short distance qcd

Nuclear Physics B (Proc. Suppl.) 3 (1988) 715-742 715 North-Holland, Amsterdam

SHORT DISTANCE QCD

James STIRLING

Department of Physics, University of Durham, Durham, England.

Some t o p i c s i n the phenomenology of p e r t u r b a t i v e QCD a r e r ev iewed . Recent e x p e r i m e n t a l d a t a a r e d i s c u s s e d and i n t e r p r e t e d . S e v e r a l p r e c i s i o n t e s t s of the t h e o r y a r e d i s c u s s e d and a c o m p i l a t i o n of h ~ v a l u e s i s p r e s e n t e d .

1. INTRODUCTION

Quantum Chromod3rnamics (QCD), the gauge f i e l d t h e o r y which d e s c r i b e s the

i n t e r a c t i o n s of c o l o u r e d qua rks and g l u o n s , i s one of the components of the

SU(3) x SU(2) x U(1) S t a n d a r d Model. At s h o r t d i s t a n c e s , e q u i v a l e n t l y l a r g e

momentum t r a n s f e r s , the e f f e c t i v e c o u p l i n g i s smal l and the t h e o r y can be

s t u d i e d u s i n g p e r t u r b a t i o n theo ry . The g o a l s of con tempora ry s h o r t d i s t a n c e

QCD a r e t h r e e f o l d : ( i ) to u n d e r s t a n d p r e s e n t d a t a , ( i i ) to measure a s

p r e c i s e l y as p o s s i b l e the fundamen ta l p a r a m e t e r s of the t h e o r y ( A ~ , the

d i s t r i b u t i o n s of p a r t o n s i n hadrons . . . . ) and ( i i i ) to make a c c u r a t e

p r e d i c t i o n s fo r the n e x t g e n e r a t i o n of had ron c o l l i d e r s . The l a t t e r i s

e s p e c i a l l y i m p o r t a n t , s i n c e QCD i s now known to be a v i t a l component of many

S t a n d a r d Model "new p h y s i c s " s e a r c h e s .

Th i s s h o r t r ev iew w i l l d e s c r i b e s e v e r a l t o p i c s i n modern QCD phenomenology.

Recent e x p e r i m e n t a l d a t a w i l l be d i s c u s s e d and i n t e r p r e t e d . The t o p i c s which

w i l l be covered a r e :

( i ) deep i n e l a s t i c s c a t t e r i n g

( i i ) l a r g e PT hadron p r o d u c t i o n

( i i i ) W and Z p r o d u c t i o n

( i v ) heavy qua rk p r o d u c t i o n i n hadron c o l l i s i o n s + - -

(v) e e a n n i h i l a t i o n .

There w i l l n a t u r a l l y be some o v e r l a p w i th o t h e r t a l k s a t t h i s Con f e r e nc e .

In p a r t i c u l a r , many i m p o r t a n t a s p e c t s of QCD have been cove red i n the rev iews

by Wu, L e e - F r a n z i n i , J e n n i , Voss, R icha rd and Hofmann.

0920-5632/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

716 W.J. Stirling / QCD at short distances

2. QCD S c a l e Dependence

Befo re c o n s i d e r i n g the e x p e r i m e n t a l d a t a i n d e t a i l , i t i s i m p o r t a n t to

remember the t h e o r y which u n d e r p i n s the s o - c a l l e d QCD " p r e c i s i o n

measu remen t s " . The b a s i c r e s u l t i s t h a t p r e c i s i o n s t u d i e s can o n l y a p p l y to

q u a n t i t i e s f o r which the n e x t - t o - l e a d i n g c o r r e c t i o n s have been computed. We

can i l l u s t r a t e t h i s by means of a s imp le " toy" p r o c e s s . C o n s i d e r a

c r o s s - s e c t i o n which can, i n p r i n c i p l e , be computed to a l l o r d e r s i n QCD

p e r t u r b a t i o n t h e o r y :

a = Aas(Q ) + Ba~(Q) + . . . ( 2 . 1 )

] 'he c o e f f i c i e n t s A,B . . . . depend i n g e n e r a l on k i n e m a t i c v a r i a b l e s and a r e

computed i n some c o n v e n i e n t r e n o r m a l i s a t i o n c o n v e n t i o n ( e . g . MS). I f B i s

unknown, t h e r e i s an a m b i g u i t y i n the p r e d i c t i o n be c a use the r e n o r m a l i s a t i o n

s c a l e Q i s n o t d e t e r m i n e d . One may i n t u i t i v e l y choose a " t y p i c a l " s c a l e

c h a r a c t e r i s t i c of the e n e r g y s c a l e s i n the p r o c e s s (PT,mQ,V~ . . . . ) , b u t t h e r e

i s no way to make the p r e d i c t i o n p r e c i s e . I f , on the o t h e r hand, the n e x t -

to-leading coefficient B is known, then the variation of o with changes of

scale is much reduced. This is because B contains a Q-dependent term B =

-A(~o/2v)lnQ + ... which compensates the Q dependence of the leading term.

The more higher order corrections are known, the weaker is the Q dependence.

Nowadays, there is a sizeable class of processes for which the next-to-

leading corrections are known and these provide the precision measurements of

the fundamental parameters, e.g. h~. Note that some arbitrariness still

persists in a cross-section truncated to next-to-leading order. Several

schemes have been proposed for "optimising" the predictions. For example, one

can in general choose a scale QFAC for which the next-to-leading order

correction vanishes [1]:

a (2) a (1) (2 .2 ) ]Q--QFAc = ]Q--QFAc

where a (n) d e n o t e s the c r o s s - s e c t i o n t r u n c a t e d to n th

i s the s c a l e QP]/~S

[ 2 ] :

o r d e r . Another cho ice

f o r which the n e x t - t o - l e a d i n g o r d e r p r e d i c t i o n i s s t a t i o n a r y

Q2 0 a(2){ 0 . ~ 2 Q=QpI,~S =

( 2 . 3 )

W.J. Stirling / QCD at short distances 717

Fig . 1 i l l u s t r a t e s t he se p o i n t s f o r a r e a l i s t i c c r o s s - s e c t i o n : the v a l e n c e

s c a t t e r i n g p a r t of the W t r a n s v e r s e momentum d i s t r i b u t i o n i n pp c o l l i s i o n s

[ 3 ] . The c u r v e s a r e the O(as) and O(a~) c r o s s - s e c t i o n s a t p$ = 50 GeV/c as a

f u n c t i o n of the s c a l e Q. The s t a b i l i s i n g e f f e c t of the n e x t - t o - l e a d i n g

c o n t r i b u t i o n i s e v i d e n t . The s c a l e s QFAcand QPbIS' as d e f i n e d above , a r e a l s o

i n d i c a t e d . I n common w i t h many o t h e r c a s e s , the d i f f e r e n c e be tween the

p r e d i c t i o n s c o r r e s p o n d i n g to the two c h o i c e s i s r a t h e r s m a l l .

q,,

1.5

I..0

t-.-

'-" 0 ~ 1"

X

~ , _ O'S "ID

I0 "10

I I i I ! I I I I I

p~ = SO 5eVIc

m

I I I m J J i m i I

118 II~ II 2 I 2 & 8 16 32 64.

W (11 PT

F i g u r e 1

The O(as) and O(a~) n o n - s i n g l e t t r a n s v e r s e momentum d i s t r i b u t i o n s fo r

pp ~ W + . . . a t v~s = 630 GeV as a f u n c t i o n of the (~f) s c a l e .

3. QCD IN DEEP INELAgrlC SCATTERING

The original quantitative test of perturbative QCI) is the breaking of

Bjorken scaling in deep inelastic lepton hadron scattering. In the leading

logarithm approximation the measured structure functions Fi(x,Q 2) are related

to the quark distribution functions [4]:

Fi(x,Q2 ) = ~ c i jq j (x 'Q2) • J

( 3 . 1 )


In describing the way in which scaling is broken in QCD it is convenient to

define singlet and non-singlet quark distributions:

FNS = qi - qj

FS = ~ (qi + qi ) " (3.2)

i

The variation of these and the gluon distribution with Q2 is described by the

familiar Altarelli-Parisi equations [5]:

Q2 OF NS as (Q2) pqq.l~S o ~ 2 - ~ r

- lP J l G J " (3.3)

Explicit expressions for the splitting functions can be found in [6]. The

precision of contemporary data demands that higher order corrections also be

included. This amounts to including O(as) corrections in the coefficients cij

in eqn. (3.1) and in the splitting functions pij in eqn. (3.3).

A detailed review of the current status of the experimental data has been

presented at this conference by Voss. From eqn. (3.2) it is clear that a

non-singlet structure function offers the most precise test o£ the theory

since the Q2 evolution is independent of the unknown gluon distribution. In

practice, however, such a measurement involves taking differences between

cross-sections (e.g. F 3 in neutrino scattering). Until recently this has

meant that the most accurate measurements, involving singlet dominated

structure functions (e.g. F 2 in muon scattering), have led to correlated

values for A~and the gluon distribution. The recent BCI)MS muon-carbon data

[7] is characterised by high statistics at large x and Q2. This means that

(a) the singlet contamination of F 2 is small and (b) there is a negligible

contribution from higher twist effects. As a result A~can be measured very

precisely. Fig. 2 shows the BCDMS data on the logarithmic Q2 derivative of

log F 2 as a function of x, together with the predictions of QCD for various

A~values. A detailed fit gives [7]

^ ~ = 230 ~ 20 ~ 6o ~eV. ( 3 . 4 )


N

o 0 f-

-0.1 c~

w

M_ TM

= -0.2

-0.3 0

I I I I I I I I I

m

÷ BC I I I I I I I I I

0.2 0.4 0.6 O.B 1.0

X

Figure 2 The logarithmic derivative d log F2(x,QZ)/d-- log Q2 measured by the BCDMS

collaboration [7]. The lines are non-sir~let QCD predictions for

A~= 100 MeV (upper line). 230 MeV (middle line) and 400 MeV (lower line).

10 H e Y )

i

lOMeV

A . ~ meosuremenfs

lOOMeV 1GeV I ' I

: ; BCOMSIH z )

c ; BCDMS(C )

• I WAS9

= t EMC(H 2)

: = ; EMC(Fe)

= : CDHS

= ; CCFRR

c : CHARM

: = : Re. e -

I.--- e---~ EECA

T d e c o y s

: = : F2 Y

- - - - e - - - large PTY I , , I , ,

100MeV 10eV

F i g u r e 3

A c o m p i l a t i o n o£ r e c e n t A ~ m e a s u r e m e n t s from deep i n e l a s t i c s c a t t e r i n g

e x p e r i m e n t s end from o t h e r p r o c e s s e s d e s c r i b e d i n t he t e x t .


This r e s u l t for h ~ is compared with other publ ished values from deep

inelastic experiments in Fig. 3. There is very satisfactory agreement between

the different experiments.

As a by-product of the structure function analysis one can also extract

parton distributions at a reference momentum scale. These can then be evolved

to arbitrary Q2 and used for hadron collision phenomenology. The parton

distributions of Duke and Owens [8], Gluck et al. [9] and Eichten et al. [lOJ

have been used in this way for several years. The data on which these

distributions were based have now been superseded by more accurate

measurements. Consequently more up-to-date distributions have recently been

derived by Hartin et al. [11] and by Diemoz et al. [12]. The former will

generally be used in the phenomenology which follows. Note that while for

most processes the differences between the "first generation" and "second

generation" parton distribution predictions are not large, there are some

cross-sections - notably W and Z production cross-sections - for which the use

of the most reliable distributions is crucial. This will be discussed in more

detail below.

4. QCD IN LARGE PT HADRON PRODUCTION

The hard scattering of quark and gluon constituents in hadron-hadron

collisions produces jets o£ hadrons with large transverse momentum. The most

striking evidence for this comes from data on the inclusive jet cross-section

at the CERN pp collider. In leading order QCD, the cross-section is given by

Ej ~ - a,b,c,d~ f~ dXldX2 Ga/p(Xl'Q) Gb/p(X2'Q)

=q,g

167r2-----~ I ab d 12 (4.1)

where the i d e n t i f i c a t i o n " j e t = par ton" i s assumed. E x p l i c i t express ions for

the spin, colour averaged 2 ~ 2 par ton s c a t t e r i n g ampli tudes can be found in

the review by Owens [13]. Unfor tuna te ly the h igher order QCD co r r ec t i ons to

a re not ye t ava i l ab l e ; the O(a~) diagrams have been t h i s c r o s s - s e c t i o n

c a l c u l a t e d [14], but the r e s u l t s t i l l needs to be cas t in to a form appropr ia te

to the j e t c r o s s - s e c t i o n . There are a l so experimental problems ( j e t a lgor i thm

dependence, energy sca le c a l i b r a t i o n . . . . ) in making a p r ec i s i on measurement.

I~.J. Stirling / QCD at short distances 721

For t h e s e r e a s o n s , the j e t i n c l u s i v e c r o s s - s e c t i o n p r o v i d e s o n l y a

s e m i - q u a n t i t a t i v e t e s t of the t h e o r y .

F i g . 4 shows the j e t PT d i s t r i b u t i o n from the UA2 e x p e r i m e n t [15] a t the

CERN pp c o l l i d e r . The cu rve i s the l e a d i n g o r de r QCD p r e d i c t i o n c a l c u l a t e d

from eqn. ( 4 , 1 ) w i t h the Se t 1 d i s t r i b u t i o n s from r e f e r e n c e [11] and wi th the

( a r b i t r a r y ) s c a l e c h o i c e Q = PT/2. The agreement i s s p e c t a c u l a r over the

comple te PT range and p r o v i d e s pe rhaps the c l e a r e s t e v i d e n c e so f a r f o r ha rd

p a r t o n - p a r t o n s c a t t e r i n g . The j e t a n g u l a r d i s t r i b u t i o n ( i n the j e t - j e t

c e n t r e - o f - m a s s ) from the UA1 expe r imen t [16] i s shown i n F ig . 5. The dashed

c u r v e i s the " p a r t o n model" p r e d i c t i o n c o r r e s p o n d i n g to the c r o s s - s e c t i o n of

eqn. ( d . 1 ) w i t h a f i x e d Q s c a l e . The d a t a c l e a r l y p r e f e r the f u l l QCD

p r e d i c t i o n ( s o l i d l i n e ) w i th s c a l e - b r e a k i n g e f f e c t s i n c l u d e d .

10 2

o I~ ii

D.

10 .3

0 150

- - set1 with O: l l r / 2

t ~ i l i i i i i J J

SO 100 PT { GeVIc )

F i g u r e 4

The j e t PT d i s t r i b u t i o n i n pp ~ j e t + X a t ~ = 0 fo r V~s = 630 GeV. The d a t a

a r e from the UA2 e x p e r i m e n t [15 ] . The c u r ve i s a QCD p r e d i c t i o n a s d e s c r i b e d

i n the t e x t .


500

600

300 Z L~ t.~

200

100

I I I i ! I I .~'l| I I

rl ANGULAR DISTRIBUTION FOR I

I TWO-JET EVENTS PLOTTED vs cosO I

I Mzj=lS0 - 250 GeV

1142 EVENTS I I

/

LEAOiNG OROER CLF..D . / / scAu.6 CURVE )7 ' / /

. " ~ s j / ~ L E A D I N G ,NC L U DINGORDENoRR_ S~ C IOUNF, _ ~ EFFECTS

I I I I I I I I I 02 O.Z~ 0.6 0.8

CosO

10

F i g u r e 5

J e t c e n t r e - o f - m a s s a n g u l a r d i s t r i b u t i o n a s m e a s u r e d b y t h e UA1 c o l l a b o r a t i o n

i n p p ~ j e t + j e t + X a t v~s = 630 GeV [ 1 6 ] . The c u r v e s a r e d e s c r i b e d i n t h e

t e x t .

I,V.J. Stirling / QCD at short distances 723

The above d i s c u s s i o n i m p l i c i t l y assumes t h a t l a r g e PT j e t p r o d u c t i o n i s the

r e s u l t of a s i n g l e p a r t o n - p a r t o n s c a t t e r i n g . In QCD, m u l t i p l e p a t t o n

s c a t t e r i n g i s e x p e c t e d to occur a t a much s m a l l e r r a t e [17 ] . For example, the

d o u b l e p a r t o n s c a t t e r i n g (DPS) c r o s s - s e c t i o n has the g e n e r i c form

DPS o2~2~o 2~2 - ( 4 . 2 )

a e f f

where Oef f i s an e f f e c t i v e " t o t a l " c r o s s - s e c t i o n which p a r a m e t r i s e s the e x t e n t

to which the incoming p a r t o n beams o v e r l a p . N a i v e l y , doub le p a r t o n s c a t t e r i n g

w i l l g i v e r i s e to fou r j e t e v e n t s and w i l l t h e r e f o r e compete w i t h the 2 ~ 4

QCD s u b p r o c e s s . There a r e however s e v e r a l i m p o r t a n t d i f f e r e n c e s be tween the

two mechanisms. Double p a r t o n s c a t t e r i n g i s a " h i g h e r t w i s t " p r o c e s s i n the

s ense t h a t , fo r f i x e d ~ T '

DImS

2--~ ~ 1

(4.3)

For a f i x e d t o t a l j e t E T t h r e s h o l d , t h e r e f o r e , i t i s more e f f i c i e n t to s ea rch

fo r DPS e v e n t s a t s m a l l e r c o l l i s i o n ene rgy . A second d i s t i n g u i s h i n g f e a t u r e

of DPS fou r j e t e v e n t s i s t h a t the j e t s w i l l p r e d o m i n a n t l y be p a i r w i s e

b a l a n c e d i n t r a n s v e r s e momentum. In c o n t r a s t , QCD 2 ~ 4 s c a t t e r i n g g i v e s

r o u g h l y equa l numbers of p a i r w i s e b a l a n c e d and n o n - p a i r w i s e b a l a n c e d

( " t r i p o d " } e v e n t s .

The AFS c o l l a b o r a t i o n have r e c e n t l y p r e s e n t e d e v i d e n c e f o r d o u b l e p a r t o n

s c a t t e r i n g i n p r o t o n - p r o t o n c o l l i s i o n s a t the CERN ISR [ 18 ] . By compar ing the

d i s t r i b u t i o n i n the PT imba lance v a r i a b l e

I = 9- (PT1 + + ( 3 + ( 4 . 4 )

f o r a sample o£ fou r l a r g e PT j e t e v e n t s , AFS obse r ve a c l e a r exces s of e v e n t s

a t smal l I compared w i t h the p r e d i c t i o n s of a model based on QCD 2 ~ 4

p r o c e s s e s o n l y [18 ] . Good agreement i s o b t a i n e d by i n c l u d i n g a DPS component

with

Oef f = 2 . 5 mb = ~ ( 0 . 1 7 fm) 2 ( 4 . 5 )

which a p p e a r s a r e a s o n a b l e v a l u e . The AFS d a t a i s t a ke n a t V~ = 63 GeV.

E x t r a p o l a t i n g to CERN pp c o l l i d e r e n e r g i e s one f i n d s [18]

724 W.J. Stifling / QCD at short distances

o 4 j > fo r ET ( 35 GeV a t ~ s = 63 GeV 60 GeV a t v~s 630 GeV "

The UA2 c o l l a b o r a t i o n have r e p o r t e d [19] t h a t an a n a l y s i s i s i n p r o g r e s s to

look fo r e v i d e n c e fo r DPS fou r j e t e v e n t s i n t h e i r j e t sample. There appea r s

to be no e v i d e n c e y e t fo r a DPS c o n t r i b u t i o n i n a fou r j e t sample w i t h ~-T >

70 GeV, and t h i s can i n p r i n c i p l e be t r a n s l a t e d i n t o a lower l i m i t on a e f f "

5. ~ IN W AND Z PRODUCTION

I n a d d i t i o n to p r o v i d i n g some of the most fundamen ta l t e s t s of the

e l e c t r o w e a k p a r t of the S t a n d a r d Nodel , the p r o d u c t i o n of W and Z bosons i n

h i g h e n e r g y pp c o l l i s i o n s i s a l s o a u s e f u l t e s t i n g g round f o r p e r t u r b a t i v e

QCD. I n t h i s c a se , the l a r g e momentum s c a l e i s n a t u r a l l y g e n e r a t e d by the

weak b o s o n m a s s e s . The s i m p l e s t q u a n t i t y to a n a l y s e i s the t o t a l p r o d u c t i o n

c r o s s - s e c t i o n : a ( p p ~ W , Z + . . . ) . T h i s i s a D r e l l - Y a n type c r o s s - s e c t i o n ,

c a l c u l a t e d to l e a d i n g o r d e r by c o n v o l u t i n g the a p p r o p r i a t e c o m b i n a t i o n s of

qua rk and a n t i q u a r k d i s t r i b u t i o n s . The n e x t - t o - l e a d i n g O(as) c o n t r i b u t i o n s

a r e a l s o known, and i n c r e a s e the l e a d i n g o r de r c r o s s - s e c t i o n by a bou t 30%.

Both UA1 and UA2 c o l l a b o r a t i o n s have p r e s e n t e d measurements on the c r o s s -

s e c t i o n s o (pp ~ W)B(W ~ Iv) and o(pp ~ Z)B(Z ~ l + l - ) where 1 i s a charged

l e p t o n [20 ] . The p r i n c i p l e u n c e r t a i n t y i n c a l c u l a t i n g t h e s e q u a n t i t i e s comes

n o t from the u n c e r t a i n t i e s i n the qua rk d i s t r i b u t i o n s , b u t from (a) the

unknown O(a~) QCD c o r r e c t i o n s and (b) the unknown top qua rk mass and number of

l i g h t n e u t r i n o s N which e n t e r i n t o the l e p t o n i c b r a n c h i n g r a t i o s . Th i s i s D

i l l u s t r a t e d i n F i g . 6, t aken from r e f e r e n c e [11 ] , which shows the e x p e r i m e n t a l

measurements from UA1 and UA2 compared w i t h the t h e o r e t i c a l p r e d i c t i o n s as a

f u n c t i o n of the top quark mass fo r t h r e e l i g h t n e u t r i n o s . The shaded hand

t ake s i n t o a c c o u n t the u n c e r t a i n t i e s i n the p a r t o n d i s t r i b u t i o n s and i n the W

and Z masses . The dashed l i n e s i l l u s t r a t e the e f f e c t of a i10% h i g h e r o r de r

c o r r e c t i o n . The g e n e r a l agreement be tween t h e o r y and e x p e r i m e n t i s

r e m a r k a b l y good, b u t w h i l e the e x p e r i m e n t a l and t h e o r e t i c a l e r r o r s a r e l a r g e

and of the same o r d e r , t h e r e i s no p o s s i b i l i t y of any s i g n i f i c a n t i n f o r m a t i o n

on the top qua rk mass. With the expec ted r a p i d i n c r e a s e i n s t a t i s t i c s i n the

n e x t few y e a r s , the c a l c u l a t i o n of the O(a~) ~ c o r r e c t i o n i s c l e a r l y a

m a t t e r of some u r g e n c y .

The c o n v e n t i o n a l method fo r o b t a i n i n g l i m i t s on N v and m t a v o i d s the

p rob lems of unknown h i g h e r o rde r c o r r e c t i o n s and l u m i n o s i t y u n c e r t a i n t i e s by


c o n s i d e r i n g the r a t i o R of the number of W ~ ev e v e n t s to the number of Z + -

e e e v e n t s [ 21 ] :

owBCW eo) R - . (5.1)

ozB(Z-~e+e - )

The key t h e o r e t i c a l i n p u t to the r i g h t - h a n d - s i d e of eqn. ( 5 . 1 ) i s the r a t i o of

t o t a l c r o s s - s e c t i o n s R ° = aW/a Z. The v a l u e of R a depends s e n s i t i v e l y on the

r a t i o of u to d qua rk d i s t r i b u t i o n s i n the x = O(Mw/V~s ) r e g i o n . Three r e c e n t

e s t i m a t e s a r e

3 .36 ~ 0 .09 ( M a r t i n e t a l . [ 22 ] ) = 3 .41 ~ 0 .08 (Halzen [ 23 ] ) . ( 5 . 2 )

Ra 3 .28 ~ 0 .15 (Diemoz e t a l . [ 12 ] )

07 b~ co o6

OS

0.z,

120

100

80

m 60

/*0

r

i

.ev p.v xv ev UAI UA2

[ r

I e e p l ~ e e

UAI UA2

20

, i r

W p r o d u c t i o n

fl/I

0 60 80 m t

, i i

Z p r o d u c t i o n

1o Lo m t {5eV }

Figure 6

The W and Z cross-sections measured by the UA1 and UA2 collaborations [20].

The theoretical predictions [11] are shown as a function of m t for N v = 3.


F i g . 7 shows t h e t h e o r e t i c a l p r e d i c t i o n s f o r R as a f u n c t i o n o f N v and m t from

r e f e r e n c e 22. The shaded bands c o r r e s p o n d to the R v a l u e s 3 .27 < R < 3 .45 U

as d e t e r m i n e d i n [22 ] . The combined UA1 and UA2 d a t a p o i n t and 90X c o n f i d e n c e

l e v e l uppe r l i m i t a r e a l s o shown. Given the u n c e r t a i n t y i n R a , e v i d e n c e d by

eqn. ( 5 . 2 ) , t he o n l y d e f i n i t e c o n c l u s i o n a t p r e s e n t i s t h a t t h e r e a r e a l m o s t

c e r t a i n l y no more than f i v e s p e c i e s o f l i g h t n e u t r i n o s . T h i s l i m i t i s

c o n f i r m e d by s i m i l a r l i m i t s from o t h e r h i g h e n e r g y e x p e r i m e n t s ( i n p a r t i c u l a r + -

f rom the p r o c e s s e e ~ ~uu) and from a s t r o p h y s i c s . Whi le i t i s t e m p t i n g to

u se F i g . 7 to e x t r a c t an upper l i m i t on the top qua rk mass, f o r example by

n o t i n g t h a t the lower edge o f the N u = 3 band e x c e e d s t he 90X c . 1 . upper l i m i t

a t m t = 67 GeV, t he l a r g e t h e o r e t i c a l and e x p e r i m e n t a l e r r o r s p r e c l u d e any

m e a n i n g f u l l i m i t a t p r e s e n t .

G iven the t h e o r e t i c a l and e x p e r i m e n t a l u n c e r t a i n t i e s , i t i s c l e a r l y

i m p o s s i b l e to u se t he t o t a l W or Z c r o s s - s e c t i o n s f o r a measurement o f a a t S

13

12

11

10

9

B

7

6

R -

U J J J i J ~ ~

0

% B(W--ev) crz B(Z~ee)

Nv=5

UA~ l f I 1

UAz 20 ~0 60 80 100

m t CGeV)

F i g u r e 7

R a t i o o£ W,Z c r o s s - s e c t i o n s measured by the UA1 and UA2 c o l l a b o r a t i o n s [20] .

The a v e r a g e o£ the e x p e r i m e n t a l r e s u l t s i s a l s o shown ( c l o s e d d o t ) . The

t h e o r e t i c a l p r e d i c t i o n s [11] a r e a s f o r F i g u r e 6.

tV.J. Stirling / QCD at short distances 727

present. A better quantitative test is provided by the transverse momentum

distribution of Wand Z bosons. At large transverse momentum the leading

order subprocesses are qq ~Wg and Clg ~Wq. With parton distributions and a

value for ~ input from other processes, definitive predictions can be

confronted with data. Measurements of the W transverse momentum distribution

by the UA1 E243 and UA2 [25] collaborations have recently been reported. As

emphasised in Section 2. any precise perturbative prediction requires higher

order corrections. Ellis et al. [263 have calculated the O(a~} corrections

for the non-singlet (i.e. valence-valence) part of the cross-section. In

reference [27] these corrections have been combined with the recent parton

distributions of reference [11] to derive precise QCD predictions. To

estimate higher order corrections for the singlet annihilation and gluon

scattering components of the cross-section, the non-singlet part is first

"optimised" and the optimisation scale is then used in the leading order

singlet annihilation and gluon scattering cross-sections. It is estimated

[27] that the overall theoretical uncertainty thus introduced is unlikely to

be more than about 120% of the total transverse momentum distribution. Fig. 8

shows the comparison between theory and experiment. The two QCD curves

correspond to two sets of parton distributions from Ell] with h~values of

10 "2

10 .3

10. (̀

~lb 10-6

10 .7

lO~a 0

i i i I

\

l l t l i l l

40 ~ 8O

p~ (GeV/c)

' ! ' I

~ = 630GeV data +UAI

"~'UA2

100 120

Figure 8

QCD predictions from [273 for the W transverse momentum distribution, compared

with data from the UA1 [24] and UA2 [25] collaborations.

728 W.J. Stirring / QCD at short distances

107 MeV (soft glue) and 250 MeV (hard glue) (lower and upper curves

respectively). Evidently the agreement is very reasonable over the complete

PT range. However it is also clear that the data are not yet in a position to

discriminate between the two sets or, equivalently, to provide a precision

measurement of A T. A final comment concerns the tail of the UAI

distribution. The highest p~ bin contains two events - one electron, one

muon, and each with two hadronic jets - with W transverse momentum

substantially larger than the rest of the sample. The event parameters are

( in CeV) [24]:

Event p~(Z) Mjj MjjW(Z)

W ~ v A 82 ~ 12 82 i 10 299 + 28

W ~ ev B 105 ~ 14 97 ~ 12 279 ~ 28

Z ~ vv C 82 i 11 148 ~ 17 ) 295 ~ 27

(5 .3)

The expected rate of such events in QCD is roughly an order of magnitude

smaller than that observed [24,28]. The origin of this discrepancy is unclear

at present. It is important to point out that it is no longer possible to

adjust the QCD parameters to force the theoretical curve in Fig. 8 to be much

harder in the tail. The parton distributions and A~are much too well-

constrained by other processes to permit a significant variation. The most

likely explanation for the two UA1 events is, therefore, that they are either

the result of non-gaussian fluctuations in the response of the UA1 calorimetry

or a statistical fluctuation in the data [24].

At small transverse momentum the emission of soft gluons in the basic 2 W

qq ~ W process gives rise to factors of aslog (MW/PT) and low order

perturbation theory breaks down. Fortunately, these large logarithms can be

resummed to all orders and the result is a "Sudakov form factor" which

controls the small p~ behaviour [29]. The resulting cross-section is most

naturally expressed in impact parameter space. Schematically:

da

dp~ 2 db b Jo(bP~) e -S(b'M) JlodXldX 2 6(x2x2s-M2 )

q (Xl .b -1 )q (x2 ,b -1 ) (5 .4)


W To the extent that the exponent S in eqn. (5.4) depends on ~, the small PT

distribution can in principle be used as a test of QCD. In practive however

there are some difficulties - for example, some non-perturbative cut-off or

smearing must be included to make the cross-section finite, which introduces a

theoretical uncertainty, and it is also difficult to make an accurate

e x p e r i m e n t a l measurement when the t r a n s v e r s e momentum i s of the o r d e r of the

t r a n s v e r s e e n e r g y r e s o l u t i o n . F ig . 9 shows an example of a compar i son of

t h e o r y [30] w i t h d a t a from UA1 [31 ] . The d a t a appea r to be s a t i s f a c t o r i l y

d e s c r i b e d by b o t h s e t s of s t r u c t u r e f u n c t i o n s and h ~ v a l u e s b u t i t i s

e v i d e n t l y d i f f i c u l t to e x t r a c t any more q u a n t i t a t i v e i n f o r m a t i o n .

6. QCD AND HEAVY FLAVOUR PRODUCTION IN HADRONICOOLLISIONS

An important class of hard scattering processes in hadronic collisions is

the production of heavy quarks. For quarks with mQ >> ~ the production

process can be analysed perturbatively and the leading order diagrams are

shown in Fig. 10. The study of heavy quark pairs produced in this way is

important not only because it provides a test of QCD but also because the

production mechanism forms the basis for many "new physics" production

processes: qq,gg ~XX with X = sparticle, techniparticle .... It is useful to

compare and contrast the hadronic production of QQ pairs with the production + -

in e e annihilation. The advantage of the former in having higher production

thresholds generally available is partly offset by the problems in identifying

the heavy quark decay products in a hadronic collision environment. For this

reason, heavy quarks produced in hadronic collisions are looked for in their

semi-leptonic decays. As the characteristic features of charm, bottom and top

quark production are rather different, each will be considered in turn.

(i) Q = c

Unfortunately, mQ = m c = 1.5 GeV appears to be too small for low order

perturbation theory to be completely reliable. Other contributions to the

charm cross-section (higher orders in perturbation theory, higher twist

mechanisms, diffractive processes, non-perturbative contributions .... ) are

probably equally important. Although this makes charm production an

interesting and important area of study, it is certainly not a clean test of

the QCD processes in Fig. 10 and so will not be discussed further here. A

more detailed review can be found in the review by Berger [32].


i I i I I

W~ev UA1 I~" = 630GeV

t~ '* -- DO1, A : 0.26eV -- 002,A=0 ~GeV

! i 011t~ ' ~,~ QCO Atfarelli et al.

°°~hq ' f ix

0 5 10 15 20 25 w (5eVlc) P'r

Figure 9

The W transverse momentum distribution at small p; from reference [31], The

data are from the UA1 collaboration [31] and the curves are the theoretical

predictions of Altarelli et al. [30].

g Q

g'- x~ _ q Q Q

Figure 10

Leading order QCD diagrams for heavy quark pair production in hadronic

collisions.


(ii) Q = b

Data on the hadronic production of bottom quarks has recently been

presented by the UAI (pp) [33] and WA78 (TU) [34] collaboration. In the UAI

analysis the b quarks are identified by their semi-leptonic ~ decay mode.

Since the Q-value of the decay is relatively low compared to the b quark

energy, the muons are predominantly produced in jets. Thus the UA1 high PT

non-isolated dimuon event sample is dominated by bb production and decay. The

1On

.4 - -

lOOpb

lOpb

Ipb

40

~=1-STeV

~x ~x

x x x

x x

" ' . , (W--tb)

"}. x

P ~ x

l/~ : 630 GeV

I I I / I

50 60 70 80 90

m t (GeV)

2(tt)

2(th 1

" 1 i

100 110 120 130

Figure II

Theoretical top quark production cross-sections at the CERN (630 GeV) and

Fermilab (1.8 TeV) pp colliders as functions of m t.

event characteristics are well-described by Monte Carlo event simulation

(ISAJET. EUROJET .... ) based on the production processes of Fig. 10. As a

result of this comparison the UA1 collaboration derive a corrected bb

production cross-section:

I o ' (pp ~ b b X ) l ~. = 1 . 1 + 0 . 1 + 0 . 4 p.b .

IP T > s G Vic, I%1 < 2 (6.1)

This measured value can be compared with the theoretical prediction based on


the processes in Fig. I0.

a(p.b) Q2

With m b = 5 CeV/c 2 we find

^ Q2 4~ = S =

2 Q2 = mb

s e t 1

s e t 2

0 .93 1.24 1 .55

1.12 1.47 1.69

(G.2)

f o r the s e t 1 and s e t 2 p a r t o n d i s t r i b u t i o n s of r e f e r e n c e [11] and d i f f e r e n t

c h o i c e s of QCD s c a l e i n the c o u p l i n g c o n s t a n t s and p a r t o n d i s t r i b u t i o n s . A

more p r e c i s e compar i son would r e q u i r e the n e x t - t o - l e a d i n g o r d e r p e r t u r b a t i v e

c o r r e c t i o n s b u t t h e s e a r e no t y e t a v a i l a b l e . There i s some e v i d e n c e f o r

h i g h e r o r d e r p r o c e s s e s from the n o r m a l i s a t i o n of the muon PT d i s t r i b u t i o n a t

l a r g e PT and from the d i s t r i b u t i o n i n the a z i m u t h a l a n g u l a r s e p a r a t i o n of the

muons [33 ] . I n the Monte Car lo a n a l y s i s t he se can o n l y be u n d e r s t o o d by

i n c l u d i n g the h i g h e r o rde r 2 ~ 3 s u b p r o c e s s e s (gg ~ Q ~ , e t c . ) w i t h an

a r b i t r a r y c u t - o f f to r e g u l a r i s e the s o f t and c o l l i n e a r d i v e r g e n c e s . Only when

a comple t e c a l c u l a t i o n i s a v a i l a b l e w i l l the compar i son be tween t h e o r y and

e x p e r i m e n t become more p r e c i s e . F i n a l l y , the WA78 c o l l a b o r a t i o n have measured

the bb c r o s s - s s e c t i o n i n ~U c o l l i s i o n s [34 ] :

a(~U ~ bBX) = 2 . 4 ~ 0 .7 ~ 0 . 8 n b . ( 6 . 3 )

T h i s r e s u l t i s a g a i n c o n s i s t e n t w i t h the l e a d i n g o r d e r QCD p r e d i c t i o n [32] .

For a comple t e d i s c u s s i o n , the rev iew by Berger shou ld be c o n s u l t e d .

( i i i ) q = t

The o n l y p r e c i s e l i m i t on the top quark mass i s m t > 25 GeV from the n o n -

+ - -

o b s e r v a t i o n of e e ~ t t a t c e n t r e - o f - m a s s e n e r g i e s up to 50 CeV [35] .

Additional indirect limits can also be derived from precision Standard Model

measurements. The consistency of measured values of sin2e W values from

different experiments implies m t < 0 (200 CeV) [36], while the observation of

strong B-B mixing suggests m t > 0 (50 GeV) [37] with some model dependent

uncertainty. Contemporary high energy pp colliders can also be competitive in

the search for a top quark with a mass in this range. Top quark production

cross-sections at the CERN (630 GeV) and Fermilab (1.8 TeV) colliders are

shown as functions of m t in Fig. 11. The solid curves correspond to the QCD

production mechanisms of Fig. 10 while the dashed lines are the contributions

W.J. Stirling // QCD at short distances 733

from W decay. Again, the characteristic signature of an isolated lepton with

one or more hadronic jets comes from the semi-leptonic decay.

The UA1 collaboration have recently reported a search for the top quark in

this way [38]. They find that even after selection cuts which would favour a

top signal there is no evidence for an excess of events over the theoretical

expectations from c and b production. This is illustrated in Fig. 12 which

shows the muon transverse momentum distribution together with the Monte Carlo

prediction including all standard (i.e. non-top) contributions. This then

leads to an upper limit on the top production cross-section and a

corresponding lower limit on the mass. Fig. 13 shows the UA1 cross-section

upper limits as a function of m t compared to the theoretical predictions.

Both have been divided by an effective lowest order cross-section to make the

extraction of a limit more precise. The EUROJET cross-section is seen to

contain an effective "K-factor" of order 1.2-1.6 from the higher order

processes. To gauge the theoretical uncertainty the calculations are repeated

using different choices of parton distributions and QCD scales. Clearly a

large scale together with a small h~value will give a smaller cross-section

and a correspondingly lower mass limit. The following table shows the 95%

confidence level lower mass limits which are obtained in this way.

s t ruc t , fns. A(NeV) Q2 95% el lower l imit

2 2 EUROJET: EHLQI 200 mt+ PT 56 GeV

^

DO1 200 s zlzl GeV ^

bIRS 1 107 s 40 GeV

The first two figures (56 GeV, 44 GeV) are the quoted UA1 results [38] for the

upper and lower theoretical cross-sections in Fig. 13. The third (smaller)

figure of 40 GeV comes from the set 1 distributions of reference [11] which

have a smaller A~value. Conservatively, then, the 95% cl lower limit on m t

could be as small as 40 GeV, but a more realistic estimate (with the inclusion

of higher order corrections etc.) would be of order 50 GeV. Finally we note

that the same analysis can be repeated for the hypothesis that the next

heaviest quark has charge -I/3, i.e. Q = b'. There is no change in the QCI)

production cross-section but there is presumably no longer any contribution

from W decay. The lower mass limits are therefore smaller. The quoted UA1

values, analogous to the numbers in the above table, are 41GeV and 25 GeV

respectively [38].


10 2

10 - t

¢ 1 -

>~ 1~ _ '

10 -3

lff~l i 0

i J i i

UAI

pp ~ p + X ~ss = 630 OeV

• Data ~~_~_-- bb ,c~-.W,Z. DY, J/~,'y"

top (tt + tb) ..... mt, D = 2SGeV/ - . - mto~:~ 40 5eV/

, - v ~.., ~ .......... m,op= 50 5eV/

I ~ ' , , , " r . . " - , i 20 ~,0 60 80 I0

p,~ (OeV/c)

F i g u r e 12

The i n c l u s i v e muon t r a n s v e r s e momentum d i s t r i b u t i o n a s m e a s u r e d by t h e UA1

c o l l a b o r a t i o n [ 3 8 ] , t o g e t h e r w i t h Monte C a r l o p r e d i c t i o n s .

v

i i i I

2.0 K-:o/(o0) ([owesI order)

/ ~0NLi25; 7 . . , j .....

~ - r : 5 < ~ = J . . . . . = V//I////////~ "~r~///.///i/l,.¢, V//I.~ V / ' / ~

° ~~, ""'cccJ z N ~ ,o,,.,

20 I 30 40 50 60

PETRA m top(GeV/cZ) LIMIT

F i g u r e 13

The UA1 t o p q u a r k p r o d u c t i o n c r o s s - s e c t i o n 95% c . 1 . u p p e r l i m i t ( h a t c h e d

l i n e ) f rom r e f e r e n c e [ 3 8 3 , t o g e t h e r w i t h v a r i o u s t h e o r e t i c a l p r e d i c t i o n s a~

d e s c r i b e d i n t h e t e x t , a s a f u n c t i o n o f m . t


7. PERTURBATIVE QCD IN e+e - COLLISIONS + --

The total cross-section for e e -~ hadrons is obtained by multiplying the

muon pair cross-section by the factor R = 3 N e 2. The higher order QCD qq

corrections to this quantity have been calculated, and the results can be

e x p r e s s e d i n te rms of a K - f a c t o r :

N 2 ] aS + + R = R (0 ) I + ~ - C 2 . . .

[e 2 - + R (0) = 3 ~ ~ q 2eqVeVq~(l(S ) ~ ~ n n ~ J q

X1 (s) 1 s(s- I~)

16 s i n Owcos O w +

XsCS) 1 4 4

256 s i n ewcos O w

2 S

= ~(3) - nf + ~ - 11 ~'(3) . (7.1)

The c o n t r i b u t i o n from the Z p o l e has a l s o been i n c l u d e d . T h i s r e s u l t i s

s t r i c t l y o n l y c o r r e c t in the z e r o qua rk mass l i m i t . The O(as ) c o r r e c t i o n s a r e

a l s o known f o r m a s s i v e q u a r k s , bu t s i n c e t h e s e a r e d i f f e r e n t f o r t he v e c t o r

and a x i a l c o u p l i n g s o f the Z, t he s i m p l e f a c t o r i s i n g form i s no l o n g e r v a l i d .

At t he h i g h e n e r g i e s c u r r e n t l y a c c e s s i b l e (PETRA-PEP-TRISTAN), t he c o r r e c t i o n s

from QCD and Z exchange a r e comparab le . Such i s the a c c u r a c y of con tempora ry

measurements t h a t the t o t a l c r o s s - s e c t i o n p r o v i d e s one o f the most a c c u r a t e

and r e l i a b l e measurements of a . A compar i son of t he t h e o r e t i c a l p r e d i c t i o n S

of eqn. ( 7 . 1 ) ( c o r r e c t e d f o r the b - q u a r k ) w i t h a l l the a v a i l a b l e d a t a

( i n c l u d i n g t h o s e from TRISTAN a t V~s ~ 50 GeV) has been p e r f o r m e d by the CELLO

c o l l a b o r a t i o n [ 3 9 ] . The r e s u l t i s a c o r r e l a t e d measurement o f a s and sin2Ow:

a s ( 3 4 GeV) = 0.141 i 0 .021

sin20w = 0 .240 ~ 0 .019 . ( 7 . 2 )

F i x i n g s i n 2 e W a t the w o r l d - a v e r a g e v a l u e o f 0 . 2 3 then g i v e s :


a s ( 3 4 GeV ) = 0 .145 ~ 0 .019 . ( 7 . 3 )

The c o r r e s p o n d i n g v a l u e of h ~ i s shown i n F ig . 3. Two comments a r e i n o r d e r .

F i r s t , the p r i n c i p l e a d v a n t a g e of t h i s method of d e t e r m i n i n g a i s t h a t t h e r e s

i s no dependence on f r a g m e n t a t i o n models , j e t a l g o r i t h m s e t c . Second, the

measured v a l u e of R i s s e n s i t i v e to QF_2) r a d i a t i v e c o r r e c t i o n s , n o t a l l of

which have been c a l c u l a t e d . The r e s u l t i n g u n c e r t a i n t y has n o t been i n c l u d e d

i n the above e r r o r s , and i s e s t i m a t e d to be e q u i v a l e n t to a t most a s h i f t i n

the e x t r a c t e d v a l u e of a of abou t 0 .02 [39 ] . S

+ - -

The t r a d i t i o n a l method of d e t e r m i n i n g a i n e e a n n i h i l a t i o n i s from s

m e a s u r i n g q u a n t i t i e s which a r e s e n s i t i v e to the r e l a t i v e r a t e of two and t h r e e

j e t e v e n t s . There a r e many p o s s i b l e c h o i c e s of such "shape v a r i a b l e s " :

t h r u s t , e n e r g y - e n e r g y c o r r e l a t i o n s , t r i p l e p l a n a r c o r r e l a t i o n s , a v e r a g e j e t

mass, e t c . A l l of t h e s e a r e i n f r a - r e d s a f e , which means they can be r e l i a b l y

c a l c u l a t e d i n p e r t u r b a t i o n t h e o r y w i t h o u t h a v i n g to i n t r o d u c e u n p h y s i c a l

i n f r a - r e d c u t - o f f s . The s t a r t i n g p o i n t fo r a l l t h e s e q u a n t i t i e s i s the s imple + -

" t h r e e - j e t " c r o s s - s e c t i o n fo r e e ~ qqg:

2 E . 1

where x . -

2 2 1 d 2 2as Xl + x2

a d.XldX 2 - 3~ (1-Xl)(1-x2) (7.4)

- ~ a r e the centre-of-mass energy fractions of the final state

( m a s s l e s s ) q u a r k s . A d i s t r i b u t i o n i n a " t h r e e j e t " v a r i a b l e , such as those

l i s t e d above , i s o b t a i n e d by i n t e g r a t i n g t h i s d i f f e r e n t i a l c r o s s - s e c t i o n over

an a p p r o p r i a t e phase space r e g i o n fo r a f i x e d v a l u e of the v a r i a b l e .

Of a l l t h e s e measures , the one which has r e c e i v e d the most a t t e n t i o n i s the

e n e r g y - e n e r g y c o r r e l a t i o n f u n c t i o n (EEC) [40 ] . The f a c t t h a t the EEC i s bo th

s i m p l e to measure and s t r a i g h t f o r w a r d to a n a l y s e i n QCD has led to i t s

becoming the parad igm measure of a s , o r , a t the v e r y l e a s t , the benchmark to

which a l l o t h e r such measures must be compared. EEC d a t a has been c o l l e c t e d

and a n a l y s e d by a l m o s t a l l of the PEP, PETRA e x p e r i m e n t a l g roups a t e n e r g i e s

r a n g i n g from 7 to d3 GeV. The t h e o r e t i c a l d e f i n i t i o n s and a comple te l i s t of

t h e o r e t i c a l and e x p e r i m e n t a l r e f e r e n c e s can be found i n r e f e r e n c e [41 ] .

I n p e r t u r b a t i v e QCD, the p e r t u r b a t i o n s e r i e s fo r the EEC s t a r t s a t O(as)

( f o r a n g l e s n o t equa l to 0 ° , 180°) :

I d~ %(v~ ) g l (X) + [ a s ( - ~ ) ] 2 g s ( ~ ) + . . . - (7.5)

G d cos X

WJ. Stirling / QCD at short distances 737

The first two terms of this series have been calculated. The functions gi(~)

are singular at 0 °, 180 °, but away from these regions the series appears to

converge satisfactorily. This theoretical result is correct for final states

consisting of quarks and gluons. In fact it is also valid in the idealised

limit where the quarks and gluons fragment independently and collinearly into

hadrons. In practice, however, jets have a finite width and the above

treatment is too simplistic. A proper treatment requires a Monte Carlo

simulation of the final state fragmentation incorporating parton branching

(including exact matrix elements where known) and a model for hadronisation.

Most of the experimental groups have analysed their data in this way.

Before discussing the results for a obtained from EEC data, two comments s

must be made. First, there are theoretical ambiguities in the way that the

second order matrix elements are combined with parton fragmentation. These

have been a source of some confusion and have accounted for some of the

differences in the results obtained from different analyses. Fortunately,

there appears now to be some consensus and the different approaches have

converged. A more serious source of uncertainty concerns the effect of using

different hadronisation models. The leading non-perturhative contribution is

sym~netric about 90 ° and therefore drops out in the EECA. In "independent

fragmentation" models, the fragmentation corrections to the EECA turn out to

be very small, and in fact the purely perturhative result can be compared

directly to the data. In "string fragmentation" models, where the

distribution of final state hadrons is not symmetric about the jet axis in a

three jet event, the EECA has a non-negligible negative fragmentation

correction. This explains why a values obtained using string fragmentation s

Monte Carlos are in general higher than those obtained using independent

fragmentation. Fortunately, again, the situation has improved significantly

in recent years, as fragmentation Monte Carlos have been improved and refined,

and the factors of two difference in a values have gone away. Small s

differences do, however, persist and it would be fair to describe this still

as a topic of some controversy. Some experimental groups continue to quote

s e p a r a t e a v a l u e s a c c o r d i n g to the f r a g m e n t a t i o n model used . w h i l e o t h e r s s

combine the u n c e r t a i n t y w i t h o t h e r s y s t e m a t i c e r r o r s . The p r e s e n t s i t u a t i o n

i s su~anarised i n F i g . 14 where r e c e n t EECA-based a l p h a measurements from the

e x p e r i m e n t a l g r o u p s a r e d i s p l a y e d . A c o m p i l a t i o n o f a l l t he a v a i l a b l e d a t a

and a c o m p l e t e l i s t o f r e f e r e n c e s can be found i n [ 4 1 ] . A r e a s o n a b l e "wor ld

738 l~.J. Stifling / QCD at short distances

1987 a s

0"10

meosuremenfs from

I

: = :

I 0.15

EECA

I

: : CELLO (SF)

TA SSO (SF)

TASSO (IF)

MARK II (SF)

MARK-J

I 0.20

a s (346eV)

F i g u r e 14

Recent (1987) e x p e r i m e n t a l measurements of A ~ u s i n g the e n e r g y - e n e r g y

c o r r e l a t i o n asymmetry, from the r ev iew by Wu [35 ] .

average" would appear to be

a s ( 3 4 G eV ) = 0 .14 ~ 0 . 0 2 ( 7 . 6 )

w i t h the e r r o r combin ing the spread be tween the d i f f e r e n t e x p e r i m e n t s w i t h the

f r a g m e n t a t i o n u n c e r t a i n t y . No t i ce t h a t t h i s i s i n s t r i k i n g ag reemen t w i t h the

v a l u e o b t a i n e d from the measurement o£ R d e s c r i b e d above . S i n c e t he se r e s u l t s

a r e e s s e n t i a l l y c o m p l e t e l y i n d e p e n d e n t , the a s s o c i a t e d A ~ v a l u e s a r e

d i s p l a y e d s e p a r a t e l y i n F ig . 3.

F i n a l l y , m e n t i o n shou ld be made of a r e c e n t s t u d y by the JADE C o l l a b o r a t i o n

[42] which a d d r e s s e s the q u e s t i o n : does a run? The i d e a i s to d e f i n e s

t o p o l o g i c a l n - j e t c r o s s - s e c t i o n s u s i n g d i m e n s i o n l e s s i n f r a - r e d s a f e j e t

c r i t e r i a . In QCD, a s imp le c h o i c e i s to use p a r t o n c l u s t e r s i , j w i th M2. > 1j

Ymin s, w i t h Ymin a f i x e d d i m e n s i o n l e s s p a r a m e t e r . Then

anj = An(Ymin)a + ...

Oto t = ~ o . (7.7) n 2 nJ


and all the ~s dependence comes from as(~S ). The JADE Collaboration have

measured the quantity R 3 = o3j/ato t as a function of v~s for Ymin = 0.08. Over

the e n e r g y r ange 22 GeV < v~s < 44 GeV the d a t a show a c l e a r , s t a t i s t i c a l l y

s i g n i f i c a n t d e c r e a s e as v~s i n c r e a s e s , c o n f i r m i n g t h a t a does i n d e e d run in S

the e x p e c t e d way.

8. CONCLUSIONS

In t h i s s h o r t r e v i e w I have f o c u s s e d on t h o s e h i g h e n e r g y p r o c e s s e s which

c u r r e n t l y o f f e r the most q u a n t i t a t i v e t e s t s of s h o r t - d i s t a n c e QCD. The

p r e c i s i o n measurements of h ~ c o m e from t h o s e p r o c e s s e s which i n v o l v e r e a l or

v i r t u a l pho tons and f o r which the n e x t - t o - l e a d i n g c o r r e c t i o n s a r e known. F i g .

3 shows a c o m p i l a t i o n o f r e c e n t measurements of A ~ f r o m the p r o c e s s e s

d e s c r i b e d in t h i s r e v i e w . Also shown a r e r e c e n t measurements from T decay and

from l a r g e PT d i r e c t p h o t o n p r o d u c t i o n which have been t aken from the r e v i e w s

( a t t h i s C o n f e r e n c e ) by L e e - F r a n z i n i and R i c h a r d r e s p e c t i v e l y . A v a l u e of A~-

from a pho ton s t r u c t u r e f u n c t i o n a n a l y s i s d e s c r i b e d i n r e f e r e n c e [43] has a l s o

been i n c l u d e d . From F i g . 3 we see t h a t a l l t he measurements a r e c o n s i s t e n t

and p o i n t to a v a l u e o f A~-~ f o r n f = 5 of o r d e r 200 i 100 MeV. Note t h a t i t

i s n o t s t r i c t l y c o r r e c t to compare A ~ v a l u e s which m a n i f e s t l y c o r r e s p o n d to

d i f f e r e n t e f f e c t i v e numbers of qua rk f l a v o u r s . However the e x p e c t e d sma l l

d i f f e r e n c e s be tween the v a r i o u s A ~ c a n n o t be o b s e r v e d w i t h t he p r e s e n t l e v e l

o f e x p e r i m e n t a l a c c u r a c y [ 6 ] . J e t p r o d u c t i o n d a t a from h i g h e n e r g y

h a d r o n - h a d r o n c o l l i s i o n s , w h i l e no t y e t in t he p r e c i s i o n measurement c l a s s ,

d e m o n s t r a t e i n a v e r y c l e a r way the s c a t t e r i n g of qua rks and g l u o n s o v e r many

o r d e r s of magn i tude i n c r o s s - s e c t i o n .

The need f o r b r e v i t y has meant t h a t many o t h e r i m p o r t a n t t o p i c s i n QCD

phenomenology have had to be o m i t t e d . One s h o u l d m e n t i o n i n p a r t i c u l a r the

i n t e r f a c e o f s o f t and h a r d QCD, as m a n i f e s t f o r example by m i n i j e t p r o d u c t i o n

and ha rd d i f f r a c t i v e p r o c e s s e s .

For the f u t u r e , we have e s t a b l i s h e d a v e r y s o l i d f o o t i n g f o r s h o r t d i s t a n c e

QCD in h i g h e n e r g y p r o c e s s e s which e n a b l e s us to make r a t h e r p r e c i s e

p r e d i c t i o n s f o r the n e x t g e n e r a t i o n o f a c c e l e r a t o r s . For example , ba sed on

the above " w o r l d a v e r a g e " v a l u e o f A~-~we can p r e d i c t t h a t as(~Lz) as measured

a t SLC and LEP w i l l be i n the r ange 0 . 1 0 5 - 0 . 1 2 5 . P r e c i s e p r e d i c t i o n s can now

a l s o be made f o r j e t and weak boson t r a n s v e r s e momentum d i s t r i b u t i o n s , and

weak boson and heavy f l a v o u r t o t a l c r o s s - s e c t i o n s a t v e r y h i g h e n e r g y h a d r o n -


hadron colliders. It is this precision which will underpin many of the

searches for "new physics" in the future.

A O O ~ I O W L E ~

It is a pleasure to acknowledge the magnificent help and support given to

me by the organisers of this conference. I am grateful also to Professor

Maurice Jacob and the CERN Theory Division for their kind hospitality when

this talk was being prepared.

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20) UA1 C o l l a b o r a t i o n : E. Locci , In t . Europhysics Conference on High Energy Phys ics , Uppsala 1987. UA2 C o l l a b o r a t i o n : R. Ansari e t a l . , Phys. Le t t . 1948 (1987) 158.

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35) Sau Lan Wu, these Proceedings.

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37) See fo r example: G. A l t a r e l l i and P. F ranz in i , CZRN p r e p r i n t CEN-TH-4745/87 (1987). J. E l l i s , J .S . Hagelin and S. Rudaz, Phys. Let . 192B (1987) 201. V. Barger e t a l . , Phys. Le t t . 1948 (1987) 440.

38) UA1 C o l l a b o r a t i o n : C. Albajar e t a t . , CERN p r e p r i n t CERN-EP/87-190 (1987).

39) C'~I.IO C o l l a b o r a t i o n : H.J. Behrend e t a l . , Phys. Le t t . 183B (1987) 400, W. de Boer, SLAC p r e p r i n t SLAC-PUB-4428 (1987). Sau Lan Wu, these Proceedings.

40) C.L. Basham, L.S. Brown, S.D. E l l i s and S.T. Love, Phys. Rev. DI7 (1976) 2298.

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42) JADE C o l l a b o r a t i o n : W. Bar te l e t a l . , paper submit ted to t h i s Conference.

43) H. Kalinowski and P. Zerwas in "High Energy E l e c t r o n - P o s i t r o n Phys ics" ,

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DISCUSSION

Von S c h l i p p e (QMC, London): I wish to comment on the h i g h e r - o r d e r

c o r r e c t i o n c a l c u l a t i o n s t h a t you have m en t ioned : the i n c l u s i o n o f ha rd 2 ~ 3

p a r t o n s c a t t e r i n g i n t r o d u c e s the p rob lem of d o u b l e - c o u n t i n g i n t o the

p h e n o m e n o l o g i c a l a n a l y s i s o f pp c o l l i s i o n s a t h i g h t r a n s v e r s e e n e r g i e s . For

i n s t a n c e , UA1 have r e c e n t l y shown t h a t a t ~ T > 200 GeV the a v e r a g e number of

E~ e t > 10 GeV) i s abou t 3 . 6 pe r e v e n t . Double p a r t o n s c a t t e r i n g j e t s ( w i t h

does n o t s i g n i f i c a n t l y c o n t r i b u t e a t t h e s e h i g h e r t r a n s v e r s e e n e r g i e s .

T h e r e f o r e one needs QCD r a d i a t i v e c o r r e c t i o n s to e x p l a i n the d a t a and t h i s

c a n n o t so f a r be t r e a t e d c o n s i s t e n t l y t o g e t h e r w i t h h i g h e r - o r d e r p r o c e s s e s .

Answer: I a g r e e t h a t t h e r e a r e s e v e r e p rob lems in t r y i n g to a n a l y s e h i g h e r

o r d e r QCD c o r r e c t i o n s f o r m u l t i j e t c r o s s - s e c t i o n s such a s t h o s e you have

d e s c r i b e d . I b e l i e v e t h a t our p r e s e n t t h e o r e t i c a l " t e c h n o l o g y " i s no t

a d e q u a t e f o r t h i s type of p rob lem. The b e s t t o o l s f o r t h i s t h a t we have a t

t he moment a r e p r o b a b l y the QCD i n s p i r e d j e t Monte C a r l o s such as ISAJET.

Zaitsev (ITEP, Moscow): For the determination of a s from the width of the T

you used only the contributed papers. If you were to use the world average

value you would get a much smaller error. You did not use another source of

determination of a from T ~ ~gg decay. These data are available. S

Answer: I must admi t t h a t I am a l i t t l e n e r v o u s of such v e r y sma l l e r r o r s

s i n c e I b e l i e v e t h a t t h e r e a r e s y s t e m a t i c t h e o r e t i c a l u n c e r t a i n t i e s , i n the

QCD models which a r e used , which a r e p r o b a b l y much l a r g e r than the

e x p e r i m e n t a l e r r o r s . However I a g r e e t h a t I d i d n o t do the s u b j e c t c o m p l e t e

j u s t i c e . I would r e f e r you to the e x c e l l e n t r e v i e w p r e s e n t e d a t t h i s

c o n f e r e n c e by P r o f e s s o r L e e - F r a n z i n i .

short distance qcd

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