Triggering the eγ Calorimeter at the LHC

Transcription

1 Triggering the eγ Calorimeter at the LHC J. Paradiso April, 1992 Abstrat An effiient simulation of the eγ alorimeter has been onstruted for the purpose of defining and evaluating an effetive triggering sheme. The struture of the simulation pakage is disussed, and the assumed detetor models are introdued. Several triggering uts are derived, and their on-line implementation is outlined at trigger levels 1 and 2. Triggering effiienies are given for simulated H γγ events with a 19-event minimum bias pileup. The rejetion of QCD bakground is demonstrated by simulating over a million hard QCD events over pileup, and traking them through the trigger logi. Single photon and photon pair rates are alulated for trigger sums alulated with tower sizes ( η x φ) of (.05 x.05), (.1 x.1), and (.2 x.2), over energy thresholds ranging from GeV. These results are interpreted to asertain the effets of energy thresholds, topologial uts, and tower size on the trigger rate.

2 Triggering the eγ Calorimeter at the LHC J. Paradiso Marh, ) Detetor Model Figure 1 shows a side-view of the proposed "eγ" eletromagneti alorimeter layout, as installed at the L3 interation point. Sine this study has dealt only with the alorimeter, the entral traker has been omitted. The eγ is assumed to be a rystal alorimeter, forming a barrel spanning η < 1. The barrel radius is set at 3 meters. The (lateral) rystal faes are eah assumed to span 3 x 3 entimeters. The urrent rystal andidate is Cerium Fluoride, and the speified longitudinal span of 25 X 0 results in a rystal length of 42 m, giving 1.6 λ of hadron interation. The Moliere radius of CeF 3 is 2.63 m. With suh a fine-grained alorimeter at a 3 meter radius, the effets of piled-up interations on resolution and pattern-reognition will be redued onsiderably. The results of this study may be relevant to the appliation of materials other than CeF 3 ; the only rystal parameters used in the simulation are the number of interation lengths and the Moliere radius (whih is impliit in the shower-sharing sheme between rystals). The rystal elements are oriented to projet toward the interation point, as indiated in Fig. 1. This results in eah rystal spanning a onstant η interval of 0.01, and φ of approximately 0.01 radians (the φ rystal size was adjusted slightly from this value in order to fit several tower sizes onto the alorimeter geometry; the dimension used is φ =.0098 radians, 2.95 m). The η < 1 alorimeter thus ontains 200 x 640 = 120,000 rystals. A hadron alorimeter, of minimum granularity.05 x.05, is assumed to be loated behind the rystal elements. The hadron alorimeter is assumed to absorb all hadron energy that was not deposited in the eletromagneti alorimeter (sine this is the extent of the model used in this study, the partiular alorimeter design is unimportant ). The rystals are assumed to ontain the entire eletromagneti shower, with no leakage through to the hadroni array. Energy thresholds are tested on three sets of tower sums. The tower sizes adopted are.05 x.05 (5 x 5 rystals, 40 x 128 = 5,120 towers),.1 x.1 (10 x 10 rystals, 20 x 64 = 1,280 towers), and.2 x.2 (20 x 20 rystals, 10 x 32 = 320 towers). 2

3 200 (η) x 640 (φ) = 128K Xtal Elements η < 1 r = 3 meters B =0.7T (z) η = φ = 0.01 Not To Sale!! Figure 1: rθ View of the eγ Calorimeter The detetor is assumed to be immersed in a onstant magneti field of 0.7 Tesla, direted along the ẑ-axis. Figure 2 illustrates a simple means of determining the impat point of harged partiles at the alorimeter's inner radius. Rather than iteratively alulating partile trajetories using a loal Jaobian (i.e. the standard GEANT tehnique), the impat point an be readily alulated in losed form. Assuming that the radial displaement of the vertex is zero (σ x, σ y 200 µm, whih is insignifiant here), the alorimeter impat point in rφ an be determined by solving the isoseles triangle given in Fig. 2 (the p utoff is impliitly maintained by requiring r < 2 r p for the arsine to be real). The impat point along the beam (ẑ) axis is then set by the partile's Larmor frequeny, and may be alulated as: z imp = p p φ B r p + z where p is the ẑ-omponent of partile momentum (along the beamline), p is the transverse momentum, φ B is the bending angle, r p the bending radius (as in Fig. 2), and z v is the z-position of the interation vertex (σ z = 5.5 m. in this study). These alulations may be realized in a few lines of omputer ode, and exeute promptly. 3

4 P Calorimeter Impat Charged Partile Trak (q) 1 2 φ B sign(q) r r p r =3meters r p θ B r p = p (GeV) 0.3B(T) φ B = 2sin -1 r 2r p Calorimeter Cylinder (rφ) projetion Figure 2: Simplified Traking of Charged Partiles Eletromagneti showers were deposited in the rystal alorimeter aording to a simple empirial model derived from the shower sharing behavior seen in the BGO rystals of the L3 eletromagneti alorimeter[1]. The onept is illustrated in Fig. 3. Eletromagneti showers are always assumed to be ontained within a 3 x 3 rystal blok. The energy of the eletron or photon is assumed to be entirely dissipated within this blok, and is distributed aording to the matrix given in Fig. 3 when the middle rystal is hit dead-enter. As the inident partile moves away from the enter, the sharing between the 9 rystals in the blok is skewed aording to the plot given at the bottom of Figure 3. Sine most of the energy deposit is highly loal (i.e. a tightly peaked spatial distribution with long tails), no differene is injeted into the sharing funtion for a partile inidene within ±0.75 m (±25% of the rystal width) of the rystal enter. For partiles hitting outside this region, the nearby row of rystals share an inreasing amount of shower energy, until they split the shower evenly at the border. This smearing is done separately for both oordinates (η and φ); i.e. first the olumns, then the rows (of the 3 x 3 matrix in Fig. 3) are skewed by the offset of the inident partile from the nearest rystal enter. 4

5 3 x 3 Array 1% 5% 1% 5% 76% 5% 1% 5% 1% Xtal Hit Dead Center 100% Sharing Fration 75% 50% 25% -75% -50% -25% 0% 25% 50% 75% Xtal. Partile Center Inidene - 1 / W / 2 W (% Xtal Width) Figure 3: Eletromagneti Shower Sharing in the Crystal Calorimeter Although this model suffers from a variety of shortomings (i.e. no flutuations in shower distribution or density are assumed, no leakage into the hadron alorimeter is modeled, et.), it exeutes extremely quikly, and has suffiient integrity to yield an indiation of trigger performane. As other, more sophistiated shower parameterizations are developed (i.e. [2]), they may be readily inorporated into the simulation software, whih has been built in a modular fashion in order to enable ready replaement and updating of detetor models. Beause eletromagneti showers are so well ontained in the rystal alorimeter, simple assumptions suh as given above retain some validity for eletron and photon showers. The situation is quite different for hadron showers in the rystal alorimeter, however, whih tend to be muh more ompliated and heavily flutuated. In order to simulate the hadron response, an empirial model[3] was implemented, based on data from the L3 BGO and uranium alorimeters. The longitudinal shower development is 5

6 (GeV) Figure 4: Energy Deposit in Crystal Calorimeter for 20 GeV Inident Hadrons parameterized by a sum of deaying exponentials with a flutuated offset. The shower is assumed to begin after the inident hadron penetrates the rystal to a depth distributed aording to e -x/λ, where λ = 26.2 m for CeF 3. Before the shower begins, the hadron looses energy as a Landau MIP, with peak energy of 350 MeV[1]. The hadron energy deposit in the rystal alorimeter is saled by a ompensation fator (π/e) of 0.6, based on the L3 BGO data, and as ould be expeted with CeF 3 (Ref. [4]). Fig. 4 shows the distribution of energy deposited in the rystal alorimeter for 20 GeV inident hadrons. One learly sees the MIP peak at 350 MeV, resulting from hadrons traversing the rystal alorimeter without showering. The showering partiles produe a broad energy distribution, peaking at 8 GeV. This broad peak is aused by the 6

7 . signifiant amount of hadron interation length presented by the rystal alorimeter (1.6 λ); the shower maximum is thus frequently ontained in the eletromagneti alorimeter (the Landau tail is also visible at the rightmost part of this distribution). When using a alorimeter equivalent to the L3 BGO (0.93 λ), the broad peak beomes a shoulder, and the distribution of Fig. 4 looks similar to the L3 data (i.e. Fig. 24 of Ref. [3]). Xtals (3 m) Xtals (3 m) Figure 5: Lateral Energy Distribution for Hadron Showers in Crystal Calorimeter The transverse distribution of the hadron shower in the eletromagneti alorimeter is generally highly flutuated and grainy. In order to model the transverse shower development, guidane was again taken from Ref. [3]. The net energy deposited in the rystals by an inident hadron is assumed to be arried by a roughly equal mix of 7

8 large ( 2 GeV ±30%) and small ( 360 MeV ±30%) quanta. These quanta are distributed aording to the presription in Ref. [3]; i.e. the large quanta are deposited within a Gaussian smear of σ = 11 m from the point of hadron impat, and the smaller quanta are deposited within a wider zone (a "flat-top" Gaussian is used, with a width roughly double that of the large quanta; see [3]). This essentially results in a hadron shower with a hot ore and long tails. This distribution an be seen in Fig. 5, whih shows the lateral hadron energy spread over many inident partiles (the plot axes are in units of 3 m. rystals). Again, the distribution is muh grainier than this on a shower-by-shower basis, sine the energy is generally divided into a sore or two of disrete quanta. The shower parameterization is not performed for hadrons with energy under 525 GeV (1.5 MIP); in these ases, all hadron energy is dissipated in the impated rystal. While this model does exhibit muh of the behavior expeted from hadron interations in the rystal alorimeter, the simulation would ertainly benefit from a more involved parameterization and/or additional tuning. The software has been strutured to readily aommodate an improved hadron interation model. A rudimentary hadron alorimeter model was adopted in this simulation. The rystal alorimeter is always assumed to fully ontain eletromagneti showers. All hadron energy remaining after interation in the rystals is assumed to be absorbed in the hadron alorimeter (i.e. full shower ontainment). The lateral shower distribution has the same form as in the eletromagneti alorimeter (i.e. hot ore with long tails), normalized to a shorter hadron interation length of λ = 10 m (from a denser absorber). In partiular, 90% of the remaining hadron energy is distributed in a Gaussian of σ = 4.2 m, and 10% is deposited aording to a "flat-top" Gaussian with roughly double width. Sine the lateral granularity of the hadron alorimeter is muh oarser (.05 x.05), the shower is not broken into quanta, as disussed above, but spread among a 3 x 3 ell array entered at the hadron impat. Events were generated using PYTHIA at s = 16 TeV. A luminosity of was assumed, with a ross-setion that resulted in an average pileup of 19 inelasti events. The hosen minimum bias desription employs the standard "UA1" parameters[5], and is used to generate the piled up events. In order to save on exeution time, a file was generated that ontained relevant parameters from 20,000 minimum bias events. For eah event that was analyzed, 19 events were superimposed from this minimum bias file. When all 20,000 suh bakground events were read, and the end of file was enountered, the file was rewound and randomly offset (within 19 events), to provide a somewhat 8

9 ... GeV η φ (deg) Figure 6: Sample H γγ event in Crystal Calorimeter (.1 x.1 towers) different minimum bias bakground. The results presented here inlude no detetor noise in the models (although some of this effet is provided through the pileup bakground). The simulation exeutes quite quikly. The average CPU time required per event (on the ETH IBM 3090) is of order 0.6 seonds (whih inludes the trigger proessing and analysis desribed in the next setion); a signifiant fration of this interval is oupied by PYTHIA generation of the Higgs or QCD event under analysis. Figs. 6 shows the energy deposited in the eletromagneti alorimeter from a H γγ event, with a Higgs mass of 100 GeV (the rystals in this plot are lumped into.1 x.1 towers). The two photons from the Higgs deay (of roughly 50 GeV eah) are learly visible, and quite isolated. 9

10 η φ (deg.) a) Eletromagneti Calorimeter GeV GeV η φ (deg.) b) Hadron Calorimeter Figure 7: Sample H γγ event in EM and Hadron Calorimeters 10

11 GeV η φ (deg) Figure 8: H γγ event in Crystal Calorimeter (.1 x.1 towers) with Double Pileup The upper plot of Fig. 7 shows the eletromagneti alorimeter with finer towers (.05 x.05). The energy of the photon near η 1 is mainly ontained within a single tower, but the energy of the photon near η -1 is split nearly evenly between adjaent towers. The hadron alorimeter deposits (also at.05 x.05) are shown in the lower plot of Fig. 7. Considerable ativity is seen, but looking at the small sale on the vertial axis, no large deposits are present; learly, most of the energy deposited in this event is eletromagneti. 11

12 GeV GeV η φ (deg.) a) Eletromagneti Calorimeter η φ (deg.) b) Hadron Calorimeter Figure 9: H γγ event in EM and Hadron Calorimeters with Double Pileup 12

13 200 GeV η φ (deg) Figure 10: QCD event in Crystal Calorimeter (.1 x.1 towers) Another 100 GeV H γγ event is shown in Figs. 8 & 9, this time superimposed over double pileup (38 minimum bias events). Sine the photons in this event are not stritly bak-to-bak, they are aompanied by a reoil jet, whih is visible at lower left in the lego plots. The energy of the reoil is distributed over a wider region, and is assoiated with a signifiant deposit in the hadron alorimeter, as an be noted in Fig. 9b. A bakground event (generated from 200 GeV QCD jets) is shown in Figs. 10 & 11. Two energy deposits an be learly noted. Neither EM luster is isolated, and both are aompanied by onsiderable hadron alorimeter energy. This event appears asymmetri (i.e. the energy of the luster near φ = 0 is larger than that near φ = 180 ). Sine both lusters are direted toward negative η, a third jet at η > 1 (thus outside the alorimeter boundary) probably balanes the energy. 13

14 GeV GeV η φ (deg.) a) Eletromagneti Calorimeter η φ (deg.) b) Hadron Calorimeter Figure 11: QCD event in EM and Hadron Calorimeters 14

15 2) Trigger Struture and Analysis After an event is loaded into the pixel arrays representing the eletromagneti (EM) and hadron alorimeters, as disussed above, a triggering analysis proedure is invoked. The rystals in the EM alorimeter ("ECAL") are first summed into towers of dimension.05 x.05,.1 x.1, and.2 x.2, in order to observe the effets of tower size on the triggering rate. "Hot" towers are identified that surpass an energy threshold of 10, 15, 20, 30, 40, or 50 GeV. Eah suh "luster" that is found is represented by a pointer to the highest-energy ontained.05 x.05 subtower. In a typial event, most suh lusters (at various energy levels and tower sizes) point to the same set of subtowers; i.e. they all arise from the same set of energy deposits. The topologial trigger uts (i.e. isolation, hadron energy veto, et. ) are then applied to these energy deposits, reating a set of veto flags. The number of lusters surviving the trigger uts at various energy thresholds may then be effiiently traked, and "Higgs" andidates, with a pair of lusters above a given energy threshold, an be identified. This logi is applied in the trigger analysis of the simulation data, and is not meant to be used in the on-line trigger itself, whih will be highly parallel and pipelined; the pointer sheme is used to effiiently emulate the trigger on a sequential off-line omputer. The handling of adjaenies an be important in trigger shemes using fixed tower sums, partiularly with small tower sizes (suh as.05 x.05). Fig. 12 shows the simple adjaeny-handling tehnique that has been adopted in the trigger analysis used here. If two adjaent towers are above a given energy threshold, as indiated in Fig. 12b, they are made to ount as one luster, assumed to be loated at the highest energy tower. If, on the other hand, two adjaent towers are both under a given energy threshold, but above a lower threshold (here assumed to be 2 levels smaller; i.e. 20\10, 30\15, 40\20, & 50\30 GeV), they are made to ount as one luster at the higher threshold, loated at the tower with highest energy. This was only performed for energy thresholds of 20 GeV and above; i.e. lusters ould not be added that were below the 10 & 15 GeV thresholds. This logi was seen to produe signifiant improvement in the effiieny of the Higgs trigger with the small (.05 x.05) tower size. As expeted, it beomes less effetive and neessary with larger tower sizes. The addition of lusters at lower energy thresholds an begin to onsiderably inrease the bakground trigger rate for the larger towers; sine the effetive tower size is now double the original, twie the pileup is inluded in the energy sum, leading to an elevated trigger. The adding/deleting of adjaent lusters per Fig. 12 should be readily implementable in a pipelined digital trigger. 15

16 Add as Cluster at Eth Eth Eth(-2) a) Two Adjaent Clusters Under Energy Threshold Count as single Cluster at Eth Eth b) Two Adjaent Clusters Over Energy Threshold Figure 12: Logi to Handle Adjaent Clusters 16

17 CUT H γγ, 100 GeV CUT 100 GeV Jets Figure 13: Energy Thresholds for "Seezlike" Cut 17

18 All energy thresholds and values used in this study are in units of transverse energy (E T ). It is assumed that the output of eah rystal (or hadron alorimeter ell) is first passed through a lookup table that sales by sin(θ), as is the standard pratie. Clusters passing the energy thresholds are submitted to a series of five topologial uts. The first two, "Blok " and "Blok Hadron " may be pipelined and implemented in a Level 1 trigger sheme. The following two uts, " Cone" and " Hadron " will require a global aess to alorimeter data (i.e. fixed tower sums are not suffiient), thus are slated for Level 2. The last ut ("Charged Energy ") requires data from a entral traker, and would be realized in Level 2 or Level 3. Eah trigger ut is disussed independently below. Trigger thresholds are set using lusters from simulated 100 GeV H γγ events (for the aepted data) and 100 GeV QCD jets (for the bakground). Figure 13 shows satter plots for the largest (horizontal axis) vs. next largest (vertial axis) ECAL energy luster in an event. Higgs data is plotted at top, QCD bakground at the bottom. The lower energy deposited by the QCD events is evident. Sine a trigger must be sensitive to other proesses besides Higgs photons, the results presented in the next setion trak the simulated events through several different energy thresholds. When looking expliitly for a Higgs, however, the results of Fig. 13 provide guidane. The gray regions in Fig. 13 represent the regions eliminated by a ut that demands one photon over 20 GeV and another over 30 GeV. This retains the vast majority of Higgs data, and rejets most QCD bakground. These uts are a bit more relaxed than those used in the study of Ref. [6], whih demanded one photon above 25 GeV and another beyond 40 GeV These uts were seen to lower the trigger effiieny for the 100 GeV Higgs events modeled here (the ut may be made more stringent if one assumes a Higgs with higher mass), thus looser uts were retained (the ensuing trigger rate on 20/30 GeV pairs is still suffiiently low, as presented in the next setion). The first topologial ut to be attempted is the blok isolation. This ut assumes that the rystals are summed into towers of dimension.05 x.05, whih in turn are summed into.2 x.2 supertowers. The logi is depited in Fig. 14. First, the highestenergy.05 tower (the gray tower with the "R") is removed from the.2 supertower sum. If the hottest rystal inside the hot.05 tower does not reside at the tower's edge, then this is suffiient. Otherwise, the adjaent.05 tower that is losest to the hottest rystal is also removed (provided that the.05 tower to be removed is still ontained in the.2 supertower sum), thus ompensating for shower sharing aross subtower boundaries. In ases where the hottest rystal is at a orner, the urrent logi removes the 3 nearest.05 subtowers, although this may not be neessary in pratie. 18

19 R R.2 x.2 Supertower.05 x.05 Subtower Figure 14: The "Blok " Cut Using a fully digital or hybrid digital/analog trigger sheme, blok isolation may be implemented and pipelined in several fashions. One method is to ompare various sums inside the hottest.05 subtower. This is illustrated in Fig. 15. The top row shows a omparison of two sums; one of the outside edges, and one of the 3 x 3 enter. If the enter has a higher energy than the edges, then only this.05 subtower need be removed from the.2 sum. If the edges dominate the energy, the shower will bleed over to an adjaent subtower, and one an pursue a few different strategies. The simplest method may be to merely ompare the energies of all adjoining.05 subtowers, and subtrat the highest-energy neighbor from the.2 sum. Another tehnique may be to ontinue using the information ontained in the rystals omposing the hottest.05 subtower, as illustrated in the first ELSE blok of Fig. 15. The first step in this sheme is to determine whih side of the.05 subtower is losest to the shower. Three-rystal sums are ompared to determine whih edge (or orner) is dominated by the shower. The adjaent.05 luster may then be identified and subtrated. If the shower energy is onentrated in a orner rystal, then the partiular orner is identified, and the 3 adjaent.05 bloks an be subtrated. 19

20 > Then Subtrat 5 x 5 Blok Else > Then, > Then Subtrat 5x5 Blok plus bottom Else Subtrat 5x5 Blok plus top Else > Then Do same proedure with right/left Else Subtrat 3 5x5 Bloks adjoining hottest orner Figure 15: Possible Pipelined Implementation of Blok 20

21 CUT CUT H γγ, 100 GeV CUT CUT 100 GeV Jets Figure 16: Blok Thresholds The blok isolation sheme doesn't are where the hot.05 subtower falls in.2 supertower; it an be near the enter or near the edge. This proess an thus be readily "hardwired"; i.e. eah.2 supertower will exeute a pipelined blok isolation alulation after every beam rossing. As will be seen in the following setion, the blok isolation ut is very useful at reduing the output rate of the level 1 trigger. A muh more powerful isolation one ut an then be attempted at level 2. The response of the data and bakground to the blok isolation ut is depited in Fig. 16. Clusters from the Higgs events are shown at top, and the QCD bakground is shown at the bottom. The lower axis of all plots is the isolation energy; i.e. the energy of 21

22 Loation of Hot Eal Subtower.2 x.2 Tower (Hadron Calorimeter) No Centering Figure 17: Example of the Blok Hadron Calorimeter the.2 supertower with the hot.05 subtower (and possibly a neighbor) subtrated. The vertial axis of the satter plots shows the energy of the hot.05 subtower. The histograms are projetions of the satter plots onto the horizontal axis. The grayed-out region represents the lusters that are ut out by the adopted isolation ut on the residual energy of E > 4 GeV. An energy-dependent ut may produe some benefit here; i.e. demand lower isolation energy when the hot.05 subtower energy is small. For this to be effetive, however, the isolation ut will have to be tightened (for low-energy lusters) below the urrent 4 GeV, whih may be problemati for trigger implementation (the value of 4 GeV used here is probably already too low, partiularly when onsidering the presene of diffiult-to-model orrelated noise in the tower sums). With this fator under onsideration, the flat ut at 4 GeV was retained. The tail seen at high isolation energy for the Higgs lusters (top row of plots) does not neessarily arise from the Higgs photons. All lusters found in the Higgs events are plotted in these graphs, inluding those due to reoil jets that an oasionally appear (as seen in Figs. 11 & 12). The Higgs trigger effiieny is thus somewhat better than these plots may indiate. The next ut to be attempted is the Blok Hadron Calorimeter. This ut is very simple, and is illustrated in Fig. 17. A ut is made on the energy ontained in the.2 x.2 hadron alorimeter tower sum loated behind a andidate eletromagneti luster. 22

23 CUT CUT H γγ, 100 GeV CUT CUT 100 GeV Jets Figure 18: Threshold Setting for Blok Hadron Calorimeter If this energy is greater than a preset threshold, the luster is onsidered hadroni in nature, and rejeted. As with the blok isolation (and as depited in Fig. 17), this ut is essentially hardwired for level 1 operation; i.e. the hadron alorimeter sum is not entered on the hot.05 eletromagneti luster. Figure 18 shows the distributions of Higgs data and QCD bakground. The horizontal axis (in all plots) is the energy of the.2 x.2 hadron alorimeter tower behind the andidate eletromagneti luster (the vertial axis of the satter plots is the energy of this luster). One an readily see that, as expeted, the Higgs photons deposit very little hadron energy, ompared with the QCD bakground. The shaded region denotes the 23

24 r = 0.3 r = 0.05 Remove Figure 19: The Cone lusters that are be removed by the adopted ut of E < 4 GeV (beware; this threshold may indeed be somewhat low for atual implementation in situations with orrelated detetor noise and pikup problems). The remaining trigger uts no longer use the established tower struture, hene must be applied at trigger level 2 or level 3. The first of these uts is a repeat of the isolation proedure, exept we now isolate rystals within a radius r <.05 of the hottest rystal in a luster andidate (approved by level 1) from a onentri irle of radius r <.3. The level 1 trigger, in this senario, would present the loation of its andidate lusters to the level 2 trigger, whih would proeed to read out all of the rystals (whih are now digitized to full preision) within a radius r <.3, and form the needed sums. The implementation is outlined in Fig. 19. For ases with portions of the.3 disk lying outside of the η < 1 aeptane, the partial sum of rystals within r <.3 is normalized up by the 24

25 (R <.05 GeV) CUT (R <.3 GeV) (R <.3 GeV) H gg, 100 GeV (R <.05 GeV) CUT (R <.3 GeV) (R <.3 GeV) 100 GeV Jets Figure 20: Data and Bakground Distributions for Cone fration of missing area (i.e. the segment of the disk that's outside of the alorimeter). This ould also be performed by adopting a threshold that depends on the loation of the enter rystal (i.e. the threshold would drop as the enter nears the edge of the alorimeter, where full disks of r <.3 are no longer possible). The data and bakground distributions for this ut are shown in Fig. 20. The horizontal axes are the energy in the.3 one (with the hot ore of.05 subtrated). The vertial axis of the satter plots is the energy of the hot.05 ore. In order to properly separate the data from bakground, an energy-dependent ut has been adopted; a luster is rejeted if it has an isolation energy greater than [4 + (E one - E tr )/5] in GeV, where E one is the energy in the 0.3 disk, and E tr is the energy in the hot.05 disk. This has been 25

26 Loation of Hot Eal Subtower.25 x.25 Tower (Hadron Calorimeter) Figure 21: The Hadron Calorimeter Cut used with the tests at (19-event pileup); for higher luminosity, the bias term is inreased to preserve the Higgs detetion effiieny (i.e. for 38-event pileup, the bias of 4 is inreased to 8.5). This ut is extremely powerful at removing the QCD bakground, as an be noted in the data & bakground separation in Fig. 20 (the Higgs photons are learly isolated in omparison to the QCD bakground; muh of the tail in the Higgs plot is due to jets aompanying some of the Higgs events), and as will be demonstrated in the next setion. Figure 21 illustrates the operation of the "entered hadron alorimeter" ut. This ut operates exatly as its title suggests; an energy sum of dimension.25 x.25 is taken over a region of the hadron alorimeter entered at the loation of the.05 eletromagneti subtower sum that produed a luster andidate. This is similar to the "blok hal veto" ut applied at level 1, exept that the hadron alorimeter sum is now entered on the EM luster, thus it doesn't employ a fixed tower struture, and is assumed to be run at level 2. No provision is urrently made for ases where the EM luster andidate is loated at the edge of the alorimeter (i.e. near η 1). Improved performane may be attained by making the energy threshold a funtion of luster position (or by normalizing the energy sum, as was done with the isolation one). 26

27 (.05) CUT CUT (.25 x.25) (.25 x.25) H γγ, 100 GeV (.05) CUT CUT (.25 x.25) (.25 x.25) 100 GeV Jets Figure 22: Data and Bakground Distributions for Hal Figure 22 shows the data and bakground distributions. The horizontal axes show the entered.25 x.25 hadron alorimeter energy sum. The vertial axis of the satter plots shows the energy of the hot.05 tower in the eletromagneti alorimeter. Clusters whih flunk the adopted ut at 4 GeV are in the grayed-out region at right (4 GeV may be a bit tight in pratie if orrelated detetor noise is onsidered). A lear separation between data and bakground is seen (less bakground passes this ut than esaped the blok Hal veto of Fig. 18). The ation of the final trigger ut is shown in Figure 23. This is a ut on harged traks that impat the alorimeter within a blok of 3 x 3 rystals entered at the hottest rystal in a luster (assuming that we're deteting photons, we veto on assoiated harged 27

28 C U T H γγ, 100 GeV C U T 100 GeV Jets Figure 23: Higgs & QCD Distributions for Charged Energy Cut traks; if the goal is to detet eletrons, suh harged traks would be required). The ECAL luster is rejeted if it is impated by harged traks of 5 GeV or more. This ut assumes that some reonstrution has been performed on entral traker data, whih will be a nontrivial task at the LHC (thus it would be run at level 2 or level 3). 28

29 Fig. 23 shows a histogram taken against the harged energy assoiated with the ECAL luster andidate. The 5 GeV ut is indiated (the grayed region is rejeted). The bakground (whih is seldom isolated; the jets are broad) has a long tail that is totally laking in the Higgs data. The ut an be tightened and still retain effiieny, however this ut doesn't remove muh data (it will mainly serve to separate eletrons from photons), thus it was kept onservative. The implementation of these uts, partiularly those applied at level 1, will depend losely on the data aquisition tehniques. For instane, if the front-end eletronis on the rystals require several beam rossings to digitize a signal (and the trigger is all digital), a filtering algorithm will have to be run on the data to identify luster andidates with beam rossings. If, however, a prompt alorimeter signal an be fast-shaped with enough auray (i.e. 8 bits) for the trigger during eah beam rossing, it ould be flash-digitized, removing any time ambiguity. The amount of proessing that an be performed diretly in an analog fashion is urrently under debate. The.05 subtowers are omprised of 25 rystals; these may be andidates for an analog sum. The larger towers (i.e. the.2 x.2) involve too many elements (i.e. 400), making an analog sum highly improbable. Digital sums an be arried out in standard sequential fashion (i.e. using adder trees or a pipelined adder). The trigger uts desribed in this report would be implemented at Levels 1 & 2, and mainly serve to remove the dominant bakground from QCD jets. The next tier of bakground is due to isolated π partiles, whih should be produed somewhere near 1 khz (beyond 20 GeV energy) at a luminosity of (see Fig. 24; these are singles rates, the rates of isolated π pairs will be extremely low). This bakground might be attenuated, if desired, by more ompliated uts running in a level 3 (or augmented level 2) trigger; i.e. finding features that may be indiative of two overlapping photon showers, reognizing π showers via lassifiers suh as neural networks, et. Suh algorithms are a topi of ative researh, and are being developed and tested at urrently running experiments. Unfortunately they are beyond the sope of the urrent study, whih has foused mainly on the higher-level trigger. The effiieny of the trigger uts on H γγ events was tested by running PYTHIA for 100 GeV Higgs, and traking the events through all uts. Results are shown in Table 1 for a luminosity of (19-event minimum bias pileup) and in Table 2 for double luminosity (38-event pileup). Beause of the limited η overage of the alorimeter, there is an intrinsi 80% aeptane loss in H γγ events; i.e. only 20% of the generated events have both photons in the alorimeter. This fator has been normalized out of the data in Tables 1 & 2, whih show the perentages of Higgs events 29

30 (with both photons in the alorimeter) that pass the various uts. The first olumn lists the energy threshold applied to the alorimeter luster (at least two lusters of the given energy are required). Three rows of data are assoiated with eah energy threshold, orresponding to the trigger tower size that is used. The bottom set of rows (the "Seezlike Cut") requires one photon to have at least 20 GeV and the other to have at least 30 GeV (as was introdued with Fig. 13). This is assumed to be the ut applied to identify Higgs andidates. Eah olumn lists the "topologial" ut that is applied. The first 6 olumns show the response to eah ut applied separately (the "Raw" olumn has no assoiated topologial ut, and shows the perentage of events that pass the energy thresholds). The two olumns at right have several uts working at one. The "Prompt Cuts" are the blok isolation and the blok hadron alorimeter veto uts, whih would be applied at level 1. The "All Cuts" olumn shows the perentage of events that pass all uts applied together (as would be output from level 2). Looking at the "Seezlike" rows of Table 1, we an see that these uts are roughly 95% effiient (when all are applied together), with a small effiieny inrease (1.5%) when enlarging the trigger sums from.05 towers to.2 towers These figures inlude the proximity onditions outlined in Fig. 12, whih inreased the trigger effiieny by 7% for.05 towers and 1.5% for.2 towers (this effet is mainly seen on the 30 GeV luster; the effiieny inrease for.05 lusters at a 20 GeV threshold is only 1.6%). The small.05 towers are thus able to produe an effetive Higgs trigger, provided that the adjaeny ondition is properly taken into aount. The most restriting ut is the entered isolation one; this produes most of the 5% loss in net effiieny. This ut is highly effetive at reduing bakground, however, as will be illustrated in the next setion. Table 2 shows the results for double minimum bias bakground (38-event pileup). Here we see that the Higgs trigger has beome roughly 91% effiient. This loss in effiieny is distributed aross all uts (the isolation one thresholds have been inreased, as was disussed previously). Some of this effiieny may be reovered by adjusting the various ut thresholds (although the 90% passage rate may well be adequate). 30

31 H γ γ # Events: 1735 % Passing Cuts m = 100 GeV 19 MB Pileup Hit Energy 2 Hits Raw No uts Blok Blok Hal Cone Hal Charged Energy Cut Prompt Cuts All Cuts 10 GeV (.05) GeV (.1) GeV (.2) GeV (.05) GeV (.1) GeV (.2) GeV (.05) GeV (.1) GeV (.2) GeV (.05) GeV (.1) GeV (.2) Seezlike Cut 20/30 GeV (.05) /30 GeV (.1) /30 GeV (.2) Table 1: Effiienies for H γγ at m H = 100 GeV, 19-event pileup 31

32 H γ γ # Events: 1605 % Passing Cuts m = 100 GeV 38 MB Pileup Hit Energy 2 Hits Raw No uts Blok Blok Hal Cone Hal Charged Energy Cut Prompt Cuts All Cuts 10 GeV (.05) GeV (.1) GeV (.2) GeV (.05) GeV (.1) GeV (.2) GeV (.05) GeV (.1) GeV (.2) GeV (.05) GeV (.1) GeV (.2) Seezlike Cut 20/30 GeV (.05) /30 GeV (.1) /30 GeV (.2) Table 2: Effiienies for H γγ at m H = 100 GeV, 38-event pileup 32

33 3) Trigger Rates As an be seen in Fig. 24 (Ref. [7]), jets are the predominant bakground to the H γγ proess at the level 1/2 level triggers. In order to asertain the effet of the QCD bakground on the photon/eletron trigger rates, PYTHIA was run to produe hard QCD events in various prodution energy windows, as summarized in Table 3 (the atual PYTHIA dek used an be seen in the subroutine "SETPTA", that is listed in Appendix 2). The ross-setions at whih suh bakground is produed (see Table 3) were taken from the PYTHIA simulations, and are plotted in Fig. 25 (the top urve in Fig. 24 is taken for η < 2, while the data of Fig. 25 were generated for η < 10; remember that all energies quoted here are transverse; i.e. E T ). These ross-setions were saled by a luminosity of to derive the prodution rates given in Table 3. The number of simulated events generated at eah energy are also listed in Table 3, together with a "bin width" (i.e. interval between suessive prodution energies, used in the integrations; the 50 GeV width assumed beyond 200 GeV is a rude approximation to a higher-energy tail). The "minimum rate" is the raw rate divided by the number of events, thus is essentially the smallest rate that the statistis an reah. The perentage of events passing the energy thresholds was nearly idential for prodution energies below 15 GeV (the minimum energy threshold is set at 10 GeV in the trigger); at these low energies, any trigger rate is aused primarily by the 19 piled-up minimum bias events (to validate this, additional runs were taken at 5 GeV [ events] & 10 GeV [ events]). The "0 GeV" row represents a run that only looked at minimum bias events, and reflets the low-energy bakground. The totals listed in Table 3 represent integrated sums; the "minimum rate" listed here is the sum of the minimum rates averaged between adjaent rows and saled by the bin width at eah prodution energy 15 GeV (the minimum bias row gives the generi low-energy bakground at the 66 mhz beam rossing rate, and is added in separately). Sine the ross-setions are dereasing at least exponentially, this is a rude trapezoidal integration (assuming a linear dependene between data points), and may produe an over-estimate. The bin widths are reasonably narrow here, however, thus integration errors should not prove more signifiant than other error soures (i.e. errors in the assumed prodution rates, PYTHIA, et.). The minimum rate of 200 Hz (for single photons) that is reahed by these statistis (single-event level) is well within the assumed 10 khz level 1 trigger output. 33

34 Figure 24: Prodution Cross Setions for H γγ Bakground 1.00E E E+06 nb/gev 1.00E E E E E E GeV Figure 25: Calulated Cross-Setion for Jet Bakground to H γγ 34

35 Prodution Energy (GeV) Bin Width (GeV) Number of Events Cross Setion (nb/gev) Raw Rate Minimum Rate hz/gev hz/gev E E E E E E E E E E E E E E E E E E hz hz E hz hz Totals E Table 3: Statistis of Bakground Simulations The rate alulation is performed in several steps. First, events are traked through the various uts, and a table is generated at eah prodution energy giving the fration of generated events that are aepted. In order to deouple the rates arising from the 19 piled-up minimum bias events from the overlaid QCD jet event, the fration of events generated by the minimum bias "0 GeV" run that passed the uts is subtrated from the orresponding fration alulated at a higher prodution energy. This differene is then normalized by the assumed prodution rate (from Fig. 25, saled by a luminosity of ), yielding the ontribution to the trigger rate at a given prodution energy. These rate ontributions are then integrated over all prodution energies, and added with the rate expeted from the minimum bias events (the "0 GeV" run), to form a net trigger rate. This proess is illustrated via Eqs. 1 & 2 below: 1) f 0 = (N aept )/(N Gen ) for minimum bias ("0 GeV" run) f p = (N aept )/(N Gen ) at QCD prodution energy "E p " dr dp Ep = f p - f 0 dσ dp Ep L 35

36 2) R = dr dp 0 de p + f 0 (66 Mhz) Equation (2) assumes that the minimum bias events (simulated here as 19 simultaneous events) our at the beam rossing rate of 66 mhz. This orretion beomes signifiant at the lower prodution energies (i.e. 20 GeV and less), where the olletive minimum bias proesses begin to ompete with the overlaid QCD event. By performing the subtration of Eq. 1, the alulated rates show the effet of the overlaid QCD event ating together with the minimum bias pileup bakground; the effets of the minimum bias events by themselves is thus eliminated, and added separately in Eq. 2. The event flow for eah prodution energy is given in Appendix 1, where a set of tables is presented showing the event flow for eah ut, the perentage of events passing the uts, and the differential rates (in Hz/GeV). The format of these tables is similar to that used in Tables 1 & 2; i.e. the "Raw" olumn assumes no uts applied, the following 5 olumns assume that only the labeled ut is ating on the "raw" data, the "Prompt Cuts" are the blok isolation and blok hadron veto together, and the "All Cuts" boasts the onerted ation of all 5 uts. The first 4 sets of rows show the data for single-hits at varying energy threshold (i.e. at least one deposit of the quoted tower size & energy in an event), and the following 5 sets of rows are data for dual-hits (i.e. at least two deposits of the quoted tower size & energy in an event). The bottom set of rows is our andidate Higgs trigger that was derived from the data of Fig. 13; i.e. one luster of 20 GeV and another of 30 GeV. The data in all perentage and rate tables (exept for the "0 GeV" set) have the minimum bias ontribution subtrated, as illustrated in Eq. 1. Some of this data is summarized in Figs. 26, 27, & 28, whih illustrate the ation of the various uts at minimum bias and 50\200 GeV QCD prodution energies. These plots basially show a row of the orresponding table in Appendix 1; i.e. the perentage of generated events passed by the uts are plotted for eah tower size (a legend for the mapping of tower size to plot symbol/shading is given on the figures at upper right). The ut orresponding to eah loation on the horizontal axis is listed on the upper left plot. Eah row of Figs. 26, 27 & 28 are taken at the listed prodution energy, and eah olumn reflets lusters passing the listed energy threshold(s). 36

37 10 GeV Single Hit 20 GeV Single Hit % Passed Raw Blok Blok Hal Cone Hal Cone Charge Prompt Cuts All Cuts % Passed Cut Applied Minimum Bias.05 x.05.1 x.1.2 x Cut Applied % Passed Cut Applied % Passed GeV Jets Cut Applied % Passed Cut Applied % Passed GeV Jets Cut Applied Figure 26: Ation of Trigger Cuts on Generated Events 37

38 30 GeV Single Hit 10 GeV Double Hit.05 x Raw x.1 % Passed Blok Blok Hal Cone Hal Cone Charge Prompt Cuts All Cuts % Passed Cut Applied Minimum Bias.2 x Cut Applied % Passed % Passed % Passed Cut Applied GeV Jets % Passed GeV Jets Cut Applied Cut Applied Cut Applied Figure 27: Ation of Trigger Cuts on Generated Events 38

39 20 GeV Double Hit 20\30 GeV Seezlike Cut.05 x.05 % Passed % Passed Raw Blok Blok Hal Cone Hal Cone Charge Prompt Cuts All Cuts Cut Applied Cut Applied % Passed Minimum Bias % Passed GeV Jets.1 x.1.2 x Cut Applied Cut Applied % Passed Cut Applied % Passed 200 GeV Jets Cut Applied Figure 28: Ation of Trigger Cuts on Generated Events 39

40 The hange in rate with tower size is immediately obvious; the large tower size leads to an inrease in trigger rate. This effet is muh more pronouned at lower prodution energies, where the larger sums are needed to pass the energy thresholds. The relative ation of the various uts an also be asertained through these plots. The most effetive ut is the entered isolation one (ut #4), whih redues the rates from all tower sizes to roughly idential amounts. Although blok isolation (#2) is seen to perform a little better than the blok hadron veto (#3), both seem to operate at a similar rejetion ratio. Their olletive ation does ahieve some additional rate redution (i.e. they don't always rejet the same events), as an be seen by the lower aeptane of the "Prompt Cuts" (#8). This is partiularly evident at the higher prodution energy, where all uts have greater effet (the isolation and deposited hadron energies extend well above the ut thresholds). The "Charged Energy " (#6) is seen to introdue omparatively little rate attenuation, as expeted from the disussion in the previous setion (Fig. 23). These uts are seen to be very effetive in eliminating luster pairs (see Figs. 27, 28), where eah ut an square its attenuation fator in the absene of luster energy orrelation. The next stage of the alulation is the integration of differential rate over all prodution energies, as outlined in Eq. 2. This has been aomplished via Tables 4-6, whih respetively show raw rates (no uts), rates passing the prompt uts, and rates passing all uts. Eah olumn in the body of the table shows the rates resulting from the labeled prodution energy (extrated from the analogous olumn of the tables in Appendix 1). Exepting the "0" olumn, these rates have their minimum bias ontribution subtrated, as in Eq. 1. Residuals within ± a few events were set to zero to avoid introdution of noise from the limited sample of minimum bias events. This resulted in essentially no ontribution from the data taken at 5 & 10 GeV, whih were dominated by the minimum bias pileup. A possible exeption, however, was seen in the single-luster rate exeeding a 10 GeV threshold after all uts (Table 6, first row), where a potentially signifiant exess of events surpassed the minimum bias sample. The origin of this effet is unknown (i.e. the superimposed QCD event generated by PYTHIA tends to be slightly more often isolated than the minimum-bias-only sample?). Beause the prodution rates are so large in this energy region, the relatively small number of exess events doubled the integrated rates alulated in this row of Table 6. 40

41 Jet Energy (GeV) Net Rate Hit Energy 1 Hit Hz Hz/GeV Hz/GeV Hz/GeV Hz/GeV Hz/GeV Hz/GeV Hz/GeV Hz/GeV Hz/GeV Hz/GeV Hz/GeV Hz 10 GeV (.05) 62, ,346 5,728 5,478 3,996 2, , GeV (.1) 88, ,581 11,094 10,688 7,698 3,944 1, , GeV (.2) 201, ,989 30,204 27,249 17,538 7,491 2, ,132, GeV (.05) 7, , GeV (.1) 11, ,163 1, , GeV (.2) 27, ,957 2,996 3,333 2,445 1, , GeV (.05) , GeV (.1) 6, , GeV (.2) 6, , GeV (.05) , GeV (.1) 3, , GeV (.2) 3, ,107 2 Hits 10 GeV (.05) , GeV (.1) , GeV (.2) 13, ,212 1,329 1, , GeV (.05) , GeV (.1) , GeV (.2) , GeV (.05) GeV (.1) GeV (.2) , GeV (.05) GeV (.1) GeV (.2) Seezlike Cut Raw Rates 20/30 GeV (.05) /30 GeV (.1) ,394 20/30 GeV (.2) ,779 Bin Width (GeV) Table 4: Differential Rate Integration for Raw Data (No Cuts) The result of the rate integration is given in the rightmost olumn. The integration is performed in a trapezoidal fashion, with the average rate between adjaent olumns saled by their energy differene ("bin width"), and summed aross the table. The "0" olumn is not saled in this fashion, but added diretly, sine it gives the minimum bias ontribution, whih is already in absolute Hz (in order to aount for the segment of the prodution energy integral between 0 and 5 GeV, half of the 5 GeV rate is added into the integral, thus assuming a linear deay to zero at 0 GeV; this ontributes only in the ase mentioned above, sine the 5 GeV rates are otherwise zero). Admittedly, the linear integration is rude, but sine the prodution energy bins are tightly lustered where the rates hange most quikly, it shouldn't produe unreasonable results. 41