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Submitted on 1 Jan 1982
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QCD CONFRONTS EXPERIMENT
H. Politzer
To cite this version:
H. Politzer. QCD CONFRONTS EXPERIMENT. Journal de Physique Colloques, 1982, 43 (C3),
pp.C3-659-C3-669. �10.1051/jphyscol:1982381�. �jpa-00221937�
Colloque C3, supplément au n° 12, Tome 43, décembre 1982 page C3-659
QCD CONFRONTS EXPERIMENT
H. D. P o l i t z e r
California Institute of Technology, Pasadena, California 91125, U.S.A.
Résumé.- Une revue qualitative de quelques problèmes actuels est présentée en mettant l'accent sur les questions qui compliquent la comparaison directe de QCD avec l'expérience.
Abstract. - Some current issues are reviewed qualitatively with an emphasis on those problems which complicate direct compar- isons of QCD with experiment.
In the 18th Century, a real physicist (what today we refer to as an experimentalist) who did something of significance would receive considerable pub- lic recognition and become something of a celebrity. The handsome fellow in the fur- lined outfit in fig. 1 was such a personage. He mounted an expedition to measure the oblateness of the Earth and traveled past the Arctic Circle.
The results served as a drama- tic confirmation of the Newton- ian theory of gravitation by accounting quantitatively for the precession of the Earth's axis due to the torque of the moon. He was also an active geneticist, but our textbooks remember him primarily as the inventor of the principle of least action. He is Pierre Louis Moreau de Maupertuis.
You may be wondering what Maupertuis has to do with today's high energy experiments.
I have been wondering much the same about QCD. In the follow- ing, I will explain my perplex- ity and return at the end to
Maupertuis. Fig. 1. P. L. M. de Maupertuis
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982381
JOURNAL DE PHYSIQUE
I n d i s c u s s i n g QCD v i s
B
v i s experiment I w i l l f o r t h e s a k e of t h i s t a l k t a k e a v e r y narrow d e f i n i t i o n . V i r t u a l l y e v e r y d i s c u s s i o n t h a t c o n c e r n s hadrons i n some way t o u c h e s on QCD. But f o r t h e p r e s e n t I w i l l t a k e QCD t o mean j u s t t h a t which we can deduce from t h e Lagrangianv i a t h e a c t i o n p r i n c i p l e (Hommage 2 M a u p e r t u i s ) . F i s t h e gauge f i e l d c o v a r i a n t c u r l ; JI r e p r e s e n t s t h e q u a r k s , summed on c o l o r and f l a v o r ; m i s t h e mass m a t r i x ; and t h e c o u p l i n g g is i m p l i c i t i n t h e c o v a r i a n t d e r i v a t i v e D =
a -
i g A. By QCD I w i l l n o t mean s t r i n g s , p a r t o n s , p o t e n t i a l s , i n t r i n s i c k ,,
h a d r o n i z a t i o n o r o t h e r "QCD- motivated" c o n c e p t s .We a l r e a d y e n c o u n t e r o u r f i r s t s e r i o u s problem. By a l l r i g h t s L should i n - c l u d e a t e r m
OFF,
where1
= euvio Fho and 6 i s a n o t h e r fundamental parPk%er of t h e t h e o r y . Such a t e r m i s allowed and t h e r e f o r e presumably r e q u i r e d . I t s consequences i n c l u d e s t r o n g CP v i o l a t i o n . Such consequences a r e n o t e v i d e n t i n p e r t u r b a t i o n t h e o r y , b u t we a r e now s u f f i c i e n t l y s o p h i s t i c a t e d t o b e c o n f i d e n t t h a t t h e y a r e t h e r e . T h i s s t r o n g CP v i o l a t i o n d i s a p p e a r s 1 i fm,
= 0 o r i f t h e r e i s a n a x i o n . m,, = 0 i s p r o p e r l y r u l e d o u t by phenomenology ( a l t h o u g h n o t u n e q u i v o c a l l y . I d i s c u s s t h e d e t e r m i n a t i o n of m a s s p a r a m e t e r s below.). There i s a l s o no unambiguous e x p e r i m e n t a l e v i d e n c e f o r t h e e x i s t e n c e of a n a ~ i o n , ~ d e s p i t e many e x t e n s i v e s e a r c h e s . While t h e expected p r o p e r t i e s of t h e proposed a x i o n were f a i r l y w e l l determined i f o n er e s t r i c t e d c o n s i d e r a t i o n t o t h e known p a r t i c l e s , a l l o w i n g y e t o t h e r p a r t i c l e s and i n t e r a c t i o n s i n t o t h e model g r e a t l y widens t h e r a n g e of p o s s i b i l i t i e s . One p o p u l a r s c e n a r i o h a s a v e r y l i g h t a x i o n , which f o r a l l p r a c t i c a l p u r p o s e s i s t o t a l l y unob- s e r v a b l e b e c a u s e i t s c o u p l i n g s a r e s o weak. However, i t h a s been r e c e n t l y p o i n t e d o u t t h a t w i t h i n t h e c u r r e n t l y p o p u l a r cosmology t h e s e i n v i s i b l e a x i o n s a r e unaccepta- b l e o r a t l e a s t p r o b l e m a t i c a l . 4 The extreme weakness of t h e i r c o u p l i n g s p r e v e n t s a needed t h e r m a l i z a t i o n a t an e a r l y epoch. While I p e r s o n a l l y have t r o u b l e sometimes t a k i n g cosmology s e r i o u s l y , I do r e g a r d t h e p u z z l e of t h e a b s e n c e of s t r o n g CP v i o l a - t i o n a s a v e r y s e r i o u s i s s u e r e g a r d i n g QCD. For t h e t i m e b e i n g , we must simply t a k e t h e v a l u e 6 = 0 a s a n i n p u t p a r a m e t e r .
With r e s p e c t t o a l l o t h e r symmetry c o n s i d e r a t i o n s , QCD f a r e s s p l e n d i d l y . Per- haps i t s most s i g n i f i c a n t achievement i s t h e v a l i d i t y of a l l of c u r r e n t a l g e b r a with- o u t n e c e s s i t a t i n g a l i g h t
n ' .
I w i l l n o t r e v i e w h e r e a l l t h e c o l o r and f l a v o r evidence.L CD depends on t h e s i x p a r a m e t e r s g ,
m,,
md, ms, mc and mb. I n p r i n c i p l e , s i x measur?ments would s u f f i c e t o d e t e r m i n e t h e s e p a r a m e t e r s , and t h e n we c o u l d c a l c u l a t e a l l o t h e r h a d r o n i c p r o p e r t i e s . I d e a l l y , c a l c u l a t i o n means more s c i e n c e t h a n a r t . That i s t o s a y , a QCD c a l c u l a t i o n s h o u l d b e r e p r o d u c i b l e even by t h e d u l l e s t t h e o r i s t , i n any c o r n e r of; t h e world. P e r h a p s some more fundamental t h e o r y w i l l e x p l a i n t h e v a l u e s of g and mi, b u t a t l e a s t QCD a l l o w s t h e i r p r e c i s e d e f i n i t i o n (no mean t a s ki n t h e p r e s e n c e of c o n f i n e m e n t ) .
Rough v a l u e s f o r t h e heavy q u a r k masses a r e e s s e n t i a l l y s e l f - e v i d e n t . Everyone a g r e e s t h a t mc = 1 . 6
+
. 3 GeV and mb.= 5.2+
.4 GeV. However, i n some s e n s e , mu, md<< A and ms -O(A), where A i s t h e d l m e n s i o n f u l p a r a m e t e r t h a t d e t e r m i n e s t h e s t r e n g t h of g. Hence, i n t e r a c t i o n s o b s c u r e t h e d i r e c t e f f e c t s of l i g h t q u a r k masses i n h a d r o n i c p h y s i c s , and c o n s e q u e n t l y , t h e i r v a l u e s a r e p o o r l y known ( i n r a t i o o r a b s o l u t e l y ) . E x c e l l e n t work i s b e i n g done t o p i n down t h e s e masses5 u s i n g d i s p e r s i o n r e l a t i o n t e c h n i q u e s , which a r e c u r r e n t l y r e f e r r e d t o a s ITEP sum r u l e s . A n a l y t i c i t y is u s e d t o connect a m p l i t u d e s t h a t we t h i n k a r e c a l c u l a b l e t o weighted i n t e g r a l s o v e r m e a s u r a b l e c r o s s s e c t i o n s . The same t e c h n i q u e s u n d e r l i e t h e a p p l i c a t i o n of QCD t o e'e- a n n i h i l a t i o n and s t r u c t u r e f u n c t i o n s c a l i n g . O f t e n , w i t h t h e s e d i s p e r s i o n r e l a t i o n s , a u t h o r s s n e a k i n a d d i t i o n a l a s s u m p t i o n s t o b e a b l e t o e x t r a c t more drama- t i c r e s u l t s . Although we a r e p r e s e n t l y s t r u g g l i n g j u s t t o d e t e r m i n e t h e l i g h t q u a r k masses, i d e a l l y t h e y s h o u l d b e over-determined, i . e . , we s h o u l d d e v e l o p s e v e r a l independent e x p e r i m e n t a l measures of t h e s e p a r a m e t e r s a s a way t o t e s t t h e t h e o r y . One p o s s i b i l i t y t h a t h a s o c c u r r e d t o me i s t o u s e a d e t a i l e d measurement of t h e par-
t i a l decay s p e c t r a i n h a d r o n i c r-decay. We s h o u l d t h i n k of y e t o t h e r p o s s i b i l i t i e s .
There a r e many new a p p l i c a t i o n s o f t h e ITEP sum r u l e t e c h n i q u e s , and t h e i r s u c c e s s i n comparison w i t h experiment i s i m p r e s s i v e . ~ a r ~ o n ~ and g l u e b a l l * masses and p i o n form f a c t o r s 9 a r e o n l y examples of what i s b e i n g done. T h i s i s a l l v e r y good work, b u t I want t o c a u t i o n h e r e t h a t t h e p a r t t h a t i s , s t r i c t l y s p e a k i n g , d e r i v e d from QCD is o f t e n n o t a s f l a s h y a s f i r s t a p p e a r s . The most f a m i l i a r example i s t h e e'e- a n n i h i l a t i o n spectrum. F i g . 2 shows a t h e o r i s t ' s r e n d e r i n g of t h e low energy d a t a .
1
+
-F i g . 2. I n R~ v s . E, i n t e g r a l s o v e r t h e r e s o n a n c e s r o u g h l y r e p r o d u c e t h e p a r t o n model.
CD p l u s d i s p e r s i o n r e l a t i o n s do n o t p r e d i c t R(E) b u t r a t h e r t h e smeared q u a n t i t y R(E') S(E-E'; A) dE', where S is a smearing f u n c t i o n of w i d t h A , c e n t e r e d a t E.
T h i s i n t e g r a l i s c a l c u l a b l e i f A and E a r e l a r g e enough. On t h e o t h e r hand, i t c o n t a i n s i n f o r m a t i o n about t h e r e s o n a n c e s i f A and E a r e s m a l l enough. I f o n e w a n t s t o e x t r a c t s u c h i n f o r m a t i o n , a compromise must b e r e a c h e d . One c a n "compute" mp and g p t o 1 0 % o n l y i f o n e assumes t h a t t h e r e i s a s i n g l e narrow r e s o n a n c e w i t h a n e g l i - g i b l e non-resonant background, t h e n a gap, and t h e n a h i g h energy continuum t h a t i s w e l l - d e s c r i b e d by p e r t u r b a t i o n t h e o r y .
The o n l y hadrons whose v e r y e x i s t e n c e we may p r e t e n d t o u n d e r s t a n d from f i r s t p r i n c i p l e s a r e t h e heavy q? bound s t a t e s . For heavy enough q u a r k s , a n o n - r e l a t i v i s - t i c p o t e n t i a l p i c t u r e s h o u l d b e a c c u r a t e f o r t h e ground s t a t e . Can we c a l c u l a t e t h e p a r t of t h e p o t e n t i a l r e l e v a n t t o t h e observed onium s t a t e s ? It s h o u l d t a k e t h e form
1 2 3
V(r)
-7
x l o g ' s+
( 0I
FI
0 ) r. . .
where t h e l o g ' s a r e c a l c u l a b l e i n p e r t u r b a t i o n t h e o r y and t h e n o n - p e r t u r b a t i v e q u a n t i t y ( F ~ ) c a n b e e x t r a c t e d from t h e ITEP a n a l y s i s . 6 A r e c e n t e f f o r t i n t h i s d i r e c t i o n l o (whose d e t a i l s I s t i l l d o n o t u n d e r s t a n d ) comes v e r y c l o s e t o r e p r o - d u c i n g t h e phenomenologically s u c c e s s f u l ad hoc p o t e n t i a l s .
I b e l i e v e t h a t t h e c u r r e n t l y most promising a r e a of c o n f r o n t a t i o n of QCD w i t h experiment is v i a l a t t i c e Monte C a r l o c a l c u l a t i o n s . C a l c u l a t i o n s l 2 of masses of qq, qqq and g l u e b a l l s t a t e s have been r e p o r t e d , and mixing s h o u l d b e s i m i l a r l y c a l c u l a b l e . P e o p l e have a l s o computed t h e baryon magnetic moments.12 A l l of t h e s e c a l c u l a t i o n s a r e r e p o r t e d t o b e good t o 20 i f n o t 10%. With t h e same t e c h n i q u e s , o n e s h o u l d b e a b l e t o compute g ~ and a l s o t h e i n e l a s t i c s t r u c t u r e f u n c t i o n s , i n c l u d i n g h i g h e r t w i s t c o n t r i b u t i o n s . A l l of t h e s e c a l c u l a t i o n s proceed i n p r i n c i - p l e from f i r s t p r i n c i p l e s . The o u t s t a n d i n g q u e s t i o n i s whether t h e y can b e t r u s t e d . The o p t i m i s t s ' answer i s y e s , c l a i m i n g t h a t t h e s e f i r s t r e s u l t s c a n b e s y s t e m a t i c a l - l y improved i f we are j u s t w i l l i n g t o do more work ( b o t h n u m e r i c a l and a n a l y t i c ) . 1 3 The p e s s i m i s t s s a y no; a l l of t h e e x i s t i n g r e s u l t s a r e p u r e l a t t i c e a r t i f a c t s , and we a r e n o t y e t s e e i n g a n y t h i n g r e l a t e d t o t h e continuum t h e o r y . One v e r s i o n of t h i s p o i n t of view14 c l a i m s t h a t a l l c u r r e n t c a l c u l a t i o n s may b e dominated by a n e a r b y
C3-662 JOURNAL DE PHYSIQUE
p h a s e t r a n s i t i o n t h a t i s a t o t a l l y c r y s t a l l i n e phenomenon, and o n l y a much f i n e r l a t t i c e g r i d would g e n u i n e l y p r o b e t h e approach t o t h e continum t h e o r y . F i g u r e 3 i l l u s t r a t e s how t h i s would a p p e a r i n t h e Monte C a r l o d a t a .
QCD
ca\cu\ab\e
s\ope
\
\'
pessimist
Yk
F i g . 3 . Monte C a r l o d a t a d e t e r m i n e s t h e i n t e r c e p t of t h e go + 0 envelope. O p t i m i s t s and p e s s i m i s t s d i f f e r on f u t u r e p r o j e c t i o n s .
I p l o t t h e l o g o f some p h y s i c a l mass b e i n g c a l c u l a t e d v e r s u s
llg; ,
where g i s t h e b a r e c o u p l i n g . Asymptotic freedom i m p l i e s t h a t we r e a c h continuum p h y s i c sgy
t a k i n g go -t 0. The Monte C a r l o d a t a , shown i n s o l i d l i n e s , which a l s o have t h e i r own l a r g e s t a t i s t i c a l e r r o r s , e x i s t o v e r a l i m i t e d r a n g e i n g$.
I n f a c t it is o n l y t h e lower e n v e l o p e o f t h e s e c u r v e s t h a t we c a n e x p e c t t o e x t r a p o l a t e t o go = 0 t o g e t t h e p h y s i c a l mass. However, we know from p e r t u r b a t i o n t h e o r y t h a t t h e a s y m p t o t i c form of t h i s e n v e l o p e is a s t r a i g h t l i n e , and we c a n compute i t s s l o p e a n a l y t i c a l l y . So t h e r o l e of t h e Monte C a r l o c a l c u l a t i o n i s t o d e t e r m i n e i t s i n t e r c e p t . The so- c a l l e d r a p i d c r o s s o v e r i s t h e phenomenon t h a t t h e f l a t go =..
r e g i o n r a p i d l y t u r n s o v e r i n t o a r e g i o n w i t h a p p a r e n t l y t h e r i g h t a s y m p t o t i c s l o p e . O p t i m i s t s b e l i e v e t h a t y e t more e x t e n s i v e c a l c u l a t i o n s w i l l l i e a l o n g t h e same l i n e w h i l e p e s s i m i s t s s e e no r e a s o n t o r u l e o u t some o t h e r b e h a v i o r .I now t u r n t o " p e r t u r b a t i v e " QCD ( a l t h o u g h I l i k e t o emphasize t h a t t h e r e i s o n l y o n e QCD i n t h e end). A modest and c o n s e r v a t i v e a p p r o a c h is t h e f o l l o w i n g . L g i m p l i e s t h a t , a s Q~ ~ ~ +
,
g ( ~ 2 ) -+ 0 . T h i s i n t u r n a l l o w s u s t o j u s t i f y a c r t a i n t y p e of p a r t o n model f o r c e r t a i n p r o c e s s e s w i t h c e r t a i n t y p e s of c o r r e c t i o n s t h a t we c a n e s t i m a t e . The p r o p e r t y of a s y m p t o t i c freedom i s e s s e n t i a l l y u n i q u e t o QCD. (Note t h a t we c a n n o t h a v e a c o n s i s t e n t t h e o r y w i t h o n l y s c a l a r p e r t u r b a t i v e g l u o n s , and, w h i l e we can imagine s o - c a l l e d f i x e d p o i n t t h e o r i e s , no o n e knows how t o compute any of t h e i r p r o p e r t i e s . Hence, a s a l t e r n a t i v e s t o QCD t h e s e a r e o n l y p a p e r t i g e r s . )W e d o o b s e r v e t h i s p a r t o n - l i k e b e h a v i o r i n a wide v a r i e t y of c i r c u m s t a n c e s . These i n c l u d e l e p t o p r o d u c t i o n ; y-pair p r o d u c t i o n ; e+e- + x, j e t s , and h
+
x; andh a d r o n s and j e t s a t l a r g e PL i n hadron-hadron c o l l i s i o n s . Regarding t h e l a t t e r , a t t h i s c o n f e r e n c e we have h e a r d d r a m a t i c new r e s u l t s of a q u a l i t a t i v e t y p e from t h e CERN SPS c o l l i d e r and i n q u a n t i t a t i v e d e t a i l from t h e ISR. ( F i g u r e 4 shows t h e momentum f l o w from a n a p p r o p r i a t e l y t r i g g e r e d 1 5 e v e n t i n pp a t
&
= 63 GeV.)QCD could have f a i l e d a t t h i s l e v e l , b u t i t h a s n ' t . A l l t h e A ' s t h a t people d e r i v e from QCD f i t s a r e r e a l , p p s i t i v e , and l e s s t h a n 2 GeV.
And a l l t h e ad hoc phenomenological f i x e s a r e of p l a u s i b l e magnitude, e.g., i n t r i n s i c kL's of O(500 MeV).
Even on t h i s q u a l i t a t i v e l e v e l , t h e r e e x i s t s a t p r e s e n t a h o t theo- r e t i c a l c o n t r o v e r s y . Does QCD a c t u a l l y imply a p a r t o n p i c t u r e f o r hadron
+
hadron hard p r o c e s s e s ? A t i s s u e i s t h e same q u e s t i o n t h a t was r a i s e d a g a i n s t t h e o r i g i n a l D r e l l - Yan p i c t u r e . Can s p e c t a t o r i n t e r - a c t i o n s s p o i l t h e simple impulse c a l c u l a t i o n s ? One o p i n i o n i s t h a t , indeed, s o f t i n t e r a c t i o n s w i t h s p e c t a t o r s produce important e f f e c t s which we c a n only q u a l i t a t i v e l y guess. l6 Only a t super-duper Q~might t h e p a r t o n p i c t u r e be recov-
F i g . 4. The momentum flow of a s u i t a b l y ered. Another group h a s argued
t e c h n i c a l l y from a n a l y t i c i t y con- t r i g g e r e d event1' i n pp a t s i d e r a t i o n s and a u a l i t a t i v e l v from
6
= 63 GeV.c a u s a l i t y t h a t t h e impulse p i c t u r e
must b e c o r r e c t . l 7 They allow, however, t h a t t h e s t r u c t u r e f u n c t i o n s and hard s c a t t e r i n g amplitudes might b e s l i g h t l y more complicated t h a n we have imagined i n t h e p a s t . A t h i r d group d i d a n e x p l i c i t c a l c u l a t i o n i n a s i m p l i f i e d model t h a t was s u f f i c i e n t l y r e a l i s t i c t o probe t h i s i s s u e . While s p e c i f i c Feynman diagrams showed t h e f e a r e d d i s e a s e s , t h e complete sum gave a t o t a l c a n c e l l a t i o n of non-parton model e f f e c t s . l 8 I n t h e r e s o l u t i o n of t h i s c o n t r o v e r s y , it w i l l b e e s s e n t i a l t o sum s i m i l a r l y over a l l e f f e c t s because t h e n a s t y c u l p r i t s a r e s o f t exchanges. Although we draw Feynman diagrams showing s o f t gluons a s going from one p l a c e t o a n o t h e r , only a complete sum c h a r a c t e r i z e s t h e s o f t p h y s i c s which by d e f i n i t i o n t a k e s p l a c e i n d i s c r i m i n a t e l y over t h e whole a v a i l a b l e space-time. S e t t l i n g t h i s c o n t r o v e r s y , now perhaps f o r t h e l a s t time, i s of utmost importance. The i s s u e i s f a r more fundamental t h a n K-factors, schemes, s o f t gluon c o r r e c t i o n s , l e a d i n g double l o g s , h i g h e r t w i s t , o r h a d r o n i z a t i o n Monte Carlos. A t i s s u e i s t h e v e r y a p p l i c a b i l i t y of t h e p a r t o n p i c t u r e t o any p r o c e s s i n i t i a t e d by c o l l i d i n g hadrons.
I n t h e f u t u r e , we can l o o k forward t o f u r t h e r confirmation of t h e q u a l t t a t i v e ( i . e . , good t o 50-100%)
re dictions
of QCD t h a t come e s s e n t i a l l y from t r e e graphs.I t h i n k we should be c o n t e n t t o s t o p h e r e . I f w e had good t a s t e , we c e r t a i n l y would!
But some people say t h a t what i s s p e c i a l about QCD i s p r e c i s e l y t h e p e r t u r b a t i v e c o r r e c t i o n s a t h i g h e n e r g i e s . We should study t h e s e i n d e t a i l and t e s t QCD. From t h i s p e r s p e c t i v e , e v e r y t h i n g i s f o r t h e most p a r t okay. But s i n c e t h e r e a r e s e v e r a l r e p e n t e x c e l l e n t reviews, l9 I w i l l c o n c e n t r a t e h e r e on what I view a s t h e o u t s t a n d i n g problems.
The f i r s t problem i s t h e so-called scheme dependence of p e r t u r b a t i v e predic- t i o n s . T h i s i s a boring s u b j e c t , but numerically i t i s c r u c i a l . I say i t i s boring because t h e scheme dependence is always f o r m a l l y y e t one o r d e r h i g h e r t h a n t h e e x i s t i n g c a l c u l a t i o n . Compute a n o t h e r o r d e r , and t h e scheme dependence of t h e calcu- l a t i o n becomes f o r m a l l y s m a l l e r . D i f f e r e n t schemes embody d i f f e r e n t g u e s s e s about t h e a s y e t u n c a l c u l a t e d h i g h e r o r d e r s . We u s e i n t u i t i o n , e x p e r i e n c e , and common s e n s e t o make t h e s e guesses. Where "reasonable" people a g r e e , we a r e probably reasonably s a f e . But s i g n i f i c a n t disagreement l i k e l y s i g n a l s t h a t y e t h i g h e r o r d e r s might b e important. The following c a s e i s c u r r e n t l y a p o i n t of c o n t e n t i o n among t h e o r i s t s . Consider t h e T decay widths
JOURNAL DE PHYSIQUE
The parameters
X
and B a r e scheme-dependent. Armed w i t h an a p r i o r 1 philosophy f o r choosing a scheme, one can t h e n go ahead and compute X and B. Some e x p e r t s have t h e n concluded t h a t T decay i s v i r t u a l l y u s e l e s s f o r determining as20 because t h e p r o p e r l y determined B i s s o l a r g e , w h i l e o t h e r s i n s i s t t h a t t h i s is v i r t u a l l y t h e b e s t p r o c e s s f o r determining a,. T h i s , however, i s t h e p r o c e s s where disagreement i s g r e a t e s t . For many o t h e r c a s e s , t h e q u a l i t a t i v e agreement of d i f f e r e n tapproachesz2 i s encouraging.
There a r e p r o c e s s e s f o r which l a r g e r a d i a t i v e c o r r e c t i o n s a r e agreed upon by everyone. T y p i c a l l y t h e s e i n v o l v e t h e edges of phase space, such a s x ' s + 1,
qi
<< q2 i n u-pair production, o r t h e q u a s i - e l a s t i c u-pair K-factor. Such c o r r e c -t i o n s a r e due in l a r g e p a r t t o what a r e c a l l e d " s o f t gluons." There e x i s t many o l d and a v a r i e t y of new t e c h n i q u e s f o r summing t h e e f f e c t s of a l l numbers of s o f t gluons i n c e r t a i n approximations.23'24 Of t h e s e , I would s i n g l e o u t r e f e r e n c e 23 a s having fundamentally improved our understanding of t h e s t r u c t u r e of t h e QCD p a r t o n model. There a r e r e l a t e d a p p l i c a t i o n s of summing s o f t gluons where t h e d i r e c t a p p l i c a t i o n of p e r t u r b a t i o n t h e o r y i s obviously i n a p p r o p r i a t e from t h e s t a r t . These i n c l u d e t h e q u e s t i o n s of m u l t i p l i c i t y 2 5 and t h e Regge l i m i t . 2 6
However, I have a g e n e r a l complaint r e g a r d i n g summing s o f t gluons. The one t h i n g t h a t we do understand about QCD i s asymptotic freedom. And t h a t i m p l i e s t h a t t h e s o f t r e g i o n cannot b e a d e q u a t e l y d e s c r i b e d by p e r t u r b a t i v e concepts, even i f p e r t u r b a t i o n t h e o r y i s summed t o a l l o r d e r s . The s t a n d a r d example i s t h a t a l l dimensionful hadronic q u a n t i t i e s must b e p r o p o r t i o n a l t o e ~ ~ ( - l / ~ ~ ) whose power s e r i e s expansion i s 0
+ og2 + og4 + . . . .
Admittedly, i n some a p p l i c a t i o n s t h e s o f t gluons a r e only r e l a t i v e l y s o f t . For example, i n producing a u-pair of momentum q ,qp
( p e r p e n d i c u l a r r e l a t i v e t o t h e hadron c o l l i s i o n a x i s ) s e t s t h e s c a l e of s o f t n e s s of gluons summed by t y p i c a l schemes. But t h e s e schemes a r e v a l i d o n l y i n t h e l i m i t l o g q 2 >> l o g q: >> l o gn2.
We have a hard enough time s a t i s f y i n g one such inequal- i t y . Hence, t h i s double l i m i t i s experimentally v i r t u a l l y i n a c ~ e s s i b l e . ~ ~I come now t o a c r i t i q u e of t h e QCD a n a l y s e s of l e p t o p r o d u c t i o n and t h e j e t s and energy flow of e'e- a n n i h i l a t i o n . Analogous comments would apply t o a l l o t h e r a p p l i c a t i o n s of p e r t u r b a t i v e QCD, where t h e same i s s u e s a r i s e . I choose t h e s e two a r e a s because t h e y have been t h e s u b j e c t s of t h e most e x t e n s i v e study.
Regarding l e p t o p r o d u c t i o n , t h e r e a r e a v a r i e t y of t r i v i a l problems t h a t con- t i n u e t o plague a n a l y s e s , b u t I w i l l n o t d w e l l on them i n d e t a i l . These i n c l u d e 10-15% d i s c r e p a n c i e s between experiments, i g n o r i n g gluonsz8 ( i . e . , u s i n g non- s i n g u l a r e v o l u t i o n where s i n g l e t p i e c e s should be i n c l u d e d ) , assuming random v a l u e s f o r o,/cl,, i g n o r i n g quark mass e f f e c t s , 2 9 and n o t d i s t i n g u i s h i n g between d e f i n i t i o n s of A.
While any of t h e above could b e remedied w i t h some c a r e , t h e r e a l l y s e r i o u s i s s u e which plagues l e p t o p r o d u c t i o n a n a l y s e s is t h e u n c e r t a i n t y due t o "higher t w i s t , " which a r e t h e power suppressed c o n t r i b u t i o n s t o s c a l i n g v i o l a t i o n s . Tn g e n e r a l we expect f o r some s t r u c t u r e f u n c t i o n F t h a t
-
-
p e r t u r b a t i v e l o g ' s+ 3
1 f ( x , l o g Q 2 )+
0 (T) 1.
Q
0Q
There i s wide agreement t h a t t h e d a t a r e q u i r e t h e power terms and t h a t t h e l o g ' s a l o n e a r e n o t enough. Such a conclusion i s p o s s i b l e because we know a l o t about t h e allowed form of t h e l o g a r i t h m i c terms. However, n e i t h e r t h e s i g n nor t h e shape i n x of t h e h i g h e r t w i s t f ( x , l o g Q ~ ) can b e determined p e r t u r b a t i v e l y ( d e s p i t e a l l claims t o t h e c o n t r a r y ) . But we have n o t h i n g n e a r t o t h e s t a t i s t i c a l p r e c i s i o n needed t o determine f ( x , l o g Q ~ ) from t h e d a t a . Hence, it i s p o s s i b l e t o f i t t h e observed s c a l i n g v i o l a t i o n s p u r e l y w i t h s u i t a b l y chosen 1 /and ~ 1~ /terms and t h e n ~ ~
g e t A=O. O r one can g e t a f a i r l y s u b s t a n t i a l A w i t h v e r y s m a l l h i g h e r t w i s t terms.
Allowing n e g a t i v e higher t w i s t terms n a t u r a l l y improves t h e
x2
of a f i t by genera- l i z i n g t h e form of t h e allowed f u n c t i o n s . It a l s o i n c r e a s e s t h e deduced v a l u e of A--
t o a s high a s 400 MeV i n a r e c e n t a n a l y s i s . 30 So it i s probably r e a s o n a b l e t o conclude t h a t A = 200+
200 MeV. One can a l s o d r a s t i c a l l y a l t e r t h e 1 / Q 2 a n a l y s i s by allowing f o r a t i n y amount of hard i n i t i a l charm.31 The amount of i n i t i a l c quarks involved h e r e i s t o o small t o be t h e o r e t i c a l l y o f f e n s i v e and a t t o o l a r g e a n x t o b e d e t e c t e d i n e x i s t i n g muon s c a t t e r i n g experiments which look f o r a second 11 from charm decay.There i s , perhaps, some hope of untangling t h i s e v e n t u a l l y . The s t r u c t u r e of h i g h e r t w i s t terms i n l e p t o p r o d u c t i o n has t h e same g e n e r a l form a s t h e l e a d i n g term, i . e . ,
h i g h e r t w i s t = C hard s c a t t e r i n g @ s o f t p a r t .
We have known i n p r i n c i p l e how t o compute t h e hard p a r t f o r some time, although only r e c e n t l y have people begun t o study it e x p l i c i t l y . 32' 337 34 The s o f t p a r t i s in- h e r e n t l y non-perturbative. It has been estimated w i t h i n t h e MIT bag though I would c a u t i o n that t h e bag i s n o t , s t r i c t l y speaking, QCD, and t h e d i f f e r e n c e s w i l l l i k e l y be even more apparent a s we go t o h i g h e r t w i s t . I n p r i n c i p l e , we could deduce t h e s o f t p a r t by comparing l o t s of d a t a , i n c l u d i n g , perhaps someday,
d i f f e r e n t p r o c e s s e s (each w i t h t h e i r own process-dependent hard p a r t s ) . The a t t e m p t t o extend t h e l e p t o p r o d u c t i o n higher t w i s t expansion t o o t h e r hard processes i s c u r r e n t l y under a c t i v e It might work ( l i k e l y t o t h e 1 /l e v e l ) , ~ ~ b u t it might n o t . The p o t e n t i a l o b s t a c l e s a r e t h e analogs of t h e t r o u b l e s encoun- t e r e d i n hadron-hadron p r o c e s s e s and some a l r e a d y i d e n t i f i e d p e c u l i a r i t i e s a t t h e m2/Q2 The physics of higher t w i s t i n c l u d e s
rimo or dial
k,, diquarks, quark- gluons ( t h e analogous multi-parton systems), o f f - s h e l l n e s s , i n t e r f e r e n c e , and f i n a l s t a t e i n t e r a c t i o n s . A s a t i s f a c t o r y r e s o l u t i o n of t h e i s s u e must d e a l w i t h a l l of t h e s e .I would l i k e t o mention t h e Brodsky, Berger, Blankenbecler school of higher t w i s t , which, w h i l e n o t s t r i c t l y QCD under my narrow d e f i n i t i o n , has l e d t o some v e r y i n t e r e s t i n g suggestions. 37 They advocate e s t i m a t i n g t h e l e a d i n g
l / q 2
p i e c e s i n t h e kinematic r e g i o n s where they a r e expected t o dominate t h e s c a l i n g behavior, e.g., a s x ' s + 1, and doing experiments s p e c i f i c a l l y designed t o probe t h e s e r e g i o n s . While t h e t h e o r e t i c a l e s t i m a t e s may have some shortcomings, t h e proposed experiments a r e i n t e r e s t i n g . For example, they suggest v e t o t r i g g e r s such a s i n .rr+
A + B+
X+
(no r beam fragments) a s a way t o ensure t h a t both quarks i n t h e+
a r e a c t i v e i n t h e hard s c a t t e r i n g .The only p l a ~ e - w h e r e h i g h e r t w i s t c o n t r i b u t i o n s a r e t h e o r e t i c a l l y under c o n t r o l i s i n t h e t o t a l e e c r o s s s e c t i o n . There we know t h a t
The "=It s i g n i s a reminder of t h e l a r g e w e a r i n g necessary
f a r
c-paring t h e d a t aand t h e theory. The s o f t p a r t of A can b e estimated from t h e ITEF chamr~nium a n a l y s i s , which g i v e s A
-
(400 M ~ v ) ~ . Even a 100% u n c e r t a h t p would still l e a y e t h e s e a s n e g l i g i b l e c o r r e c t i o n s t o t h e l e a d i n g p a r t . R e g r e t t a b l y , even t h e r e c e n t 5% measurements of R+ -
l e a d t o only a v e r y crude measure of a.
e e
There i s a d i r e c t analog of h i g h e r t w i s t when we attempt t o study p r o p e r t i e s of t h e hadronic f i n a l s t a t e i n e+e- a n n i h i l a t i o n , such a s i n c l u s i v e p a r t i c l e d i s t r i b u - t i o n s , j e t s , and energy flow. A t some f u t u r e d a t e t h e a n a l y s i s of r e f e r e n c e 34 might be g e n e r a l i z e d t o i n c l u d e t h i s s i t u a t i o n (although a method f o r t h e c a l c u l a - t i o n of energy flow parameters is f a r from obvious). At p r e s e n t , a l l a n a l y s e s r e l y h e a v i l y on what a r e c a l l e d h a d r o n i z a t i o n Monte Carlos t o add non-scaling c o r r e c t i o n s t o t h e p e r t u r b a t i v e QCD c a l c u l a t i o n s s o t h a t they t h e n a t l e a s t resemble t h e d a t a .
C3-666 JOURNAL DE PHYSIQUE
I want t o emphasize t h a t t h e e x i s t i n g h a d r o n i z a t i o n schemes have n o t h i n g t o do w i t h QCD, w i t h f i e l d t h e o r y , o r even w i t h quantum mechanics. They embody p u r e l y c l a s s i c a l p i c t u r e s of how t h e f i n a l hadrons might be produced from t h e i n i t i a l quarks and gluons. D i f f e r e n t Monte Carlos must b e expected i n p r i n c i p l e t o g i v e d i f f e r e n t answers f o r t h e u n d e r l y i n g QCD parameters i n any a n a l y s i s i n which t h e Q~
i s such t h a t doing t h e Monte Carlo a t a l l i s important i n t h e f i r s t p l a c e . Such a p o s s i b i l i t y h a s f i n a l l y been recognized by one of t h e groups a t PETRA, who r e p o r t e x t r a c t i n g an a, from t h r e e j e t e v e n t s u s i n g t h e Lund-string h a d r o n i z a t i o n t h a t i s roughly 50% b i g e r t h a n t h a t e x t r a c t e d from t h e same d a t a u s i n g t h e Hoyer-Feynman- F i e l d scheme.38 I w i l l n o t a r g u e whether t h e y a r e c o r r e c t i n d e t a i l o r n o t , b u t c e r t a i n l y such a n e f f e c t i s p o s s i b l e . A s i m i l a r r e s u l t was r e p o r t e d elsewhere,3y w i t h a s t r i n g - i s h h a d r o n i z a t i o n t h a t i s r a t h e r c l o s e r t o QCD g i v i n g a A "1.4 GeV u s i n g e+e- d a t a . We could c e r t a i n l y make up y e t more e q u a l l y p l a u s i b l e schemes, which would no doubt g i v e y e t o t h e r r e s u l t s f o r as.
The p e r t u r b a t i v e c a l c u l a t i o n s should d e f i n i t e l y be v a l i d a s Q~ +
,
and a l l t h e s e h a d r o n i z a t i o n e f f e c t s w i l l e v e n t u a l l y become n e g l i g i b l e . The r e a s o n t h a t t h e y a r e s o important i n t h e momentum f l o w s t u d i e s of e x i s t i n g experiments is, however, s i m p l e t o understand. The momentum flows where t h e hadrons go, and t h e hadron d i r e c - t i o n s r e f l e c t P+/P,,,
where PA and P,, a r e t h e i n d i v i d u a l hadron's moments perpendi- c u l a r and p a r a l l e l t o i t s p a r e n t quark o r gluon momentum. P, is roughly l i m i t e d by A,
but P,, i s t h e momentum p e r hadron, which i s no way n e a r t h e t o t a l e+e- energy.D e s p i t e c l a i m s of how o u r understanding h a s grown, t h e o r e t i c a l e f f o r t s i n "non- p e r t u r b a t i v e " p h y s i c s have shed no l i g h t , n o t even q u a l i t a t i v e l y , on how hadrons a r e produced. So f o r t h e p r e s e n t , we must acknowledge t h a t any q u a l i t y s e n s i t i v e t o doing a h a d r o n i z a t i o n Monte Carlo i n t h e f i r s t p l a c e can o n l y be determined v e r y c r u d e l y . And I know of no a p p l i c a t i o n s of p e r t u r b a t i v e QCD i n which our ignorance of t h e quark-hadron c o n n e c t i o n does n o t g e t i n t h e way of p r e c i s i o n t e s t s a t c u r r e n t e n e r g i e s of our p e r t u r b a t i v e c a l c u l a t i o n s . However, q u a l i t a t i v e t e s t s a r e t e s t s n e v e r t h e l e s s , and t h e s u c c e s s e s a r e b o t h impressive and v e r y u s e f u l f o r doing o t h e r physics.
I r e t u r n a t l a s t t o Maupertuis, whose w r i t i n g s I perused t o t r y t o reaccivqtle my French. I came a c r o s s t h e f o l l o w i n g passage, which remained i n my mind a s somehow very 3 propos. He wrote:40
"L'Etre supr6me e s t ? a r t o u t ; mais il n ' e s t pas par t o u t 6galement v i s i b l e . Nous l e v e r r o n s mieux dans l e s o b j e t s l e s p l u s s i m p l e s : cherchons-le dans l e s p r e m i s r e s l o i x q u ' i l a imposdesl l a Nature; dans c e s r s g l e s u n i v e r s e l l e s , s e l o n l e s q u e l l e s l e Mouvement s e conserve, s e d i s t r i b u e , ou s e d 6 t r u i t ; e t n o n pas dans d e s PhdnomSnes q u i n e s o n t que d e s s u i t e s t r o p compliqu6es d e c e s l o i x .
I o f f e r t h e f o l l o w i n g p a r a p h r a s e (allowing t h a t r e f e r e n c e t o t h e supreme Being i s no l o n g e r common i n everyday p h y s i c s d i s c u s s i o n ) :
The laws of n a t u r e a r e manifested everywhere but n o t a s c l e a r l y i n some s i t u a t i o n s a s i n o t h e r s . We should s e e k them o u t through t h e i r s i m p l e s t manifesta- t i o n s and n o t p i s s around t r y i n g t o u n t a n g l e them from t h e i r most complicated consequences.
References
( C o n t r i b u t i o n s t o t h e XXI I n t e r n a t i o n a l Conference on High Energy P h y s l c s a r e r e f e r e n c e d by number, IOXXX.)
1. R. P e c c e i and H. Quinn, Phys. Rw. L e t t . 38, 1440 (19771,
2 . J . Cavaignac e t a l . , 1k0755; H, F a l s s n e r , I n P r o c e e d i n g s of tIie Lepton and Photon I n t e r a c t i o n s , Bonn, 1981.
3. M. Dine, W. F i s c h l e r and M. S r e d n i c k i , Phys. L e t t .
E ,
199 (1981).4. L. Abbott, P. S i k i v i e , J. P r e s k i l l , F. Wilczek, and M. Wise, t o b e p u b l i s h e d . 5. S. Narison e t a l . , /10259, 60839, (10849; C. Becchi, S. N a r i s o n , E. d e R a f a e l , and
F. Yndurain, Z . Phys.
2,
335 (1981).6. M. Shifman, A. V a i n s h t e i n , and V. Zakharov, Nucl. Phys.
w ,
385 (1979).7. V. Belyaev and B. I o f f e , ITEP p r e p r i n t ITEP-59-1982.
8. V. Novikov e t a l . , Acta Phys. P o l .
G,
399 (1981).9. B. I o f f e and A. Smylga, i1 0889; V. Nesterenko and A. Radyushkin, ~ 2 - 8 2 - 2 0 4 ; V. Chernyak and A. Z h i t n i t s k y , 81-74, 75, 76 N o v o s i b i r s k p r e p r i n t s ; N. C r a i g i e and J. S t e r n , #0270.
1 0 . C. F l o r y , Phys. L e t t .
H,
263 (1982).11. H. Hamber and G. P a r i s i , Phys. Rev. L e t t .
5,
1792 (1981); D. Weingarten, Phys. L e t t .m,
57 (1982).12. F. F u c i t o e t a l . , CERN p r e p r i n t CERN-TH-3288 (1982).
13. K. Symanzik, DESY p r e p r i n t DESY 811068 (1981).
14. G. Bhanot and R. Dashen, Phys. L e t t .
E,
299 (1982).1 5 . CDHW C o l l a b o r a t i o n , 10836, /10837, 110838.
16. G. Bodwin, S. Brodsky and P. Lepage, Phys. Rev. L e t t .
2,
1799 (1981); A. Mueller Phys. L e t t .H,
355 (1982).17. J. C o l l i n s , D. Soper and G. Sterman, ITP-SB-81-59, ITP SUNY Stony Brook p r e p r i n t . 18. W. Lindsay, D. Ross, and C . S a c h r a j d a , Southampton p r e p r i n t SHEP-81182-4 (1982).
19. e.g. A. Buras, P r o c e e d i n g s of Lepton and Photon I n t e r a c t i o n s , Bonn 1981.
20. S. Brodsky, P. Lepage, and P. Mackenzie, 110781.
21. P. Stevenson, i10123, 60124; G. Grunberg, il0844, 10896.
22. W. Celmaster and D. S i v e r s , Phys. Rev.
g,
227 (1981); A. Blumenfeld and M. Moshe, i10336.23. J. C o l l i n s and D. S o p e r , Nucl. Phys.
m,
3 8 1 (1981); Nucl. Phys.w,
445(1982).
24. R. K i r s c h n e r and L. L i p a t o v , /10378; A. Contogouris, S. Papadopoulos, and 5 . R a l s t o n , 10171, il0172; S. Mukhi and G. S t e m a n , ITP-SB-81-30, ITP SUNY Stony Brook p r e p r i n t ; J. R a l s t o n and B. P i r e , (10231, il0232; K. Lewin, 110501;
Y . D o k s h i t z e r , V. F a d i n , and V. Khoze, Leningrad p r e p r i n t LENINGRAD-82-745 (1982); G. Bordes and A. N i c o l i a d e s , 110869; P. C h i p e t t a et a l . , il0536.
25. A. B a s s e t t o , M. C a i f a l o n i , G. M a r c h e s i n i and A. N u e l l e r , XFUF 8 2 / 1 1 F i r e n z e p r e p r i n t .
26. A. White, 1 9 8 1 R e n c o n t r e d e Moriond ; T o p i c a l Conference on Forward C o l l i d e r P h y s i c s , Madison, 1981.
C3-668 JOURNAL DE PHYSIQUE
27. S. E l l i s , N. F l e i s h o n a n d W. S t e r l i n g , Phys. Rev.
e,
1386 (1981);J. Kodaira and L. T r e n t a d u e , SLAC p r e p r i n t SLAC-PUB-2862 (1981).
28. R. M. B a r n e t t and D. S c h l a t t e r , SLAC-PUB-2883, SLAC p r e p r i n t . 29. D. S h i r k o v , f10433.
30. F. E i s e l e e t a l . , Phys. Rev.
G,
4 1 (1982).31. R. Godbole and D. P . Roy, i'l 0158.
32. R. J a f f e and M. S o l d a t e , Phys. Rev.
g ,
49 (1982).33. E. Shuryak and A. V a i n s t e i n , i110110, #0111.
34. R. K. E l l i s , W. Furmanski and R. P e t r o n z i o , 1'10744; Ref. TH 3254 CERN p r e p r i n t . 35. A. Efremov and A. Radyushkin, c o n t r i b u t i o n t o t h e XX I n t e r n a t i o n a l Conference
o n High Energy P h y s i c s , Madison, 1980.
36. R. D o r i a , J. F r e n k e l and J. C. T a y l o r , Nucl. Phys.
w,
93 (1980); B. B a n e r j e e , A. C h a t t e r j e e and M. Sengupta, #0366.37. E. Berger, f10454, ANL-HEP-PR-81-51 Argonne p r e p r i n t ; S. Matsuda, 10030, i10031, KEK TH 37 KEK p r e p r i n t ; J. Bagger and J. Guinion, UCD 8113 UC Davis p r e p r i n t ; J. Gunion, P. Nason, and R. B l a n k e n b e c l e r , f0506.
38. CELLO C o l l a b o r a t i o n , i10555.
39. R. F i e l d and S. Wolfram, CALT 68-909 C a l t e c h p r e p r i n t .
40. P. L. M. d e M a u p e r t u i s , Les Loix de Mouvement e t d e Repos, 1746.
Acknowledgement. T h i s work s u p p o r t e d i n p a r t by t h e U.S. Department of Energy u n d e r C o n t r a c t No. DE-AC03-81ER40050.
D i s c u s s i o n
S. DRELL (SLAC).
-
Following on the disnission at Bonn last gear would you say that there is now any evidence that the strong QCD coupling constant runs according to asymptotic freedom with Q~ ?You are referring to the arguments based on the energy flow as a function of opening angle.
D.
POL1TZLR.-
Myanswer i s no. I t h i n k the analysis presented a t the Bonn conference was f a r too naive. The running of us i s i t s e l f o(a2). On t h e same page of the Bonn proceedings where the running of
a,i s prese ted, &other f i g u r e shows t h a t h
asmust be varied by over l o % , i.e. O(a), a t fixed t o f i t the data used in the running analysis. Also the of the analysis goes from
0.5t o
5GeV where various corrections are certain1 y important.
T.N. TRUONG (EcoZe Polytechnique).- Would you elaborate how the quark masses can be detemnined from e decay ?
D.
