ATL-DAQ /09/99

Transcription

1 AL-note DAQ-98-0 HD-IHEP AL-DAQ /09/99 Level{ Rates for riggers Using the -Signature R. Dubitzky and K. Jakobs University of Mainz, Germany E. Bagheri, K. Mahboubi, and M. Wunsch University of Heidelberg, Germany 0 August 998 Abstract In the ALAS experiment the trigger will be used in conjunction with other triggers like the single jet, the single electron and the tau trigger. In the present note rates for various combinations of such triggers are estimated for both low and high luminosities. hese rates are dominated by background events from QCD two jet production. In comparison to these background rates, also the rates from processes with genuine missing transverse energy, like W- and top-production and the production of supersymmetric particles are given.

2 Introduction resolution. his resolution is mainly determined by the the detector acceptance, the calorimeter response and resolution and the hardware realization of the trigger. Missing transverse energy will be one of the distinct signatures at LHC to select interesting physics processes. Many extensions of the Standard Model include weakly interacting particles which, if produced at LHC will escape detection. heir presence will however be signalled by an imbalance of transverse momentum. Among the basic building blocks of the level{ calorimeter trigger is the summation P of the total transverse energy deposited in the calorimeters. ogether with the scalar sum E also the components E x and E y in the plane transverse to the beam axis are computed in the jet/energy-sum processor of the level{ trigger. Although the trigger itself is not included in the basic level{ triggers [], it's combination with the single jet and tau triggers is important to allow for triggering on interesting events with low jet or tau thresholds. Due to the large cross section QCD 2{jet events dominate the trigger rate at low values of missing transverse momentum. heir contribution depends strongly on the achievable hese eects have been studied [2] using the same simulation chain as the one presented here. After a brief description of the simulation in Section 2, the rates for the various processes considered are presented in Sections 3 and 4 for low and high luminosity. 2 he Simulation Chain he present simulations are based on the ALAS fast simulation programme ALFAS [3]. he physics generator PYHIA [4] is used to generate the physics events. With respect to the standard version some modications have been made to ALFAS, which are described in Ref.[5]. hey mainly concern the response and the resolution of the calorimeters together with a correct description of the longitudinal energy sharing between the electromagnetic and the hadronic calorimeters. he calorimeter response and resolution functions have been determined from a full ALAS GEAN simulation for both single charged pions and photons in the full energy range of interest, from 200 MeV up to 00 GeV. In the same simulation the energy dependent longitudinal energy sharing in the calorimeters has been determined. Whereas the response and resolution curves have been parametrized the distributions obtained for the longitudinal sharing were directly used in the fast simulation. Random numbers are taken directly from the obtained distributions. It should be noted that all eects of energy losses in the tracking detectors and in the insensitive material are taken into account in the response and resolution functions. he deposited energies in the calorimeters are summed into trigger towers with granularities in according to the proposed trigger cell granularities over the full range of pseudorapidities(mainly 0. 0., except in the endcap regions). Electronic noise is added for each trigger tower, assuming Gaussian distributions with standard deviations as given in the ALAS calorimeter DRs [6]. Pileup from minimum bias events is added onto the hard collisions, as described below. In this procedure correct shaping functions of the various calorimeter types are taken into 2

3 account. he complete electronics chain as realized in the level{ trigger preprocessor, consisting of a 0-bit FADC with a dynamic range up to 255 GeV, bunch crossing identication (BCID), as well as the data calibration and conversion in a look{up table are simulated [9]. In a nal step the calorimeter energies are summed into a map with a granularity of = his map contains the basic energy information for the jet/energysum processor, whereas the e.m. cluster processor uses the original maps with a granularity of = Pileup Simulation Pileup eects due to multiple interactions within one bunch crossing are crucial, especially for the trigger, because summing must be performed over large detector areas and, hence, uctuations in the pileup of uninteresting events degrade the resolution. Pileup eects have been taken into account in this simulation in the following way. Minimum bias events are generated using PYHIA 5.7 with the parameter settings as used by ALAS for the full GEAN simulation. he number of events per bunch crossing follows apoisson distribution with a mean of 2.3 (23.0) events for low (high) luminosities. he energy deposits E are derived in the same way as already described, and summed up to form trigger towers of = hen calorimeter specic shaping functions f shape (t) are applied. he signal part of the shaped calorimeter signal extends over a few bunch-crossings followed by a long undershoot, which extends over 20 bunch-crossings. herefore the history of previous events to the event of interest occuring at a time =BX 0 must be taken into account. he contributions of events earlier in time are added up resulting in an eective energy E e () for a given bunch-crossing =BX: E e ( = BX) = X t=bx t=bx 25 E (t) f shape (t) his procedure is repeated for every bunch-crossing including at least the expected occurence of the signal maximum plus the three following minimum bias pile-up events to allow correct identication of the interesting bunch-crossing. he energies of the last seven bunch-crossings are written to disk in order not to repeat for every event this time consuming procedure. Afterwards these pseudo-events are read back and can be used in the further analysis. 3 Level{ rigger Rates at Low Luminosity 3. Contributions to the Spectrum from QCD Jet Events he calculation of the inclusive spectrum is aected by large uncertainties, since in addition to the contributions from physics channels, also contributions from instrumental eects are important which can not be calculated reliably at present. Among such eects are machine induced backgrounds, beam gas interactions as well as contributions resulting from extreme tails in the detector performance. 3

4 In the present note an attempt is made to calculate the contribution of QCD jet and minimum bias events to the spectrum. hese events will add a signicant contribution to the trigger rate given their high production cross section together with the resolution of the missing transverse energy measurement in the trigger. In order to simulate the total inelastic proton-proton cross section of 70 mb, the following procedure has been applied: in the QCD jet simulation using the PYHIA Monte Carlo program the P cuto value, which has to be introduced in order to cuto the divergent treelevel cross sections, has been chosen such that the total QCD jet cross section corresponds to 70 mb. his cross section value is obtained for a cuto value of 4.3 GeV. Applying this procedure assumes that typical minimum bias events can be described by low P tree level QCD jet production. Since in any case the contributions of low P jet or minimum bias events to the spectrum are small for large values of missing transverse momentum, the uncertainty introduced by using this method is considered to be small. For the low luminosity simulation the spectrum as well as the trigger rates have been calculated without pileup as well as with the superposition of 2.3 minimum bias events on average. he reconstructed spectra at the trigger level for the simulated events are shown in gure. Due to the degraded resolution the spectrum is found to be slightly harder if on average 2.3 minimum bias events are added. d σ / d E (mb / GeV) (GeV) Figure : Contribution of QCD two jet events to the superposition of low luminosity pileup. spectrum with and without the hese spectra can be directly turned into level{ trigger rates. hey are shown in gure 2asa function of the threshold. In gure 3 the P spectrum of the generated leading parton is plotted for the case where 4

5 trigger rate (khz) (GeV) Figure 2: Inclusive threshold used in the level{ trigger. trigger rates from QCD jet events as a function of the 2.3 minimum bias events have been addded. On the same gure the accepted cross sections of events passing thresholds of 40 and 60 GeV are shown. As can be seen, no events with low P partons contribute to the accepted trigger rates for high at low luminosity. 3.2 Combined rigger Rates: Jet + A combination of the trigger in association with the single jet trigger is among the basic level{ triggers of ALAS. Before the combined trigger rates are evaluated, it is importantto establish the relation between the jet energy scale and the level{ jet trigger scale. Dierences between these scales might arise from the dierent geometrical size of the jet windows, since a cone with a radius of 0.4 or 0.7 is used in the reconstruction while a xed window of = is used in the trigger. In the following a comparision is made between the jets reconstructed oine by using the ALFAS algorithm[3] and the so called level{ jets. In gure 4 the trigger acceptance is shown as a function of the reconstructed oine jet transverse momentum. Only jets with a P above 5 GeV are used in the comparison. he aceptance has been determined for various trigger thresholds with values at 5, 0, 20, 30 and 50 GeV. In additon, gure 5 shows the ratio between the energies reconstructed at the trigger level to the ones reconstructed oine using the full calorimeter information. Part a) shows the correlation between the ratio of trigger energy to jet energy as a function of the jet P. In part b)-f) this ratio is shown for various bins of the jet P. As can been 5

6 d σ / d P (mb/gev) P parton (GeV) Figure 3: he P spectrum of the leading parton of the generated QCD jet events. he fraction of events accepted passing various thresholds is indicated by the dashed curves. seen, the distributions are broad at low P values, which indicates that low thresholds have to be used to trigger with high eciency on low P jets. his on the other hand will lead to a signicant increase in trigger rate resulting from uctuations in the underlying event structure. From these curves, the trigger cluster thresholds have been determined such that the reconstructed jets of a given E will be accepted with an eciency of 95%. Using these thresholds the trigger rates have been determined. he results are shown in gure 6 for the case where 2.3 minimum bias events have been superimposed on average. he rates are given as a function of the threshold for dierent jet thresholds. rigger rates for specic combinations of jet and thresholds are also given in table for the case where no pileup events are superimposed and in table 2 for the case where on average 2.3 minimum bias events are added. As mentioned above, these rates have been determined for a threshold setting on the trigger clusters which correspond to an eciency of 95 % with respect to the oine jets. As can be seen, for low thresholds there is a signicant increase in trigger rate due to the pileup addition. his increase is moderate for thresholds beyond 50 GeV. If instead of the trigger clusters the thresholds of the reconstructed jets are used directly, i.e. with an ideal threshold curve, the rates as given in table 3 are obtained. hey can be considered as lower limits for the combined jet+ trigger rates at level{2. he deviations from the true level{2 rates will be smaller the closer the level{2 scale is to the oine jet scale. 6

7 able : Level{ trigger rates (in khz) for various combinations of and jet E thresholds, without the superposition of minimum bias pileup. (GeV) E 0 (jet) > 0 GeV E 0 (jet) > 20 GeV E 0 (jet) > 30 GeV E 0 (jet) > 40 GeV E 0 (jet) > 50 GeV E 0 (jet) > 60 GeV E 0 (jet) > 80 GeV and jet E thresh- able 2: Level{ trigger rates (in khz) for various combinations of olds, including 2.3 minimum bias events (low luminosity). (GeV) E 0 (jet) > 0 GeV E 0 (jet) > 20 GeV E 0 (jet) > 30 GeV E 0 (jet) > 40 GeV E 0 (jet) > 50 GeV E 0 (jet) > 60 GeV E 0 (jet) > 80 GeV able 3: Level{ trigger rates (in khz) for various combinations of and jet E values, assuming an ideal threshold behaviour. On average 2.3 minimum bias events have been superimposed. hese rates can be considered as a crude estimate (lower limit) of the level{2 rates. (GeV) E 0 (jet) > 0 GeV E 0 (jet) > 20 GeV E 0 (jet) > 30 GeV E 0 (jet) > 40 GeV E 0 (jet) > 50 GeV E 0 (jet) > 60 GeV E 0 (jet) > 80 GeV

8 trigger efficiency 0.75 trigger efficiency P jet (GeV) P jet (GeV) trigger efficiency 0.75 trigger efficiency P jet (GeV) P jet (GeV) Figure 4: Examples of trigger eciency curves for trigger cluster thresholds in the range between 0 and 60 GeV. he reference scale is the reconstructed jet energy of ALFAS using a cone algorithm with a radius of

9 Figure 5: Ratios between the energy in the trigger cluster and the reconstructed ALFAS jet energy using a cone algorithm with a cone radius of 0.7. Plot a) shows the ratio as a function of the jet E, plots b) - f) show the ratio for various bins of the jet E. 9

10 trigger rate (khz) (GeV) Figure 6: Level{ trigger rates using the combined jet and signatures. he rates are given as a function of the threshold for dierent jet thresholds. On average 2.3 minimum bias events have been added to the hard collision. 0

11 3.3 Physics Processes with Large Many interesting physics processes with a signicant amount of missing energy will be selected through the inclusive lepton/di-lepton and jet triggers. When combining them with a missing energy trigger, it might be possible to reduce the thresholds for those objects, while keeping a high signal eciency and reducing the background rate. he eect of combining the signature of the physics processes of interest with the inclusive single electron or jet triggers will be studied in detail in the next sections Combined rigger Rates: e/ +, jet + Emiss and e/ + jets + First we analyzed the combination of missing energy and electron candidates by generating a sample of W! e decays. In order to investigate the contribution of QCD background to the level{ inclusive electron trigger rate, a sample of QCD events is also generated following the procedure described in section 3.. When requiring electron triggers, eciencies are calculated taking into account the limited acceptance of the electron trigger, i.e. only those events are analyzed containing a generated electron within jj < 2:5 he inclusive trigger rates for these samples are plotted as a function of the trigger threshold and are shown in gure 7. he eect of combining the e/ trigger with the signature could also be read o from this gure and is shown for some thresholds in table 4. he rates of QCD background for a sample of trigger combinations when applying dierent cuts on the missing energy are given in table 5. Rate (khz) QCD jets QCD jets ( EM2I ) QCD jets ( EM5I ) QCD jets ( EM7I ) QCD jets ( EM20I ) W eν W eν ( EM7I ) E miss,trigger(gev) Figure 7: Level- trigger rates for W! e and QCD events, including pileup, versus the trigger threshold for dierent trigger combinations (EMxxI: an isolated electron candidate with E e;trigger >xxgev is required.

12 It is important to note that the QCD background rates for the e/ trigger are higher compared to those given in the DR [7] and the rigger Performance Report [8]. his is related to the fact that in the fast simulation { contrary to the full simulation quoted in the DR {, some eects of the calorimeters are not taken into account in full detail like the lateral shower development, which does especially aect the isolation criteria for the electron trigger. Furthermore, no attempt has been made so far to adjust single cell thresholds and the isolation thresholds within the fast simulation. In order to estimate the uncertainties due to these decencies we studied the rates for a set of thresholds (2 to 20 GeV) in the vicinity of those used in the DR applied to the electron candidates while keeping the isolation requirements the same as used in the DR. A following note [0] will be devoted to a detailed study of the rate dependencies on these parameters. he inclusive shown in gure 8 for some trigger eciency curves for the W events studied in this section are trigger threshold settings. efficiency E miss,trigger: 20GeV E miss,trigger: 40GeV E miss,trigger: 50GeV E miss,trigger: 60GeV E miss,trigger: 80GeV E miss,generated (GeV) Figure 8: Level{ inclusive of the generated for dierent trigger eciency curves for W! e events as a function trigger thresholds. For the trigger thresholds the value of the generated at 95% eciency is extracted from gure 8. hese values are given in parantheses together with the nominal thresholds in table 4, which contains the eciencies for dierent combinations of the single electron trigger with the signature. As seen in table 4 the electrons from the W decays are found by the level{ system with an eciency of 86 %, when applying an electron trigger threshold of 7 GeV. As already mentioned the limited eta coverage of the electron trigger has been taken into account. Selecting only those events, which in addition show a signicant amount of missing energy 2

13 able 4: Level{ trigger eciencies for W! e events for various combinations of and electron candidate's E. (GeV) ( = 95% ) 0 20 (33) 40 (63) 60 (85) 80 (02) 00 (5) inclusive 00.% 83.3% 42.4% 3.9% 0.6% 0.% e2 90.7% 8.9% 44.5% 2.7% 0.3% 0.% e5 88.2% 8.2% 44.2% 2.7% 0.3% 0.% e7 86.2% 80.4% 44.2% 2.6% 0.3% 0.% e % 78.5% 44.0% 2.6% 0.3% 0.% in the level{ trigger system (e.g. > 20 GeV, corresponding to an eciency of 95 % for a generated of 35 GeV), results in an eciency drop of 4 %, while at the same time the rate of the QCD background events is lowered by an extra factor of 65/9 to 9 khz as can be seen in table 5. When requiring an electron candidate of 2 GeV together with a signicant amount of missing energy (e.g. > 20 GeV), we observe that the QCD background is rejected by a factor of 40/2 with respect to the inclusive electron trigger, resulting in a rate of 2 khz. his rate has be compared to the inclusive electron trigger rate of 25 khz, obtained when applying a threshold of 20 GeV. he eciencies are comparable in the two cases. Rates below khz can be obtained when requiring a combination of missing energy above 30 GeV together with low energy electron candidates, but then the eciencies will drop rapidly. We conclude, that an ecient trigger can be made using isolated electrons and the signature to trigger on W decays into electrons and neutrinos using lower thresholds for electrons than for the inclusive electron trigger. Still high eciencies can be obtained when compared to the isolated electron trigger, but the QCD background rate is signicantly lower. If a rate of khz of an inclusive missing trigger is acceptable, a threshold of approximately 50 GeV must be applied. Although the main trigger for W's is the isolated electron trigger, an inclusive trigger may be used to trigger W decays with an eciency of 2 to 4 %. hose events can be used in the oine analysis to calculate trigger eciencies for electron and or jet signatures without any bias and to calibrate the missing energy seen in the level{ trigger system. 3

14 able 5: Level{ trigger QCD background rates for various combinations of jets and/or electron trigger for dierent trigger threshold values; exx means: electron candidate with E e;trigger > XX GeV, 2jXX means: 2 jet candidates with E jet;trigger > XX GeV. (GeV) ( = 95% ) Inclusive rate (khz) < 0. e2 rate (khz) < 0. < 0. e5 rate (khz) < 0. < 0. e7 rate (khz) 65 9 < 0. < 0. < 0. e20 rate (khz) 25 < 0. < 0. < 0. 2j20 rate (khz) < 0. < 0. 2j35 rate (khz) 0. < 0. < 0. e2+2j20 rate (khz) < 0. < 0. < 0. e5+2j20 rate (khz) < 0. < 0. < 0. e7+2j20 rate (khz) < 0. < 0. < 0. e20+2j20 rate (khz) < 0. < 0. < 0. e2+2j35 rate (khz) 4 0. < 0. < 0. < 0. e5+2j35 rate (khz) < 0. < 0. < 0. e7+2j35 rate (khz) < 0. < 0. < 0. e20+2j35 rate (khz) < 0. < 0. < 0. 4

15 3.3.2 Combined trigger rates: /had. + In addition to the combination with jets, it is also planned to combine the trigger with the tau trigger at level{. his allows for example to trigger on W! decays with lower thresholds compared to the individual tau or triggers. Also in this case the trigger rate is dominated by QCD jet events, which give a fake missing energy signature in association with jets that pass the tau criteria at level{. In order to evaluate the rates for such a trigger, the rejection factors of the tau selection against QCD jets have been applied. hey have been evaluated from a full GEAN Monte Carlo simulation for various thresholds of the E of the tau []. he trigger rates have then been determined from the previous jet + sample by applying the eciency to pass the tau criteria to each trigger cluster. he results at are shown in gure 9 for three thresholds of the tau E as a function of. At low luminosity tau and thresholds around 30 GeV lead to trigger rates in the khz range. trigger rate (khz) (GeV) Figure 9: Level{ trigger rates using the combined tau and given as a function of the E miss bias events are superimposed. signatures. he rates are threshold for dierent thresholds. On average 2.3 minimum 5

16 3.3.3 op Production and the rigger he top production rate would be very large at LHC even at low luminosity. In order to calculate eciencies and background rates a sample of tt events, with a top mass m t = 70 GeV, has been generated. he produced top is forced to decay exclusively into a bottom quark and an intermediate vector boson, i.e. t(t)! bw + ( bw ) decay channel which is the only signicant decay mode expected within the framework of the standard model. One W coming from the top is then forced to decay into an electron and a neutrino, whereas the W coming from the anti-top is forced to decay hadronically. he presence of the one neutrino in the nal state calls for a genuine signature which could be triggered on. A plot of the inclusive trigger rate for the generated tt sample is shown on gure 0. he QCD-jet production rate, which is one of the main backgrounds for the analyzed decay channel, is also superimposed on the same plot. Rate (khz) QCD jets QCD jets (J35x2) QCD jets (J35x2 + EM7I) tt - eνbjjb tt - eνbjjb (J35x2 + EM7I) E miss,trigger(gev) Figure 0: Level{ inclusive trigger rates for tt events. he rates are plotted as a function of the trigger threshold. he inclusive eciency curves for dierent trigger thresholds have been analyzed in one of the previous sections. here, for each trigger threshold the value of the generated missing energy has been extracted, at which the eciency reaches 95 %. hese values are given in addition to the nominal thresholds applied in the level{ trigger system in table 5 and 6. When requiring electron and/or jet triggers, eciencies are calculated taking into account the limited acceptance of the electron and/or jet trigger, i.e. only those events are analyzed containing a generated electron within jj < 2:5 and/or oine reconstructed jets within jj < 3:2 6

17 he rates of the QCD background for dierent trigger combinations, relevant to the top study, have been given earlier in table 5. Considering the nal state decay products of the channel analyzed here, it is clear that tt events decaying semileptonically could be selected by requiring a high-p electron candidate and/or high-p jet candidates and in addition. We investigated the possibility to apply lower thresholds of the electron and/or jet triggers when requiring in addition the signature. Obviously the thresholds should be chosen such, that a high rejection against jets could be achieved and, at the same time, as much of the signal as possible is retained. able 6 summarizes the obtained eciencies after the application of dierent combinations of the jets and electron triggers as a function of the threshold. In our examples, we required two jet candidates and/or one electron candidate in addition to missing energy. We have chosen the jet thresholds such (20 and 35 GeV), that an eciency of 95% will be reached for the transverse energies of the reconstructed jets of 30 and 50 GeV. For the electron candidates the thresholds were chosen such, that the range covers the threshold settings as given in the DR. able 6: Level{ trigger eciencies for tt events for various combinations of jets and/or electron trigger for dierent trigger threshold values; exx means: electron candidate with E e;trigger > XX GeV, 2jXX means: 2 jet candidates with E jet;trigger > XX GeV. (GeV) ( = 95% ) 0 20 ( 5) 40 (84) 60 (6) 80 (30) Inclusive 00% 93% 72% 44% 24% e2 90% 84% 64% 39% 2% e5 88% 82% 62% 37% 20% e7 86% 80% 6% 36% 20% e20 84% 78% 59% 35% 9% 2j20 99% 93% 7% 43% 24% 2j35 92% 86% 66% 40% 23% e2+2j20 90% 84% 64% 39% 2% e5+2j20 87% 82% 62% 37% 20% e7+2j20 86% 80% 6% 36% 20% e20+2j20 83% 78% 59% 35% 9% e2+2j35 84% 78% 60% 36% 20% e5+2j35 82% 77% 58% 35% 9% e7+2j35 8% 75% 57% 34% 9% e20+2j35 79% 73% 56% 33% 8% As can be seen in the table, the requirement of a signicant amount of missing energy ( > 20 GeV) in combination with other signatures helps in rejecting eciently the QCD background by keeping a high eciency for the top production. For instance, requiring two jets with more than 20 GeV and an isolated electron candidate of more than 2 GeV results in a rejection of QCD background of 40, while the eciency drops only by 6 %. If only 2 jets of 20 GeV are required in addition with missing energy ( > 20 GeV) an acceptable rate of 3.8 khz is expected with an eciency of 93 % for the top production. 7

18 3.4 Production of SUSY Events and the rigger One of the main topics of the ALAS experiment is the search for supersymmetric particles. he signature of the SUSY events, in the case of R-parity conservation, would be a large, resulting from the two nal state LSPs produced through the cascade decays of the other SUSY particles, together with multiple high-p jets and high-p leptons. Final states not containing leptons could be selected by considering the combined jets + trigger. he ALAS collaboration has decided to investigate in more detail ve points in the parameter space of the minimal supergravity (SUGRA) model. In this note three representative points, namely points 2, 3 and 4, corresponding to three dierent M SUSY scales, are considered. he parameters for these three points are given in table 7. he SUSY event samples used for the simulations in this note are generated using the SPYHIA Monte Carlo program. he generated events go through the complete simulated level{ trigger chain as explained in this note. able 7: SUSY parameters and the corresponding M SUSY for the three points considered in this note. m 0 (GeV) m =2 (GeV) A 0 (GeV) tan sign() M SUSY (GeV) Point Point Point he inclusive trigger rates together with the combined + jet trigger rates, as a function of the trigger, for the three points considered here are shown in gure. Also included is the rate of the QCD background. he standard model backgrounds have ususally a lower, lower jet multiplicities and less energetic jets. he eciency curves of the inclusive trigger for the three SUSY points studied here are shown in gure. When requiring jet triggers, eciencies are calculated taking into account the limited acceptance of the jet trigger, i.e. only those events are analyzed containing oine reconstructed jets within jj < 3:2 As can be seen in table 9, requiring two jets in excess of 50 GeV brings the background rate down to khz. he eciency is 78.6 % to trigger on SUSY events of the most critical parameter point3. If in addition missing energy in excess of 20 GeV is required the eciency drops only slightly to 76.3 %, whereas the QCD background rate will then be reduced to 0.5 khz. Requiring two jets above 00 GeV results in a drop of eciency for the most aected, low sparticle mass Point 3 of more than a factor of 2 to 36.6 %. If instead missing energy ( > 40 GeV) would be required together with jets above 50 GeV the eciency is kept at 70.3 % while the rate is around 00 Hz as in the case when requiring two jets above 00 GeV. We conclude, that it is favourable to use the missing energy signature with low energy jets to trigger eciently on SUSY events even at low sparticle masses while keeping the background rate at an acceptable level. LSP stands for the Lightest Supersymmetric Particle, which in most of the R{parity conserving supersymmetric models is the absolute stable lightest neutralino 0. 8

19 Rate (khz) POIN 2 POIN 2 (J50X2) POIN 3 POIN 3 (J50X2) POIN 4 POIN 4 (J50X2) QCD jets QCD jets (J50X2) QCD jets (J00X2) QCD jets (J50X2) E miss,trigger(gev) Figure : Level{ inclusive and combined + jet trigger rates for three SUSY points and the QCD background jets. he rates are plotted as a function of the E miss threshold. trigger able 8: Level{ trigger eciencies for SUSY events for various combinations of jet triggers. 2jXX means: 2 jet candidates with E jet;trigger XX GeV. and (GeV) 0 20(45) 40(78) 60(03) 80(25) 00(56) inclusive 00.% 99.6% 98.3% 96.0% 93.6% 90.8% POIN 2j % 95.7% 94.8% 93.0% 9.2% 88.9% 2 2j00 87.% 86.9% 86.3% 84.9% 83.3% 8.5% 2j % 72.8% 72.3% 7.% 69.8% 68.2% inclusive 00.% 96.4% 87.6% 75.6% 63.2% 50.9% POIN 2j % 76.3% 70.3% 6.6% 52.3% 42.6% 3 2j % 35.5% 32.9% 29.4% 25.2% 20.9% 2j50 6.0% 5.5% 4.4% 3.0%.2% 9.3% inclusive 00.% 96.7% 89.6% 82.% 74.8% 67.5% POIN 2j % 87.9% 85.0% 80.6% 75.% 68.7% 4 2j % 77.7% 75.6% 72.% 67.3% 6.8% 2j % 58.% 56.5% 54.% 50.4% 46.3% 9

20 able 9: Level{ trigger QCD background rates for two jet triggers at dierent thresholds for dierent trigger threshold values; 2jXX means: 2 jet candidates with > XX GeV. (GeV) Inclusive rate (khz) < 0. < 0. 2j50 rate (khz) < 0. < 0. < 0. 2j00 rate (khz) < 0. < 0. < 0. < 0. efficiency efficiency E miss,trigger: 50GeV E miss,trigger: 80GeV E miss,trigger: 00GeV E miss,trigger: 25GeV E miss,trigger: 50GeV E miss,trigger: 50GeV E miss,trigger: 80GeV E miss,trigger: 00GeV E miss,trigger: 25GeV E miss,trigger: 50GeV E miss,generated(gev) E miss,generated(gev) efficiency Figure 2: Level- inclusive of the generated E miss,trigger: 50GeV E miss,trigger: 80GeV E miss,trigger: 00GeV E miss,trigger: 25GeV E miss,trigger: 50GeV E miss,generated(gev) for dierent trigger eciency curves for SUSY events as a function trigger thresholds. 20

21 4 Level{ rigger Rates at High Luminosity 4. Combined rigger Rates: Jet + he analysis described above has been repeated for a high luminosity scenario at LHC. In this case 23 minimum bias events have been added on average on the hard scattering process. he calorimeter shaping functions, the complete pulse history and the BCID algorithm are applied as described in Section 2. he results obtained for the spectrum and for the accepted events at the parton level are given in gure 3 and gure 4. Clearly visible is the degradation in the resolution, which is reected by the much broader spectrum. At high luminosity also events with small parton E values pass the cuts of 40 and 60 GeV. d σ / d E (mb / GeV) (GeV) Figure 3: Contribution of QCD two jet events to the spectrum, high luminosity. he inclusive trigger rate and the combined rates including jet requirements are given gures 5 and 6. In order to obtain trigger rates in the khz range, threshold around 00 GeV have to be set. As in the case of low luminosities the trigger rates for specic combinations of jet and thresholds are given in table 0. hese rates have been determined for a threshold setting on the trigger clusters which correspond to an eciency of 95 % with respect to the oine jets. If instead of the trigger clusters the thresholds of the reconstructed jets are used directly, i.e. with an ideal threshold curve, the rates as given in table are obtained. hey can be considered as lower limits for the combined jet+ trigger rates at level{2. he deviations from the true level{2 rates will be smaller the closer the level{2 scale is to the oine jet scale. 2

22 able 0: Level- trigger rates (in khz) for various combinations of and jet E thresholds, including 23 minimum bias events (high luminosity). (GeV) E 0 (jet) > 60. GeV E 0 (jet) > 80. GeV < 0. E 0 (jet) > 00. GeV 2 58 < 0. < 0. E 0 (jet) > 20. GeV 0 58 < 0. < 0. E 0 (jet) > 50. GeV < 0. < 0. able : Level- trigger rates (in khz) for various combinations of and jet E values, assuming an ideal threshold behaviour. hese rates can be considered as a crude estimate (lower limit) of the level-2 rates. (GeV) E 0 (jet) > 60. GeV < 0. < 0. E 0 (jet) > 80. GeV. 0.2 < 0. < 0. E 0 (jet) > 00. GeV < 0. < 0. E 0 (jet) > 20. GeV < 0. < 0. E 0 (jet) > 50. GeV 0. < 0. < 0. < 0. 22

23 d σ / d P (mb/gev) P parton (GeV) Figure 4: Fractions of accepted events in the thresholds, high luminosity. trigger from QCD jet events for various trigger rate (khz) (GeV) Figure 5: Inclusive of the trigger rates at high luminosity from QCD jet events as a function threshold used in the level{ trigger. 23

24 trigger rate (khz) (GeV) Figure 6: Combined trigger rates at high luminosity, jets +. 24

25 4.2 Physics Processes With Large Also at highest luminosities many physics processes with a signicant amount of missing energy will be selected through the inclusive lepton/di-lepton and jet triggers. But again, the thresholds may belowered for these objects when combining them with a missing energy trigger keeping high eciencies and reducing the background rate. he eect of combining the signature of the physics processes of interest with the inclusive single electron or multiple jet trigger will be studied in detail in the next sections Combined rigger Rates: e/ +, jet + Emiss and e/ + jets + he eect of combining the signature of the physics processes of interest with the inclusive single electron trigger is analyzed again by generating a sample of W! e decays. In order to investigate the contribution of the background jets to the level{ inclusive electron trigger rate, a sample of QCD events is generated taking into account the enhanced pileup contribution of 23 events in one bunch crossing expected at high luminosities. he analysis follows closely the one described in the previous sections. Again the inclusive trigger rates for these samples are plotted as a function of the trigger threshold and are shown in gure 7. Rate (khz) QCD jets QCD jets ( EM5I ) QCD jets ( EM20I ) QCD jets ( EM26I ) QCD jets ( EM30I ) W eν W eν ( EM26I ) E miss,trigger(gev) Figure 7: Level{ trigger rates for W! e and QCD events, including pileup, versus the E miss trigger threshold for dierent trigger combinations (EMxxI: an isolated electron candidate with E e >xxgev is required he inclusive gure 8. trigger eciency curves for the case of high luminosities are shown in 25

26 efficiency E miss,trigger: 20GeV E miss,trigger: 40GeV E miss,trigger: 50GeV E miss,trigger: 60GeV E miss,trigger: 80GeV E miss,generated (GeV) Figure 8: Level{ inclusive of the generated for dierent trigger eciency curves for W! e events as a function trigger thresholds. he eciencies to select W! e decays at high luminosities at level{, using both the inclusive trigger and the combination of the single electron trigger with the signature for dierent thresholds are given in table 2 able 2: Level{ trigger eciencies for W! e for various combinations of electron candidate's E. and (GeV) ( = 95% ) 0 20 (35) 40 (69 ) 60 (90) 80 (2) 00 (25) inclusive 00.% 83.7% 45.2% 9.8%.6% 0.3% e5 86.7% 78.% 44.6% 8.7%.2% 0.% e20 8.3% 74.9% 43.9% 8.6%.% 0.% e % 68.7% 42.5% 8.2%.% 0.% e % 62.9% 40.7% 7.9%.% 0.% As seen in table 2, the electrons from the W decays are accepted by the level{ system at high luminosities with an eciency of 73%, when applying an electron trigger threshold of 26 GeV. Selecting only those decays, which in addition show a signicant amount of missing energies in the level{ trigger system (e.g. > 20 GeV) results in a 4% drop of the eciency, while at the same time the QCD background is rejected by an extra factor of 76/45 to 45 khz as can be seen in table 3. When requiring an electron candidate of 20 GeV 26

27 able 3: Level- trigger QCD background rates for various combinations of jets and/or electron trigger for dierent trigger threshold values; exx means: electron candidate with E e;trigger > XX GeV, 2jXX means: 2 jet candidates with E jet;trigger > XX GeV. (GeV) ( = 95% ) Inclusive rate (khz) e5 rate (khz) < 0. e20 rate (khz) < 0. e26 rate (khz) < 0. < 0. e30 rate (khz) < 0. < 0. 2j35 rate (khz) j55 rate (khz) < 0. e5+2j35 rate (khz) < 0. < 0. e20+2j35 rate (khz) < 0. < 0. e26+2j35 rate (khz) < 0. < 0. e30+2j35 rate (khz) < 0. < 0. e5+2j55 rate (khz) < 0. < 0. e20+2j55 rate (khz) < 0. < 0. < 0. e26+2j55 rate (khz) < 0. < 0. < 0. e30+2j55 rate (khz) < 0. < 0. < 0. together with a signicant amount of missing energy of > 20 GeV, we observe that the QCD background is rejected by a factor of 92/79 with respect to the inclusive electron trigger, resulting in the same rate and eciency. We conclude, that also at high luminosities an ecient trigger can be made using isolated electrons and the signature to trigger on W decays into electrons and neutrinos using lower thresholds for electrons than for the trigger using only isolated electrons. Still high eciencies can be obtained when compared to the isolated electron trigger, but the QCD background rate is signicantly lower. If a rate of khz is acceptable, a threshold of approximately 40 GeV together with an electron candidate of more than 26 GeV must be used. Such rates are not achievable with an ecient inclusive electron trigger. 27

28 4.2.2 Combined trigger rates: /had. + he rates for the combination of the trigger and the tau trigger by adding high luminosity pileup. he results are shown in gure 9, again for three thresholds of the tau E as a function of. At high luminosity the trigger rate can be kept at the level of khz threshold are raised to provided that the thresholds on the E of the tau and the 60 GeV. trigger rate (khz) (GeV) Figure 9: Level{ trigger rates using the combined tau and given as a function of the threshold for dierent tau thresholds. signatures. he rates are 28

29 4.3 op Production and the rigger In order to calculate eciencies and background rates at high luminosities, again a sample of tt events, with a top mass m t = 70 GeV, has been generated. he produced top is forced to decay exclusively into a bottom quark and an intermediate vector boson. In the following decays the W coming from the top is then forced to decay into an electron and a neutrino, whereas the W coming from the anti-top is forced to decay hadronically. In these events the pileup of 23 minimum bias events per bunch crossing has been taken into account. A plot of the inclusive trigger rate for the generated tt sample is shown in gure 20. he QCD-jet production rate, which isthemain source of background for the analyzed decay channel, is also superimposed on the same plot. Rate (khz) QCD jets QCD jets (J55x2) QCD jets (J55x2 + EM26I) tt - eνbjjb tt - eνbjjb (J55x2 + EM26I) E miss,trigger(gev) Figure 20: Level{ inclusive trigger rates for tt events. he rates are plotted as a function of the trigger threshold. he rates of the QCD background for dierent trigger combinations, relevant to the top study, have been given in table 3. Considering the nal state decay products of the channel considered here it is clear that tt events decaying semileptonically could be selected by requiring, in addition to trigger, a high-p electron trigger and/or two high-p jet triggers. he aim of this study was again to investigate combinations of these triggers with the signature. Again, the thresholds should be chosen such that a high rejection against jets could be achieved and, at the same time, as much of the signal as possible is retained. In our examples we have chosen the jet thresholds such (35 and 55 GeV), that an eciency of 95 % will be reached for the transverse energies of reconstructed jets of 50 and 80 GeV. For electrons candidates the thresholds (5, 29

30 20, 26, 30 GeV) were chosen such, that the range covers the threshold settings as given in the DR [7] and the rigger Performance Report [8]. he result of the application of dierent trigger combinations on the rates of the jet background and on the tt signal is superimposed on gure 20. able 4 summarizes the obtained eciencies after the application of dierent combinations of the jets and electron triggers as a function of threshold. able 4: Level{ trigger eciencies for tt events for various combinations of jets and/or electron trigger for dierent trigger threshold values; exx means: electron candidate with > XX GeV, 2jXX means: 2 jet candidates with > XX GeV. (GeV) ( = 95% ) 0 20 (53) 40 (92) 60 () 80 (38) Inclusive 00% 93% 73% 47% 24% e5 87% 8% 62% 40% 22% e20 82% 76% 59% 37% 20% e26 76% 7% 54% 34% 8% e30 72% 67% 5% 3% 7% 2j35 93% 86% 67% 44% 25% 2j55 67% 62% 48% 33% 9% e5+2j35 82% 76% 59% 38% 2% e20+2j35 78% 72% 56% 36% 20% e26+2j35 73% 67% 52% 33% 7% e30+2j35 70% 64% 49% 3% 6% e5+2j55 59% 55% 43% 29% 7% e20+2j55 57% 53% 4% 27% 6% e26+2j55 54% 50% 38% 25% 4% e30+2j55 52% 48% 37% 24% 3% As can be seen in table 4, the requirement of a signicant amount of missing energy ( > 20 GeV) in combination with other signatures helps also at high luminosities in rejecting eciently the QCD background by keeping a high eciency for the top production. For instance, requiring two jets of more than 35 GeV and an isolated electron candidate of more than 5 GeV results in a QCD background rate of 6 khz and a top selection eciency of 82 %. Requiring in addition an in excess of 20 GeV would result in a rejection of QCD background with a factor of 6:=2:5, while the eciency drops only by 5 %. At high luminosities it is not possible to simply trigger on 2 jets and missing energies, because either the rate will be too high or the loss in eciency is unacceptably high. 4.4 Production of SUSY events and the trigger he signature of SUSY events at high luminosities is the same as that for the low luminosities and therefore the same trigger sets could be applied in order to select these events. At high luminosities it is expected that higher thresholds must be set in order to achieve an acceptable trigger rate. Due to this fact the search for the SUSY particles at the LHC design luminosity would be more suitable for the high mass sector of the supersymmetric particles. 30

31 he inclusive trigger rates, as a function of the trigger, for the three SUSY points considered in this note and for the QCD background are shown in gure 2. Rate (khz) POIN 2 POIN 2 (J200X2) POIN 3 POIN 3 (J200X2) POIN 4 POIN 4 (J200X2) QCD jets QCD jets (J00X2) QCD jets (J50X2) QCD jets (J200X2) E miss,trigger(gev) Figure 2: Level{ inclusive E miss and combined E miss + jet trigger rates for three SUSY points 2, 3 and 4, and the QCD background jets. he rates are plotted as a function of the trigger threshold. As mentioned earlier, the standard model QCD processes, which are the background source and aect the selection of the SUSY events, ususally have smaller values. hey also tend to have, in most of the cases, fewer and softer jets. herefore applying high threshold multi-jet triggers will be an ecient method to select SUSY events. But it would be quite interesting if the large signature, inherent to the SUSY processes (in the case of R-parity conserving supersymmetric models), could be utilized in order to lower these trigger thresholds. his possibility isstudied by generating three dierent SUSY event samples as before but this time including high luminosity pileup. Likewise a sample of QCD background jets has also been generated and been subject to the same set of trigger combinations as the signal of interest, namely the SUSY events. Figure 2 also shows the eect of requiring two energetic jets at the trigger level for the signal and the QCD background rates. It could be seen that by requiring two 50 GeV jet triggers the rate of the QCD background drops dramatically whereas the rate for the SUSY events is not aected very largely. Most aected are POIN 3 events with a low mass particle spectrum, which must have been fully studied at lower luminosities. he eect of requiring an inclusive trigger or two jet triggers in combination with an signature are summarized in table 5 for some trigger thresholds. It could be seen that in the case of POIN 2 and POIN 4 the requirement oftwohigh threshold jets, 3

32 e.g. 50 GeV and, does not result in a signicant degradation of the eciency, whereas going up from two 00 GeV to two 50 GeV jets would bring the eciency down from about 87 % (79 %) to 73 % (59 %) for POIN 2 (POIN 4). able 5: Level{ trigger eciencies for SUSY events for various combinations of jet triggers. 2jXX means: 2 jet candidates with E jet;trigger XX GeV. and (GeV) 0 20 (50) 40 (82) 60 (0) 80 (35) 00 (60) inclusive 00.% 99.6% 98.2% 96.5% 93.8% 9.% POIN 2j % 87.2% 86.4% 85.4% 83.8% 8.9% 2 2j % 72.8% 72.2% 7.4% 70.0% 68.5% 2j % 56.6% 56.2% 55.5% 54.4% 53.3% inclusive 00.% 96.7% 88.0% 76.4% 63.8% 5.9% POIN 2j % 35.5% 32.9% 29.5% 25.4% 2.3% 3 2j50 5.7% 5.4% 4.3% 2.7%.2% 9.3% 2j % 7.2% 6.7% 6.0% 5.3% 4.4% inclusive 00.% 96.7% 90.3% 82.8% 74.7% 67.6% POIN 2j % 78.0% 75.9% 72.5% 67.6% 62.2% 4 2j % 58.2% 56.7% 54.3% 50.7% 46.8% 2j % 37.3% 36.6% 34.9% 32.8% 30.3% By applying the above mentioned trigger combinations to the QCD background, the contribution to the level{ trigger rate from the QCD events has been estimated. hey are summarized in table 6. his should be compared with the reduction obtained for SUSY events. Inspection of table 6 shows, that the QCD jet background rate has been reduced by a factor of 80 3, resulting in a total rate of 5 khz, when requiring at least two jet in excess of 50 GeV. Now, by requiring two jet triggers with a lower threshold of 00 GeV, plus an trigger with a threshold of 40 GeV, we observe, that the eciency to select POIN 4 events has only slighly decreased, while the QCD background is rejected by a factor of and is expected to amount toonly 80 Hz. able 6: Level{ trigger QCD background rates for two jet triggers at dierent thresholds for dierent trigger threshold values; 2jXX means: 2 jet candidates with > XX GeV. (GeV) Inclusive rate (khz) j00 rate (khz) < 0. < 0. 2j50 rate (khz) < 0. < 0. < 0. 2j200 rate (khz) < 0. < 0. < 0. < 0. he eciency curves of the inclusive are shown in gure 22. trigger for the three SUSY points studied here 32

33 We conclude, that also at high luminosities it would be desirable to use the missing transverse energy signature with low energy jets to trigger eciently on SUSY events while keeping the background rate at an acceptable level. efficiency efficiency E miss,trigger: 50GeV E miss,trigger: 80GeV E miss,trigger: 00GeV E miss,trigger: 25GeV E miss,trigger: 50GeV E miss,trigger: 50GeV E miss,trigger: 80GeV E miss,trigger: 00GeV E miss,trigger: 25GeV E miss,trigger: 50GeV E miss,generated(gev) E miss,generated(gev) efficiency Figure 22: Level- inclusive of the generated E miss,trigger: 50GeV E miss,trigger: 80GeV E miss,trigger: 00GeV E miss,trigger: 25GeV E miss,trigger: 50GeV E miss,generated(gev) for dierent trigger eciency curves for SUSY events as a function trigger thresholds. 33