Nuclear Instruments and Methods in Physics Research A297 (1990) 111-120North-Holland

Muon rates at the SSC

Dan GreenFermi National Accelerator Laboratory, Batavia, IL 60510, USA

David HedinNorthern Illinois University, DeKalb, IL 60115, USA

Received 13 February 1990 and in revised form 28 June 1990

l . Introduction

There are five sources of particles which produce hitsin a SSC muon detector :(1) it t, K t and K L decays,(2) prompt muons (c, b, t and W decays);(3) hadron punchthrough ;(4) cosmic rays ;(5) low energy particle backgrounds.This paper will discuss items 1-3. It will give muondistributions in angle and PT for a range of detectorthicknesses from each source. In particular, we willattempt to make a crisp definition of the absorberthickness which is needed for good muon detection inSSC detector environments. This paper is a continua-tion of previous studies [1] .

The rates from 1 and 2 are straightforward to esti-mate. The iT and K decay rates depend on the pathlength to their first interaction point, while those muonsfrom heavier particle decays (prompt) depend only uponthe production mechanism . What are not particularlywell understood are the backgrounds due to punch-throughs, by which we mean the existence of particles

deep in hadronic showers which escape into the muondetection system___ As we will see later, these particles

can be either hadrons or muons. For thick absorbersthey are most likely to be muons . Punchthroughs can bereduced relative to other muon sources by adding ab-sorber . Thus an important question in designing SSCmuon detectors is the necessary thickness .We will first discuss the rate and kinematic distribu-

tions of particles produced by hadronic interactions . Wewill compare measured distributions to a simple model

of hadronic interactions . This model is then used to

0168-9002/90/$03 .50 © 1990 - Elsevier Science Publishers B.V . (North-Holland)

2. Hadronic interactions in thick absorbers

This paper presents calculations of muon rates at the SSC. It will give muon distributions in angle and PT for a range of detectorthicknesses and will separately give the rates from various sources . In particular, we will attempt to make a clear definition of theabsorber thickness which is needed for good muon detection in SSC detector environments.

justify our use of the data measurements to differentabsorber thicknesses and hadronic energies . We willthen integrate over the particle distributions in pp inter-actions at 40 TeV to give us the rate and kinematicdistributions of particles in an SSC muon detector . Wewill do this in two ways. The first uses a semianalyticalmodel which will aid in understanding the varioussources. The second uses ISAJET and has a more de-tailed integration over kinematic distributions. Thesecalculations allow us to estimate the absorber thicknessneeded for muon identification and triggering .

In order to begin to understand the punchthroughphenomenon it is important to first gather up existingdata and try to understand the general characteristics

that emerge. In fig. 1 is shown data from Lab E neu-

trino experiments [2] taken during test runs with inci-

dent hadrons . The probability of finding a muon at a

momentum fraction z of the hadron is given, where the

incident hadronic energy varies from 50 to 200 GeV.

The "fragmentation function", D(z ), is defined suchthat the muon momentum is referred to the front of the

absorber. The total absorber thickness [3] in this data is

26XO and the mean density of the detector is 4.2 g/cm3 .

The first thing that strikes you is that there is an

approximate scaling law. The fragmentation function is

roughly independent of the incident hadron momentum,

at least within the accuracy of the data .Other data [4] from experiment E-379 are shown in

fig . 2 for incident hadron energies of 40, 75, 150, and

225 GeV. Again there seems to be a scaling behavior . It

is also clear that the two data sets shown in figs . 1 and 2

agree . For E-379 the total absorber depth was 18.5X0and the mean density was 6.1 g/cm3 . Later we will seethat we expect D(z) to be proportional to the density.These two data sets are not of sufficient accuracy tosupport this prediction.

First let us see if we can understand this scalingbehavior with the most simple minded model that wecan make. Assume that a hadron of momentum p isincident on an absorber. It begins to shower at a depthof 1X0 . That shower creates a mean multiplicity ofhadrons, (n>, with momentum k. Those hadrons (pions)must decay into muons of momentum q before the nextshower, that is within one more X0 . We will ignore thedifference betwe,n k and q . The relationship betweenthe laboratory momentum of a secondary, a primary,and the Feynman scaling variable x is approximatelyk = xp. In this simple minded model the muons fromthe decay of first generation pions constitute punch-through . If one goes deeper in the absorber, one simplyranges out muons of higher momentum. Obviously, thispicture ignores multigenerations, and so it will do apoor job on pileup at low momentum. Fluctuations inthe showers are also totally ignored .

The assumptions in this model for production aregiven below in eq . (1) . An additional assumption is that

10 2

Nô

10 4

t

D. Green, D. Hedin / Muon rates at

L

.

I

1

I

1

0.1

0.4Z= PY./Ph

Fig. 1 . Data from Lab E on D(z) for 0 50, 0 100 and v 200GeV incident hadron energy .

IÔ '

1ô2

N

- je,

the SSC

t

Fig . 2 . Data from E-379 on D(z) for o 40, 0 75, v 150 and o225 GeV incident hadron energy .

there is a rapidity plateau . The production cross sectionis constant in y up to the kinematically allowed maxi-mum value Ymax :

du/dy = a,

Ymax = ln(vrs- /m ),

x = (MT/4) ey .Obviously the mean multiplicity is proportional to

the width of the rapidity plateau . The differential crosssection as a function of Feynman x is :(n> = 2ayma,

dx/dy=x,

0.1

0.4Z= PN./Ph

do/dx = [(n )/2Ymax ](1/x) .

Clearly the idea is to relate the observed scalingbehavior of the punchthrough fragmentation functionto the well known scaling behavior of secondary pro-duction processes in hadron collisions . "Jets" are alsoknown to fragment with a scaling behavior [5] .

As mentioned before, Feynman x is approximatelythe laboratory momentum fraction carried off by the

secondary, which is defined to be z . The secondarydecay probability is approximately proportional to oneover the laboratory momentum and therefore :x=k/p=z,

Pp = (A/er)(m/k),

D,t(z) = [ <nil2 ym.](AlcT)(mlp)(1/z2 ) .

(3)

This simple expression for the fragmentation func-tion depends on the density of the material, and has arough scaling shape. However, it is explicitly dependenton the momentum of the incident hadron . Since thedata in figs. 1 and 2 only span a factor of 5 in momen-tum, we will pick (for a numerical comparison) 25 GeVincident momentum . This simple expression for thefragmentation function is shown in fig. 3 .

Surprisingly enough, both the shape and the magni-tude roughly agree with the data shown in figs . 1 and 2 .If anything, the data falls more rapidly, which appearsto be a reflection of the fact that the rapidity plateaudoes not extend to the kinematic limit. Typically thisbehavior is par:tmeterized in the form of a power law in

IÔ'

162

NC

1(54

0.1

0.4Z= PfL/ Ph

D. Green, D. Hedin / Muon

Fig. 3 . Simplistic D(z) model for O rapidity plateau and .(1- z)4 at 25 GeV incident energy .

rates at the SSC

1 .0 r

16 2mam0F 163

1(54

10 100

P(GeV /c

/6

1000

Fig. 4. Probability for detection at a depth of 14Ao due to 41decay in R = 2 m, and o punchthrough . Also shown is the

integral of a curve, O, which fits the data of figs. 1 and 2.

(1 - x) . Hence, we also show in fig. 3 the simple frag-mentation function multiplied by (1 - z)4 . This mod-ified form is in much better agreement with the data athigh values of x or z, i.e. values around 0.5 .

Another comparison of interest is to look at therelationship between this data, which is for muonsescaping from thick absorbers with incident hadrons,and data which only ask for something to punch throughinto a detector element downstream of an absorber. Ifwe parameterize the data of figs . 1 and 2 using afragmentation function which iz; the sum of two ex-ponentials, then this form is easily integrated to get themuon punchthrough probability as shown below:

D,,(z) .-. ale- b 1Z + a2e_b2Z,

Pw(X, p) -" (allbl) e-blkmm/P+ (a2lb2) e-b2kmm/P

kmin -^" - (dE/dx)L,

(4)

where L is the absorber length .Shown in fig. 4 is the probability for a pion to decay

in a 2 m decay length as a function of momentum . Incomparison, the probability for the pion to punchthrough

bso_L .r ot

thicknesstotaltotal t hit.t~ta1.JJickness ltirA,e isis auliovso111 an CiVSVI Vi ":

shown . First note that punchthroughs, in this situation,dominate over decays for momenta > 20 GeV . Nextnote that the punchthrough probability is effectively 1for momenta above about 600 GeV. This means that, ifone only measures the appearance of some particleexterior to a 14XO thick absorber, one essentially has norejection power against hadrons above 600 GeV . Atrapidity y = 3 this means hadrons with transversemomenta > 60 GeV .

The hadron punchthrough points are a fit [61 to theWA1 data :

P(X, p)=exp[(,\ -X')/Xett~

X' = 1 .53p(GeV)0'33X0,

Xett = 0 .89p (GeV)0'165

A0

(KT ) -= 2/a = 0.33 GeV,

D. Green, D. Hedin / Muon rates at the SSC

The punchthrough probability is 1 for depths

< A'.Beyond a depth of X', the punchthrough probabilityfalls off exponentially with an effective absorptionlength which is greater than X 0 . What is extremelyinteresting is that the integrated muon fragmentationfunction agrees well with our parameterization of theWA1 hadronic punchthrotl%h data in the region ofvalidity, which means for momenta between about 20and 100 GeV . Note that a depth of 14X0 of iron rangesout decay muons from pion secondaries up to about 2.8GeV . This means that for 100 GeV incident momentum,the minimum value for z is roughly 0.028. There are nodata for z < 0.03 in figs . 1 and 2. Low z means multi-generation pileup, so we expect that the comparisonbetween the integrated muon fragmentation function,eq . (4), and the WA1 fit, eq. (5), may not be valid there.

The success of this comparison (within factors of 3)leads us to believe that deep punchthrough consistslargely of low energy muons from the decay of showerproducts rather than unquenched hadron showers them-selves . This is certainly true at large depths where thehadron showers are quenched, i .e ., the mean number ofshower particles falls below 1 . To set the scare, at 14X 0depth, the mean number of hadronic shower particles isless than 1 for incident hadron momenta less than 1TeV . Thus, at this depth, and for hadrons below 1 TeV,the punchthrough consists mostly of muons ['71 .

If punchthrough consists of muons, and we are try-ing to detect muons, what more can we do to get rid ofthem aside from measuring their momentum and/orranging them out . Obviously, one thing is to track theincident particle and the outgoing muon and see if theexit position and angle are consistent with pure Coulombscattering of an incident muon. For example, for 14X0in steel, multiple scattering causes a projected transversemomentum impulse of 163 MeV. This means that a 100GeV muon has a one standard deviation angular match-ing error of 1 .6 mrad . By comparison, the secondarypions in the shower have a mean transverse momentumof about 333 MeV :

da/dy dKT = [ (n>a2/4ymaxI e -aKT .

6

Given the production characteristics for low trans-verse momentum inclusive pion production, it is easy to

work through the joint fragmentation function formomentum fraction z and angle 0 shown below:

0

KT/k = KTlzp

D,,(z,0) = [(n >(«p)2/Zymax](XlcT) [ Oe-azop7,

(7)

As an immediate check, if one takes the expressiongiven in eq . (7) and integrates over all angles onerecovers the muon fragmentation function given in eq.(3) . Conversely, if the momentum fraction is integratedover, the fragmentation function as a function of angleis :

DW(O) = [(n)(am)/2ymaJ (X/cT) e-aBkn,in~

(0N,> z 1lkmina .

(8)

Note that so far we find that the mean angle formuon punchthrough depends on the minimum value ofthe momentum of the muons due to the depth of thematerial . Otherwise, the angular fragmentation functionis a scaling object, which is independent of the momen-tum of the incident hadron. For example, at a 14X 0depth in steel, the mean angle is 74 mrad for the spaceangle or 50 mrad for the projected angle .

Test beam data [81 taken from DO are shown in fig .5 . What is plotted is the Lorentzian half-width, T/2, ofthe punchthrough for hadron showers at depths of7.3X 0 and 15.6X0 for hadron momenta of 100 and 150GeV. The first thing to note is that the width is ratherindependent of momentum, as one expects from ourprevious estimate, eq . (8) . The production radius, usingeq . (8), is roughly Rprod = [a(dE/dx)1 -1 , which is aconstant independent of momentum and depth. Thisprediction is shown in fig . 5 as the dashed line . Obvi-

DISTANCE (m)Fig. 5 . DO test data on shower widths for 100 and 150 GeVincident hadron energy at depths of 7.3X 0 and 14.6X0 . Thedashed curve is the simplistic shower width due to production,while the solid curve is the shower width due to multiple

scattering .

ously, it is not a good representation of the data . Wemust improve the model.

So far we have ignored the multiple scattering of thesoft decay muons as they pass through the absorber .Assuming that the exit size is due to scattering, and thatit is dominated by particles with z near '-min (given the1/z2 distribution), then :

f = 0.021 GeV,

Rms - [ß/(dE/dx)] L/xo .

This dependence on depth is also shown in fig . 5 . Itappears to be qualitatively correct, in that it is indepen-dent of incident momentum and weakly (F) depen-dent on depth of absorber. The magnitude is also inrough agreement . More detailed data from Lab E hasrecently been published . This data [9] indicates a weakdependence of R on L ( - FL ), and a rather weakdependence of R on p, as expected in our very crudemodel .

Clearly, one can use the difference in width of thespatial distributions of isolated muons incident on theabsorber and of the punchthrough muons from incidenthadrons to get another rejection factor . One asks ; is thisthe parent or is it a momentum reduced multiplyscattered secondary decay muon?

m8

10 2

1a-3

F . ~EG5369 .Oao( .

IeIa/~WAI

16-5L20

E636F .

I I

),(574a/cm

..

WA I

P (GeV /c)

D. Green, D. Hedin / Muon rates at the SSC

STATION APb

7 .3ao(413g/c,2)

STAT'ON

UUUL3MB

4-- _

50 100 200 300

Fig . 6 . DO test beam data for punchthrough probability and forreduction due to a "Coulomb cut" . A simplistic model esti-

mate, O, is also shown.

Data taken to study the DO muon system are shownin fig. 6 . The curves are punchthrough probabilities forhadrons as a function of hadron momentum at a depthof 7.3Ao and 14.6Ào . In addition, the probability ofdata also surviving a two dimensional Coulomb cut isshown. This cut leaves a residual punchthrough prob-ability after making a 2a cut in the exit position of thetrack, requiring the punchthrough track to be withinthat cone . Clearly, there is a substantial rejection to behad . The rejection factor also increases with momen-tum, since the punchthrough radius is roughly momen-tum independent (as we saw in fig. 5), while the Coulombcone has a radius that decreases with momentum.

Also indicated in fig . 6 is the result of a roughcalculation using a two standard deviation multiplescattering error, and defining the rejection factor to bethe square of the 2a multiple scattering width, dividedby (0,,)/r2.That rejection factor, as plotted in fig . 6, isreasonably close to what is observed in the data :

REJECTION =- [2ks1(<01,)1V_2)12,

9ms = (IQ L/xo )`P .

(10)

Clearly, if the momentum of an incident track isknown, then a "Coulomb cone" can be defined for theexit position with respect to the incident position . Theresulting cut improves with momentum, thus tending tocancel the rise of the punchthrough probability withmomentum (see fig. 6) .

3 . Rates in SSC muon detectors

The studies of existing test beam data presentedabove allow us to make a parameterization of the spec-trum of exit momentum and angle for a hadron incidenton a block of absorber . This means that we can quanti-tatively compare various sources of prompt muons andselect an absorber thickness in a decisive way . Theselection criterion chosen here is that punchthroughmuons should be reduced below decay muons and be-lo . . the signal due to prompt muons from some interest-ing physical process .

In principle, with isolated muons the task is ratherstraightforward, but it seems unlikely that one shouldrestrict oneself to that sort of envirnnment for a bench-mark process . What is appealing about muons is thatone can identify them in hostile environments such as inthe core of jets . In fact, for jet flavor tagging it isnecessary to work in that envirc Ement . Therefore, it isincumbent on the designer of a muon system to retainthat advantage and be able to tag and identify muons inthe core of jets.We have chosen to do this calculation in two ways .

We will first use a semianalytical model . This will allowus to qualitatively understand how the produced jets

fragment into hadrons, which then give muons . We willthen repeat this using an ISAJET-based model . Thiswill have better integration over items such as fragmen-tation and structure functions. The two techniques yieldsimilar results for the relative contributions of differentsources . The ISAJET calculation gives more precisevalues for the rate at different angles and PT-

The jet cross section at the SSC (at least at 90 °) hasa momentum spectrum that goes like 1/p3, which is dueto the elementary 2-to-2 Rutherford scattering process[10] . Heavy flavors, in lowest order, arise from gluon-gluon fusion. Prompt muons arise from heavy flavorproduction followed by three body semileptonic decay,with branching ratios of order 1 (which follows fromsimple quark counting) .

Shown in fig. 7 are the differential cross sections(do/dy dPT)v=o for jets, heavy flavors, and promptmuons from semileptonic decays. Clearly, a physicsdriven criterion is to design a muon system in which theprompt muons from heavy flavors can be tagged cleanlywith respect to all other background sources . The crosssection scale is also important [11]. If the SSC runs atits design luminosity of 1033 cm -2 s-1 , then in a oneyear run at efficiency (107 live seconds), there will beone muon at a PT of 1 TeV per unit of rapidity per

t 33

I

I'll ~I

I

I

I "I 1 1 1

1

1

1

1

11 111

Pl (TeV)

Fig . 7 . Differential cross section estimates for jets, heavyflavors, and prompt muons from heavy flavor decay at V-s = 40

TeV.

D. Green, D. Hedin / Muon rates ai the SSC

do/d p = 1/p3,

kT (TeV)

do/dk= fx[dQ/dpJD(z) dplp ,k

Fig. 8 . Differential cross section estimates for jets, rr from jetfragmentation, and w from pion decay in a R = 2 m space .

GeV. Thus it seems unlikely that one needs to worryabout large samples of muons with transverse momenta> 1 TeV.

What about hadronic backgrounds? First one needsto let the jets fragment into pions. The differential crosssection estimate for that is shown in fig. 8 . Havingfragmented the pions, one can get a decay backgroundestimate for a 2 m decay length . That background isalso shown in fig. 8 . In making this estimate, the parentjet spectrum was assumed to be Rutherford-like. Thefragmentation function for jets fragmenting into pionswas taken from UA1 data [5] . That data was approxi-mately fit to an exponential fragmentation function :

One of the nice properties of an exponential frag-mentation function is that such a soft fragmentation,convoluted with a power law production spectrum, leadsto the same power law spectrum for the fragment with areduced cross section [10] :

(da/dk)/(do/dp) ,= 2a,,/b,,',

(12)

with k being the momentum of the fragment, in thiscase the exiting muon as opposed to p, the momentumof the particle incident on the absorber.

Comparing fig . 7 and fig. 8, one can see that decaysdominate over the signal for transverse momenta below10 GeV. This statement assumes that the central track-ing has no kink rejection factor, i .e. no additionalrejection against decays . Above kT of 10 GeV, themuons from heavy flavors in jets dominate over decaysand do so by at least a factor of 10 for kT > 350 GeV.This means that decay muons are under control as asource of background if we look at reasonably highmass dijet events .

What about punchthrough backgrounds? In princi-ple, this is the dominant background . For a depth of14XO we know the punchthrough exceeds the decaybackground (fig. 4) for transverse momenta greater than20 GeV. Using the integrated muon fragmentation func-tion (eq . (4)) and the pion spectrum (fig. 8), we find therejection fraction for any hit beyond a depth of 14X0 .That rate is shown in fig. 9 .

The total punchthrough rate exceeds the prompt ratefor transverse momenta > 30 GeV . Then for all PT, acombination of decay and punchthrough backgroundexceeds the prompt rate of muons . This is clearly un-

~6 3

EO

abv

~~ 38

00f

01

Lo

10

k T (TeA

Fig . 9 . Differential cross sections for -n punchthrough at a14X O depth, o, if momentum is measured,

, and if a "Coulombcut," O, is imposed.

D. Green, D. Hedin / Muon rates at the SSC

acceptable . We assume that, for flavor tagging, you arein the core of a jet and thus cannot depend on a centraltracker to give you the momentum . In any case, themomentum must be measured after the absorber.

In many systems such as DO [12], the last fewabsorption lengths of material exterior to the precisioncalorimetry are in the form of magnetized iron and areused to make a modest momentum measurement so asto reduce punchthrough . In this case, instead of usingthe integral punchthrough probability (eq. (4)), we usethe differential probability (figs . 1 and 2) folded intothe pion spectrum (eq . (12)) . The rejection factor, for afragmentation function consistent with the data shownin figs . 1 and 2, is = 4 x 10-5 . This reduction assumesthat you have indeed measured the momentum. Whataccuracy does one need? Also shown in fig . 9 is theresult of smearing the muon momentum by ±20%which is appropriate to 1 m (= 6A o ) of magnetized steelexterior to 8Ao of precision calorimetry . The steeplyfalling input spectrum means that a very crude measure-ment is quite dangerous. A crude measurement alsocomprimizes the triggering scheme since it allows leakagefrom the enormously higher rates at low kT. But evenfor kT > 300 GeV, the prompt rate still exceeds themomentum measured punchthrough assuming a 20%momentum measurement . In all detectors, the resolu-tion will be degraded at the highest momentum due tomeasurement errors and we have not considered anyspecific designs.

Moreover, one may also use the vertex position ofthe event, and the tracking before and after the mag-netized iron (which comes for free with the momentummeasurement) in order to improve a two dimensionalCoulomb cut . We have already discussed the rejectionfactor for those cuts . Note that one need not depend onfinding the associated track in the core of a bet usingcentral tracking . It is important to have stand alonemuon capability up to a luminosity of 1034 cm - ' s - 'since the SSC luminosity is only limited to 1033 cm - `s-1 by synchrotron radiation . Hence, upgrades inluminosity are likely, and a dependence only on centraltracking appears to be a bad bet .

Using the rejection factors which we roughly ca cu-lated using the simple model (or using the DO test datashown in fig . 6), we can estimate a maximum reductionin the momentum measured nunchthrough rate by im-posing these Coulumb cuts [131 . The resulting spectrumis shown in fig. 9 . This estimate implies one can alwaysreduce the punchthrough rate (above about 20 GeV) tobe well below the prompt rate . This is the criterionwhich we set out to achieve, to be able to cleanlymeasure muons from heavy flavors in a jet environment .We have also used the ISAJET program (version

5 .20) to generate proton-proton interactions at 40 TeVand then determine the rates from items 1-3. For thiscalculation, we used twojet and W events with PT from

5 to 10000 GeV/c. Those pions and kaons which decaybefore interacting in the calorimeter and whose decaymuons have enough energy to penetrate the absorberare defined as decays . The decay rate is directly propor-tional to the size of the central tracking region . Weassume a cylinder with a 2.5 m radius and 10 m totallength . This is the size of the largest central region wehave seen considered (14] .

Prompt muon rates from heavy quark decays and Wdecays are also straightforward to estimate . Top and Wdecays can be differentiated from b or c decays (andfrom other muon sources) by their isolation . As such,they are usually a more important source of backgroundto other heavy particle decay to muons (such as Z's) .We have assumed a top mass of 120 GeV. The rateversus absorber thickness for both decay and promptmuons is only a function of energy loss in the absorber .

In determining the punchthrough rate, four differentdetection scenarios are possible :a) Measure momentum only in inner region, no exiting

measurement ;

N-

Io

r

10 40

IÔ 42

. . .0001

-001

.01

kT (TeV)

D. Green, D. Hedin / Muon rates at the SSC

Fig . 10. Punchthrough rate in cm2/GeV versus k T assuming(a) the hadron is only measured in the inner tracking ; (b) thehadron's momentum is measured in the inner tracking but atrajectory is measured after the absorber ; and (c) the momen-

tum is measured after the absorber .

Z 102

0 10 20 30 40 50 60 70 80 900 (degrees)

Fig. 11 . Angular rates in Vb/deg of particles exiting 15, 25, 35and 45X0 of iron .

b) Measure momentum only in inner region, measure-ment of exiting position and angle ;

c) Measure momentum exiting absorber ;d) Measure momentum before and after absorber .Fig . 10 shows the kT distribution for punchthroughsafter 14X0 in the region I -l I < 1 assuming a), b) and c) .Those in a) assign each hadron (pion, kaon or baryon)the WA1 weight and use the hadron's PT as the muon'skT. Item b) multiplies the weighting factor using theCoulomb cut discussed above but still assigns the hadronPT to the muon. For this figure, we used a factor of125/p2 up to 200 GeV (and assume that above 200GeV the reduction factor is the 200 GeV value) . Thecurve for c) uses the WAl weight with the D(z) distri-bution in figs . 1 and 2 . As discussed above, an outermeasurement of the muon momentum even with resolu-tion of order 200 will dramatically decrease the rate atlarge k T. Given a momentum measurement both beforeand after the absorber (which is feasible in the centralregion of a solenoidal detector), it should be possible toreduce the punchthrough rate even further .

The angular rates for particles exiting 14, 24, and40X0 of iron are given in fig . 11 (with the two hemi-spheres being summed) . The same thickness is assumedat every angle . Table 1 sulnrnarlze szes the râteS for ti'uck=ness from 97 0 to 45X 0 and for various pseudorapidityintervals.

Fig. 12 gives the kT distribution for an absorberthickness of 14N0 assuming punchthroughs are mea-sured using technique c) . Decays dominate the rate andare predominantly at low kT . The total rate is 13 mbwith 30 Rb having kT greater than 5 GeV/c. Fig . 13gives the relative fraction of exiting particles fromprompt, decay and background sources . Above about15 GeV/c, prompt sources (heavy quarks) begin to

b

Fig. 12 . Rates in cm2/GeV vs kT for particles exiting a 14A0absorber for I q I < 3.

Table 1Muon rates a) versus absorber thickness

Ij 2e

10

30

,632

103.

10 3e

642

0 001 001

k T (Te\, )

a~ Rates in Wb summed over PT .

01

D. Green, D. Hedin / Muon rates at the SSC

I

z 1020

103W

Q

IQ

200 400 600 800 1000

kT (GeV)

Fig. 13 . The relative fraction of particles exiting a 14X0 absorber with I i1 I < 3 vs kT from (a) prompt decays ; (b) -rr/K

decays ; and (c) punchthroughs .

dominate with the rate from either iT/K decays orpunchthroughs falling to about 10-3 above a fewhundred GeV.

Thickness Source o<InI<3 0 < Inl <1 1 < Inl < 2 2 < I-qI < 3

All 28000 400 4100 23 0009A0 punchthrough 4900 70 420 4400

prompt 400 16 130 250All 18 000 250 2700 15 000

12X0 punchthrough 430 5 30 400prompt 400 16 130 250All 11000 130 1500 9600

15X0 punchthrough 40 0.4 3 40prompt 380 13 120 250All 6800 80 700 6000

18X0 punchthrough 5 - 0.4 5prompt 270 13 70 190All 4400 50 460 3900

21A0 punchthrough 0.7 _ _ n7

prompt 270 10 70 190All 2700 30 270 2400

25A0 punchthroughprompt 270 10 70 190All 900 12 70 800

35A0 punchthroughprompt 150 7 10 135All 400 2 24 340

45X0 punchthroughprompt 140 0.6 7 130

120

The conclusion from the above rate estimates is thatone must measure the momentum exterior to the ab-sorber, but that this measurement need not be particu-larly accurate . The total absorber need not be exces-sively thick . Depths for calorimetry and magnetizedsteel comparable to those which are used in the DOdetector should be adequate . DO was optimized forelectroweak energy scales, which are at least an order ofmagnitude below those which are of interest in SSCdetectors . If one does not measure the momentum exte-rior to the main absorber, then one is restricted tophysics in which one studies isolated muons . Even inthe case of isolated muons, the redundant (though crude)exterior measurement protects you against mismeasuresin the central tracker, which notoriously tend to pro-mote lower momentum tracks to high momentum tracks .It is cheaper to measure punchthrough than to range itout, as a glance at eq . (4) tells you . The optimal proce-dure is perhaps to have a fairly thin absorber (14X0 ).After removing the 8X0 to 10X0 needed for precisioncalorimetric measurements, that leaves of order 6X0which is sufficient to make a modest momentum meas-urement using magnetized iron as the absorber . Thatmeasurement buys you between four and five orders ofmagnitude in punchthrough rate. Simply stated it ap-pears to be cheaper to get that factor from the momen-tum measurement than from adding tens of thousandsof tons of steel [1] .

References

[1] D. Carlsmith et al ., Proc . 1996 Summer Study on thePhysics of the Superconducting Supercollider, Snowmass,1986, p . 405 .

D. Green, D. Hedin / Muon rates at the SSC

[2] B . Schemm, Ph.D . Thesis, University of Chicago (1988) .[3] Unless stated otherwise, we assume throughout this note

that 1X0 of absorber is 1' .8 cm of iron and gives anenergy loss of 195 MeV to minimum ionizing particles .K. Lang, Ph.D . Thesis, University of Rochester (1985) .V. Barger and R.J . Phillips, Collider Physics (Addison-Wesley, 1987) .

[6] D . Green, Proc. Workshop on Triggering, Data Acquisi-tion and Computing in Hadron-Hadron Colliders,Fermilab (1985) p . 402.Monte Carlo calculations using GÉANT confirm this aswell as reproducing the measured fragmentation functionof particles exiting a thick absorber . R. McNeil, privatecommunication .

[8] D. Green et al ., Nucl . Instr. and Meth . A244 (1986) 356 .[9] P.H . Sandler et al., Phys. Rev. D42 (1990) 759 .

[10] D . Green, Fermilab CONF-89/70.[11] R.K. Ellis and J. Rohlf, Proc. 1984 Summer Study on the

Design and Utilization of the Superconducting Super Col-lider, Snowmass, 1984, p . 203 .

[12] DO Design Report, Fermilab (1984).[13] This estimate assumes that there is no correlation between

the Coulomb cut and the fragmentation function. Thoughthere are some cases where this is wrong (e.g. a noninter-acting hadron), we feel that it is a good first approxima-tion .

[14] For example, The Large Solenoid Detector, Report of theCollider Group, submitted to the Proc . Workshop ofPhysics at Fermilab in the 1990s, Breckenridge, 1989 .

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