Nuclear Physics B (Prec. Suppl.) 25B (1992) 19-25 Nortll-Holland

PROCEEDINGS SUPPLEMENTS

A Measurenmnt of the ~ p total cross section at ~/s = 1800GeV

Sei)as t iml W h i t e , Rockefel ler Un ive r s i ty

for the ('.DF C ollalmration

A b s t r a c t

The [)p differential elastic scattering cross section was measured at V~ = 1800 (-~eV. using an improved arcelt.rator lutvinosity

determination and CDF small angle data in the range of 0.05 < t < 9.2((h'V[e) ~-. By extrapolating the differential cross

sections to t=0 anti using the optical theorem we ohtain a total cross section of f f to t (PP) -~ 72.04-3.6 mh. This result is

preliminary in the sense that we expect to filrther reduce the systematic error on the optical point.

1 Introduction 2 Method

The goal of the CDF small angle physics program i.-

to measure the diffractive processes of elastic scattering.

diffraction dissociation and atot(pp) at V~=ltg0O GeV [I].

For this purpose CDF da ta wore recorded during special

stores with higil-/~ optics (f:I~72 m), using triggers derived

from small angle detectors sensitive to the leading parti-

cles, mounted in Roman Pots.

In this paper we present results from tile analysis of

elastic scat ter ing data recorded (luring one such store.

In tile past year we also completed a s tndy of tile ac-

celerator hmfinosity calibration in collaboration with the

Fermilab acclerator del)artmont [2]. This work is do-

scribed hriefly in section 5 and lies resulted in an improwd

hnninosity measurement.

ln(lepmldent of the total cross s.~ction measurement,

we find tha t tilt, effective cross section seen by tile CDF

minimum bias trigger, which is primarily sensitive to

non-diffractive inelastic events, increases hy a factor of

1.30 -I- 0.06 in the energy range 5.16 _< V/~ _< 1,~00 GoV.

This increase is small enough to constrain estimates of

mini-jet i)roduction at our energy [3].

We inca.sure tim differential pp olastic scattering cross sec-

tion d ~ t -I dNrl

dt = i l L ) ~ (2.1)

where

2 .02 -t ~-- Pb, nm fiT,it

and the scattering angle, Oli,,,t ,was mea~sured wh, h Ifi-

dinmnsiona] detectors at various 'stations" in the Teva-

tron.

The measured differential ~.lastic srat ler ing distrihntion

was extrapolated to t = 0 ant! tile total cross section was

calculated using the optical thcr~om:

dn, l .~ot = 16~(bcff(i +/,2)-~_~__ It=o (2.2)

A preliminary nmasnrenmnt of p has btn°n l)res~nted at

this conference [4]. We used a vahw p=0.145 (consistent

with [4]) to obtain atot = 72.0=1= 3.6 rob. It shouhl he noted

that our deternfination of ¢rtot using eqn. 2.2 changes by

only -I-I~ for 0.1<p<0.2.

2.1 Track M e a s u r e m e n t

The detector stat ions were located in non-cryogenic in-

serlions of tile Fermilab Tpvatron I)pyoml tile CI)F Iow-l~

(luadrupole magnets. A simplified plan view of tile ( ' I )F

forward spectrometers is shown ill figure I.

0920-5632/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved.

20 S. W h i t e / ~ p total cross section at v ~ = 1800 G e V

Pb t Alifl iq i 5~m

z

, O , I h , l r

Sl. $2 $3 ~ ' - - " l )WC~SI $7, S6

BEND

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i l t l~ t It rt l( It/.', tH'I n o t ,h[I tslr l t .

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amdy,g,~ with a ri.solulion ,)f 2 ... 0.2,~',Z. For the elastic t '

scatll.ring a.alyxix, data fr(ml thix I{'ading parlich" spe(--

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2. inh.rct .p! o f lh,-. p t rack w i l l , lh , . i n l o r a c l i . n vor l ( .x .

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I } Wt' IIsOd l ] ,o ro ] ; l l i ( i l i

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. u s l y I)y .5 d t , l ,wh , r s l a l i o n s i l l olasl i(" vv t , i l l s , lhP..;t. ( l a la

ab.o p r - v i d , ' a l l i t j l~q' l lal (-hf.(k (in l ho h w a l i ( m - f lh , . (Io-

h.lhJl 'S. I : i ~ . r , . 2 shows l lw r , .s i(hial . f I racks f r i . n ( . las t ] (

soaltering; ('amli(lalt's in xlalioli 3. An iuicou'rocl (I,,1~rmi-

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wo,h l It.nil I . va l . i a l i ons of Ira';in r<,sidual w i lh impacl

]mini . .%;f~ such v a r i a l i t m ix ol)sm'v,,(I,

2.2 Event r e c o . s t r . c t l o n

l{fq'~'ring I . fig. l . (lo1,,(-Icw . ' ; la l i t ) l ls .%'i..5'~..5~..5',~ and .%'7

( ' (mla i i , s i l ic(m s IHp (h, l , ,( ' i ,w.,. d r ] h wir~, ch;inlbPr.,-; ; l l l ( ]

s r h i l i l l a l . l I r i ~ , w ( ' tH ] l l l o rs . T h t ' d , , l ( , ( 'h ) rs w o r o l ] l i 'H] l l l r . ( l

in J l t . . a l . i . , I s and i , , . , i l i ,m t 'd rh,s<, i , , lht . s u m , d I)r,aln.,.

t ,nr t , s l . I )h , , ' ,md i l i ,ms wt.r,. , ,s l ; l l ) l is l l t , , I .

Th,, I't'Xllll:'4 I)rt,:.,Ollh'(I hi ,r , , ar t , I )asml t i l l d a l a r ro l l l o11,,

..l(,r~, (I., i ,J~ whi,'h wt, r..-,,,'(h,d ]fi.993 ,,hlslic l r igg~,rs, ro-

qui r in-g a r , f i l , c id , . i . , , , , f s ( ' in l i lbJ l i (m c t ,unh, rs in a l l 5 d,,-

S, W h i t e / # p total cross section at v~ = 1800 GeV 21

t~,( ' tor s t a t i o , ~ . "l'ln~, trip;~;,,r .~cJrdi l la lor.~. wh i r l n In~'a.~u]',,d

['i.;:l:'~ X ~.70 CIII i l l X ; l l ld y. (]et i [ ,r l l l l l l ,p t i l l , ~t ,Ol l lPtr i ( - ; l l ; ic-

C'ol)taln('~. o f th( , Sl)(.cl r o l lm l ( , r .

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n.cnr~h,d d , r i . g lh~, ~am. . r . . w i t h d i l f l , r~. . t trip;~;~.r n,-

q u i r ~ m , , . t . ~ m i d f i ) . n d to I)P 0. ! INJ: .01.

h i th." d a t a aHa ly~ i~ , w~, (l¢,t,~,l'lVlili,,(I t i m I ] l i l l i l l ( ' l ' ( I f I t ' l l , '

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th f ' h i gh n , d l ] i i d a , l c y al ' i .~i i l~ f r o m tin-" l a r ~ ] l l l ]nib~,r o f

I l iea:"; l l l ' t~l l l l~l l l~ III thr , t r ; - l l ' k ] l l ~ I,o dot f ' r l l l J l i , " I),~.~,~ibl~ n'-

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Wel'e II.~,d i l l r ( , ( 'Ol i .~ l l ' i lc t io l i , a l t h o l i l h ~l ~l l 'J I) d l , l~c lo l '~

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i l l I d r i f t i t i id ( i f ' l ay Ihi+, vNr i r i t i , ' .~ .

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,~,~111+,111.~ f~i i l l ld i l l ,~ la t i l l l l I ~t,~ 7 Wl,l'~, il.~r,iI l ( i dt, l i , l ' l l l i iH,

l i ra i l l l ~ l l i l , l l l l l i l i i l l i ( I .~cal l~ ' r i l i~ i i l l ~ l l ' ( i t Ihr , p (l l .~il l l Ih~,

i i l t n l ' ac l i , l i i l l ( l i l i l ;in ~1 i ' l l l l .~l r~ihi l i I i l l h f , f i t ) . " l l i l . pl ' ( I t ( l l l

~cat t~ ' l ' i l l~ i l l l~ [ f ' W;I.~ ;il.~ll d( ' l~ ' l ' l l l i l l~ 'd I INiII~ , ,g l la l i~ l l i 2 .3

a l l d Ihr , Ioca l l~ l l i elf l i ra l r a c k .~,~nl , , l i l i l l ~ l a l j , l i l 6, W~'

Ih+' l i l l h l l I lie, c ( l l l h l~ 'a i ' l l y .

, ~ " = 0"'1, - ~,"' (9 . . i )

f i )r a l l ,,,w, nv.~ (,,-,.,,, l ip. l i t , , : I l l ) . T h - r , - i..i ~l ,rl. ',ar l l . "ak i l l

c~}]] i l i~,ari l ,y w i t h ~,<,{->, = 2 0 f l r a d i l l ; i lv '~,~l ] l l , l l l w i l h tl i~'

r l i h ' i l l a l~ ,d r~ .~o l l l t i on fo r i, la.~ll( ' r,W,lii.~. Th , , r l , i~ ;i l.~.

a .~ i l l l .~ la l i lb l ] l la ( -k t~rn i l i id wli(i.~, .~]i;illr, i.~ li~ll. ;i pr } l l r i .

k l l ( iWI i .

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ll~'l'l'Ol'liir,d fii.~ lo an ; i .~ i l l i l~ 'd I ta l l l ; i ck~ r¢ i i l i l d + ~;lll,~.~l~ill

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7. ;i I ' l l r l h l , r ( ' i l l i l l i l ) ; i¢ ' l l l a ra l l i ~ ' l ~ ' r . . r l l , ca lC i l la l~ 'd i i.~il i~

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r !

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0 t , - 0 . 2 -0 .1 0 0.1 0.2

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3°° I 200

100

- 0 . 2 -0 .1 0 0.1 0 2 x 10 -1

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I'111.

012 ' ' • I 0 "3

collinx, i,~elast;c veto

rOl l~ i~ l~ ' l l l d~ , l~ . r i l l i l i a l i . l i . f thr , l l , m b r , r , i f , , ] as l i r ~,W,ll l~

w i t h t Im u . r . I ~,;tlvnpJ~.. I a khip., j . h l a('l',~.lllll l Inr" ,.fli,'i~mri~'.~

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1 h,,.~, , ' l lh ' i r 'wc i , 's [6].

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~'V¢'lll (']~l~s I l l l l l lb l 'F o f pw'I I | .~

t i-~,rk ~,'S4m."llt:-, iw .~'n..'~'.'..~. I ' - . . d

INin~,iH~ .~'1 ~/'.~':

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l(llJ + / - I:'l

I ; i3 + / - 11

J.~ + / - ~

223 + / - I l l l )

] '~v,',. l~ f i , r v , 'h i lh ..,P , r . l l im ' ,a r , . l~>, lh cand ida te , wa~ f i )mHI

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r .d l iv t , 'a j ' i l y w l rbd l l . ' , v.'a~ p l . l i , . d . Thi. ' . s.',,'.~.td r,,,,r',~.~:.l r , , ' -

IhJri pa l h v,,';t~ a l~o ii~l'.d 1 . i,~l h n a h ' fv lr l h,,r (J,,,,~li~ild,,.) r, '-

, rO l lMf ' l lC l io l i I~r~,~i.,~. Tahl.-, I ...iillnlli;iriz...,.i l h l , rl;~:-,.,-ii l iralit,l l

~d" , ' l ; l~t ](" t ,w,wl~ a r r . r d i w ~ 1 . w h ~ . l l . , r th~'y w~,ro f i ) l l l l ( I i l l

thr , i ) r i lv i iBry n ,co l i~ l r l lCl i l l l l pa l h. n, t i . i ,w,,d w i l b ~t;-iti~Jll~ ;~

; l l ld T lI.~,l";lll~r, r , f I v'ar ki 1114 hl , ' , l f i r i , , ]nry. , ." r.',t ri,.v,r,d lib'.Call..-,,.

22 S. W h i t e / p p total cross section at v ~ = 1800 G e V

of extra track segments were found in the event (ususally

due to upstream interactions).

Elastic candidates satisfying collinearity cuts on 0~ and

0~ were binned in t and the distribution was corrected for

trigger and reconstruction efficiency.

A geometrical acceptance correction was applied to

events in each t-bin taking into account the limited cov-

erage of the detectors in azimuth

The corrected differential elastic scattering rate was di-

vided by the integrated Luminosity of ( 1.24 -I- 0.0S) • lfi s°

and is plotted in figure 4. The data are well described by

a simple exponential dependence on t, whose coefficient is

found to be,

b = 16.5 + 0.5(statistical)(GeV/c) 2 (2.5)

T , I

1 0

, I . . . . i . . . . ! . . . . I . . . . I , i i t l t l l l l . . . .

0.06 O.OS 0,1 0.12 0.14 0,16 0.18 0.2 t-(GeV/c).-2

S1TOT CORR.

Fi~zre 4: Differential elastic scat ter ing cross section.

Data f rom A n n 0 attd A r m I are contbined.

3 S y s t e m a t i c Errors on the Opt ica l

Po int

We now consider the remaining systematic errors on the

optical point measurement.

The contribution from possible errors in the effective

lengths was found to be less than 3%. We used the rela-

tive alignment of detectors with elastic tracks to find the

maximium possible discrepancy from measured positions.

Then a simple Monte Carlo calculation was used to find

the effect of these discrepancies on the optical point.

Luminosity and the beam trajectory are discussed in

more detail below.

The beam trajectory affects the elastic scattering dis-

tribution in the following sense. Our internal alignment of

the detectors within the spectrometers using elastic tracks

doesn't constrain the overall angle of the apparatus rel-

ative to the beam direction. On the other hand, such

an offset would change the relative rate in detectors on

either side of the beam, giving rise to 2 different elastic

cross sections. Intuitively we expect this effect to partly

cancel when data from both sides (Arm0 and Arml) are

combined.

3 .1 B e a m t i l t a n g l e

The beam tilt angle is determined by comparing data in

the 2 spectrometer arms. This is done by starting with an

angle +~ for a possible offset and then rebinning in terms

of a new t variable.

t' = to + 2 . p " - ( 0 ~ - 6 ) (3.1)

A new acceptance, is also calculated for each spectrom-

eter arm and the resulting corrected t-distribution is fitted

to the form:

d N el = c A • t '~'t (3.2)

dt

The fitted total numher of events is then:

N ~t = , A / b (3.3)

The elastic cross section integrated from 0.05 < t <

0 . 2 ( G e V / c ) 2 is plotted for Ann 0 and Ann 1 data in figure

• 5 using different choices for the beam tilt angle. Clearly

the best choice for the beam tilt angle is in the ran~,e -.5.0

p r < b < 0.0/27".

When data from both arms are averaged, the fitted

slope and intercept parameters (b and ~ It=0) are

insensitive to ~ well beyond its possible range of uncer-

tainty. This is evident from figure 6 , which show the

dependecc,~ of the fitted intercept on the beam tilt angle.

S. White / pp total cross section at v~ = 1800 G e V 23

8.5

,E

~ 8

7.~

6.5

,~ ARM-O

* ~ u - 1

0 +

5 . 5

. , . I .... I .... I, , ...... I . . . . . . . . . . . .

5-20 -15 -10 -~ 0 5 1#0 1t~ 20

BEAM TILT ANGLE-MICRORADIANS

Figure 5: Elastic scattering cross scction intcgrated over

the range 0.05 < t < 0.2(GeV/c) 2 vs. the assumed beam

tilt parameter.

The statistical error on a~t is 4-1.5 %. Combining uncer-

tainties from Luminosity (4- 6.~%), reconstruction losses

and background (4- 3.0 %) and trigger efficiency (4- 1.0% )

we obtain

~ 300 o

-,~o 290 E

2 8 0

270

26D

250

240

230_2q

1 I a

. . . . I . . . . I . . . . I . . . . I . . . . ! . . . . g . . . . g • • , n

-1,~ - 10 - 5 0 5 10 15 20 beam t ~ t ongte

Figure 6: Dcpcndcne¢ of thc optical point (data from both

spcctromctrr arms combined) ,n thr a.~.~umcd brain tilt pa-

ratartt'r.

5 L u m i n o s i t y Cal ibrat ion and t h e In-

e las t ic Cross Sec t i on

cr, t = 16.5 4- 1.3rob. (3.-I)

4 T h e Tota l Cross Section

The optnral theorem can now 1)e used to derive trtot(pp )

from tire fit parameters to figure 4 yielding

2 -I dcr'l ct'Ztot = 16~r(hc)2( 1 + P ) ~ I,=o

= 19.53.( i + (.145)'~) -~

2 ~ 7" mb • ((271.0+ 1 3 . 1 4 - ' : . ) ~ )

ctt,, t = 72.0 4- 3.6rob (4.1)

The errors contril)uting to the overall uncertainty in th,"

optical point are liswd seperately in equation 4.[. The

(second) systematic error results from tlw comlfiv0d un- certainties from Luminosity, background~reconstruction

efficiency, and trigger efficiency.

The instantaneous hmfinosity from stored p and p beams

in the Tovatron can be calculated from accolerator based

lneasiIl 'fqlleltts of bunch intensity and pllll)litallce arid the

known hetalron al | lpli tude and inomentum dispersion at

ar given interaction region. This calculation is estimated

to 1)e accurate to 4-11% and the dominant ,n~er ta inty

c o m e s front tht" I)liltch intensity lllPasllrPIllel | ts [7].

We have reduced this imninosity uncertainty by using

data taken with tile ( ' I )F d~-tector at ~ = 5 . 1 6 GeV with

a mininnnn bias trigger and coral)acing our measured in-

elastic cross sm'tion with tha t of UA,I. This indopendont

chock on the luminosity, when comlfinml with the accelpr-

at, or calculation, reduced the uncertainty to +5 .6~ at 5.16

GeV. The rHative luminosity o r r . r when the Iwam onerg2¢

was increased to v ~ = IX00 GeV was found to be 4-4.3%.

Itonce an overall luminosity uncertainty of 4-6.8% was as-

sig, ned to . , r integ, rated luminosity at fldl beam ~'nergv.[21

24 S. W h i t e / O p total cross section at xls = 1800 G e V

5 . 1 M i n l n i u m B i a s C r o s s S e c t i o n

The ('liF l i lh i i lnUl l i bias t r igger requires at least i charged

track lit each of 7 xots o[" . l leal i l -Real i i cOil liler.~ ( l l l l ( "s l

cover ing the l lseudora l l id i ty raligO :1.:1 ~ q ~ .5.9 till e i ther

ship of the h l te ra r t i on point .

This trigger is p rhnar i l y sensit ive to nondi f r rac l ive in-

elastic e','enl~ al id is lie, ar ly ident ica l i l l coverage Io the

I 'A-I doul l lo al.' l l t f iggt.r which spali.~ l lSelldo rapid i t ies o f

:l.o < ,# < 5.(i [~1.

- ~ " ( 0 -

: : ( " - -

i F

6

L

OILl,

30 40 50 GO

RB~c/LAc c 1800 GeV Data (mb)

b

i t , , I . . . . t . . . . ! . ~ . ~

30 40 50 60

RBsULA¢ c 546 GeV Data (rob)

Pigur- 7: I h h r m i , a t i m t "s lbt , d n i m u n t bism h'itj-

!u r( BB( ' ) r f[~ rtil'< rross .~ , ' t i , n f r , m lumim,.~it!/ .~,ali,tj.

dt.~cribtd in tlu It.ft.

Figur+, 7b shows t lw rate of l i B ( ' ci'llllil.~ d iv ided hy

lh~. i l l i ro r rec lod l l l i i l i l iOSily c; l lc l l la l i t i l i . [ )a le l lo i l i ts r~ll'-

rosp. i id to a tTo lera lo r iiIOlt..illrlHilellls or lint, sh)rod ] leal l l

ll~lralilOlPrs called " l l yh ig wire st'ellS" w h i d i al'P l i lade lie -

rh, lh 'a l l .v d l l r i l i~ ( ' I l l : da ta lakh lg . " r h . . × l ) O r i o d rali',

for this l l . i ~ , r was ca icu la l .d frol l l l he I 'A-I d~niblo ; ir l l l

cross sPctioll and IlSed 1o correct l l i~ accnlol-alt ir Ii i i l i i lHiS-

i l y scale, tlas~,d til l a de la ih , d sl udy Cti l l l l lar i l l ~ acce lera tor

calculat io l is w i th observed rales a l ld eVel l l vl~rtex d is t r i -

l l l l l iOliS t inder a var let ) ' o f beani coi id i l io l iS we assigi led ~ll

e r ror Io l l io re la t ive h i in inos i t y at d i [ ferenl ~ol l ider r l l l i -

n ing ¢.llergies.

The rorrespolidiiig ('ross seciiOll at. ~ s : l , q 0 0 (;~,"

(shown in lig. 7a ) inc reases by 1.30 4-0.06.

| i i ( le l le i idonl o f t i le elast ic a l id t o l a l cross sectiOli niea-

Sll l 'ell ieil l ~ discu.~sed above, th is d i rect l i lea.~llrOll lel l l o f t i le

hierease o f the "n i in i lnuni I)ias" cross section Ihn i ls llOsslli le

IIr'V¢ thresholds i l l the i l ie las t i r rl'os~ secl ion. I :or ~xa ln l i le ,

eal( ' l l la l ions o f Q ( ' I ) i i i i l l i - j lq cross ~ecliOllS [31 im, dic l al l

ill('l 'easo o f 73-.1.1 n lh i l l Ollr Oll~,rgy l';llll~P, a I'alhlq- dl';i.

i l la l ic illCroase COlll i larod lip Ollr .l,.~erv,.d rise o f "~ 10 I l ih

for oi l her the Io la l i l ie last ic t)l" " i l l i l l i l i l i i l l l bias" cross sec-

t iol is.

~ ~0 SIGMA TOTAL PBAR-P

d

{3

80

?0

60

50

40

[] Corrol- 76 .." Rl rlen;sov-71 .+" 0 Amos-85 .-" • , -UA4 ." lit UA| ." ¢t E-710 (L-ini:lependenl.prellrn;nory} ." ~c CDF (L-OepenCen(. pfellmlnory )

1/:I .2'

. ~ :

C ; . . . . . . . . . . . . . . . . . . . . . . . . . . . J l0 1ff 10 = ~o'

CfdS ENERGY(GeV)

Hgure ~: I ' - I ' t . m / rr..~.~ s tc t iml r.w. ('.115; I']urrg!l.

6 C o n c l u s i o n

W~, h a w lilt,;isilr,,d trt,,l(/jp) = 77.0-1-'|.(i l i lb. ;11 ~ / ~ : l ~ ( } 0

( few iiSilig all in i l l l 'oved ac('t.h,r;l lr lr l i l l l i i l lt i.~il.y ca l i l l r ; i l l ( l l i

a l id C I )F ~,hlslh. da la . O i i r resil l l is COilsislelil w i t h lhe

va]uo i.~,ll.rh,d I>y ]']7]1"i and s l i i t lo ih { rough ly ;is In s )l:l] PXI l 'al lolaliOllS frol l i h)wer ellrgiP.~ as ('lilt l ie sef, ln fl'~llll [ig. III'P <~.

S. W h i t e / ~ p total cross section at v~ = 1800 G e V 25

lP.~lllg i i i l ind+' l l+ ' l idel i l iiit~ii.~llr~'ln~,llt o f 1.li~, r ise o f tiff ,

iil++];i.~iie Cl'OS,~ ~t~cliOll i l l lJit ~ i'alil~+" 5<1(i _< ~ ~ I S 0 0 ( i l+W

all ili('l'<~ltsl TM by il f3c t f l r i l l 1 .30 - I -0 .0f i wa,~ I' ltil i l l l w h i d l

i.Psl i'h't,s llO,s+sibh + n P w ihl'+sli~lhl.s hi I l l+ + hie la .s lh ' cro,~s sP('-

1 io l i .

R e f e r e n c e s

[1] for f u r t h o r detail .s ou t l w ( ' l ) l " sma l l ang le appa ra tus s~,e coutz'ibution II b' G.Ap~llinari iu Proce~,dings of th~ Third lutol-naiional ('oilfi,ronc~ on Elastic aiid ])ilrractiw Scattoriug -Nud.Phys.l|(Proc.Suppl)12 (1990)p1:2 and S.Whito in Elastic and l)i[['ractivo Scattoring II, Editions l:rowltior,,s{ 19~,~) p27.

[2]" ( ' I )F Lumirkosity Calibration " .(LPih'hor and .¢;.Whito, Formilab preprint FN-550.

[3] "Q( ' l ) mini jet cross sections". I.Sarcovic.S.I).l:;llis and P.('arruthors. Phys.li~,v.I) .I0 (19n9) 1116.

[.1] "Status l{,,porl on ETI0", i,r~,sonled by S. Shukla. 111e.~+ + l i roc l ,ed ings.

[.'5] Tll~, T¢,vl41rtln J)l,;iiii i~lll~l'~y hlis ;i s.'v'~tr'iil;llil + lillCl~l "- t a h i t y o f on l y :t:0.f) ( ~ V a l v]:~= IX00 ( ; ~ , V . . ~ col i- I . l ' i l l i l t iOl i J)y ] {o lJal id .Iolin.~on i l l l Jil, l)l.OCe~dillg+~ +if Ilia, I f i ~ ( ' E I I N - I ! ~ j oh i l ac(-~loral~ll + +~ctiool.

[6] 'tVe +,×ill+el, a lii<ii't TM r~ lhwd aliaJl,'.sis, currr, n l l y i l l lli'ol~r+',~,~, li,~ilip_.; l lo l h I ) i ,V( ' a l id .~ilicoii Jiil,s Io y i d d a slnall++r ,sy,~t<+nial.J~! i~l-i'i+)i " . ] ' l l i s i.~ l i ke ly Io l'Odllcl TM l.h~' l , l 'roi' l i l l i'J't<,t fl'Olll ,~l,~l,ll+).l~.

[7l N.(i++ll 'aud, " ( ' ( l i n j i l i l a i~ l l i °l+ Tl~vali 'Oil L l l i i i inoPi i iy liS- i l i [ lii<,a,,illi'l,d MaC]l i l l l , jiai'aliif'l.<,r.~" ,I:N-.q:IP4 (1.<t90)

[,~] I~li.v.s. I,~,it. 1.17]1 ( I .q~ . l )392 . I IA. I fhid,~ l h a l ~2.7-I- I).,~I~ o f i ii~,]a,sl.ic oV+,lils sal i,sfy 1 li~,il" dol l l i l r , ;ll+iil l i'i l - ~('1'.

[9] M . I l h w k and l l . ( ' ah l i . Iq iy ,~ . l .~ , l l . l~x l l (19,'47! p.l.13. l:it.~ 5 a i id (i ar~ l ih l l l~ 'd Jii [igUl'O ~.