the 1.’s for Trigger Towers above thresholds EM LTA and HD LTA for the TOWER Algorithms requires a third pass lookup in the CAL Adder trees. This will fit within the 396 ns bunch crossing time, but NOT the 132 ns bunch time. Use of this algorithm will not be possible when we go to 132 ns. • One could, with a 4th lookup, arrange to sum Trigger Towers separately for the CC and for the EC at their natural boundaries (I find no great utility in doing this.) • Cost for implementation of the TILE or TOWER ALGORITHMS are estimated to be within the $25K now in the L1CAL cost estimate.

  6. Rate Studies • Study rates for central J/Y e+ e - triggers from BdYKS , using elements: • Level 1: 2 CC trigger towers ET >CALEM (GeV) • 2CTT tracks over low pT threshold (1.5 GeV) with opposite charge • 2 CPS clusters overCPSTHR (MIPs) • Match CTT and CPS to within 3 strips • (Optional) match CTT/CPS quadrant with CAL quadrant with TILE Algorithm with thresholds { EMLO, EMHI, HADLO, HADHI } • orTOWER Algorithm with thresholds {EMLTA, HDLTA} • Level 2: (see D0Note 3506) • Isolation for each electron • CAL - CPS h - f match • maximum DR between electrons • transverse mass less than 4 GeV/c2 Compute for both dijets (2 - 500 GeV/c) and for J/Y samples. Use ISAJET/UP_GEANT ntuples from Lucotte/Bhattacharjee. Rates are for 2 minbias events overlaid, appropriate for L = 2 x 1032. We require oppositely charged electron candidates. We require the two candidates in the same or adjacent quadrants in f.

  7. Rate Studies For fixed CPSTHR, interpolate CALEM to give fixed J/Y Level 2 rate ( 13.3 mHz) -- for several algorithm choices. These rates are thus all for the same collection rate for J/Y. EM Had Algorithm CPS Thrsh. Veto Thrsh Rate (MIP) (GeV) (GeV) (Hz) TOWER 2.0 2.0 2.0 407 “ 2.0 2.0 none 533 “ 2.5 2.0 2.0 249 “ 2.5 2.0 none 330 TILE 2.0 2.0 2.5 580 “ 2.0 2.0 none 819 “ 2.5 2.0 2.5 371 “ 2.5 2.0 none 524 No QUAD2.0 -- -- 1430 Match 2.5 -- -- 1113

  8. Interpretations • Rates for central J/Y into dielectrons at 2E32 are manageable with quadrant matching (hundreds of Hz) • Quadrant matching gives a factor of about 3 - 4 for TOWER algorithm; factor of about 2 - 3 for TILE algorithm. • For fixed J/Y rate, we do better with larger CPS threshold and lower CALEM tower threshold within range studied. • TOWERAlgorithm better than TILE by factor of about 1.5 in Level 1 rate for fixed J/Y yield. • Application of Hadron veto buys about a factor of 1.3 - 1.4 in L1 rate (5 - 10% loss in J/Y rate) • Lucotte studies of FPS/ECEM quadrant matching for single and dielectron triggers show similar reductions in Level 1 rates.

  9. Recommendations • Results of June 9 Trigger meeting discussion : • Hadron veto may be dangerous -- may be rate dependent, give more difficulty in getting trigger efficiencies. • ImplementTOWER algorithm for running at 396 ns. We would have to change to the Tile algorithm when and if the Tevatron goes to 132 ns. However, we note that the physics of J/Y , calibrations etc. are probably topics that are dominant early in the run. The switch to the TILEalgorithm is simply achieved by modification to the firmware.

  10. OR’ing Needs • Effective use of the Quadrant matching requires the use of Ors -- the proliferation of trigger elements for each quadrant would break the bank for the current limitation to 128 coupled Level 1 and Level 2 specific triggers. • To simplify the work in programming the Framework, there should be a limited number of ORing types. In the current list we have: • Basic quadrant OR of two terms A and B: • SUMnR(A,B) = A1*B1 + A2*B2 + A3*B3 + A4*B4 • where the notation A1 means term A for quadrant 1 etc., • and n = 1,2 is the number of objects in the term; • For quadrant ORs with a calorimeter term (A = CEQ(n,q) • R = eta region (N, C, S) ( C = h < 1.6) (N = h 1.6) • For ORs involving Calorimeter, the SUMnR definition would also include the term ECR(1,lo,R) to define which cryostat the EM deposit was in. • Regions R and T below are considered to be different.

  11. OR’ing Needs Same quadrant OR’s for two objects (e.g. dielectron): In same eta (cryostat) or different eta regions: SAMRR(A,B) = Sum2R(A,B)* ECR(2,lo,R) (4 OR’s) SAMRT(A,B; C,D) = Sum1R(A,B)*Sum1T(A,B) (8 OR’s) where Regions R and T are different, and terms (A,B) refer to Region R and (C,D) refer to Region T Adjacent quadrant OR’s for two objects: define OddR(A,B) = (A1*B1 + A3*B3) * ECR(1,lo,R) and EvenR(A,B) =(A2*B2 + A4*B4) * ECR(1,lo,R) Then in same or different eta regions: ADJRR(A,B) = OddR(A,B) * Even(A,B) (4 OR’s) ADJRT(A,B; C,D) = OddR(A,B) * EvenT(C,D) + EvenR(A,B) * OddT(C,D) (10 OR’s)

  12. OR’ing Needs Opposite quadrant OR’s for two objects : OPPRR(A,B) = [(A1*B1 * A3*B3) + + (A2*B2 * A4*B4)] * ECR(2,lo,R) (2 OR’s) OPPRT(A,B; C,D) =[(A1*B1 * C3*D3)+(A3*B3 * C1*D1) + [(A2*B2 * C4*D4)+(A4*B4 * C2*D2) *ECR(1,lo,R)*ECR(1,lo,T)(5 OR’s) Unequal quadrant OR’s for two objects : NEQRR(A,B) =[(A1*B1)* (A2*B2+A3*B3+A4*B4) (8 OR’s) +(A2*B2)*(A3*B3+A4*B4)+A3*B3*A4*B4]*ECR(2,lo,R) NEQRT(A,B; C,D) =[(A1*B1)* (C2*D2+C3*D3+C4*D4) +(A2*B2)*(C3*D3+C4*D4)+A3*B3*C4*D4] + [(C1*D1)* (A2*B2+A3*B3+A4*B4)+(C2*D2)*(A3*B3+A4*B4) +A3*B3*C4*D4] *ECR(2,lo,R)(16 OR’s) All quadrant OR’s for two objects : ALLRR(A,B) = SAMRR(A,B) + NEQRR(A,B) (13 OR’s) ALLRT(A,B; C,D) = SAMRT(A,B; C,D) + NEQRT (A,B; C,D)(25 OR’s)

  13. Other OR uses Can OR calorimeter terms (CEQ) with preshower terms FQN/FQN to associate calorimeter and forward preshower -- or CEQ with TPQ/TNQ to associate calorimeter and central preshower/central track -- or CEQ with TIQ to associate isolated track and calorimeter -- All appear in the current trigger list. All OR structures are of form Sq (Aq* Bq) or (TermA + TermB ) where TermA,B are some collection of ANDed terms.

  14. Conclusions • Quadrant ORing gives very useful Level 1 rate reductions both for low ET and high ET triggers. • An algorithm using trigger towers above a threshold in a large tile approximates a fully trigger tower-based algorithm and can be used for 396 operation. A somewhat poorer algorithm (TILE algorithm) can be used at 132 ns. • Quadrant matching requires extensive use of OR’s, believed to be available in the framework. • Recommend adoption of the TOWER algorithm and L1 AND/OR term ORing.

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