TRACKING AT THE SSC/LHC HF-W. SADROZINSKI, A. SEIDEN and AJ WEINSTEIN 1987 SSC ...

13 Pages·2002·0.89 MB·English

(cid:9)(cid:9)
NuclearInstrumentsandMethodsin PhysicsResearch A279(1989) 223-235 223
North-Holland, Amsterdam
TRACKINGAT THE SSC/LHC
H.F.-W. SADROZINSKI, A. SEIDEN and A.J. WEINSTEIN
Santa Cruz InstituteforParticle Physics, University ofCalifornia, SantaCruz, CA 95064, USA
We presentthedesign of atracking system fortheSSC/LHCbased on siliconmicrostrip technology with excellentmomentum
resolution andgood multitrack resolution.Theparameters ofthetracking device arebased on an analysis of therequirements of 1
TeVphysics. Theperformanceof the silicon trackerhasbeen investigated in a MonteCarlo study.An ongoing R&Dprogramto
develop radiation-hard fast readoutchips forthesiliconmicrostripsis described.
1.Introduction the function of the tracking to includeresolvingtracks
inside dense jets and measuring momenta of isolated
In the past [1,2] thediscussion of detector capabili- high energy leptons with precision comparable to the
ties at the next generation large hadron collider calorimeter in order to momentum-analyze both elec-
(SSC/LHC) has been biased towards calorimetry. In trons andmuons with the same resolution.
mostphysicsstudies, informationfromcalorimeters has
beenused to define the topology of the event (number
of jets, missing E etc.) and to measure the energy of 2. Physicsmotivation forhigh precision tracking
theelectrons and the mass ofjets. In contrast, tracking
hasbeen reducedto aminimalrole as abackup for the On can measuretheperformance of generalpurpose
calorimeter, to detect detached vertices and identify SSC/LHC detectors on their ability to discover the
multiple interactions within onebeam crossing. Only a Higgs boson, if its mass is in the 100 GeV to 1 TeV
modest momentum resolutionwasrequired. Inspired by range, and to studyits decays. Depending on itsmass,
the work of the Compact Detector Subgroup of the the Higgs search will focus on different signatures and
1987 SSC Detector Workshop [3j,wepropose toextend thus will require different detector capabilities. This is
shownin table 1 [3], where as a function of Higgs mass
8000 800
(a) (b)
6000 600
s.
r
v
r
4000 400
m
G
2000 200
0
60 80 100 120 60 80 100 120
Jet Mass [GeV] Jet Mass [GeV]
Charged Event Multiplicity
n~h Fig. 2. Mass of jets recoiling against Wbosons (solid histo-
Fig. 1. Charged multiplicity n~h in jets recoiling against W gram: W+W events from a Higgs with 1 TeV mass, dotted
bosons in ppcollisions (PYTHIA4.8):(a)W+Wevents from histogram: W+QCDjets events with 1 TeV mass, both nor-
aHiggswith 1TeVmass,(b)W+QCDjets events with1 TeV malized to one SSC year), (a) all events, (b) events with
mass. n,h< 40.
0168-9002/89/$03.50 CC Elsevier Science Publishers B.V. V.TRACKING DEVICES
(North-Holland Physics Publishing Division)
224 H.F.-W Sadrozinskietal./TrackingattheSSC/LHC
Table1
H°detectionin acompactsolenoid detector
Detected
MHo Advantages of Compact RatesPerYear
(GeV/c2) Signature Solenoid Detector (1040cm 2)
60
H0 -yy Good7r°/-y separation 500
in microconverter
100
F_ tv -Vertex detection (b tag)
H'W GoodN/e ID in Jets 400
L- bb Goodmissingpt
150
H0-ZZ' - GoodZmass reconstruction
2MZ inboth upandee
300 140 (Z -"eonly)
560 (Z - tc,e)
H0--> ZZ -4t+ Good Zmass measurement
-ZZ -t+t-vv in both eeandPWup 1 TeV
-WW -evty Good missingpt
500 29 (Z ->eonly)
116(Z -+ p,e)
r ev,py,TV
H'-WW - Bestjet capability:
700 L-. qq - Calorimetry 5000
Precise, hi resolution
t+t- analysis ofcharged 1000
tracks andneutrals
L- qq insidejets
1TeV W+Wt Preciselepton measure-
ment in TeVrange
thedetector requirements areshown.ForthelightHiggs nch=32, and fig. lb shows nch for the background
decaying into bb onemust have excellentvertex recon- (W Iv)+QCDjets with a mean of noh=75.Acutat
struction to tag b decays [4]. For the intermediate n,h<40 retains78%of the signal whilerejecting92% of
Higgs, which decays to ZZ pairs leading to a 4-lepton the background. Fig. 2 shows the effect of this multipl-
final state, goodpair mass resolution in both electrons icity cut on the mass distribution of thejets recoiling
and muons is necessaryto increase the rate bya factor against the leptonically decaying W. Fig. 2a shows the
of four over the electron-only case [5]. At large Higgs signal around 84 GeV and the background before the
masses, where in the WW decay one of the W's is cut (signal/background =1:7), and fig. 2b shows the
detected in its hadronic decay, the ability to track result of the multiplicity cut (signal/background =
efficiently charged particles of the underlying event 1:0.7).
allows one to discriminate between the signal (WW) A precision tracking device which allows the de-
andthemajorbackground (W +QCDjet). To quantify terminationof thechargedmultiplicitydown to pt=0.5
this, we show in fig. 1 the charged event multiplicities GeV thus provides crucial information complementary
n,h fromPYTHIA 4.8 [6]forthe two cases (onlytracks to the calorimeter to suppress the background suffi-
with rapidity JYJ<2.5 and transverse momentum pt > ciently. This is possible becausethetracking device has
0.5 GeV in events containing ajet with the massof the potentiallymore sensitivityto thesoft componentof the
Ware counted). Fig. la is thecharged multiplicity for event (tracking is possible down to 250 MeV) and has
H -->(W --iIv)+(W -jets) with a mean multiplicity of much better spatialresolvingpower.
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H.F.-W. Sadrozinskietal. /Trackingat theSSC/LHC 225
3. Design ofa 1 TeV tracking system
The environment at the SSC/LHC will be a chal-
lenge to a tracking device. It can be characterized by ¢~+ 'k 'k
lcoalrlgiesimounltriaptleic.iJteitess,widtehnsaenjeetnse,rgsytifofft1raTceksV awinldl haavhiegah titi y¢++fti++~iÍfl¢+~ +++ili+~' yv',,,í ~~\\\\\
charged multiplicity of n.h=50-100 and a mean angu-
lar track separation in thecore of (B) =0.5 mrad (i.e.,
500 wm at 1 m radius!) [5]. On the otherhand,isolated
leptons from Z or W decays will have transverse
momentaofthe orderupto p, =1 TeV.Additionally, if
the readout is not accomplished within the time be-
tween beam crossings (16 ns at the SSC) so-called
minimum-bias events will be added to the interesting 0 10 20 30 40 50
events, increasing the occupancy. This calls for adetec- Fig.3. Beam view of silicon tracking system. The outerradius
tor which has small cells commensurate to the track is 50cm.
separation, good intrinsic position resolution, and fast
collection time.
A tracker consisting of Si microstrips with 25 Wm
pitch fits these requirements. It was shown [7] that a sponds to about 0.6 Mrad per year [8]. Clearly, the
double hit resolutionof100 Pmand an intrinsic resolu- design of sufficiently radiation-resistant electronics is
tion ofbetter than 5wm canbe achieved.Thecollection critically important. Note that for high momentum
time can be made assmallas10 ns. tracks, theimpact parameter erroris still - 5 [Lm, even
Amodelfor the organizationof such detectors is the starting 8 cm from theorigin, since thelong leverarm
vector tracking chamber, made of jet cells. Thejet cell of the tracking device provides a very well measured
geometry was introduced by the JADE collaboration. angle and curvature.
The first of such chambers incorporating stereo wires, (3) We assume each layer is 150 [Lm thick and has
and smaller jet cells to aid in pattern recognition, was double sided readout, a technological development
used bythe MARK III detector. Subsequent examples which seems to be realistic [9]. This gives 2.5% of a
are the trackers for the MARK II, CDF, SLD and radiation lengthofmaterial for the silicon and probably
ZEUS. Note also, that the use of a vector tracking about 4-5% Xo in total if we include a support struc-
chamber allows a crude local calculation of the trans- ture. It is of great importance to keep the amount of
versemomentum, using tracksegments; this allows the material in this range to avoid creating many soft
reconstructionofhightransversemomentumtracksonly, electron-positron pairs from photon conversions (see
in an efficient manner. This would vastly shrink the section 5). In addition, B meson vertex reconstruction
computer timeneeded fortrackreconstruction for events for the light Higgs scenarioinvolves lower momentum
in which onlyhigh p, tracks aredesired. tracks and is sensitive tomultiplescattering errors. For
our design the multiple scattering contribution to the
3.1. Parameters of the tracking chamber impact parameter error is about 80 [tm/p with p in
GeV. Requiring an error <20 ~tm implies B tagging
Theparametersofthetracker areas follows (see fig. usingtracks with p>4GeV. For the lightHiggssearch
3): discussed above, we find that the efficiency for recon-
(1) It is made of 16 layers of silicon strips (25 wm structing a 100 GeV Higgs -> bb with at least two
pitch) organized into 8pairs (superlayers) ofdetectors. charged tracks falling within the central f2 units of
The detectors are assumed tobe double sided(one side rapidity is reduced by only 14% if we do B tagging
with axial strips, the other with small angle stereo) so requiring two tracks with p> 4GeV.
the total number of measurements is 32. Thus the
detector can be thought of as 8 axial and 8 stereo 3.2. Patternrecognitionrequirements
superlayers, although the axialand stereo measurements
are grouped together locally. This can be compared to We showin fig. 4 two pairs of detector layers. The
typical vector drift chambers, such as the new MARK detector arrangement isspecified by the distances 8 and
II chamber, whichhas 6 superlayers ofeach type. A, which are the separation between pairs in a super-
(2) The radius varies from 8 to 50 cm. The inner layer and between superlayers, respectively. The con-
radius is determined by the amount ofradiation damage flicting demands on 6 and A are as follows:
that can be tolerated. For the SSC operating at a (a) would like 6 small enough to make matching of
luminosity of 1033 CM-2 s-1, this inner radius corre- points on atrack simple;
V.TRACKING DEVICES
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226 H.F.-W.Sadrozinskietal. / TrackingattheSSC/LHC
excellent double track resolution of the silicon strip
trackeris fulfilled for only theouter5 superlayers(out
of 8 total) with radii ri>_ 20 cm.Thus thedevice should
be able to yield a sufficient number of distinct hits for
nearly allof thetracks.
(2) To match points into a segment we choose the
simplest algorithm illustrated by thedashed line in fig.
4.Toeach pointin theinnerlayerofapair we associate
the pointwith theclosest (p angle in the outer member
of the pair. For a curving track the deviation in space
froma perfect match, usingthis algorithm, is given by:
[ 2PtrackIs.
However, in thejetcore we canexpect nearby hits from
very stiff tracks with a mean spacing of (B)ri. These
can cause incorrect associations in segment formation.
Thus, the simple algorithm for matching points into
Fig.4.Atrackpassingthroughtwoadjacentlayerpairs. vectored segments will work provided:
ri
S<(B)ri,
2Ptrack
(b) would like 8 large enough that the track angle or
(tangent vector)is well measured;
S
(c) would like 4 big enough to fill a given space; and
2(9) <Ptrack
(d) would like d small enough to allow frequent sam-
pling. This relation needs to bevalid for all momenta within
For thepattern recognition we require that: thejetcore and provides the motivation for asmall S.
(1) differenttracks give distinct hits; (3) The basis for linking vector segments [10] is
(2) hits in the paired layers, separated by S, can be illustrated in fig. 5. The angle between the tangent
locally associated into correct vector segments; and vectorsandachordconnecting thesegmentsis thesame
(3) vector segments from different pairs can be cor- for both vector segments belonging to the same circle.
rectly linked into tracks. Each angle Bt or 02 is measuredwith a precisiongiven
We define: by C2a.18. Linking can be done if this accuracy is
Ptrack=track's radius of curvature; adequate.We show in fig. 6thetrajectories of twovery
(0) =typicaltrack separation angle; high momentum tracks separatedbyaproduction angle
a, =position resolution of measuringelement; of (0). An incorrectlink yields thedashed trackwhose
E, =twotrackresolvingpowerin space, locally,fora
measuring element;
5 =separation of elements used to measure track
vectors;
r =outerradius of device; and
m
(cid:9)=ri mean radius of the ith pair.
From the physics considerations discussed earlier,
(0)=0.5 mrad. Forasiliconstrip detector with 25 ~tm
pitch, am=5 Wm and E,.=100 ttm. Suitable signal
processing could distinguish tracks entering adjacent
microstrips, giving Em=25 Wm at the expense of a
slightlydegraded position resolution.
We nowquantify therelation betweenparameters so
that the three pattern recognition requirements can be
met:
(1) To seedistinct hits from different tracks in layer
i we need:
Em< ri(B).
This is avery stringent requirement, which even forthe Fig.5.Relation forvectorsegmentslyingononetrack.
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H.F.-W. Sadrozinski et al./ TrackingattheSSC/LHC 227
Bt = AZ + <8>
Fig.6.Angular relations foraspurious track(dashed) created
from hitsfromtworeal tracks.
Fig.8.High pt ISAJETeventin a3Tfield.
angles donotmatchby an amount (B). Thus, the goal
forthelinking to work is:
< (6).
S B mesons, b::5 300 gym. To avoid errors in association
forpairs, we requireas before:
This provides themotivation for alarge S.
For am =5 wm and S=1 cm, we get am/8 =0.5 b8
d= <r,<0> or b< r2<0>
mrad, which is - (0). We will see below, using a full
Monte Carlo simulation, that S=1 cm is indeed close
to optimum. Taking S=1 cm,and rt >8cm impliesthat thereis no
problem for b<320 pm even for the innermostlayer.
In theabovewehaveassumedthat tracks come from
There is aproblem Ks, which mighthaveto bepicked
the origin when we match the two hits into a vector
up in asecond pass,if they arecloseto thejet axis.
segment (but not in the vector segment linking). We
show in fig. 7what happens for a trackwith animpact
parameter b. 3.3. MonteCarlostudies
The displacement of the second hit in a closely
spaced pairof detectorsat radius ri foravery stifftrack In ref. [5], we have looked in more detail at the
with impact parameter b, with respect to astraight line ability to do tracking in 1 TeV jets with a silicon
through the origin,is d=bS/ri. For thedecayof D or tracker.TheprogramISAJET [111 wasused to generate
events with two quark or gluonjets, each with pt >_1
TeV. The mean multiplicity within JYJ<2 in these
events is 330, of which 118 have pt >1 GeV. Fig. 8
shows ahigh eventin a 3 Tmagnetic field.Aregion
pt
near the core of the tight 1.5 TeVjet in thelower left
quadrant of the event, at a radius of 26 cm, has been
blownup as fig.9. Thescaleis matchedto thesize of a
single strip detector containing 1024 25-~tm elements.
(Note the strips have beentilted to compensate for the
Lorentzangledue to themagnetic field.) At this scale,
which is the one relevant to track finding, the stiff
tracks arenotconfusing.
To quantify this further, we have performedthefirst
two steps of the pattern recognition for events with 1
TeVjets as outlined in section3.2.Detailscanbefound
in ref. [5]; we report here only the results. For tracks
Fig. 7. Relation of points to be associated into a vector with pt >1 GeV, we evaluate the efficiency vs pt for
segmentforastifftrackwith impactparameterb. findingtracks if we require at leastNVEC=4, 6, or 8
V.TRACKING DEVICES
228 H.F.-W. Sadrozinskietal. /Trackingat theSSC/LHC
Fig.9.Blowup ofhigh p, eventshowingthejetcore.
correctlyfound vector segments to call thetrack found.
Theresults forS chosen equal to 1 cm are shownin fig.
10, wherethelast binincludes overflows.Theefficiency
approaches 100% for high momentum tracks. In con-
trast to conventional drift chamber trackers, which are
most efficient for lowp, tracks which separate from
jets, the silicon trackerwe describe is most efficient for
the high-pt tracks in the core of jets. We find that a
S=2 cm is noticeably worse than S= 1 cm. Choosing
S=5 mm wouldgive abouta10%increase in efficiency
if all 8 segments are required and little change for the
case of 6or 4segments found.
Oncevectorsegments arefound, theymust be unam-
biguouslylinked together to formtracks.Onewayto do
this is to use a techniqueemployed successfullywith the
Mark II jet-cell central driftchamber at the SLC [12].
The idea is to calculate the curvature (K = 1/2ptrack)
andazimuth at the origin $o of atrackpassing through
the origin and tangent to the vector segment. A vector
segmentprovides a measure, at averageradius r, of the
track azimuthq) and rate of change of azimuthd.o/dr
We thus calculate
-dS5/dr
K=
do/dr)2
~1 +(r
op =4>+árcslnKi.
This will produce a mapping in which all vector
segments found for a given track should he near one Fig. 10. Tracking efficiency vs pt as a function of number of
point in the K-$o plane. Thevector segments found for segments reconstructed (8=1 cm). The error bars are 95%
the eventshownin fig. 8 havebeenplotted in fig. 11a. confidence levellimits, from thestatistics of theMonte Carlo
Up to eightvector segments areplotted foreach track. run.
H.F.-W. Sadrozinskiet al./Trackingat theSSC/LHC 229
0.4 one side of the detector at a small angle (the stereo
angle a) with respect to the axialdirection. For detec-
0.2
tors of length 1=10 cm, a stereo angle of a=5 mrad
0.0
yields a "stereo displacement" s=la =500 lim. We
-0.2 assume each pair of strips is organizedas shown in fig.
-0.4 12, with u stereo strips on one detector of apair and v
0 2 4 8 stereo on theother(a= -a).
00 (a) 5 mm spacing The goal forthepattern recognitionis to measure z
coordinates locallywithin each pair. Each of the8pairs
0.05 making up the full detector would then have space
coordinatesandtangentvectors assigned locally to each
0.00 track.Thesewould then have to bematched fromlayer
i to layer, as discussed above.
-0.05 Tracks separated by more than the stereo displace-
Y
ment s in theaxialprojection donotinterferewith each
-0.10 3.84 3.88 3.88 3.9 3.92 other at all. A value of s=500 wm is probably small
00 (b) 5mm spacing enough to guaranteethat most stereo hits canbeassoci-
ated by selecting from a small number of alternative
0.05 assignments.
The matching problem in z locally can come form
0.00 twotracks whichcanbe confused or from many tracks
causing accidental matches.
-0.05 C
Y Ingeneral, we can minimize the z matching confu-
sion by taking a very small stereo angle a, trading off
-0.19
3.84 3.88 3.88 3.9 3.92 resolution in z. This does not significantlydegrade the
. . .o (c)10mm spacing momentum or mass resolution forasolenoidal field. In
Fig.11. Plot of u vs $0 forvector segments foundin theevent addition, we only need 1 mm resolution in z at the
in fig. 8. Up to 8 vector segments per track, and vector vertex to separate most multiple interactions. The very
segments found incorrectly are also shown. (a) The entire good 5 gm resolution of the strips, giving oz= 1.4 mm
event, 8=5mm. (b)Blow-upof oneof the1.5 TeVjets, 8=5 for a=5 mrad, will yieldaresolution in z at thevertex
mm,(c)sameas(b), but8=10mm.
of 835 pm.
The confusion from many tracks can be quantified
in terms of the detector andphysics parameters. Recall
One canimmediately seethetwojets in theevent. The that within ajet, themean displacement betweentracks
effect of resolution in curvature is also seen from the at aradius r is r(B). If apair of axial strips havebeen
spread in points for each track. For this plot we have successfully associated within thejet, all tracks within
used am=5 l.Lm and 8=5 nun. the stereo displacement region s (defined above) will
Fig. llb is a blowup of the region around thejetat leavestereo hits whichcanconfusethe z matching.The
(po=3.9 rad. The effect of resolution is now more number of tracks entering this region is Ns=s/(r(B)).
obvious, and it is also clear that the error in ic is All of these tracks will leave stereo hits in the u plane
strongly correlated with the error in $o. The improved which could accidentally associate with another hit in
vector segmentresolutionobtainedbyincreasing 8 from the v plane falling within a region of full width tam,
5 to 10 mm resultsin clearlyseparatedtracks within the
jet, as shown in fig. llc. Note the spread in measured
$o values is Fam/8, the parameter introduced earlier
to quantify the ability to link vector segments. After Axialstrips
ontop
looking at plots for many events with 1 TeV jets, it
becomesclearthat 1 cm is agood choice for 8 andwill u, smallanglestereo
strips onbottom
usually allow vector segment linking for the tracks in
thejetcore.
v, smallanglestereo
strips ontop
3.4. zmeasurement
Axialstrips
onbottom
In ref. [5] we have looked at the use of stereo
measurementsto determinethe zcoordinate. Sinceeach Fig. 12. Orientation of strips for a closely spaced pair of
strip detector is double sided, we orient the strips on detectors.
V.TRACKING DEVICES
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230 H.F.-W.Sadrozinskietal. /TrackingattheSSC/LHC
"2 -,TT-~------ 1.2 closely spaced tracks in theouterlayers, or degradethe
10 efficiency bycausingtracks to cross in theouterlayers,
leading to confusion.
It appears that whether the tracks are relatively
isolated, in the periphery, or in the core of ajet, the
dominant effect of themagnetic fieldis to causetracks
to cross, leading to confusion and inefficiency. It is
G 0 10 20 3040 _50_60_70_80 0 0 10 20 3040 5060 7080 therefore desirable to have the lowest magnetic field
Pr(GeV/c) P,(GeV/c) possible to obtain the needed momentum resolution.
Fig.13.Efficiencyvs p, forcorrectlymatching thez strip s in With afieldof 2.5 T, theinefficiency forvector segment
a vector segment found correctly in 4p. (a) a=5 mrad. (b) finding in the inner layers due to the close spacing of
a=20mrad. tracks is approximately thesame as theonein the outer
layers due to trackcrossings [5].
Themagnetic fieldcanalso degradethedouble track
whichis theresolution characterizing thecorrectchoice. resolution by spreadingthe charge (electrons andholes)
Theprobabilityof therebeing such ahit in the v plane over several strips due to the Lorentz drift of the
is therefore P=NS 2am/s, and thenumber ofpotential chargesin themagnetic field.This effect canbereduced
incorrect z pairings is Ni.,-, =NP. Thus we arrive at by orienting the detector elements so that theirnormal
thescalingrule for stereo association to work well vector makes an angle 0, with respectto the xy-radius
Ninc-z =Ns2 2Qem = 2amsz <1. vdeectteocrto.rsToatmainnainmgilzeewhtihechpirsotbhleema,verwaegecoafnthoeriLeonrtentthze
angles for each charge (electron andholes),and choose
For the detector considered above, Ninc- =0.5 at a a magnetic fieldwhich is low enough so that theresid-
radius of20cm. Thus, atlarger radii, it maybepossible ual Lorentz drift spreads thecharge over a strip width
to uselonger detectors(e.g., bondingtwoorthree10cm or less. A detector of 150 Wm thickness in a field
long detectors together) or larger pitch in order to B=2.5 Toriented at tanBL=(0e+A,h)B/2will spread
minimize the number of electronicschannels required. thecharge by22.7 gm on either side of thedetector,just
In order to test our scalingrule for z matching, we less than one strip width; thus theimpact onthedouble
use the same events containing 1 TeVjets as were used track separation will be small. Larger magnetic fields
in section 3.3 above, where the finite beam length with worsen theproblem.
vzo =5 cm is included. We apply the z matching al- We look at the expected momentum resolution for
gorithmabove to vector segments that were found cor- the silicon tracker discussed above. We will assume a
rectly in theaxialprojection. The efficiencyfor making vertex constrained fit as would be appropriate for the
thecorrect z match, as a function of p, of the track, is high momentum leptons from the heavy Higgs decay.
shownin figs. 13aand13bforthecases a =5mrad and Assuming that the four measurements in a superlayer
20 mrad, respectively.Theefficiency in theformer case give aneffectivemeasurementwith anerror Q, andthat
is >95% for all tracks, falling at high p, where tracks the eight superlayers are approximately equally spaced
are in the center ofjets. It is clear that the efficiency out to a maximumradius rm gives[5]
begins to degradesignificantly when thestereo angleis
QP, 5.5a
increased to 20 mrad, as predicted by our scalingrule,
andwe have verified that theeffect continues at larger pt 0.3Br
stereo angles. Taking a=3 wm, after averaging over the four mea-
We conclude that choosing S=1 cm, a=5 mrad surements in asuperlayer, rm=0.5 m and afieldof 2.5
provides a good match to the physics demands at 1 Tyields
TeV.
apt
=8.8%p, (TeV
Pt
4. Effectof themagnetic fieldandmomentum resolution For the intermediate mass Higgs search we wish to
reconstruct Z° masses using leptons with a resolution
We assumethepresence ofanaxialmagnetic fieldto better than the natural Z° width limit which implies
measure the momentum of the tracks. Because the that we want
momentum resolution varies inversely with the mag- apt
netic field, it is desirable to have the largest field <2% at about200 GeV.
possible. However, the magnetic field also has an im- Pt
pact on the pattern recognition efficiency. The field Thus,theresolution found aboveis adequate and, again,
mayimprovethereconstruction efficiencyby separating we find that a fieldof B=2.5 T is sufficient. Sincewe
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H.F.-W. Sadrozinskiet al. / TrackingattheSSC/LHC 231
50 0150 ~-
40
0.125
30- Silicon_ Microstrip Tracker
U
20
10 10° y0.075
10 20 30 40 50 60 70 80 90 100
0.050
Z (cm) R.
k
Fig.14.Planofsilicontracking system,with azimuthalsymme- e
try. 0.025
0 0.5 1 1.5
want to minimize the tracking inefficiency and the RAPIDITY Y
Lorentz angleforelectron motion in thesilicon, 2.5 Tis Fig. 15. Momentum resolution vsrapidity for silicon tracking
probably an optimumchoice for thefield. system.
For such good resolution the multiple scattering
contribution totheresolution willdominateup torather
high momentum. Assuming 5% of a radiation length
and a 50 cm path length themultiple scattering contri- contains about 40 m2of silicon detectors. Going out in
bution is approximately ap/p1=0.8% for B=2.5 T. 0 this arrangementgives:
This number is comparable to the number typical of (a) tracking with >_ 6 superlayers for 170°>0>10 °
presentdaycentraldriftchambersystems. (IYI-< 2.3);
Fig. 14 shows apossible arrangement for the track- (b) tracking with 8superlayers for160° _> 0_> 20° (IYI
ing detector in r vs z, having azimuthal symmetry. It < 1.75);
Table2
Detector parameters andscalingrules
Physicsparameters for: 1TeVjets 50GeVjets
Trackangularseparation(0)(mrad) 0.5 10
Jetangularwidth812(mrad) 10 40
Trackptinjetcore(GeV) 50 10
Detectorparameters Si tracker Driftchamber Mark II/SLC
Magnetic field B(T) 2.5 2.5 0.5
Radiusofcurvaturep=3.3p,/B (m) 66 66 66
Radialdetectorspacing 8(cm) 1 1 0.8
Superlayerthickness8SL(cm) 1 4 4
Maximumradius rm(cm) 50 160 150
Innerradiusrl (cm) 8 50 20
Detectorlength l(cm) 10 >100 230
Doubletrackseparationem 100 Jim 3 mm 4 mm
Stereoanglea(mrad) 5 50 74
Position resolution am(ILm) 5 100 100
z position resolution a,=Y2Qm/a (mm) 1.4 2.8 1.9
Momentum resolutionup/Pt2(1/TeV) 0.09 0.26 1.0
Occupancyfromminbias (TeV-1) 0.003 0.26 0
Scalingrule requirements
Resolvehits:em/r(0) <1 0.7 6.0 0.45
Findvectorsegments: 8/(2p(0)) <1 0.15 0.15 0.006
Linkvectorsegments:Vf2am/(SSL(B)) <1 1.4 7.1 0.4
Matchzhits:2amla/(r(0))2<1, or: 0.24
forla>2r81/2:4an,01/2/(r(B)2)<1 16.0 0.2
V. TRACKING DEVICES
232 H.F.-W. Sadrozinskietad. /Trackingat theSSC/LHC
(c) tracking over a fixed radius of 50 cm for 154°>_B trapped in the field if thediameter of curvature is less
>_ 26' (JYJ51.44); and or equalto theouterradius ofthechamber: 2Ptrack_< rm.
(d) tracking with axial strips for 143° >_ 0>_ 37° (1YJ 5 Thus, for example, trapping will occur for: pt<190
1.10). MeV for the compact solenoid [3] with rm=50 cm,
Assuming ap/pt=8% pt (TeV-1)at 90' andignor- B=2.5; orp<<_600MeVfor thelargesolenoid detector
UP/p2
ing multiple scattering, fig. 15 shows vs rapidity, with rm=160cm, B=2.5 T[13].Alargefraction of the
forp in TeV. tracks in minimumbias events occurin this momentum
Theuseof silicon, combined with amoderatelylarge range, so trapping can be important. The ranges for
magnetic field, allows very good resolution. It is essen- trapping are indicated in fig. 16 for the two detector
tial, however, to alignthesilicontoanaccuracy ofafew configurations with 2.5 T fields. (Trackswith diameter
microns in order to achievethis resolution in practice. of curvature less than the inner radius, 2Ptrack <rinner,
A comparison of the parameters of the proposed Si are curled up withoutreaching thechamber.)
tracker with the scaling rules (see table 2) shows that To estimate the effect we have calculated the effec-
the SI tracking chamber is well suited to the require- tive tracklength seen in thedetector perminimum bias
mentsof physics at 1 TeV. On theotherhand, atracker event using the ISAJET MINBIAS model (with =5.1
based on conventional technologies like the one pro- charged tracks per unit rapidity at SSC energies, which
posed for the large solenoid [13] will not be suited for maybea significantunderestimate). We havelooked at
the TeV scale due to problems with occupancy (see both a compactand large solenoid [13].
below) and double track resolution e. For comparison, We havefound that the occupancyis increased bya
the performance of the MARK II chamberat the SLC factor between 2 and 2.5, as compared to B=0, for
is shown, whichis designed forphysicsat 100 GeVand both detectors at B=2.5 T. For the compact solenoid
very low duty cycle. the occupancy is not a problem because of the large
segmentation and excellent time resolution. Silicon de-
tectors are able to resolve the hits from every beam
5. Occupancyof thetracking chamber crossing separately. Even at the innermost radius of 8
cm, with aluminosity of 1033, theoccupancy is -., 2X
The occupancy of the tracking chamber is de- 10-3 in a two-hit resolution element of 100 Wm (4
teriorated by (a) pile-up of minimum-bias events, (b) strips) of 10 em length. This contrasts with an oc-
trappedtracks,and(c)photon conversions. cupancy of about 20%, at a 50 cm radius, for a 4 turn
If the collection and readout time of the tracking diameter cell in a large solenoidal detector covering
device is larger than the time between beam crossings, JYJ< 1.5, assuming a pileup of only 4.8 events (3 beam
several events will pile up in the detector, thus in- crossings). In thecentral rapidity region JYJ51.0,con-
creasing the occupancy correspondingly. The presence tainingthe siliconstrips nearest thebeam in fig. 14, the
of a large magnetic field tends to trap particles in the spiralingtracks would increase theoccupancy andradi-
field increasing theoccupancy and radiation damage. ation damage by40% for a2.5 TB field.Theradiation
Fig. 16 shows the transverse momentum spectrum damage issue would argue for the smallest magnetic
fromISAJET forminimumbias events.Atrack will be fieldconsistent with thephysicsgoalsof the detector.
Finally, we consider theeffect of photonconversions
in the tracking system. This will be a serious problem
fora tracking detector containing asubstantial fraction
ofaradiationlength of material.Theconvertedelectron
PT (JYI s 2, Minbias Events) o
spectrum is very soft since each ir decays into two
photons and each photon converts into two charged
particles(the ir° momentum spectrum is taken tobethe
same as thecharged primaries, fig. 16). We assume that
because the conversion electrons are so soft, they all
spiral in the detector for nearly any radius of conver-
sion. There are roughly half as many m°'s as charged
particles, giving 2X, converted electrons per primary
charged track, where Xo is the amount of material in
the tracking system in radiation lengths. We estimate
the number of track lengths per spiralling track r=4
forboth detector configurations. This results in atrack
Fig. 16. Transverse momentum spectrum for minimum bias length due to photon conversions of 8Xo for every
events. The ranges indicated by arrows are described in the charged primary for both detector configurations.
text. Clearly avalue of Xo_< 5% is very desirable. Note that