a measurement of the pp total cross section at √s = 1800gev
TRANSCRIPT
Nuclear Physics B (Proc. Suppl.) 25B (1992) 19-25 Nort h- Itoiland
U C L E A R P H Y S I C S
P R O C E E D I N G S S U P P L E M E N T S
A Measurement of the p p total cross sect ion at ~/-s = I 8 0 0 G e V
So|)a.~tian W h i t e , Rockefeller Univers i ty
for the ( :I)F ( 'ol lahoration
A b s t r a c t
The lip difh,rontial ,'la.~tie stat tor i i ig cross sect i.lil was (ilPa.~ilrl,~! .,i , ~ : I tttl(t { ;oV, ii~iiil~ :ill iUilirove,I a¢c¢'l,'ratnr ItiillillO~it v
d,'i l 'ri i i i l iali~qi and ( : l )P sit,all angle dala iu the raligO elf (I.(i:) < t < O.2((;rl"ir)". I ly l 'x l ral- i la l in l4 the diff~,r,,utial cross
,~eelioiis Io I :1) ;iii(I usilig ill+' nplieal theory,Ill wl, ~dll,ain a lota l erl~..-;,,; secliliu rd" a l . l (pp ) = 72.1i:t:3.6 nih. 'l'lli~ rl,.~lilt i~
prel inihiary in the .~Oil.~e lhal wo eXll~Cl Io fur lher rod,ice l l lo .~ysl.eniali( .,rnir on t iw (.piieal i>~/inl.
1 Introduction 2 Method
The goal o f the CI)F small anglo physics linlgrani i.-
to nloa.~ure the diffractive procossos of el&~lriC scattering.
diffraction dissociation and atot(pp) at ~/~= IMO0 (:eV [I].
For this p . rposo (!I iF da ta woro recorded during sporial
stores wi th h igh- / i opt ics ( l t , , ,72 nt ), i ishl I I r i~gors ( l¢i~iod
f ronl smal l al igl~ de toc i . r s ,~elisil, ivo Io t i l l ' Ioadin I par l i -
clos, lUOii l i lod in l ion ,an Ihl ls.
|It th is l lapi.r wl, lirosi, nt rosi l l ts f ronl t im ;i,lialysis (l l
elast ic scat torh ig d a t a nwon lod du rh ig o11o such ~ loro.
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14,rinil; ib acc lerator do l la rhnPi i l I')1. Th is work is do-
scri l lod l i r io l ly lit .,;octioii .% al ld l ias rosl l l lo l l it, ;ill i l l i l l row, i I
lulnino,~ity inoa~il roli iOllt.
[ , idol)oi l( lol l , o f l l io t (d;d cross .~oction tllOas,,rot,iolit,
wo f ind tha t t l to o|l'octiv~', ¢-ros.% .~,('tif)l, sop,, by tho ( ' I ) F
ntinitl,lttn bias triggor, which is i)riln;irily soltsitivo t .
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1.30 :it 0.06 in the Oliprp~v rat,go 5.16 < v~ <_ IN(}() ( ; o r .
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[ . . . . . . . . . . . . . . . . . . . . . . . I i, 'Vl,lll i+l;i>~ 1 - t l l ; i< ~ ~.l ,~ll l l+ll l~ i i i N I . .+"f+. :+',it. I , l l l l l l l
i I l l i > . ; l l ~ .l~lll;,i';>
I l l l i>,+,ill~ ,%.. i l l i i . ,~hi l~ i . . I h .q .~ l l l l , l l l~
i,~[ 1 i+;i ~sl.~l ii1,ii I ~
l l l l l l l h + , r , + f t++,++<,lll -+
l : i : ' l~ It+/ Pql
IIIII i / 13
13 : i ÷ / I I
I- , + / fi
97+ ÷ ! I ( l l i
lZv,',,l~ I~,I" ~ l,i,l, ,., ,,,llim';~r ,*I;,~Ii, ,';,i,dbh~i,, ~;,~ lhul,d
;,,',',,z(lil,~4 h, th,. m,.lh,.l d,.>ri'i,),,d M.,v,, ~,'r,. r,.lil ,J~.
ili~+ Ir;ll'k ~,,~iii,,iiI~ l'riilll M;lli¢ill~ .%:I ~llld .~" ;illd ;i li+,w
,',,lli.,,~,rily v+,ri.hl,, ~+ ,~ l)h,lh.d. 'i'hi~ .,'<,,i,d r,.,',.,~IH,'-
l i l i l i i m l h ~;i~, ; i l ~ , u>,,d h , +,~I i i l l ; l h ' [ l i r l h(,r ( i w ~ l i ~ i b l , , } r,,
(+ii|l:q 1'11(I ii Jli llJm,~l,~. ' I 'M , I , , I ~ l i l l i l l i ; i f i~ l ,~ I h, , ,'l;i~,,,ili,'+sl i lHl
i l l ' i'l~l~|Ir ~W('III~ ;ilTllrll]ll~ If) wll,.lh,,r lh,.v wl.rl, f, lhild ill
I h,' lil*il,l;il~' r,.,'(,ll~l rll('l il,ll i);il h. r,,i l'i+.vi+d wit h ~l ;il ],ili~ 3
;ilid T h,.r;,ii~,. ,,l'tl ;wkill- ii,,.lliri,,i.'y. ,,i' l'l,l ri,w,.d l.,r+,li~.
22 S, W h i t e / # p total cross section at x/s = 1800 GeV
due to ui)strpa.m i~ltor&ctioTis).
//u were binned in t and the distribution was corrected for
t t ; ~ l ~ n t a n t i p~e~r ic i~ i le l t ; l~ l l r l ~l~la-inttetJ
A g~ometrical acceptance correction was applied to
events in each t-bin taking into account the limited cov-
erage of the detectors in azimu@.
The corrected differential elast ic scatter ing rate was di-
vided by the integrated Luminosity of ( 1.24 4- 0.08) • 103o
and is plotted in figure 4. The data are well described by
a zimple exponential depel:denc~, on t, whose coefficient is
found to be,
b = 16.5 + 0.5(statistical)(GeV/c) 2 (2.5)
E lOz
T I
lO
. I . . . . I . . . . ~ . . . . I . . . . I . . . . I . . . . I . . . .
0.06 O.O~S 0,1 0.12 0.14 0.16 0.18 0.2 t -(GeV/¢)**2
SITOT CORR,
Figure 4: Diffl:rtntial elastic scattt'rin9 cross section.
Data from Arm 0 avd Arm I nr~ combined.
3 Systematic Errors on the Optical
Point
We now consider the remaining systematic errors on the
optical point measurement.
The contribution from possible errors in the effective
lengths was fontal to be less than 3~A. We used the rela-
tive alignment of detectors with elastic tracks to find the
I . . . . . . . . . . . . . . . . . . . . 1 . . . . . . , . . . . . . . . . . . . . . . . . . . . l . . . . . . . . . .
The~ a ~impie M.onto ( ' ado caF.-ubdi,.;u wa~ ~sed ",o ii~,:]
Lummoslty and the beam trajectory at discussed in
lllfi~ l l g | a l l hOlfi~L'
The beam trajectory affects the elastic scattering dis-
tribution in the following sense. Onr internal alignment of
the detectors within the spectrometers using elastic tracks
doesn't constiain 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 ti,e beam. giving rise to 2 different elastic
cross sections. Intuitively we expect this effect to partly
cancel when data from Loth sides (~rmO and Arnll) 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
or a new t variable.
t' = to + 2 . p2 . (0~. • ~) (;I.1)
A new acceptance, is also calculated for eacb spectrom-
eter arm and the resulting corrected t-distribution is fitted
to the form:
dN'l = (a . ~s.t (3.2) dt
The fitted total numbor of events is then:
N 't = r a /b (3.3)
The elastic cross section integrated front 0.05 < t <
0.2(G(V/e) 2 is plotted for Arm 0 and Artu I data ill figure
5 using different choices for tile beam tilt anglo. Clearly
the best choice for the Imam tilt angle is in the range -5.0
ttr < b < O.Oltr.
When data from I)oth arms are averaged, tile fitted
slope and intercept parameters (b and ~ It=o) are
insepsitive to b welt beyond its possible range of uncer-
tainty. This is evident from fignre 6 , which show the
dependence of the fitted intercept on the bean, tilt angle.
S. Whi tc /~ ,p total cross section at x/s = 1800 GeV 23
[
= .
+ I[ + e I - * ~ u - + °[
, +
6.5
, +
l++I 5..5
i
+ +
.5 . . . . i . . . . i . . . . I . . . . . . . . i . . . . l . . . . i . . . .
- 2 0 - t 5 - t O - ,5 5 10 15 20
BP-AM TILT ANGLE - MICRORADIANS
Figure 5: Elastic seattcri~g cross section iut~ gmtcd m,~r
the range 0.05 < t < 0 .2(( ;cV/c) ~ vs. the assttnu'd I~ram
tilt parameter.
r
P o, 'a I"
280 ~
270
260
250
240
2 ~ 0 I . . . . I . . . . I . . . . i . . . . I J . . I I . . . . I . . . .
- 2 0 - 1 5 - 1 0 - 5 0 ~ IO 15 20
beom tilt ongle
Figure 6: D(prmhm'( of Ihc optirul iminl (data [corn bwh
sl)( c t ~ m l ~ ' l l r (U'tIL°¢ combh, dj . , I th~ a.,~.,~utn~d b¢ ~lnZ l i l t p l t -
t ' l l l f l ( t¢ I',
Tlno statistical error on a,l is + 1.5 (/~,. (:ovnlfining Ulicer-
tainties from [.unlinosity (4- 6 . ~ ) , reconstruction losses
anti backg round (+ 3.0 %)all(I trigger efficiency (4- I.O(Z~)
we obtain
Luminos i ty Cal ibrat ion and the In-
e last ic Cross Sec t ion
a,I = 16.54- 1.3mb. (3.1)
4 T h e Tota l Cross Sec t ion
Tim optical theorelli <'all IlOW I)e ll~etl 1o <lPrive #t,a(PP)
from the fit parameters to figure 4 yiPhling
. da' I rr~+t = 16~r(hc)+(I + I f l ) - I - -~ - It=o
= 1 ! ) . 5 3 . ( 1 + (.I.15)2) - I . I m l l )
• ((271.04- 13.1 4- 23.A ) ~ - ~ )
rh,,t = 72.0 4- 3.6n+b ( . t . l )
"rile errors rotltril)llt illg to thP .vorall tlncPrtaiiv y iu t hP
optical point are listed sPperatPly in Pqual i .n 1.1. The
(second) syst~'ulatic error r,,sults from thP r.nlhil:Pd un-
certaintios frmn I u:,d,msily, backgr.und/rPcor,struction
efficiency, and t r igs . , ,,lliciency.
T h e iti.M all t ~tleimllX Jlllliilli~,~i[y frOll l st.red p aIId I m beal l l~
in t i le "J'Pvatroll ra i l J)e ca lcu la ted t ro is a r c , I P r a t o r ImsPd
IlIP~iSlIrPIIIPIItS fm[ J)llllCJl i I l lP I is i fy ati(J Pl l l l t l i ta l lCe and f l ip
known I)olairon anlpl i tude and nloniPntum di~pPrsioil at
a given inforaction region. Thin calculation is estimated
to ImP a c t ' t l r a l P t o ~ J l ~ al ld f i le th )n l i lmnt un( 'Pr ta i i l t y
('OIIIPN fr i t l l i t he hl: / l i 'h i l l lP I Is i ty II iPi lSllrPll lel l tS [~'].
WP h,vP rPdured l l l is huninosity un('Prtahlfy by using,
data takPn witil the ( ' I l l : dPh,cf .r at J~=51(i (;eV with
a mi,finlum bias t riKgPr and cttmlmr!n~, tmr nleasurPd in-
Plastic cross .~P<'iiOll with tJlat . [ UA.I. "l'lli.~ i,(Iol.,udt, l l t
chock on the luminosity, when combined wit h the arcolor-
a t . r calculation, rPduced the unrPrtaild, y It) ::f:5.6'/, at 5,1G
( ; IV . Tim rPlati" t. h lmin.s i ly Prr-r wt.,l l ttl,, I.,am onPrKv
was increased 1. vC= I.~(10 (;eV wan f t . . id t . Imp :L.I.3%.
lloncP an .vPrall luminosity llncPrlaii, l y tmf -}-6.,~c~, was as-
sigw'd t,t Ollr i l l l eg ra ted hl l l l i l l ( tSi |y al [llJJ be;t i l l e l lor~v. [~]
24 S. W h i t e / ~ p total cross section at v~ = 1800 GeV
Jh+, { ' I )F )++bfi+,)++))) hian + +'+~,~+,+" r+,g~)ir+,s al i+,a>d ~ cha)'~+,d
t 5:++=!~ +11 +-;~¢-h ++. "--- ;P. :+ ++_ .+++;++t+ +{++;~t)t +:++tll+tt~;=m (===. t++:~)
cow,r ing the p.,,(,udorapidily Pal)St'. 3.3 < I! < 5.9 on o i lhor
si(Jt" of lilt'+ i l l loracl ion ] ) O i l i t .
This Ir+~¢++,r is p r imar i ly +,+elisitivo to nondi l [ rac l ivo in-
r.la.,+tic ovt,lltn a)ld is ))early id(';)tica) i)) coverago to t im
I ' A I doul ) l , a l m trig~('r which s p a n s i)s(,ul(Io ral)idit ios o f
3.0 _< ,i _< +.(~ [s].
i
:,+, +
22
:j -
] I ,~ ,,
: / (a.
o . . . . . . . . -=-- , ++=.~ ' , .:-.l ~ . . ~ - + L ~ _ - ~ i 30 40 ~0 CO
RBac/L~c c 1800 GeV Da ta ( rob)
.~ a F
++P-
++i ~ , r
30 40 50 60
RBBc/L~c c 546 GeV Da ta ( rob)
I'iK))r,, 7: Ihhrnt+'m)lio, uf th+ mi td t ,mn bia., Iri!l-
[i + r( BIH ') t ff++'lirt' ~'./'¢t,,~.,, ..~(. vii,t+ fcom lumin+).,il!l .~+'oli,!l.
d++~vrib+d h) Ihr h.rl.
l : iguro 717 ..,how+,+ lh+, rah , t)f BB¢' co)nil.~ divid, 'd l)y
l h . llllC1')rro(('lod hl)llilZO.,,+ily cah'll]aliOll, ] )a la poh)t.,, cor+
r+,njiOlZd I o ; l l . ( , o i t ' , r a f O l + lll(';l+'~llrt'qllOllln ( I f tilt +̀ P,l()r,'(] i ) l q I ) l l
l)aram+,l+,rn ('all,,d "f lyhi~ v,'h'c s cans " +,,l)i,l, ar , ' mad+, p,,-
r i o d h ' a l l y d l l l + i l l g ( ' I ) I : , ) , . a lakh)g. "l+h, ' ,+'Xl)+'cl+'d rat+"
for l ids t ri~g+.r was . ah ' , ) l a t .d Iron) lho I ' A I d,),)l)l+' a r m
l'l'ot+>, S O l ' t i l ) l l alt(J Um+.(I 111 ('+)rr<'( I tlff, alTP1Orahlr h l l ) 1 1 1 1 0 ~ -
i i y . '+ca)0 . i~,ay.+,d ))i a d + , t a i b , d >4 l)+))-' <'<) ~ , a r i t + ~ a(c+,J+,t '+!+++r
( a [ ( ' l ! j a i i o t m V , i t b +!bnor '~ 'o{] rate~ a t l l ] P~,oltl ~-Ol' l ."X <])?,!l'++ + , , , ; ; . . . . . . . . . . + . . . . . . . . . . . . ; . . + . . . . F + . . . . . . . . . . . . . . . : + : . . . . . . . . . . : . . . . + . . . . . . . . . . . . . . . . . . . . ~.+ . . . . . . ++
+.rror h) lho r+.lativo h]miu<)sitv al difF,,ron) ,',+dlMor r,n~-
l)+|l~ ( , l ' lOl-~[t ' .~.
T h e co r ros l )ond ing cross soclioll al ~/~=lXO0 t+I+,V
(showll ill fig. 7a) ) )crease 's l)y 1.30 :t: 0.06.
Indol)ond, ,n/ o f I h,, +'lactic and to la l c ross so(.lion moa-
+'r;IIPPIIIV')il)+; discUns<'d al),)v¢'. I his d i r o ( ' l 111PasllrO)llol)l o f l h P
i l lcroasq o f t l iP " i l i i l i i l l i l l l l i I)ian" (-ross nocliOII l imi ts posnil)h,
nl 'w threq ioh ls in I Iw i)wlasl ic cross n+,clion. I"()r ,,xaml)lo.
, 'ah')i lal ions ()f Q ( ' I ) mi)li+j+,l cross s,,('li,)nn [3] I)r, 'dir l atl
i l lCl+Oaso (l|" '2"~- [ | I1+!) il l (Hit" +',llerg3" i'illlgt',, it | ';ttllof dl';i-
Illali<" ill('ro;l+'+o ( 'ol) l :al , ,d )o (1111" ob:,oT'vod rin,, o f + 10 IIII)
f - r , ' i lhm' lh<, Iohd hwla+lh" or "miui t )mm bias," cro~,s +,,c+
llon>,.
S)GMA TOTAL P~A~-p
9o
$0
70
$0
r'Z CorroI- 76 Oen~sov-71 ""
) ~ o s - 8 5 .. *0) "UA4 • llr UAI
E- 710 (L-+n(Jepeo(lent,;~relitn[~ory) .." cOF {L-OepenCl~:~t. prellmlnor I~ )~ IIII/[..~ .-
, .@:'
CMS ENERGY(CeV)
I,'i~uro ,~: I ' - I ' h d a l vro.~.~ ,~+clim~ v.~. ~ ".~1,0" I "mrf l~ l .
6 Conc lus ion
W. haw, m,,a~ur,,d ,~,,dPp) = T2.0:E3.6 nlb. a! v(~= I.~00
G+4," using an iml)row,d ac¢.,h,v'at.r hllnino.~ily (a l ib ra l lon
and ( ' I ) I : (,laslic data . ( ) q r r , ,null i~ ('OllP+i~|t'ql| wi lh l l i ,,
v a h w r , ) lmr l vd by l '710 aml ~m<,oth (ro l i~h/y a~ It, s )[9]
,'x! rap()la!inlls froln hm','r ollr~io.~ aP, ('all I)(' hI'oh fl'olll lig-
lit(, N .
S. Whi t~ ' /pp total croqs section at ~ = 1800 GeV 25
i i lm.
R e f e r e n c e s
[ I ] for fl lrt h(~r (h, tail~ ,m lli,, ( ' I ) I : .~mall a .gh. al)paratu- ~,~,' C()ll lri l)l/tJ(,l i hy ( ; . A p , J l i . a r i i,, Proc(,~,diHg~ o f thf, Th i rd l . t~ , r r la t i , .m l (',mf,,r~,.r~. (.u I ' ]as! ie a . d D i f f rac t ive Scaft~,ril iR -N,c l . lULv.~. l | ( l ' roc. ,~ luq) l )12 (I,q.90)p12 arid S.%Vhitr' i . I'la.~tic attd I) i | f r ; i r t iv~, Scatt , , r in~ I I . L 'd i f io .~ I 'roiHi,,r,,s{ l : )xx) p2T.
[ 2 ] " (°1)1" I . , m i . o ~ i t y ( ' a l i h ra t i ( . i "" . ( ' . l ' ih 'h~' r aml ,~ .Whi t , , . I : , ' rmi la l) pr~,pril lt I :N-S50.
[3] " Q ( ' I ) mi. i j~. t , ' r ~ .~,,rti(,,.~". I .Sar r r ' v i r .S . I ) .H l i~ a . d I ' . ( ' a r r . d . , r s . I 'hy~.Rfw I) 10 (19,~9) I l i f t .
[ I 1 ",~f;ifll~, R,,i)or! ,,,i 1~710". pr,,s,,r,l~,d hy S. Sh,nkla. t I. '~,' pr . . ' , , . ,d in/~.
[;~] "l'h~' " l ' , ,valr , . i h, 'am ,,n~,rgy ha.~ a .~.v~lr~lliHlic Ull('('r+ l a i l l l y fir ()lily ~(}..() ( ; ( ,V a| % / ~ : i,~O0 ( ; , 'V . ~,',' e,m- lr ihl l l iol l h v Ro l laml Jllhll.~Oll ill the, I)l',)('(,,,(IJli~; I)f
[6] ~,%'r" ,'Xl){'cl a m , . ' , ' r~,lim'd ;nmly.~is. C,lrl '~'l l l ly i,~ prl.~r,,.~..I.,,i.~ h(~th I )W( ' a .d ,~ili('(m hils I~ yi,,hl a ~.nalh,r ~y.~h,malic ~,rror. Thi~ i~ lik~'t.v h~ r~,d.c~. II.,
[?] .X.(i(, l l 'and. " ( ' a m l ) u l a i , m ,)f 'l',,w.llv'~m l.,n.iun~)~iiy ~n~- i l l~ Iil(,a~lll'¢,(I .~.|a('hill,' I)aralll(,l(,l'.~'" .1:~-.().|.~ (I f lgO)
[,~] PiLv.~. L, ' l t . I IT i l ( l . ( IXl) ;I.(12. I".'%1 ii.(I.~ tha i x2,? 0..~(/( ,~i" iw,las! i(" (.v,,nat.~ ,~ali.~i'y t i . , i r ( l( .d)l , , a rm Ir ig- ~('l'.
[.9] .M.IIh.'k aml I{ .( 'ahm I 'hy~,. I . ," i t . l~h (19'<7" p.I I:L I"il,~ ;) ;iOl(I G al'(, i)l()ll~,(I i . li~ur(" x.