PRODUCTION OF HEAVY QUARKS

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PRODUCTION OF HEAVY QUARKS

F. Halzen

To cite this version:

F. Halzen. PRODUCTION OF HEAVY QUARKS. Journal de Physique Colloques, 1982, 43 (C3),

pp.C3-381-C3-405. �10.1051/jphyscol:1982369�. �jpa-00221924�

JOURNAL DE PHYSIQUE

Colloque CS, supplément au n° 12, Tome 43, dêoerribve 1982 page C3-381

PRODUCTION OF HEAVY QUARKS

F. Halzeti

Department of Physios, University of Wisconsin, Madison, Wisconsin 53706, U.S.A.

Résumé. 1. Vue d'ensemble du sujet. 2. Annihilation e e et production par neutrinos. 3. Production par photons et leptons. 4. Production par hadrons. 5. Problèmes pour le modèle standard. 6. Conclusions.

Abstract. - 1. Introduction: a perspective on the subject. 2. e e annihilation and leptoproduction by neutrinos. 3- Photo- and leptoproduction. 4. Hadroproduc- tion. 5- Problems for the standard model. 6. Conclusions.

1. Introduction: A Perspective on the Subject. - My goal is to construct a

"house of cards" that pulls together the wealth of experimental information on the production of heavy quarks under the umbrella of perturbative Q.CD and the standard electroweak model. 1 will almost succeed; failures are potentially very important and will be discussed at the end of the talk. If the structure collapses by the next conference, I will be only mildly disappointed; this is how progress is made.

a) Theoretical £e_rspect_i_ye_1 In the days preceding the advent of QCD the statistical model provided us with a framework to compute particle yields. The probability for producing a particle of mass m is given by

P * e '2 m / T , (1)

where T is a universal temperature of about 160 MeV. We obtain

TT : K : D * 1 : Iff1 : icf5 . (2)

Alternatively, one can consider the hadronic production of heavy quarks as a tunneling problem, i.e., the probability that a string breaks up into a pair of heavy quarks of mass m_. Here

2 -am_

P ^ e (3) 2 2 ^

where m = (m. + pT) and a = TT/K. K is the string constant. The result is

(u,d) : s : c = 1 : 1 : lo"i0 . (4)

The small estimates for charm production in the "old" physics result from the difficulty in localizing the large energy required to produce a heavy quark pair.

This leads to a dynamic exponential suppression of the cross section when in- creasing the quark mass. Such a suppression is absent in QCD due to the flavor-

independent point coupling of quarks to gluons. Much higher rates for charm production, compared to those obtained in Eqs. (2) and (3), are expected. The production of heavy quarks provides us with one of these rare opportunities where the "old" and "new" physics differ qualitatively. The experimental verdict is clear. At the highest energies charm is produced at the 10 ^ 10"-' level of

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982369

F i g . 1 : To$al i n c l u s i v e c r o s s sec- t i o n s f o r T-,K and charm p a r t i c l e s i n pp c o l l i s i o n s . My b e s t e s t i - mates f o r t h e t o t a l charm c r o s s s e c t i o n s depend on t h e assumptions made f o r the A~ dependence i n ex- periments u s i n g n u c l e a r t a r g e t s (A ^2/3 f o r t r i a n g l e s

,

AI f o r squares).

lo2

CI

n E

V

*

C ^f

6-

16.-

Events / Day

,+_s

pions ++Y,-

- ^{+/*2:-- -}

5,

(/ klcn-ls

./f -

- _{/ . G o}

/*

charm

- / *

- ₊ ,++4 _-

/(+

^{I I I}

^-

F i g . 2: S i g n a l / n o i s e and events per day f o r charm p r o d u c t i o n i n v a r i o u s i n t e r a c t i o n s denoted by a c i r c l e . Hadronic i n t e r a c t i o n s have been d i v i d e d i n t o ISR and lower energy SPS/FNAL experiments

T-mesons (see F i g . 1 ) . QCD i s a t present t h e o n l y framework t h a t can accommodate these o b s e r v a t i o n s . The discrepancy between t h e e x p e c t a t i o n s f o r b-quark p r o d u c t i o n based on QCD and estimates based on Eqs.

0)

and (3) i s even more dramatic. I n t h e llord'l p h y s i c s b-quarks a r e p r a c t i c a l l y unobserwable i n hadronic i n t e r a c t i o n s , c o n t r a r y t o t h e evidence which w i l l be presented f u r t h e r on.

b) llTechnological" p e r s p e c t i v e The

potent 7--- r---J

technolocr I c a p p a y - o f f fmom a d e t a i l e d understanding o f t h k product i o n mechanisms and s i g n a t u r e s o f heavy quarks i s what makes t h e c o n s i d e r a b l e e f f a r t s on t h i s problem d e f i n i t e l y worthwhile. I n e+e- c o l - 1 i s ions

9

nb ( f o r ece- ^i13.n;05 i s a c arm ^{% 10 nb}

B

f a c t o r y . What about t h e

a c c e s s i b l e i n hadron c o l l i s i o n s ? The p o s s i - b i l i t y o f e x p l o i t i n g these l a r g e r a t e s w i l l r e q u i r e a v e r y d e t a i l e d understanding o f p r o d u c t i o n mechanisms and s i g n a t u r e s . Pro- gress i s e s s e n t i a l i n o r d e r t o design t r i g g e r s t h a t can overcome t h e u n f a v o r a b l e s i g n a l / n o i s e i n t h e c o l l i s i o n s w i t h t h e h i g h e s t r a t e s (see Fig. 2 ) .

The q u e s t i o n o f heavy quark p r o d u c t i o n touches some o f t h e "great" p h y s i c s issues p r e s e n t l y a w a i t i n g d e f i n i t e answers: ( i ) Are w e a t t h e t h r e s h o l d o f a p r o l i f e r a t i o n o f fiew quark f a m i l i e s o r i s our w o r l d indeed

'dmited t o t h r e e f a m i l i e s w i t h o r w i t h o u t t h e t o p quark? T h i s q u e s t i o n c o n s t i t u t e s an experimental a t t a c k on t h e issue o f whether quarks a r e composite o r t r u l y fundamental.

Progress i n our understanding o f charm and beauty p r o d u c t i o n i s e s s e n t i a l i n o r d e r t o p e r f o r m "generat ion-counting" w i t h pp-col1 i d - e r s , a m i s s i o n which has been f o r e c a s t n o t t o be an easy one.3 ( i i ) Heavy quarks c o u l d be used as s i g n a t u r e s i n t h e search f o r weak bosons. T h e i r l e p t o n i c decays are, however, t h e dominant background4 i n searching f o r t h e l e p t o n i c s i g n a t u r e s Z ^-+

~ 3 ,

W ^-+ Rv. ( i i ) The search f o r n e u t r a l s c a l a r s which appear

i n electroweak gauge t h e o r i e s e i t h e r as Higgs bosons o r as dynamical bound s t a t e s r e - mains a h i g h p r i o r i t y task.5 U n t i l o p e r a t i o n o f a new g e n e r a t i o n o f e+e- c o l l i d e r s o n l y hadron beams have a r e a l i s t i c s h o t a t t h e i r d i s c o v e r y . We w i l l i l l u s t r a t e how t h e s t u d y o f charm p r o d u c t i o n has generated novel and v e r y p r o m i s i n g techniques f o r Higgs h u n t i n g .

C) Exper i m e n t a l - e $ w ~ p $ ~ t i y $ . The advent o f S i o r Ge l i v e t a r g e t s and C C D de- v i c e s opens up t h e p o s s i b i l i t y o f c o n s t r u c t -

i n g v e r t e x d e t e c t o r s f o r f i x e d t a r g e t as w e l l as c o l l i d e r experiments. A S i - t a r g e t , p r e s e n t l y o p e r a t i n g a t t h e SPS, has achieved t r a c k r e s o l u t i o n o f o r d e r

l o 2

microns and has become a s u c c e s s f u l t o o l i n d e t e c t i n g t h e a s o c i a t e d p r o d u c t i o n o f charm p a r t i - cles.' A1 though v i s u a l d e t e c t o r s ( f a n c y

F. H a l z e n C3-383

b u b b l e chambers, streamer chambers) can p o s s i b l y compete i n r e s o l u t i o n t h r o u g h t h e use o f h o l o g r a p h y , t h e i r o b s e r v a t i o n r a t e i s l i m i t e d t o 10 % 50 msec by f i l m ad- v a n c i n g . The S i - t a r g e t , p r e v i o u s l y mentioned, has on t h e c o n t r a r y a deadtime o f l e s s t h a n

l o 2

nsec, a1 l o w i n g beam i n t e n s i t i e s exceeding t h o s e f o r v i s u a l d e t e c t o r s by a t l e a s t two o r d e r s o f magnitude. P r o g r e s s on v e r t e x d e t e c t o r s c o u p l e d w i t h i n c r e a s e d t h e o r e t i c a l i n s i g h t i n t h e d e s i g n o f t r i g g e r s w i l l h o p e f u l l y l e a d i n t h e n e a r f u t u r e t o h i g h s t a t i s t i c s heavy q u a r k p h y s i c s w i t h photon and hadron beams and t o m e a n i n g f u l searches f o r new g e n e r a t i o n s .

+ -

2. e e A n n i h i l a t i o n and L e p t o p r o d u c t i o n by N e u t r i n o s .

-

The p r o d u c t i o n o f heavy q u a r k s i n t h e s e r e a c t i o n s i s so w e l l understood t h a t t h e y a r e used as " f l a q s " t o s'tudy o t h e r p h y s - c s issues.7 T h i s i s i l l u s t r a ed by a r k c e n t a n a l y s i s o f ;he CDHS group o f o v e r I 0 opposi r e - s i g n dimuon events.'

4

The p r o d u c t i o n o f heavy q u a r k s by n e u t r i n o s proceeds v i a t h e diagram shown i n F i g . 3. The dominant c o n t r i b u t i o n s a r e summarized i n T a b l e 1. For n e u t r i n o beams r o u g h l y h a l f o f t h e charm

L e p t o n v e r t e x Quark v e r t e x Coup1 i ng

v, F

v ⁺ p - v a l e n c e d -t c 2

s i n Bc

sea S + C 2

c o s

e

-

^-

v ^-+

v+

sea s ⁺ c 2

q

cos

ec

F i g . 3: P r o d u c t i o n o f heavy T a b l e 1: Dominant c o n t r i b u t i o n s t o charm produc- q u a r k s by n e u t r i n o s . t i o n by n e u t r i n o s and a n t i n e u t r i n o s .

F i g . 4: B j o r k e n x - d i s t r i b u t i o n o f o p p o s i t e s i g n dimuon e v e n t s . The shapes r e f l e c t t h e i r charm o r i g i n , as summarized i n T a b l e 1.

p a r t i c l e s o r i g i n a t e f r o m t h e ( ~ a b i b b o - suppressed) t r a n s f o r m a t i o n o f a v a l e n c e d-quark i n t o a c - q u a r k by t h e weak i n t e r - a c t i o n . The o t h e r h a l f i s due t o t h e ( ~ a b i b b o - a 1 lowed) t r a n s i t i o n o f a sea S-

q u a r k t o a charm quark. For a n t i n e u t r i n o beams t h e c h a r g e c o n j u g a t e o f t h e l a t t e r t r a n s i t i o n i s t h e dominant s o u r c e o f charm. Charm p a r t i c l e s a r e d e t e c t e d v i a t h e i r l e p t o n i c decay w h i c h c o n t r i b u t e s a p o p p o s i t e i n s i g n t o t h e p r i m a r y

u.

The d a t a a r e shown i n F i g .

4;

t h e shape o f t h e B j o r k e n - x d i s t r i b u t i o n c l e a r l y r e - f l e c t s t h e p r o d u c t i o n o f charm o f f sea- q u a r k s i n t h e 7 case and t h e presence o f an a d d i t i o n a l v a l e n c e d -t c mechanism f o r v-induced p r o d u c t i o n . From t h e s e d a t a t h e s t r a n g e component o f t h e n u c l e o n can be deduced, t h e KM m a t r i x elements Ucd, Uc, can be determined and t h e shape o f t h e charm f r a g m e n t a t i o n f u n c t i o n has been o b t a i n e d . 8 ^{I t} has a "hard" d , i s t r i b u t i o n p e a k i n g a t <z> = 0.68

+

0.08 i n agreement w i t h t h e e x p e c t a t i o n o f B j o r k e n and

~ u z u k i

.9

The p h y s i c s p o t e n t i a l o f charm t r i g g e r s c o u l d be f u r t h e r enhanced h y t h e s t u d y o f b-quark p r o d u c t i o n , e.g., c -t b o f f charm

ic

t h e nucleon. V i a t h e cas- cade decay b -t c + p same-sign dimuon e v e n t s r e s u l t f r o m w h i c h t h e KM element

Ucb (Uu i n 7 - i n t e r a c t i n g ) can be determined.'' U n f o r t u n a t e 1 y, same-sign dimuons should be approached w i t h care. We r e t u r n t o t h i s issue a t the end o f t h e t a l k .

1 1

3. Photo- and L e p t o p r o d u c t i o n

. -

A t y p i c a l diagram f o r t h e p r o d u c t i o n o f a heavy quark p a i r by p2oton o r l e p t o n ( i . e . v i r t u a l photon) beams i s shown a t t h e t o p o f T a b l e 2. The cc p a i r i s detected as a DD,

A,D ...

p a i r o r as a $ bound s t a t e . i t

i s v e r y important i n d i s c u s s i n g t h i s . . problem t o separate events whe;e t h e [REAL AND VIRTUAL PHOTOPRODUCTION] $ o r charm p a i r c a r r y t h e incoming

Or

y2

p h o t o n ' s energy ( e l a s t i c events,

z

-

1) from events where t h e y c a r r y

1

^{9 or DD,}

^{AP ....}

o n l y a f r a c t i o n o f t h e beam energy ( i n e l a s t i c events, z < 1). The v a r i a b l e z measures t h e f r a c t i o n o f

N-'*

'-- E

t h e y,y* energy c a r r i e d by t h e p r o -

duced c F p a i r . E l a s t i c events a r e ELASTIC

cF corries Y- energy ( z = I )

yp-cF

...

(elastic)

'7

INELASTIC b e a u t i f u l l y described by t h e l e a d i n g o r d e r diagram y g -+ cc. As p i c t u r e d ( z < 1 ) on t h e l e f t i n Table 2, t h i s i s t h e

and energy dependence o f e l a t i c charm p r o d u c t i o n by p h o t o n s l S as i l l u s t r a t e d i n Fig. 5. I t i s imper-

Yp- cF

...

(elastic)

2- z

l b

0

10 102 103

dynamic color B e t h e - H e i t l e r process o f QCD. l2

(0s in lifetime colt.) Given t h e gluon s t r u c t u r e f u n c t i o n ,

t i t c o r r e c t l y d e s c r i b e s t h e magnitude

Bethe- Heitler of OCD

Works ! (m,' 1.5)

Fig. 5: E l a s t i c cF p r o d u c t i o n by photon Fig. 6: Same as F i g . 5. The choices o r l e p t o n beams

(a2

⁼ 0 ) . A1 so shown i s mc = 1.2 and 1.5 GeV i n t h e photon- t h e r e s u l t o f a c a l c u l a t i o n based on t h e gluon f u s i o n c a l c u l a t i o n a r e l e a d i n g o r d e r diagram Yg ⁺ cc. c o n t r a s t e d .

a t i v e t o use mc = 1.5 GeV as shown

exoct color i n F i g . 6. The same c a l c u l a t i o n

s u c c e s s f u l l y accommodates data on e l a s t i c $ I s p r o v i d e d one i n t r o d u c e s a phenomenological parameter f = l o - ' d e s c r i b i n g t h e frequency t h a t c F p a i r s m a t e r i a l i z e i n t o $ I s .

order ah higher I n i n e l a s t i c events t h e c F p a i r large p, c a r r i e s a f r a c t i o n o f t h e beam

energy. The r e s i d u a l energy i s c a r r i e d by a gluon, as i l l u s t r a t e d on t h e r i g h t - h a n d s i d e o f Table 2.

Table 2: "Road map" t o t h e s t r u c t u r e o f I n e l a s t i c p r o d u c t i o n i s t h e r e f o r e a charm p h o t o p r o d u c t i o n i n t h e c o n t e x t o f h i g h e r o r d e r process i n v o l v i n g

p e r t u r b a t i v e QCD. ~(clcl?) diagrams o f t h e t y p e yg+(cF)g.

F. H a l z e n C3-385

I n t h e case o f J, p h o t o p r o d u c t i o n one can a g a i n i n v o k e some d u a l i t y f a c t o r f 1 con- v e r t i n g c F ' s i n t o $ I s . One hereby e x p l i c i t l y d e n i e s t h a t c o l o r p l a y s a fundamental r o l e i n t h e p r o d u c t i o n mechanism, a t r e a t m e n t o f t h e c o l o r quantum number o f t e n encountered i n l i f e t i m c a l c u l a t i o n s . A l t e r n a t i v e l y , one can t r e a t c o l o r as a n e x a c t quantum number,'' i .e. o n l y diagrams where t h e c c p a i r i s i n a c o l o r s i n g l e t w i t h t h e J, quantum numbers a r e i n c l u d e d . T h i s l e a v e s one d i a g r a m f o r t h e i n e l a s t i c

p r o d u c t i o n o f $, shown i n F i g . 7. Whatever t h e d e t a i l s , b o t h approaches a g r e e t h a t t h e i n e l a s t i c c r o s s s e c t i o n i s O(as) o f t h e e l a s t i c . I t i s t h e r e f o r e e x p e c t e d t o b e r o u g h l y 0.2 o f t h e e l a s t i c . T h i s r e s u l t i s r e a d i l y o b t a i n e d f r o m t h e "bleach-

i n g " d i a g r a m i n F i g . 7 w h i c h i s r e l a t e d by c r o s s i n g t o t h e decays $ + ggy o r J, + ggg. T h i s r e s u l t i s , however, a t v a r i a n c e w i t h t h e data. E l a s t i c and i n e l a s - t i c y i e l d s o f open o r bound charm a r e r o u g h l y e q u a l , as i l l u s t r a t e d i n T a b l e 3.

C o r r e c t i n g t h i s d i s a s t e r by changing t h e mass o f t h e charm q u a r k would r u i n t h e agreement o f t h e l e a d i n g o r d e r diagram w i t h t h e e l a s t i c d a t a ( F i g . 6 ) .

E l a s t i c I n e l a s t i c

y " ~ ⁺ J, (209 GeV u-beam)

0.36

+

0.08 nb 0.28

+

^{0.08 nb}

.56f 6 :: i l b > 1 ~ b

F i g . 7: "Bleaching" d i a g r a m channels

f o r t h e i n e l a s t i c photo- p r o d u c t i o n o f $ I s .

T a b l e 3: Comparison o f e l a s t i c and i n e l a s t i c c r o s s s e c t i o n s f o r bound and open charm.

E x p e r i e n c e has t a u g h t us, however, t h a t n o r m a l i z a t i o n s a r e r a t h e r f l e x i b l e when e v a l u a t i n g QCD diagrams e x p l i c i t l y . Another f e a t u r e o f i n e l a s t i c charm p r o - d u c t i o n i s t h a t once a g l u o n has been e m i t t e d t o s h a r e t h e beam energy w i t h t h e

( c c ) p a i r , t h e l a t t e r can r e c o i l a g a i n s t t h e g l u o n and o r i g i n a t e w i t h l a r g e p ~ . I n F i g . 7 t h e J, r e c o i l s a g a i n s t t h e accompanying g l u o n : i n c r e a s e i n i n e l a s t i c i t y t h e r e f o r e i n e v i t a b l y r e s u l t s i n an i n c r e a s i n g p o p u l a t i o n o f t h e h i g h p ~ r e g i o n w i t h $ I s . H i g h s t a t i s t i c s BFP data15 f a i l t o show t h i s e f f e c t by d i r e c t l y compar- i n g t h e shapes o f the p T - d i s t r i b u t i o n i n b i n s 0.7 < z < 0.9 and z < 0.7 (Fig. 8 ) .

F i g . 8a: Comparison o f t h e p T - d i s t r i b u t i o n s f o r t h e p r o d u c t i o n o f e l a s t i c and

i n e l a s t i c a ' s .

A l t h o u g h e a r l i e r EMC d a t a showed h i n t s i n t h e r i g h t d i r e c t i o n ( F i g . 8 ) , t h e same c o l l a b o r a t i o n shown in s u b m i t t e d t o t h i s conference a b e a u t i f u l s e t o f every z-bln d a t a w i t h i n c r e a s e d s t a t i s t i c s 1 6 a l l o w i n g a more

d e t a i l e d a n a l y s i s o f t h i s p r blem. We can indeed compare t h e l a r g e - p T t a i l (pf = 1 ⁵ 10 G ~ Y ~ ) f o r 6 d i f f e r e n t b i n s i n z. E l a s t i c $ I s a r e d e s c r i b e d by a f i t PT-3'87, w h i c h I s i m p l y superimposed i n F i g . 8b on t h e f i v e i n e l a s t i c b i n s . No e v i d e n c e

to-2

t64

- '*\ '\

f o r i n c r e a s e d pT o f t h e $ I s w i t h i n c r e a s e d i n -

+, ,

b 0 . 9 - 0 . 9 5 e l a s t i c i t y ( s m a l l e r z - v a l u e s ) can be found. I

-

^\

_\

xto-' a t t e m p t e d v a r i o u s ap roaches t o a n a l y z e t h e d a t a : e.g., c a l c u l a t i n g <pT> f o r p+

5'

> 1 o r f i t t i n

-"

- '

^t\0.B-0.9 i n e v e r y b i n . N o t ~ c e , e.g.. how w e l l t h e pT

9. %-

x

lo-'

pendence f o r 0.4 < z < 0.6 i s d e s c r i b e d by t h e

- kt\+\

^0.7-0.8 EMC f i t t o t h e pT d i s t r i b u t i o n f o r e l a s t i c $ I s . Two c o n c l u s i o n s a r e p o s s i b l e : ~(aa;) o n l y des-

\

)\t

X I O - ~ c r i b e s i n e l a s t i c $ p r o d u c t i o n a t l a r g e pT. I n

-

+\ \0.6-0.7 t h i s k i n e m a t i c r e g i o n t h e b l e a c h i n g diagram o f

+\

^{x F i g . 7} c o r r e c t l y p r e d i c t s t h e n o r m a l i z a t i o n ( w h i c h i s h e r e i n s e n s i t i v e t o t h e e x a c t v a l u e o f I I

mc), b u t t h e b a s i c l a r g e pT c h a r a c t e r o f t h e d i a - gram a w a i t s c o n f i r m a t i o n . T h i s c o n c l u s i o n s t i l l 1 2 5 10 l e a v e s 80% o f t h e i n e l a s t i c d a t a u n e x p l a i n e d .

p: ( G ~ v * ) A l t e r n a t i v e l y , one m i g h t c o n c l u d e t h a t t h e l a r g e y i e l d o f i n e l a s t i c $ I s p o i n t a t t h e e x i s t e n c e o f n o n - p e r t u r b a t i v e sources o f charm q u a r k s . F!g. 8b: The l a r g e p produc- H i n t s t h a t abundant s o u r c e s o f charm quarks t r o n o f ^{$ J ' S} i s n o t a f r e c t e d by e x i s t i n t h e v e r y s m a l l z r e g i o n ( p r e s e n t l y i n - i t s i n e l a s t i c i t y . a c c e s s i b l e by muon d e t e c t o r s as EMC and BFP) can

be found by comparing charm c r o s s s e c t i o n s i n e x p e r iments w i t h v a r y i n g acceptance. The WA4 experiment ,'7 u s i n g a tagged y beam and t h e Omega s p e c t r o m e t e r , has a v e r y broad x acceptance and i s v e r y u n l i k e l y t o m i s s any source o f charm due t o t h e l a c k o f coverage. I t s measured photoproduc- t i o n c r o s s s e c t i o n (now c o n f i r m e d by ~ ~ 5 7 ' ~ ) exceeds t h o s e measured by muon de t o r s w h i c h a r e o n l y s e n s i t i v e t o e l a s t i c charm ( F i g . 9 ) . The WA58 e x p e r i m e n t ,

FBc-

d e t e c t i n g charm p a r t i c l e p a i r s i n an ~ m u l s i o n exposed t o t h e same beam, observes AcD e v e n t s YN-charm (el.+ inel.) w i t h XF < 0. Again, t h e s e t y p e s o f e v e n t s 2 a r e n o t d e t e c t e d by e x p e r i m e n t s l i k e EMC o r

BFP.

These l a r g e p h o t o p r o d u c t i o n c r o s s sec- t i o n s o f heavy q u a r k s a r e a complete m y s t e r y f r o m t h e p o i n t o f v i e w o f p e r t u r b a t i v e QCD.

We r e c a l l t h a t a t b e s t 20% o f t h e i n e l a s t i c e v e n t s observed by t h e s m a l l acceptance muon

b d e t e c t o r s c o u l d be accommodated by p e r t u r b a -

t i v e c a l c u l a t i o n s . I s e r t u r b a t i o n t h e o r y o n l y p a r t o f t h e s t o r y ?

B 9

The answer i s

/

'

p o s s i b l y a f f i r m a t i v e ; I w i l l i l l u s t r a t e t h i s , , , , ,,,I

,

, , , , , , i n a s t r i k i n g way by showing how t o c a l c u l a t e

O d

10' 103 a l l p h o t o - and h a d r o p r o d u c t i o n c r o s s s e c t i o n s

10 i n a n o n - p e r t u r b a t i v e framework.20 We w i l l

E, (GeV) b a s i c a l l y e x t e n d t h e a d d i t i v e q u a r k model t o i n c l u d e photons and g l u o n s . The p r o c e d u r e i s F i g . 9: Evidence f o r abundant p i c t o r i a l l y d e s c r i b e d i n F i g . 10. I n photo- p h o t o p r o d u c t i o n o f i n e l a s t i c p r o d u c t i o n t h e photon fragments i n t o a q u a r k - charm quarks. The d a t a i s com- a n t i q u a r k p a i r ( a s d e s c r i b e d by t h e photon pared t o a n o n - p e r t u r b a t i v e s t r u c t u r e f u n c t i o n ) ; one o f t h e q u a r k s sub- e s t i m a t e o f t h e t o t a l ( e l a s t i c s e q u e n t l y s c a t t e r s o f f t h e t a r g e t ( w i t h a + i n e l a s t i c ) p h o t o p r o d u c t i o n nominal q N c r o s s s e c t i 6 n o f 10 mb). The c r o s s s e c t i o n . h a d r o p r o d u c t i o n c r o s s s e c t i o n i s t h e n o b t a i n e d

F. H a l z e n

N N - charm

"m

F i g . 10: N o n - p e r t u r b a t i v e c a l c u l a t i o n F i g . 11: A n o n - p e r t u r b a t i v e e s t i m a t e o f heavy q u a r k photo- and hadro- o f h a d r o p r o d u c t i o n o f charm f o l l o w i n g p r o d u c t ion. t h e c a l c u l a t i o n d e s c r i b e d i n F i g . 10.

by p h o t o n - g l u o n s u b s t i t u t i o n [see F i g . 1 0 ) . I t i s i m p o r t a n t t o r e a l i z e t h a t t h e heavy q u a r k s c a t t e r i n g o f f t h e t a r g e t i s o f f - m a s s - s h e l l ; f o r d e t a i l s see Ref. 20.

The r e s u l t s a r e i n t r i g u i n g (see F i g s . 9, 11) and a r e a w a r n i n g t h a t p e r t u r b a t i v e QCD m i g h t n o t be t h e end o f t h e w o r l d i n t h i s s u b j e c t . Even more p u z z l i n g i s t h e f a c t t h a t t h e s e c a l c u l a t i o n s can d e s c r i b e l i g h t q u a r k s as w e l l , e.g., f o r

Ey = 170 GeV we f i n d

g i v i n g a r e a s o n a b l e v a l u e o f t h e t o t a l c r o s s s e c t i o n o f 110 wb. I f t h e s e arguments have some element o f t r u t h , t h e y w i l l p r o v i d e f u t u r e h i g h - e n e r g y , l a r g e acceptance e x p e r i m e n t s w i t h o v e r t w i c e t h e number o f e v e n t s e x p e c t e d on t h e b a s i s o f conven-

t i o n a l y - g l u o n f u s i o n models.

2 1

4. H a d r o p r o d u c t i o n o f Heavy Quarks

. -

a) E x p e r i m e n t a l s t a t u s o f open charm. 22,23 Up t o now a m u l t i t u d e o f e x p e r i m e n t s e m p l o y i n g a w i d e v a r i e t y o f t e c h n i q u e s has g i v e n us a t b e s t a nebulous v i e w o f t h e s y s t e m a t i c s o f open charm p r o d u c t i o n . I w i l l f i r s t a r g u e t h a t t h e c o n f u s i o n i s m o s t l y ( p o s s i b l y e x c l u s i v e l y ) c r e a t e d by a n absence o f s u f f i c i e n t c a r e i n comparing v a r i o u s e x p e r i m e n t s . Problems emerge when ( i ) comparing e x p e r i m e n t s u s i n g n u c l e a r t a r g e t s w i t h t h o s e u s i n g e x c l u s i v e p r o t o n s and f o r g e t t i n g t h a t t h e Aa c o r r e c t i o n s i n v o l v e d have n o t been e x p e r i m e n t a l l y de- t e r m i n e d , ( i i ) i n v o k i n g l i m i t s on charm p r o d u c t i o n f r o m t h e observed l e p t o n / p i o n r a t i o and ( i i i ) u s i n g words l i k e " c e n t r a l " and " d i f f r a c t i v e " p r o d u c t i o n w i t h o u t g i v i n g them a p r e c i s e meaning. B e f o r e c o n f r o n t i n g t h e d a t a , I w i l l a t t e m p t t o remedy t h i s s i t u a t i o n .

What i s t h e Aa dependence o f charm p r o d u c t i o n ? N o n - p e r t u r b a t i v e o r t r u l y d i f f r a c t i v e models24 a r g u e f o r a = 2/3, whereas models based on p e r t u r b a t i v e QCD 2 5

( w h i c h t h e d a t a s t r o n g l y f a v o r , as w i l l be argued f u r t h e r on) r e q u i r e A'. Such arguments a r e , however, d a n g e r o u s l y o v e r - s i m p l i f i e d , as i l l u s t r a t e d by t h e

A'

for p p

--A a K

0

F i g . 12: A' dependence o f s t r a n g e p a r t i c l e p r o d u c t i o n as a f u n c t i o n o f Feynman x.

f o l l o w i n g example. Everybody knows t h a t a s h o u l d be 2/3 f o r t h e d i f f r a c t i v e produc- t i o n o f s t r a n g e p a r t i c l e s . Well

...

^{i t i s}

n o t z 6 as shown i n F i g . 12. Around Feynman x o f 0.6 t h e v a l u e o f ^ci becomes as s m a l l as 0.45 f o r b o t h K and

A

p r o d u c t i o n . So even i f one e x p e c t s A1

,

" n u c l e a r p h y s i c s "

m i g h t p l a y t r i c k s on us and make t h e ob- s e r v e d v a l u e say, A o e 7 . Aoa3 makes a l o t o f d i f f e r e n c e when one i s u s i n g a t u n g s t e n t a r g e t ! I w i 11 assume A2l3 and t h i s i s n o t n e c e s s a r i l y a bad v a l u e i f you l i k e p e r - t u r b a t i v e QCD as i l l u s t r a t e d by g l a n c i n g a t t h e s i t u a t i o n f o r s t r a n g e p a r t i c l e s . M e a s u r i n g a i s , however, a h i g h p r i o r i t y t a s k f o r t h e f u t u r e .

My message r e g a r d i n g l i m i t s on charm c r o s s s e c t i o n s f r o m l e p t o n / p i o n r a t i o s i s s i m p l e : approach w i t h c a r e ! M p o i n t i s i 1 lu s t r a t e d i n F i g . 13 where we'7 have c a l c u l a t e d R/n f r o m t h e l e p t o n i c decay o f D mesons assuming a 8% l e p t o n i c b r a n c h i n g r a t i o and a nominal (and i n t e n t i o n a l l y o u t r a g e o u s ) t o t a l y i e l d o f 1 mb. D's a r e produced a c c o r d i n g t o a momentum d i s t r i b u - t i o n

F i g u r e 13a i l l u s t r a t e s t h e s e n s i t i v i t y of R/n t o t h e d e t a i l e d shape o f t h e D decay d i s t r i b u t i o n by a l t e r n a t i v e l y assuming D + K ( o r K")RV. F i g u r e 13b i l l u s t r a t e s t h e same p o i n t r e g a r d i n g t h e e x a c t v a l u e o f b i n E q . ( 5 ) . F i g u r e 13c f i n a l l y i l l u s t r a t e s how one can s t r e t c h t h e e r r o r b a r s on n, b and t h e decay d i s t r i b u t i o n t o s l i p a I mb c r o s s s e c t i o n under t h e observed R/n r a t i o .

F i g . 13: R/n r a t i o s a t

& =

62 GeV f r o m D + K ( o r K"9.v) assuming Eq. ( 5 ) , a l e p t o n i c b r a n c h i n g r a t i o o f 8% and a nominal v a l u e o f t h e D p r o d u c t i o n c r o s s s e c t i o n o f 1 mb.

I ' " " " r l i I I 1 1 1 1 1 1 1 1 ~ I

(I-X)\-~~T u,= 1 rnb ( ~ - x ) " e - ~ ~ r u c = l m b - x n P I uc=lmb

1c3 -

-

- - -

n.3. b.2.5

I 1 < 1 1 1 1 1 1 1 I

,

^{8 <} s a , ' J J

0.1 1. to. 0.f I 1. 10

-

^{n = 3}

-

^{b = 3} _\

\ \

\

F. H a l z e n C3-389

F i n a l l y , l e t us a g r e e on a w o r k i n g d e f i n i t i o n o f t h e words " c e n t r a l " and

" d i f f r a c t i v e l ' . As a guide (and as a g u i d e o n l y ) we use t h e diagrams f o r l e a d i n g p a r t i c l e p r o d u c t i o n shown i n F i g . 14. I t i s easy t o c a l c u l a t e t h e i r l a r g e x

U softer: F i g . 14: Working d e f i n i t i o n not

** ^q.

^.ff r a c t i v e " charm p r o -

d u c t i o n . I n t h i s language c e n t r a l l y produced p a r t i c l e s f o l l o w a (1-x15 d i s t r i b u t i o n .

b e h a v i o r , e.g., ;sing t h e c o u n t i n g r u l e s o f Ref. 28. P r o t o n s produce l e a d i n g A C 1 s w i t h ( I - x ) ' and D 1 s w i t h ( 1 - x ) 3 . I t i s easy t o u n d e r s t a n d t h a t D ' s a r e r e l a t i v e l y

s o f t e r : t h e y c o n t a i n I f a s t v a l e n c e quark, n o t 2 as i s t h e case f o r A,. T h i s s i t u a t i o n i s f a m i l i a r : d i f f r a c t i v e K ' s a r e s o f t

e

r t h a n A ' s . T- beams produce an e q u a l amount o f Do and D p a r t i c l e s w i t h a ( I - x ) d i s t r i b u t i o n . I n t h i s p i c t u r e t h e Feynman x dependence o f c e n t r a l p r o d u c t i o n i s (1-x15. These e s t i m a t e s n e g l e c t t h e masses o f t h e charm p a r t i c l e s . E s p e c i a l l y a t l o w e r e n e r g i e s t h e observed x - dependence c o u l d t h e r e f o r e be s i g n i f i c a n t l y s o f t e r . We d i s c u s s t h e d a t a n e x t .

The o b s e r v a t i o n o f " d i f f r a c t i v e " o r l e a d i n g charmed p a r t i c l e s , produced w i t h l a r g e Feynman x , was f o r a l o n g t i m e t h e monopoly o f ISR e x p e r i m e n t s . T h i s s i t u - a t i o n has r a d i c a l l y changed. L e a d i n g D ' s f r o m a p i o n beam a r e now obserxed i n f i v e e x p e r i m e n t s . I l l i n o i s e t a1.29 and A C C M O R ~ O see l e a d i n g D ' s f r o m D decay, produced w i t h a broad x d i s t r i b u t i o n c o n s i s t e n t w i t h ( I - x l . These o b s e r v a t i o n s a r e c o n f i r m e d by p r e l i m i n a r y d a t a f r o m t h e F e r m i l a b MPS.3' t h e y o b t a i n as a b e s t f i t t o t h e l o n g i t u d i n a l momentum d i s t r i b u t i o n ( 1 - x ) 1 ' 5 f d ' 7 . The LEBC e ~ p e r i m e n t ~ ~ f u r t h e r m o r e p r e s e n t e d e v i d e n c e f o r two components i n t h e x - d i s t r i b u t i o n (I-x)",

w i t h n s h i f t i n g from a t y p i c a l c e n t r a l v a l u e a t s m a l l x t o a v a l u e c o n s i s t e n t w i t h u n i t y when x approaches 1. Beam-dump e x p e r i m e n t s as a group23 have been u n a b l e i n t h e p a s t t o f i n d any t r a c e o f l e a d i n g charm p a r t i c l e s . T h i s s i t u a t i o n i s f i n a l l y r e v e r s e d by t h e d e t e c t i o n o f l e d i n g D p a r t i c l e s f r o m a 278 GeV ^T- beam w i t h t h e Fermi l a b u-beam dump f a c i 1 i t y . 3 j L e t us r e c a l l t h a t we e x p e c t ( F i g . 14) a

n

beam t o fragment i n t o equal numbers o f l e a d i n g Do and D p a r t i c l e s f o l l o w i n g a ( I - x ) ' d i s t r i b u t i o n . The e x p e r i m e n t observes D ' s t h r o u g h t h e i r s e m i - l e p t o n i c decay i n t o

.

I t i s i m p o r t a n t t o remember t h a t

i . e . , t h e l o n g e r l i f e t i m e o f charged D ' s w i l l be r e f l e c t e d i n t o a l a r g e r l e p t o n i c b r a n c h i n g r a t i o . T h e r e f o r e , t h e observed l e p t o n i c decays o f D-, DO w i l l d i f f e r , w i t h

The e x p e r i m e n t indeed observes an excess o f prompt

u-

w i t h i n acceptance. T h i s number has t o be i n t e r p r e t e d w i t h c a r e , t h e v a l u e b e i n g - x-dependent. C l e a r l y t h e b e s t p l a c e t o d e t e c t a l e a d i n g charm component i s i n P e v e n t s (Eq. ( 7 ) ) . T h e i r d a t a a r e shown i n F i g . 15. The momentum d i s t r i b u t i o n o f t h e U i s compared w i t h t h e expected d i s t r i b u t i o n

They o b t a i n

BU(D-) = 2.9 t 0.2 p b ( x > 0 o n l y )

.

⁽¹⁰⁾

Here I used a g a i n A 213

.

Assuming r o u g h l y equal c r o s s s e c t i o n s f o r x > 0 and x < 0 and a nominal b r a n c h i n g r a t i o o f

l o % ,

Eq. (10) t r a n s l a t e s i n t o a " d i f f r a c t i v e "

c r o s s s e c t i o n o f o r d e r 50 pb, o n l y a f a c t o r 4 below t h a t observed a t t h e ISR.

F i g . 16: Leading Acls observed i n an exposure o f LEBC t o a 360 GeV p r o t o n beam.

F i g . 1.5: Momentum dependence o f p

-

l e p t o n s f r o m D- p a r t i c l e s i n t h e F e r m i l a b beam-dump e x p e r i m e n t . The d a t a a r e d e s c r i b e d by a " d i f f r a c t i v e "

d i s t r i b u t i o n ( I - x ) ' e - 2 . 5 p ~ .

Four e x p e r i m e n t s now s u p p o r t t h e o b s e r v a t e o n o f l e a d i n g A: a t t h e ISR i f one i n - c l u d e s t h e i n d i r e c t e v i d e n c e f r o m a CDHS34 r e s u l t . Indeed, t h e i r o b s e r v a t i o n o f a

V,T

asymmetry i n t h e beam-dump r e s u l t s can be i n t e r p r e t e d as a consequence o f lead- i n g A, decay. A Serpukhov experiment35 o b s e r v e s a 100 A, peak i n t h e decay

Ac ^-t ~ K O T + T - . A1 l e v e n t s a r e c o n t a i n e d i n a 3 0 MeV b i n . P u z z l ing, however, i s t h e f a c t t h a t t h e i r p r o d u c t i o n c r o s s s e c t i o n s a r e as l a r g e as t h o s e obs r v e d a t t h e ISR, d e s p i t e t h e low energy o f t h e i r n e u t r o n beam. The T a t a group3' p r e s e n t e d new e v i d e n c e f o r Ac from an e m u l s i o n exposure a t F e r m i l a b . The p r o d u c t i o n a n g l e i n t h e e m u l s i o n r e f l e c t s t h e l e a d i n g c h a r a c t e r o f t h e A C 1 s . A l t h o u g h backgrounds a r e f o r m i d a b l e , t h e o b s e r v a t i o n o f a s s o c i a t e d D ' s i n two e v e n t s l e n d s f u r t h e r s u p p o r t t o t h e i r a n a l y s i s . F u r t h e r e v i d e n c e f o r A, p r o d u c t i o n i s shown i n F i g . 16.

F. Halzen C3-391

Although t h e s t a t i s t i c s a r e low, t h e LEBC experiment32 u s i n g hydrogen i s v e r y c l e a n . One n o t i c e s t h e c l u s t e r i n g o f Ac events a t a l a r g e r x - v a l u e when com- p a r i n g t o D events shown i n t h e same f i g u r e .

The absence of any d i r e c t evidence f o r l e a d i n g & I s from p r o t o n beam-dump experiments i s s t i l l p u z z l i n g . Before jumping t o c o n c l u s i o n s , one should keep t h e f o l l o w i n g p r e c a u t i o n s i n mind: ( i ) The v a l u e f o r t h e l e p t o n i c branching r a t i o o f t h e Ac ((4.5%) i s o n l y known w i t h i n l a r g e e r r o r bars; t h e a c t u a l v a l u e m i g h t be smal l e r . ( i i ) The l e p t o n from Ac-decay c o u l d be much s o f t e r than one e s t i m a t e s assuming a three-body decay. A h i g h e r m u l t i p l i c i t y o f hadrons i n the f i n a l s t a t e o f t h e A,-decay (as observed f o r D s e m i l e p t o n i c decay) would reduce t h e e s t i m a t e d acceptance o f t h e experiments. ( i i i) As al'ready mentioned, even l e a d i n g Acls c o u l d have an x - d i s t r i b u t i o n s i g n i f i c a n t l y softer t h a n ( I - x ) ' , an e s t i m a t e t h a t n e g l e c t s t h e heavy quark mass. ( i v ) Leading D ' s , expected t o be s o f t e r than (1-x) 3 , c o u l d be confused w i t h those c e n t r a l l y produced.

Fig. 17: Ac and D p r o d u c t i o n i n NN F i g . 18: U n i v e r s a l t h r e s h o l d r i s e o f c o l l i s i o n s . heavy p a r t i c l e m u l t i p l i c i t i e s : s t r a n g e

and charm p a r t i c l e s i n hadron c o l l i - s i o n s , s t r a n g e p a r t i c l e s i n e+e- anni- h i l a t i o n .

F i g u r e 17 shows a c o m p i l a t i o n o f experimental values f o r Ac and D p r o d u c t i o n i n NN c o l l i s i o n s ( a d d i t i o n a l nN d a t a a r e shown i n F i g . 21). To t h e e x t e n t t h a t t h e t o t a l i n e l a s t i c c r o s s s e c t i o n i s r o u g h l y independent o f energy i n t h e g - r a n g e under c o n s i d e r a t i o n , t h e t h r e s h o l d represents t h e r i s e o f t h e charm p a r t i c l e m u l t i - p l i c i t y . T h i s t h r e s h o l d dependence i s very r e m i n i s c e n t o f t h e observed increase o f K,A m u l t i p l i c i t i e s a t ISR energies,37 as weld as t h e sharp r i s e i n K,A m u l t i p l i - c i t i e s observed i n e+e- a n n i h i l a t i o n a t PETRA. T h i s i s shown i n F i g . 18, where we have converted t h e e+e- a n n i h i l a t i o n energy t o an e f f e c t i v e NN energy u s i n g

Equation (11) t r a n s l a t e s hadron-hadron energy t o p a r t o n - p a r t o n energy by removing t h e beam j e t s . The procedure i s f a m i l i a r i n t h e study O f t o t a l m u l t i p l i c i t y where

o charm A'

lo0

F i g . 19: Same as F i g . 18 assuming A ' i n deducing charm c r o s s s e c t i o n f r o m e x p e r i m e n t s u s i n g n u c l e a r t a r g e t s .

QCD

fusion

+

flavor excit.

a E b

/

-

F i g . 21: Data on h a d r o p r o d u c t i o n (TN and NN) o f charm a r e compared w i t h a c a l c u l a t i o n e v a l u a t i n g t h e f u s i o n diagrams o f F i g . ZOa, b (dashed 1 in e ) and w i t h a f u l l ~(ci:) c a l c u l a t i o n ( s o l i d 1 in e ) .

N spectotor

F i g . 20: L e a d i n g o r d e r QCD diagrams f o r t h e p r o d u c t i o n o f heavy q u a r k s .

one concludes39 t h a t <x> = 0.2. The u n i v e r s a l t h r e s h o l d f o r heavy p a r t i c l e p r o d u c t i o n d i s p l a y e d i n F i g . 18 i s i n - deed r e m i n i s c e n t o f t h e u n i v e r s a l be- h a v i o r o f charged p a r t i c l e m u l t i p l i c i - t i e s 3 9 p r o v i d e d a comparison i s made between e'e- and NN induced r e a c t i o n s u s i n g Eq. ( 1 1 ) . F i n a l l y , F i g . 19 shows how e x p e r i m e n t a l v a l u e s f o r charm p r o - d u c t i o n on n u c l e a f T a r g e t s " f a 1 1 t h r o u g h t h e f l o o r " when A I S assumed. T h i s can be t a k e n as e v i d e n c e f o r an A@ depen- dence c l o s e r t o A ~ ' ~ , b u t by n o means d i m i n i s h e s t h e need f o r an e x p e r i m e n t a l measurement.

b

Ps~Lu_rba_t~veG!-con2~~!ts_-

25 t h e data. The O(as) graphs w h i c h con-

---

s t i t u t e t h e l e a d i n g o r d e r QCD mechanisms f o r p r o d u c i n g heavy quarks a r e l i s t e d i n F i g . 20. N e g l e c t i n g t h e charm s t r u c t u r e i n s i d e t h e p r o t o n , i.e., n e g l e c t i n g t h e diagrams o f F i g . 20c, we a r e l e f t w i t h t h e f u s i o n model where charm i s hadro- produced by t h e f u s i o n o f q u a r k s

( F i g . 20a) and g l u o n s ( F i g . 2 0 b ) . U s i n g s t a n d a r d c h o i c e s f o r t h e l i g h t q u a r k and g l u o n s t r u c t u r e f u n c t i o n s we o b t a i n t h e charm c r o s s s e c t i o n l a b e l l e d " f u s i o n " i n F i g . 21. The f u s i o n diagrams under- e s t i m a t e t h e observed charm y i e l d s by o v e r one o r d e r o f magnitude. I t i s

F. Halzen

I \\\

- -

^no

.P+ I

^{quark in beam}

^/

F i g . 22: S t r u c t u r e o f t h e x-depen- F i g . 23: Close-up o f a f l a v o r e x c i t a t i o n dence o f charm p a r t i c l e p r o d u c t i o n diagram.

i n p e r t u r b a t i v e QCD. Recombination o f valence quarks w i t h t h e s p e c t a t o r charm quarks (see F i g . 23) y i e l d s l e a d i n g charm p a r t i c l e s .

academic t o d i s c u s s whether t h i s discrepancy can be f i x e d up, e.g., by assuming a charm quark mass as low as 1 GeV, because a second glance a t t h e data r e v e a l s t h e abundant p r o d u c t i o n o f charm p a r t i c l e s w i t h l a r g e Feynman x. The f u s i o n diagrams o n l y p o p u l a t e t h e c e n t r a l r e g i o n (xF 0) w i t h charm, as t a n be seen i n Fig. 22.

Faced w i t h t h i s f a i l u r e we should c l e a r l y r e c o n s i d e r O t h e f a c t t h a t we ne- g l e c t e d t h e f l a v o r e x c i t a t i o n graphs o f F i g . 20c. The f i r s t o f these diagrams i s shown i n d e t a i l i n F i g . 23: a quark i n the beam s c a t t e r s by g l u o n exchange o f f a charm quark i n t h e t a r g e t . The o r i g i n o f t h i s charm quark i s QCD e v o l u t i o n , as shown i n F i g . 23. The s t r u c t u r e o f t h i s diagram i s s c h e m a t i c a l l y g i v e n by

e x h i b i t i n g t h e f a c t t h a t these diagrams d i v e r g e when

t"

^{-t 0} and one h i t s t h e gluon exchange p o l e i n F i g . 23. However, t h e g l u o n p l a y s t h e same r o l e as t h e v i r t u a l photon i n l e p t o p r o d u c t i o n ; t h e r e f o r e ,

f

i s s i m i l a r t o t h e Q~ c o n t r o l l i n g t h e QCD e v o l u t i o n o f t h e s t r u c t u r e f u n c t i o n . When + 0 no charm i s presen: i n t h e t a r g e t and t h e r e f o r e t h e divergence i n E q . (12) i s c o n t r o l led. Only when t = -m: have enough charm p a i r ? evolved t o g i v e a non-vanishing v a l u e f o r t h e diagram I n F i g . 23.

By t h i s argument tmin = -m: i n Eq. ( I Z ) , s t i l l y i e l d i n g l a r g e c r o s s s e c t i o n s from f l a v o r e x c i t a t i o n . A q u a n t i t a t i v e e v a l u a t ' o n i s d i f f i c u l t because o f our ignorance

1

o f t h e charm s t r u c t u r e f u n c t i o n C ( X , Q ~ = mc!. 0 d o r i c 0 ~ ~ used a Monte-Carlo t o ex- p l i c i t l y generate t h e charm s t r u c t u r e f u n c t ~ o n from e v o l u t i o n . The r e s u l t i s shown i n Fig. 21.

F l a v o r e x c i t a t i o n diagrams n o t o n l y a l l o w us t o b r i d g e t h e gap between t h e f u s i o n diagrams and t h e d a t a , they "impersonate" d i f f r a c t i v e p r o d u c t i o n o f charm.

Leading Acls, absent i n t h e f u s i o n model, can now be obtained by t h e recombination o f t h e s p e c t a t o r c-quark i n Fig. 23 w i t h a valence (ud) p a i r i n t h e proton. A l t e r - n a t i v e l y , a s p e c t a t o r c can p i c k up a u o r d valence quark t o form a l e a d i n g

D.

I t w i l l be s o f t e r than t h e A, because i t c o n t a i n s o n l y one valence quark. The p i c t u r e emerging i s s i m i l a r t o t h e one presented i n Fig. 14 which we used t o summarize t h e experimental data. A sample c a l c u l a t i o n i s shown i n Fig. 22. However, u n l i k e t r u l y d i f f r a c t i v e mechanisms, f l a v o r e x c i t a t i o n does n o t have a l o g a r i t h m i c energy t h r e s h o l d (which would be c l e a r l y a t v a r i a n c e w i t h t h e data; see Fig. 21) and p r e - d i c t s a suppression o f t h e cross s e c t i o n w i t h i n c r e a s i n g quark mass which i s sub- s t a n t i a l l y s t r o n g e r than We r e t u r n t o t h i s p o i n t when d i s c u s s i n g b-quarks.

I t s h o u l d be c l e a r from t h i s d i s c u s s i o n t h a t p e r t u r b a t i v e QCD i s used as a t o o l t o d e s c r i b e t h e d a t a and cannot be s u b j e c t e d t o q u a n t i t a t i v e t e s t s . The framework i s , however, s u f f i c i e n t t o d e s c r i b e t h e data. The s i t u a t i o n i s s i m i l a r t o t h a t f o r t h e h a d r o n i c p r o d u c t i o n o f l a r g e - p T hadrons. I t i s i n f a c t q u e s t i o n - a b l e

whethe&-the

p e r t u r b a t i v e approach t o heavy q u a r k p r o d u c t i o n i s c o m p l e t e l y understood; t h i s makes i t an i n t e r e s t i n g s t u d y case. The p e r t u r b a t i v e approach

i s indeed v a l i d i n t h e ( i m p o s s i b l e ) 1 i m i t where s + a w i t h m2/3 f i x e d (see F i g . 24).

Q

I t i s o f c o u r s e i m p o s s i b l e t o keep t h e r a t i o m2/$ unchanged w i t h o u t i n c r e a s -

e 2 4

I n s m, as w e l l a s

2 .

T h i s i s what i s done Yn t h e D r e l l - Y a n p r o c e s s and t h e resemblance o f diagrams as t h e f i r s t one i n F i g . 24 t o D r e l l - Y a n a n n i h i l a - t i o n i s m i s l e a d i n g . The p r o b l e m i s

Q i l l u s t r a t e d by t h e second diagram. I t

i s indeed eazy t o show t h a t w i t h o u t

s-a,,

fixed

i n c r e a s i n g mL, t h e momentum t r a n s f e r

+ D when sQ+ ^rn. Some p r o p a g a t o r s become s o f t and p e r t u r b a t i v e r e s u l t s a r e s u s p i c i o u s when s > > m c . T h i s s h o u l d be k e p t i n mind, e.g., when c a l c u l a t i o n s o f c- o r b - p r o d u c t i o n a r e e x t r a p o l a t e d t o c o l l i d e r e n e r g i e F i g . 24: The p e r t u r b a t i v e l i m i t o f heavy What about i n t r i n s i c charm?

32

q u a r k p r o d u c t i o n . F i r s t , and most i m p o r t a n t : we do n o t need i t . What I mean by t h i s i s v e r y p r e c i s e : a l l observed l e a d i n g p a r t i c l e s c o n t a i n v a l e n c e quarks. The d a t a com- p l e t e l y s u p p o r t s o u r c l a i m t h a t l e a d i n g charm p a r t i c l e s have l a r g e Feynman x be- cause t h e y c o n t a i n v a l e n c e q u a r k s w i t h l a r g e x; t h e charm q u a r k i t s e l f i s a s o f t p r o d u c t o f a o f f - s h e l l g l u o n ( ~ i g . 2 3 ) . I f t h e c-quarks themselves were v a l e n c e - l i k e , as i n t h e i n t r i n s i c charm p i c t u r e , t h i s c o n s t ~ a i n t on t h e quantum numbers o f l e a d i n g p a r t i c l e s i s l i f t e d and, e.g., l e a d i n g ~ + ( c d ) c o u l d emerge f r o m p r o t o n beams. There i s no e v i d e n c e f o r t h i s . I n s t e a d o f c o n t i n u i n g t o r u l e o u t i n t r i n s i c charm, we s h o u l d l o o k f o r i t i n t h i s way and t r y t o e s t a b l i s h whether i t e x i s t s a t some l e v e l .

A r e valence-1 i ke c c components i n t h e p r o t o n wave f u n c t i o n a f e a t u r e o f QCD?

The answer i s no; t h e argument i s d e p i c t e d i n Fig. 25. The f i g u r e shows (uud c a Fock s t a t e s o f t h e p r o t o n . I n t h e t o p diagram t h e c c p a i r m a t e r i a l i z e s f r o m a g l u o n w i t h l a r g e Q'. Such diagrams can be computed p e r t u r b a - t i v e l y and a r e i n c l u d e d i n t h e p r e v i - ous c a l c u l a t i o n s . I n t r i n s i c charm c o u l d be g e n e r a t e d f r o m diagrams o f t y p e shown i n F i g . 25b.- Here a s o f t

large Q

g l u o n produces a s o f t c c p a i r t h a t e v e n t u a l l y shares t h e momentum o f t h e v a l e n c e q u a r k s a f t e r m u l t i p l e i n t e r - a c t i o n s . The problem i s , however, t h a t t h e c - q u a r k s a r e f a r o f f - s h e l l and a r e t h e r e f o r e s h o r t - t ime f l u c t u a - momentum t i o n s : t h e r e i s n o t enough t i m e t o

P

a c h i e v e t h e momentum s h a r i n g w i t h t h e

v a l e n c e q u a r k s t o b u i l d up an i n t r i n - s i c uudcc Fock component o f t h e p r o - ton. How f a r t h e c-quarks a r e o f f - s h e l l i s g i v e n i n t h e model of

-5

Brodsky e t a l . and one can d e r i v e an

upper l i m i t o n t h e l i f e t i m e o f t h e c F p a i r

F i g . 25: c F components o f t h e p r o t o n wave f u n c t i o n .

' I - . c

I ^\

F i g . 27: Candidate i n t e r -

\ ^{/ \}

I

p r e t a t i o n s o f TN ^-+ @$X

N.j.,,-

F

-\

N

-A-'

B - $ K x ...

e v e n t s .

where p i s t h e p r o t o n momentum. T h i s t i m e i s much s h o r t e r t h a n a t y p i c a l l i g h t q u a r k f l u c t u a t i o n p / u 2 ( w i t h = 300 MeV), p r e v e n t i n g t h e c F p a i r f r o m b e i n g an

i n t r i n s i c p a r t o f t h e p r o t o n . B u i l d i n g v a l e n c e - l i k e c F components i n t o t h e p r o t o n i s i n t r i n s i c a l l y i m p o s s i b l e .

C) Evidence f o r b-quark productio:. F i g u r e 26 summarizes t h e e x p e r i m e n t a l s t a t u s o f t h e h a d r o p r o d u c t i o n o f b-quarks. A l s o shown a r e p r e d i c t i o n s f o r b- and

t - q u a r k p r o d u c t i o n based on t h e f u l l 0 ( a 2 ) c a l c u l a t i o n s d e s c r i b e d i n c o n n e c t i o n w i t E

103 1 1 ^I charm p o d u c t i o n . F i r s t , t h e r e a r e upper

-

cascades In

cosmic rays=

l i m i t ~ . ' ~ NAlg o b t a i n s a 100 nb l i e i t a t 400 GeV f r o m an e m u l s i o n exposure. Cas- cade decays of heavy q u a r k s have been ob-

i n emulsions exposed t o cosmic

?

They cannot be charm; t h e most

c o n s e r v a t i v e assumption i s t h a t t h e y a r e b ^-+ c ^-+ s cascades. A l s o , n a r r o w p a r a l l e l muon bundles have been i n t e r p r e t e d as cas-

-

cade decays o f b-quarks. T h i s e v i d e n c e p u t s t h e b-quark c r o s s s e c t i o n i n t h e 1 0 % 1 0 ~ TeV range a t t h e l e v e l o f 100 u b . T h e r e i s t h e e v i d e n c e from t h e BCF group a t t h e I S R . ~ ~ T h e i r r e s u l t i s shown assuming t h a t t h e b r a n c h i n g r a t i o i n t h e observed mode i s g i v e n by B(Ab + PDT) =

/ B (Ac ⁺ pKn)

.

^{B(Ab -+} pDn) has t o be o f

o r d e r 1 t o 2 q v o i d c o n f l i c t w i t h t h e l e p t o n /

I p i o n l i m i t o n Ab p r o d u c t i o n a l s o shown

10'

lo2 to3

i n F i g . 26.

f i

(GeV) But e r e i s new i n f o r m a t i o n . The NA3 group@ has observed a p o s i t i v e s i g n a l f o r t h e r e a c t i o n 'IT-N + $@X. The $ I s a r e F i g . 26: Summary o f t h e e x p e r i m e n t a l d e t e c t e d b y t h e i r

u+u-

decay. The s a l i e n t i n f o r m a t i o n on t h e h a d r o p r o d u c t i o n o f f e a t u r e s o f t h e e v e n t s a r e as f o l l o w s : b-quarks i s shown a l o n g w i t h p r e d i c - ( i ) t h e c r o s s s e c t i o n i s 30

+

10 pb a t t i o n f o r b- and t - q u a r k p r o d u c t i o n 280 GeV; ( i i ) t h e e v e n t s show d i f f r a c t i v e based on p e r t u r b a t i v e QCD. c h a r a c t e r i s t i c s , w i t h one l e a d i n g $ (<x>

i s i n excess o f 0.4!) and a s l o w $; ( i i i ) t h e $$ i n v a r i a n t mass i s spread f r o m 6.5 t o 8.5 GeV; ( i v ) t h e < p ~ > o f t h e $$ p a i r and t h e i n d i v i d u a l @ I s a r e o f o r d e r 1 GeV. The most o b v i o u s i n t e r p r e t a t i o n i n - v o l v e s t h e f i r s t mechanism shown i n F i g . 27. A f t e r p r o d u c t i o n o f a charm q u a r k p a i r , a n o t h e r s o f t cc p a i r i s p i c k e d up o u t o f t h e sea t o form two $ I s . I t i s c l e a r t h a t b o t h $ I s w i l l be c e n t r a l l y produced ( x

-

0) w i t h an i n v a r i a n t mass c l u s - t e r e d around 29,. The NA3 e v e n t s seem t o e x c l u d e t h i s i n t e r p r e t a t i o n . he k i n e m a t i c f e a t u r e s o f t h e e v e n t s s u p p o r t , however, t h e a l t e r n a t i v e i ~ t e r p r e t a t i o n shown i n $7 F i g . 27 t h a t b - q u a r k p r o d u c t i o n w i t h subsequent B + $ and B + $ decays i s t h e s o u r c e o f @$ e v e n t s . The observed

$9

r a t e i s i n agreement w i t h t h e p r e d i c t i o n shown i n F i g . 26 p r o v i d e d t h a t t h e decay f r a c t i o n B ^-+ $X i s o f o r d e r 1%. I t i s i m p o r t a n t t o remember t h a t a t t h e e n e r g i e s under c o n s i d e r a t i o n f l a v o r e x c i t a t i o n ( n o t f u s i o n ) i s t h e dominant s o u r c e o f b-quarks. The l e a d i n g B w i l l be t h e s o u r c e o f a l e a d i n g $;

t h e o t h e r B (and $) w i 11 have lower l o n g i t u d i n a l momentum. T h i s i s i n

.

p,inbalance agreement w i t h t h e d a t a (see F i g . 28)

.

leading B T h i s r a p i d i t y gap between t h e B a s , as

w e l l as t h e random o r i e n t a t i o n o f t h e two $ decay p r o d u c t w i l l l e a d t o a l a r g e , spread o u t i n v a r i a n t mass m The r e s u l t s o f a c a l c u l a t i o n a g a i n $$.

a g r e e w i t h e x p e r i m e n t (see F i g . 28).

12 F i n a l l y , t h e $ decay p r o d u c t s a r e n o t

s u b j e c t t o any c o n s t r a i n t s f r o m t r a n s -

C

3 v e r s e momentum c o n s e r v a t i o n . The b-

\ 8 q u a r k s r o u g h l y conserve t r a n s v e r s e

-

V) c momentum, t h e $ ' s do n o t . The e v e n t

aJ

z

⁴ d i s p l a y e d i n F i g . 28 shows t h e s e c h a r -

a c t e r i s t i c s . F o r a d e t a i l e d a n a l y s i s we r e f e r t o Ref. 47. I f t h i s i n t e r p r e -

0 t a t i o n o f $$ e v e n t s i s c o r r e c t , e x p e r i -

0 0.4 0.8 0.4 0.8 ments d e t e c t i n g muons o n l y can be used

i n t h e f u t u r e t o s t u d y heavy q u a r k p r o d u c t i o n .

d) Bound f l a v o r s . The " b l e a c h i n g "

o f t h e c F c o l o r quantum number when t h e q u a r k s m a t e r i a l i z e i n t o a $ has made t h e u n d e r s t a n d i n g o f bound f l a v o r p r o - d u c t i o n v e r y d i f f i c u l t . We a l r e a d y en- c o u n t e r e d t h i s i s s u e when d i s c u s s i n g $- p h o t o p r o d u c t i o n . New, v e r y c l e a n and 6 7 8 10 h i g h s k 8 t i s t i c s e v i d e n c e has been ob- (GeV) t a i n e d f o r t h e p r o d u c t i o n o f $ ' s v i a

t h e r e a c t i o n pp ⁺ x + $ y . x ' s a r e a F i g . 28: b - q u a r k p r o d u c t i o n f o l l o w e d d e f i n i t e p i e c e o f t h e u z z l e i n under- by B + $ and

B

+ $ decays c o n f r o n t s s t a n d i n g $ - p r o d u c t i o n 4

5

and c a l c u l a - T N ⁺ $$X d a t a f r o m t h e NA3 e x p e r i m e n t . t i o n s a l o n g hese l i n e s a r e now v e r y

s u c c e s s f u

.

⁵⁵

There i s a l s o t h e s c a l i n g law o f G a i s s e r e t i t i s a f a c t t h a t a l l d a t a on t h e p r o d u c t i o n o f bound f l a v o r s can be u n d e r s t o o d on t h e b a s i s o f t h e two f o l l o w i n g a s ~ u m ~ t i o n s : 5 ~ ( i ) c o p i o u s decay o f a ( Q m s t a t e i n t o hadrons r e s u l t s i n c o p i o u s p r o d u c t i o n by hadrons; ( i i ) l e t dimensions do t h e r e s t . T h i s l e a d s t o t h e s t a t e m e n t t h a t

r

^M2

o ( ~ a =

- F(F)

( 1 4)

M3

Here

r

i s t h e d i r e c t [ ( Q T ) + 3 g l u o n s ] w i d t h o f t h e QZ) bound s t a t e . The suc- cess5' o f t h i s approach i s shown i n F i g s . 29, 30. M / T - 0 i s indeed a u n i v e r s a l f u n c t i o n o f M2/s. A1 1 a t t e m p t s t o d e r i v e Eq. ( 1 4 ) , e. f r o m QCD, have f a i l e d . To dd t o t h e m y s t e r y , i t has been r e c e n t l y discoveredgi'that t h e s c a l i n g f u n c t i o n F(M

t

/s) i s i d e n t i c a l i n shape t o t h a t observed i n t h e D r e l l - Y a n process ( s e e F i g . 3 0 ) , l e a d i n g t o t h e r e l a t i o n

Here y i s t h e r a p i d i t y o f t h e bound s t a t e v ( Q ~ ) .

e) Higgs-hynyig. To show t h a t a t l e a s t some o f t h e g o a l s announced i n t h e b e g i n n i n g o f t h i s t a l k a r e n o t f r i v o l o u s , I would l i k e t o show t h e i m p o r t a n t i m p l i - c a t i o n s o f what we l e a r n e d about heavy qu$sk p r o d u c t i o n f o r Higgs h u n t i n g .

F i g u r 31 shows an example o f a f o r g o t t e n (Higgs e x c i t a t i o n ) diagram and a s t a n - d a r d ~ ~ d i a g r a m f o r H i g g s p r o d u c t i o n . F o r a dynamics1 l y g e n e r a t e d Higgs mass o f about 10 GeV, t h e two mechanisms have a s i m i l a r c r o s s s e c t i o n ( u n f o r t u n a t e l y i n t h e

F. H a l z e n

F i g . 29: The s c a l i n g law o f Eq. (14) c o n f r o n t s t h e data.

Same as F i g . 29. The f u n c - ) i n Lq. (14) i s t h e same as t h e e q u i v a l e n t s c a l i n g f u n c t i o n i n t h e D r e l l - Y a n process.

pb range, a l t h o u g h i t c o u l d be s i g n i f i c a n t l y l a r g e r 5 5 ) . N o t i c e t h a t t h e c a l c u L a - t i o n o f gc + Hc t y p e diagrams i s v e r y r e l i a b l e as t h e Higgs mass c o n t r o l s a l l t + 0 d i v e r g e n c e s . Comparing c r o s s s e c t i o n s i s , however, b e s i d e t h e p o i n t . Indeed, t h e o l d - f a s h i o n e d f u s i o n diagram r e q u i r e s f i n d i n g a H + cF,

TY

peak i n a l a r g e back- ground o f such p a i r s o r i g i n a t i n g f r o m o t h e r sources (e.g., gg + c a

.

T h i s i s hope- l e s s g i v e n t h e r a t e . The s i g n a t u r e o f p r o d u c t i o n and d e t e c t i o n o f t h e H i g g s e x c l u - s i v e l y v i a heavy p a r t i c l e s 5 3 ( f i r s t d i a g r a m i n F i g . 31) i s , however, s p e c t a c u l a r .

F i g . 31 : Examples o f a f o r g o t t e n (a) and a s t a n d a r d (b) diagram f o r H i g g s p r o d u c t i o n .

Four f a s t , l o n g - l i v e d p a r t i c l e s c F c z o r CFTY s i g n a l t h e e v e n t s . We c a l c u l a t e d t h a t no competing backgrounds e x i s t . I n t h e CFTY channel t h i s r e s u l t i s a g a i n v e r y r e - l i a b l e . A few events can t h e r e f o r e e s t a b l i s h t h e s i g n a l ! I n t i m e s o f f i n a n c i a l r e s t r a i n t , program committees become v e r y c o n s e r v a t i v e , b u t i s n ' t t h e H i g g s w o r t h a gamble?