PHOTON-PHOTON COLLISIONS

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PHOTON-PHOTON COLLISIONS

D. Burke

To cite this version:

D. Burke. PHOTON-PHOTON COLLISIONS. Journal de Physique Colloques, 1982, 43 (C3), pp.C3-

513-C3-524. �10.1051/jphyscol:1982373�. �jpa-00221928�

JOURNAL DE PHYSIQUE

Colloque CZ, supplément au n° 12, Tome 43, décembre 1982 page C3-513

PHOTON-PHOTON COLLISIONS*

D. L. Burke

Stanford Linear- Accelerator Center, Stanford University, Stanford, California 94205, U.S.A.

Sommaire — Des études des collisions photon-photon sont revues avec une attention particulière donnée aux résultats nouveaux présentés â cette conférence. Ceux-ci incluent des résultats sur la spectroscopie des mësons légers et sur la diffusion inélastique profonde électron-photon. Un travail considérable a été jusqu'à maintenant accompli sur la production de résonances dans les collisions yy.

Des études préliminaires, à grandes statistiques, de la fonction de structure du photon F 2 ( X , Q 2 ) sont présentées et des commentaires sont faits sur les problèmes qu'il reste â résoudre.

Abstract — Studies of photon-photon collisions are reviewed with par- ticular emphasis on new results reported to this conference. These include results on light meson spectroscopy and deep inelastic ey scat- tering. Considerable work has now been accumulated on resonance produc- tion by Y Y collisions. Preliminary high statistics studies of the photon structure function F^CXjQ^) are given and comments are made on the problems that remain to be solved.

1. General Remarks — The advent of high-energy high-luminosity e e- storage rings has led to productive studies of photon-photon collisions. As shown1 by C. F.

Weizsacker and E. J. Williams, the electromagnetic field produced by a charge moving with relatlvistic velocity is equivalent to a flux of virtual photons with a charac-

teristic spectrum,

dN /dk °= i/k , (1) and with an angular divergence that is quite small for large energies,

9 ~ m/E . (2) It is clear that colliding electron beams, such as those at PEP and PETRA, have

associated with them well-collimated colliding beams of nearly-real photons. As illustrated in Fig. 1, various final states can be produced by these photon-photon collisions; for two real (massless) photons, the state X is restricted to have even charge conjugation and, by Yang's theorem, the spin cannot be J = 1. The latter condition is relaxed if one of the beam electrons is scattered at a finite angle so that the q^ of the corresponding photon is not zero.

Detailed analyses of the kinematics of the process shown in .Fig. 1 can be found in the literature,2 but we note here that invariant masses pro-

duced by photon—photon collisions range continuously from threshold values up to the maximum allowed by the beam energy E^. The differential cross section in sx = m^ is determined predominantly by the bremstrahlung spectrum noted in (1).

Roughly,

Fig. 1; Illustra- By contrast, the annihilation channel is characterized by events tion of the process that occur at one invariant mass s = 4E^ (ignoring radiative ee •+• eeX.

*Work supported by the. Department of Energy, contract DE-ACO3-76SF00515.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982373

JOURNAL DE PHYSIQUE

corrections), and the cross section falls like 11~2. The logarithms in formula (3) arise from integrations over the phase space allowed the motion of the yy center of mass. Note that 2.ln(2 Eb/mx) is just the length of the rapidity interval avail- able for a state with mass mx. The cross section for the production of X by two

2 2

real photons is ayy +,(six). More generally, if a(sx,ql,q2) depends upon the masses of the incident photons, then relation (3) must be rewritten in terms of a sum over photon helicities and helicity dependent cross sections. As noted above, however, unless one of the scattered beam electrons is detected at a finite angle, most of the observed events correspqnd to q$- q:- 0, and replacing ~(s~,q$,~$) -+ o(sx,O,O) is not too bad of an appro~imation.2~3

The problem for the experimentalist is to detect the final state X (notice that the yy CMS is not at rest in the lab), and to separate the two-photon produced states from backgrounds due to the annihilation channel. This latter problem is solved in two distinct ways. Exclusile measurements, in which all final state particles are detected, can be isolated from the annihilation channel by making use of the kine- matics of the two-photon process. Events are selected that display masses

mx << 2Eb and low net transverse momenta relative to the beam

I

^pt

1 -

0 (typically

lpt( < 100 EleV/c). This latter property is due to the small divergence of the equiva- lent photon beams (Eq. (2)). Two-photon events can also be "tagged" by detecting one of the outgoing beam electrons at small angles with respect to the beam line.

Both of these techniques have been successfully used to study two-photon collisions.

The list of topics for which data have been reported in the literature covers most aspects of strong interaction physics. It includes:

*: (yy 3 1i)

spectroscopy: (yy +

Iqq>)

hadronic pair production: (yy + &) total hadronic cross sections:

high-pt phenomena:

- single particle inclusive distributions (yy -+ ~,K,etc.

+

^anything)

-

jet structures (yy -+

qq)

deep inelastic ey scattering: (ey -+ e f hadrons)

-

photon structure functions

I have chosen to present in this talk results from only two of these areas

-

spec- troscopy (Section 2) and deep inelastic ey scattering

-

(Section 3). These are extremely interesting subjects and are areas in which the study of photon-photon collisions can play an important role in our understanding of the strong interaction.

The most glaring omission in this talk will be the absence of any discussion of the studies of high-pt phenomena. No new results on this topic were reported at this conference, andathe interested reader is referred to the review given at the Bonn Conference last year.4

2. Spectroscopy

A. Introduction

-

The production of a quark-antiquark meson resonance R (spin 3 # 1 and C = i-) by two

6

photons is described by the diagram shown in Fig. 2a. The production cross section is related to the partial width of the decay process R-+yy,

( a ) ( b )

Fig. 2: Two-photon production of (a)

1 ,.,+ 1 )

quark-antiquark bound states and (b)

Y glue-glue bound states. The quantum

numbers of a state that couples to two

( C = i - , I , = O , J f I ) real photons are shown in the figure.

10 - 8 2 439142

D.L. Burke C3-5 15

where BW(s) is an appropriate Breit-Wigner line shape, and the spin factor is needed since the partial width is defined in terms of an average over the various possible initial spin states in the decay process. Hence a measurement of the production rate for ee+eeR is also, by (3) and ( 4 1 , a measure of the partial width of R into two photons (if the spin of R is known).

Knowledge of rR+ yy is of interest because it is a probe of the lqi> bound-state wave function,

The quark charge is eq (n! units of e) and the matrix element is written for unit charges. The wave functions of bound states of light quarks are highly relativis- tic, and the problem is usually approached within the theoretical framework of SU(3).

The assumption of nonet symmetry implies that the overlap integral is the same f-or all members of a given multiplet, so the ratios of various partial widths are given by the quark charges and mixing angles derived from mass formulae. The partial widths of heavy quark resonances (e.g., the nc(2980)), 'should be computable with the non-relativistic potential models that are used to describe the appropriate -onium spectrum. Unfortunately, no data exist yet on the two-photon production of any of these heavier states.

One of the more interesting problems in the study of the light meson spectrum is to arrive at an understanding of the role played by the purely gluonic bound states

Igg>

expected to exist due to the non-Abelean nature of QCD. As noted above, the coupling of a resonance to two photons is determined to first order by the charge of the constituents that make up the state in question. The coupling of a gluonic bound state to yy proceeds only through the OZI-suppressed box diagram shown i6 Fig. 2b. Somewhat more generally5 if

IR>

is a linear combination of Iqq> and Igg>,

IR>

⁼ cos8 Iqq>

+

^sine

Igg>

⁽⁶⁾

then we would expect

rR+ I

^cos8

1

2

.

By comparison, the production of

1

R> in a

"glueball favored" channel, such as the prompt photon decay J/$+yR shown in Fig. 3,

( a ) ( b l

Pig. 3: Prompt-photon decays of an ortho-

3s

1

quarkonium bound state, for example,

>

^3s*

^{> Iq.}

^{J/(J +} y + (a) glue-glue and (b) quark-

antiquark.

would proceed with rates

1

sin8

12.

Naively then, states that are easily produced by photon-photon collisions would seem to not be good candidates for states that are predominantly

1

gg).

Four quark resonances

Iqqqq>

are expected to be rather loosely bound and quite broad. These states literally "fall apart" into pairs of vector particles,

If this is the case, then the vector-meson-dominance model of the photon leads one quite naturally to look for four-quark states in yy c~llisions.~

B. Pseudoscalar Mesons

-

Measurements of the yy partial width of a number of known resonances have now been reported in the literature, and in fact, are beginning to appear as standard entries in the Particle Data Group

table^.^

The first resonance to be detected8 in photon-photon collisions at e+e- machines was the

n'

(958). Along with results for the a0 and 11(550) partial widths obtained from Primakoff production experiments, this provided the complete set of values for the pseudoscalar multi- plet given in Table I. The beautiful agreement between the measured widths and those

C3-5 1 6 JOURNAL DE PHYSIQUE

e x p e c t e d from SU(3) i s p r o b a b l y t h e T a b l e I. R a d i a t i v e Widths o f t h e Pseudo- s t r o n g e s t e v i d e n c e t o d a t e t h a t q u a r k s s c a l a r Mesons

c a r r y f r a c t i o n a l c h a r g e . Tyy (keV)

Data

C. Tensor Mesons and t h e O(1650)

-

F r a c t i o n a l I n t e g r a l ^TheoryC Measurements of p a r t i a l w i d t h s f o r t h e

2++ t e n s o r mesons f (1270) and A2 (1310) Quark Quark

Charges Charges

have been on t h e market f o r some t i m e

now, b u t r e p o r t e d 1 ' a t t h i s c o n f e r e n c e no 7.95 x i n p u t i n p u t i s a f i r s t measurement f o r t h e f ' ( 1 5 1 5 ) .

11 0.324 + 0,046a

T h i s measurement h a s been made by s t u d y - 0.390 0.720

i n g t h e

KK

f i n a l s t a t e . L i m i t s i r e a l s o r l t 5.8 t l.lb 6 . 1 26 s e t on t h e c o u p l i n g of t h e O(1650) t o 5.0 k 0 . 5 ~

yy. T h i s l a t t e r r e s o n a n c e h a s been ob- 5.4 2 1.0b s e r v e d 1 ' i n t h e prompt-photon decay

J / + + - y O , w i t h t h e s u b s e q u e n t decay o f aRef. 7 b ~ e f . 8 ' ~ e f . 9 t h e - 8 i n t o b o t h

nn

and KK. The produc-

t i o n and decay a n g u l a r d i s t r i b u t i o n s o b s e r v e d i n t h e prompt photon s t u d i e s somewhat f a v o r a JPC = 2* a s s i g n m e n t , and s o d i s c u s s i o n o f t h i s s t a t e i s i n c l u d e d i n t h i s s e c t i o n .

Shown i n Fig. 4 a r e t h e

s p e c t r a o b t a i n e d by TASSO" f o r t h e 40

two-photon p r o d u c t i o n of

K+K

^and

- -

I @ ? : .

The K%- e v e n t s a r e s e l e c t e d 30 >

t o h a v e n e t p t < 100 MeV/c and t h e $ lo

kaons h a v e been i d e n t i f i e d by t h e ;.20

-

8 _-.

t i m e - o f - f l i g h t t e c h n i q u e . There i s

2

^m +

a c l e a r peak a t t h e p o s i t i o n of t h e

5

z w 5 f '(1515) w i t h few e v e n t s s e e n a t

&

^lo 2, t h e e(1650). Some c a r e s h o u l d b e

t a k e n h e r e s i n c e t h e e f f i c i e n c y of 0 0

t h e t i m e - o f - f l i g h t i d e n t i f i c a t i o n ^{1 . 1 1.3 1.5 1.7 1.0 1.2 1.4 1.6 1.8 2.0} of t h e kaons f a l l s a t t h e h i g h e r $0-n M (KR) M (KR) . , 9 ( ~

masses and i s e s s e n t i a l l y - z e r o a t

mm = 1.9 G ~ v / c ~ . The K:K~ spec- Fig. 4: ( a ) The K+K- spectrum produced by yy trum s e e n i n F i g . 4b ( o b t a i n e d from c o l l i s i o n s , and (b) t h e c o r r e s p o n d i n g spectrum e v e n t s w i t h f o u r c h a r g e d prongs f o r

KZKZ.

w i t h n e t pt < 150 MeV/c) a l s o

e x h i b i t s a peak a t t h e mass o f t h e f ' ( 1 5 1 5 ) . The p a r t i a l w i d t h s o b t a i n e d from t h e s e two s p e c t r a a g r e e w i t h e a c k o t h e r w i t h i n s t a t i s t i c a l u n c e r t a i n t y , and t h e TASSO group r e p o r t s ,

and

.

^{BRO ,& < 0.5 keV} (95% C.L.)

re

^{+ Y Y (9)}

where t h e b r a n c h i n g r a t i o s i n c l u d e b o t h kaon c h a r g e s t a t e s . The Mark I1 group h a s made a s i m i l a r s t u d y w i t h a b o u t o n e - t h i r d of t h e l u m i n o s i t y o f t h e TASSO experiment and g i v e s o n l y t h e l i m i t s ,

and,

i- O + y y B R O + e < 0.4 keV (95% C.L.)

.

⁽¹¹⁾

The v a l u e s g i v e n i n (8) through (11) assume t h a t t h e s p i n of t h e 8 i s J = 2 and t h a t t h e f ' and t h e 8 a r e produced w i t h h e l i c i t y A = 2 by r e a l photons. The r e s u l t s a r e s e n s i t i v e t o t h e h e l i c i t y s t r u c t u r e of t h e p r o d u c t i o n r e a c t i o n b e c a u s e t h e a c c e p t a n c e

D.L. Burke

of the detectors depend upon the angular distribution of the produced kaon pairs.

If the f' is assumed to be created entirely with A = 0, then the partial width ob- tained by TASSO from the K+K- channel wouldlo be 0.5

+

^{0.1 keV.}

A summary of the r e p ~ r t e d ~ , ~ ~ , 12* l 3 measurements of the partial widths of the 2* tensor mesons is given in Fig. 5; new

results reported at this conference are under- I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 l l r l

lined in the figure. The error bars are the 1-0+ PLUTO

reported statistical contributions only, so the I.I MARK n scatter in rhe data are an indication of the f(1270) w TASSO

level of agreement between the various experi- +O- CB

ments. Note also that all points, except the H JADE Crystal Ball (CB) measurement of the f(1270), I assume that the production process for J = 2

-

^{cB \(INPUT)}

proceeds through helicity X = 2. The Crystal

Ball was able to study the helicity structure ^{A2(1310) +oi} of the process yy + f + .rr0nO and found the data ⁰ _/ consistent with A = 2, although the best fit

included a contribution from A = 0 of -10%. _/ #' This multiplet is bslieved to be ideally mixed a =,/

f'(1515)

with the f = (u;+ dd)/fi and the A2 =

-

(u;

-

dz)

fi,

while the f' is the purely strange A' ^{- - -}

-

SU(3)

I

ss> state. These quark assignments predict s t a t ~ s t ~ c a l

that the yy partial widths of these resonances

(

^errors only)

should be in the ratio 25:9:2. With the

average of the measured values of the f(1270) I I I I I I I ~ I ~I I I 1 1 1 1 1 1

as input, this SU(3) prediction is shown in 0. I I 10

Fig. 5. Since the mass of the f'(1515) is ^Em-Bz Try (keV) .xetl~

larger than the other two states, a phase

Fig. 5: Summary of measured space correction (scaled like m3) has been

partial widths of the 2* tensor included in the figure. The agreement is not

mesons. The underlined results perfect, but given the uncertainty regarding were reported at this conference.

the helicitv structure of these reactions. it

is actually~remarkably good. It has been'argued14 that the yy partial width. of the f1(1515) is extremely sensitive to the fraction of non-ss quark pairs in its wave- function. The value reported above places10 an upper limit of 1% on the amount of non-ss quark admixtures in the f' (1515).

The limits (9) and (11) on the coupling of the 8(1650) to yy are actually not yet very stringent. The branching fraction of the 6 to KK is not known, but may be as small as 10-20%, while that of the f1(1515) is probably quite large. If the 0 is predominantly a spin-2 ss state, then its coupling to yy would presumably be comparable to that of the f'. The data cannot rule out a partial width I'(e-+yy) of the order 0.1-0.2 keV. If the 8 is a 2* glue-glue resonance, then a rough estimate of its width can be made by noting that the presence of two electromagnetic vertices in the quark loop in Fig. 2b means that the process is dominated by the u-quark.

The rate for the decay Igg; J = 2>+yy should be of the order of that for f(1270) +

yy times an OZI suppression factor. This latter suppression can be estimated as the square root of the Zweig factor of the $(1020), which is ~ 1 0 0 . Roughly then, r(lgg; J = 2>+yy) may be of order a few tenths of a keV. This is certainly con- sistent with the data. Unfortunately, it also appears to be about the same size as that for the sE hypothesis.

+ - + -

D. The .rr .rr rr n Final State

-

The four pion final state produced by photon-photon collisions was one of the first to be studied.15 It was found that the cross section exhibits a large enhancement near m48 ¹ 1.5 G ~ v / c ~ . The early data are shown in Fig. 6. This enhancement was found to be mostly due to pop0 production, but the statistics of these data limited the sophistication of the analyses that could be done by the experimenters. The magnitude of the cross section, however, is extremely large for a single channel, and vector-meson-dominance cannot easily explain this effect.15

Preliminary, high-statistics data (70 pb-I) have been reported at this con- ference by the TASSO group.10 The observed spectrum of events, uncorrected for detection efficiency or photon flux, is shown in Fig. 7. High-lighted in this

JOURNAL DE PHYSIQUE

+ - + -

Fig. 7: High statistics n n T a spectrum reported by TASSO. The curve is a polynomial fit to the region 1.6 Gev/c2 to 3.0 Gev/c2.

+ - + -

Fig. 6: The a T a n cross section as first observed in yy collisions.

figure is the presence of a narrow peak with a mass of 2.10 ? 0.01 Gev/c2, and a measured Gaussian width of 94 k 21 M ~ V / C ~ FWI. This latter value should be compared with the intrinsic resolution of the TASSO detector which is -60 Mev/c2 FWHM. The

statistical significance of the signal is derived by fitting the background with a polynomial as shown in the figure. Simply counting the number of events above this background in the mass range 2.0-2.2 Gev/c2 yields 342-258 = 84 events, or a 5.2 standard deviation effect. This is a rather conservative technique since it ignores the tails of the Breit-Wigner which would contribute to a signal derived from a fit to the data. The TASSO group also estimates the partial width as

(23+1)

. ^r

_YY ~~(n+rr-a+a-) = 1.6 ? 0.4 (statistical) keV

.

⁽¹²⁾

The spin factor (see Eq. (4) and discussion) has not been determined and the detec- tion efficiency was computed by assuming that the four pions are produced according to phase space. The established resonance closest to this peak is the h(2040), a 4* state with m = 2.040 3 0.020 and total width = 150 2 50 Mev/c2 that has been observed7 in high-statistics spectrometer experiments in the na, KK, and perhaps pp channels. Although the mass of the h is reasonably close to that quoted above the width of the peak in the xy process may be considerably smaller than 150 MeV/c

1 .

^No

limits are given in the PDG table for a possible decay of the h(2040) into four pions. The most direct way to resolve this possibility will be to examine the yy-tna and KK channels in this mass range. The experimental resolution on the mass of the two-body final state will be considerably better, but this channel is compli- cated by the QED process yy + Ufu- and yy + efe- which are large and must be suppressed experimentally. No results have been reported yet.

The TASSO group has also done a more detailed analysis of the complete set of events in Fig. 7. They filnd that the spectrum below e2.0 Gev/c2 is almost totally dominated by the pop0 final state while above 2.0 Gev/c2 the 4n final state is prevalent. Little porn is seen anywhere, and the peak at 2.1 ~ e v / c ~ does not appear to contain any pO's whatsoever. A two-body partial wave analysis of the pop0 spec- trum below 2.0 Gev/c2 rules out significant 0- and 2- contributions, while either an isotropic distribution or a combination of

of

and 2' give equivalently good fits to the data; the limited geometrical acceptance of the detector makes it difficult to separate these two possibilities. A particular limit has been set on the production and decay of the 8(1650),

i- _@+YY B R 8 + p ~ p ~ < 1.2 keV (95% C.L.)

.

D.L. Burke

The 9 a p p a r e n t l y can account f o r no more t h a n about one-third of t h e p o p 0 e v e n t s found i n t h e r e g i o n between 1.5 G ~ V / C ~ and 1.9 Gev/c2. This ma b e of i n t e r e s t i n

8

l i g h t of a r e c e n t l y r e p o r t e d 1 6 o b s e r v a t i o n of t h e decay J/$+ yp pO. The pop0 spec- trum seen i n t h i s decay i s c o n c e n t r a t e d a t masses below 2.0 Gev/c2, but l i m i t e d s t a t i s t i c s p r e v e n t any d e t a i l e d s t u d y of t h e pop0 system. Work by t h e Mark 111 a t SPEAR may u l t i m a t e l y p r o v i d e a l a r g e r d a t a sample.

3 . Deep I n e l a s t i c ey S c a t t e r i n g : The Photon S t r u c t u r e Function A. I n t r o d u c t i o n -We t u r n now t o a r a t h e r d i f f e r e n t

view of photon-photon c o l l i s i o n s . A s mentioned i n t h e opening remarks, i f one of t h e s c a t t e r e d beam e l e c - t r o n s i s d e t e c t e d a t f i n i t e a n g l e s a s shown i n Fig. 8, t h e n t h e mass of t h e corresponding photon i s n o t n e a r z e r o , and some c a r e must b e taken i n w r i t i n g t h e pro- e d u c t i o n c r o s s s e c t i o n . P a r t i c u l a r l y i f Q2 = -q2 i s l a r g e , t h e n t h e p r o c e s s i s more c o r r e c t l y thought of a s deep i n e l a s t i c ey s c a t t e r i n g , where t h e t a r g e t i s chosen from t h e f l u x of n e a r l y - r e a l photons Y a s s o c i a t e d w i t h t h e undetected beam e l e c t r o n . I n

.Less

q 2

o

~ 4391A7 10-82

complete analogy w i t h deep i n e l a s t i c electron-nucleon

s c a t t e r i n g , t h e ey process can b e w r i t t e n i n terms of Fig. 8: Diagram f o r t h e deep p a r t i c u l a r combinations of l o n g i t u d i n a l and t r a n s - i n e l a s t i c s c a t t e r i n g p r o c e s s v e r s e s t r u c t u r e f u n c t i o n s t h a t d e s c r i b e t h e unknown e y + e

+

^hadrons.

hadronic v e r t e x i n Fig. 8. With t h e p u r e l y QED fac-

t o r s from t h e upper v e r t e x e x p l i c i t l y i n c l u d e d , we can w r i t e q u i t e g e n e r a l l y , 1 7 2

d a ( e y + e + h a d r o n s ) = l 6 ~ a E E

dxdy Q [xy2 F:(x,Q2)

+

( 1

-

Y )

.

^{F:(X,Q~)] (14)}

where x and y a r e t h e u s u a l s c a l i n g v a r i a b l e s ,

and,

Formula (14) must be convoluted w i t h spectrum of t a r g e t photons t o d e s c r i b e t h e over- a l l p r o c e s s e e + e e + h a d r o n s . A s i n t h e c a s e of electron-nucleon s c a t t e r i n g , t h e v a r i a b l e y i s approximately t h e f r a c t i o n a l energy l o s t by t h e d e t e c t e d beam e l e c t r o n and, i n t h e p a r t o n model, x i s t h e momentum f r a c t i o n of t h e t a r g e t p a r t o n s t r u c k by t h e high Q2 probe. I n t h i s c a s e t h e t a r g e t p a r t o n i s q u i t e l i t e r a l l y a c o n s t i t u e n t of a r e a l photon. Before d i s c u s s i n g t h e p h y s i c s i n Eq. (14) we n o t e t h a t i n experi- ments done t o d a t e t h e f a c t o r xy2, which i s p r o p o r t i o n a l t o s i n 2 ( 0 / 2 ) , i s s m a l l com- pared t o ( 1 - y ) . A t t h e l e v e l of s t a t i s t i c s c u r r e n t l y a v a i l a b l e , t h e observed c r o s s s e c t i o n i s s e n s i t i v e only t o F:. Experimenters have s o f a r ignored t h e c o n t r i b u t i o n of F: and have used measurertlents of t h e c r o s s s e c t i o n t o e x t r a c t F;.

The f u n c t i o n FZ(x,Q2) h a s t h e well-known i n t e r p r e t a t i o n a s t h e momentum and charge weighted d i s t r i b u t i o n of hard c o n s t i t u e n t s i n t h e t a r g e t photon. I n t h e absence of gluon bremstrahlung, t h e s i m p l e s t diagram i s shown i n Fig. 9 w i t h ,

The charge of t h e s t r u c k quzrk i s e q , and q ( x , ~ 2 ) , which d e s c r i b e s t h e d i s a s s o c i a t i o n of t h e t a r g e t photon i n t o qq, a l s o c o n t a i n s a f a c t o r of e i . To s e e t h e form t h a t q(x,Q2) w i l l t a k e , f i r s t c o n s i d e r t h e p u r e l y QED p r o c e s s ey - t e + l i . This i s des- c r i b e d by Fig. 9 w i t h t h e quark-antiquark p a i r r e p l a c e d by a l e p t o n p a i r . The

C3-520 JOURNAL DE PHYSIQUE

distribution of leptons in a photon, l(x,Q2), is just the familiar1' double-peaked function that describes pair production,

10-82 4391A8

Shown in Fig. 10 are measurements made by PLUTO'~ and

CELLO'^

of the leptonic structure function of the Fig. 9: Quark-parton photon. The data agree well with the simple form model for the hadronic implied by (17) and (18). vertex shovm in Fig. 8.

I a ) 0'5 _PLUTO

0.4

-

X

- _,

_0.3

LL -10

Fig. 10,: Leptonic structure function of the photon. The curves are QED calculations.

B. Hadronic Structure of the Photon

-

It is clear that the quark-parton model pre- diction for the hadronic structure function F; is given by Eqs. (17) and (18) with the lepton mass replaced by the appropriate quark masses,

where a color factor of 3 has been included. This corresponds to the simplest point- like behavior -the photon enters directly into the hard-scattering process as in Fig. 9. By contrast, if the photon behaves strictly as a hadron (VDM), then instead of rising at large x, we would expect F; to fall with increasing x as nuclear struc- ture functions are known to do. One estimate17 gives

Equations (19) and (20) are compared in Fig. 11, and are seen to be drastically dif- ferent for x 2 0.2. The real interest in measurements of F2 stems from the fact that, at large Q~ and W and for x 2 0.3, the hadronic (e.g., VDM) contributions to

FI

are expected to be small, thus possibl~ allowing perturbative QCD calculations to successfully describe the deviations of F2 from the simple Born parton model pre- diction. Leading-log calculations have been completed20 and estimates of the next order contributions have also been madeq21 The leading-log calculation gives (for light quark contributions)

"

D.L. Burke

and 250 mrad. Only events with >0.75 GeV of energy visible in the remainder of the detec- tor were used in the measurement. The pub- lished results, based on 2500 nb-', are shown in Fig. 12. What is shown is the value of F;(x,Q') averaged over the range 1 < Q2 < 15 GeV;

the average value < Q ~ > for these data is 5 ~ e ~ 2 . where A is the scale parameter of QCD. The

function h(x) is quite similar to the parton model prediction, but differs at large x where gluon bremstrahlung softens the spec-

trum of quarks in the photon. The function (21) is shown in Fig., I1 for Q2 = 3 G ~ V ~ and the relatively large value A = 500 MeV.

For smaller values of the QCD prediction is closer to the parton model curve.

Notice that

FT

in (21) exhibits an explicit scale breaking = In Q2. For heavier quarks (e.g., charm) it is probably more correct to use the parton model form In w2/m;, but

Fig. 11: Comparison of the hadronic structure function of the photon as expected from three different models of the photon. The QCD curve is the leading-log prediction for A =

500 MeV.

an exact treatment of the threshold has not been given.

The earliest measurement of F; was made22 bythePLUTO collaboration. The scattered beam

\

\

\ -

\

The lowesf order (L.-0.) QCD prediction for this range of Q2 is shown in the figure for ALO = 200 MeV, and the higher order expectation is

given for = 200 MeV. Notice that these com- 0.7 putations were done with different renormaliza- 0.6 tion schemes, so the H.O. curve cannot be

directly compared with the L.O. one. The QCD 0.5 scale has essentially been adjusted in each

case to fit the data. A major uncertainty 0.4 in these data arises because the mass W must L?

be reconstructed from the hadronic system ^0.3 that is seen in the central part of the 0.2 detector. Since all detectors have limited

geometrical acceptance, only a "visible" W _{0. I} is measured and it is necessary to unfold

xtrue from xvis with a model for the produc- 0

tion of the hadronic system. The PLUTO 0 0.5 I .O

analysis was done by generating qq pairs ^{0 - 8 2 X 4391111} (Pig. 9) and then decaying the hadronic sys- Fig. 12:

PI(;)

averaged over tem according to a phase-space model with 1 i Q2 < 15 GeV measured by PLUTO.

limited-pt about the qq direction in the yy The curves labeled QCD also in- CMS. The final results are claimed to be clude the VDM contribution.

insensitive to the details of this model.

Despite this problem, these data are clearly inconsistent with the VDM prediction, and indicate that a real photon contains a considerable component of large x con- stituents.

Preliminary, higher-statistics data were presented at this conference by the

CELLO^^

and JADE^^ collaborations. These groups have not attempted to unfold the true x distribution from the observed events, but instead have compared various Monte Carlo calculations to the raw data. These are shown in Pigs. 13 and 14.

The CELLO data correspond to 11.2 ~ b - l with an average <Q2> = 8.4 G ~ v ~ , while the JADE results are from 20 pb-l with < Q ~ > = 23 G ~ v ~ . The Q2 values differ because the two experiments had different acceptances for the scattered beam electrons.

Both measurements were made by requiring Wvis > 1 GeV, and since xvis = Q2/ (Q2

+ w&)

then the higher Q2 data from JADE are peaked at higher xvis than the CELLO data.

electrons were detected in electromagnetic lo-2 ^{I I I I} \ calorimeters arrayed along the beam line and 0 0.2 0.4 0.6 0.8 1.0 covering the angular range between 100 mrad 0 - 8 2 x 4 3 9 1 1 1 0

I I I l ( I I I I -

-

PLUTO

-

QCD (L.0)

QCD (H.0)

- <@>=5 G ~ V ' VDM -

-

+t+-

-

-

/.

L...

... ...

-

...

-

I I I I I I 1 I b . -

C3-522 JOURNAL DE PHYSIQUE

CELLO

1

0

0 0.5 I .O

10-82 X ~ l ~ 4391112

Fig. 1 3 : D i s t r i b u t i o n i n x b i s of e v e n t s s e e n by t h e CELLO d e t e c t o r . The c u r v e s are p r e d i c t i o n s f o r ( i ) t h e QPM, ( i i ) a combination of QCD f o r ( u , d , s ) q u a r k s and t h e QPM f o r t h e charm q u a r k , and

( i i i ) QCD f o r a l l q u a r k s p e c i e s . The t h r e e c a s e s a r e i n d e p e n d e n t l y n o r m a l i z e d t o t h e d a t a .

Fig. 14: D i s t r i b u t i o n i n xvis of e v e n t s s e e n by t h e JADE d e t e c t o r . The s o l i d c u r v e i s t h e p r e d i c t i o n of a second o r d e r QCD c a l c u l a t i o n w i t h

& s

= 200 Mev. The u p p e r dashed c u r v e i s t h e same c a l c u l a t i o n done w i t h A= = 100 Mev, and t h e lower c u r v e c o r r e s p o n d s t o A= = 400 Mev.

The CELLO d a t a i n Fig. 1 3 a r e compared w i t h t h e s h a p e s e x p e c t e d from t h e p a r t o n model (Eq. ( 1 9 ) ) , t h e l o w e s t o r d e r QCD c a l c u l a t i o n (Eq. ( 2 1 ) ) , and a combination i n which t h e c o n t r i b u t i o n o f t h e charm q u a r k i s t a k e n from (19) and t h e l i g h t q u a r k s a r e t r e a t e d w i t h (21). I n a l l c a s e s t h e c u r v e s a r e n o r m a l i z e d t o t h e d a t a . The s h a p e s of t h e d i s t r i b u t i o n s a r e n o t v e r y d i f f e r e n t . The a b s o l u t e n o r m a l i z a t i o n , however, of t h e QCD p r e d i c t i o n i s d e t e r m i n e d by t h e v a l u e of A and t h e s e d a t a a r e c o n s i s t e n t w i t h v a l u e s 0.1 < ALO < 0.2. The s e n s i t i v i t y of F$ t o t h e v a l u e o f A i s shown more d i r e c t l y i n Fig. 14. Here t h e JADE d a t a a r e compared f o r t h r e e d i f - f e r e n t v a l u e s of A i i i ~ w i t h a QCD c a l c u l a t i o n t h a t i n c l u d e s t e r m s a I n ( l n ~ ~ / ~ & ) ) . A f i t t o t h e d a t a f o r xvis > 0.4 g i v e s ,

It s h o u l d b e n o t e d t h a t i n t h e s e c a l c u l a t i o n s , t h e charm q u a r k was t r e a t e d a s a l i g h t quark. I f (19) i s used i n s t e a d of (21) f o r t h e charm q u a r k , t h e n t h e v a l u e of

& ?

from t h e JADE d a t a becomes13 0.18

-

a change of about: 20%.

Fig. 15: The JADE d a t a b i n n e d i n Q ~ . Only e v e n t s w i t h xvis > 0.3 have been i n c l u d e d i n t h i s p l o t . The c u r v e i s t h e I n Q~ b e h a v i o r e x p e c t e d from p o i n t - l i k e c o n s t i t u e n t s i n t h e photon.

D.L. Burke

A second distinctive feature of both the parton model and QCD is that F; is expected to be proportional to In Q~ (at fixed x), rather than vanish like a power of l/(ln Q2) as do structure functions of nucleons. The JADE data, binned in Q2 and averaged over the region xvis > 0.3, are shown in Fig. 15 and are seen to be consis- tent with the expected point-like behavior. The PLUTO results were also examinedzz in this way and found to display this property.

C. Promise and Problems of Deep Inelastic ey Scattering- The data above represent a relatively small amount of luminosity and it can be expected that, in the near future, data samples 4-10 times as large will be available. At that time measure- ments of the photon structure functions will no longer be statistics limited. In principle, this could become a very sensitive way of determining the QCD scale param- eter A in whatever renormalization scheme is desired. There are, however, several serious theoretical and experimental problems, some of which have already been alluded to in the above discussion of data. Firstly, it hasn't been proven yet that the perturbative QCD series converges anywhere in x. It is known that for x < 0.3 the lowest order QCD prediction is unstable, thus indicating that non-perturbative contributions are important in that region. Also, values of x very near 1.0 cor- respond to the lowest W values and various threshold effects not described by perturbative diagrams become important.23 Secondly, there is no proper treatment yet of the heavier quarks. As noted above, the value of h , ~ derived from the JADE data changes by ~ 2 0 % when the contribution of the charm quark is evaluated with the parton model instead of QCD.

On the experimental side there should be some concern that events with invariant masses as low as 1 Gev/c2 are included in the measurements of

FZ.

Indeed, the measurements are dominated by invariant masses between 1 and 3 Gev/c2. It could be expected that contributions from resonances and thresholds will be suppressed at large Q2, but this is somewhat dangerous. It must be noted that some discrepancies exist between the observed invariant mass distributions and those predicted by the QCD Monte Carlos used by the experimenters. This is particularly true in the CELLO data12 which is at a lower Q2 than the JADE results. But certainly the most im- portant task facing the experimentalists is to successfully unfold the true x dis- tributions from the observed events. The problem is that events produced at low x, where perturbative QCD calculations are unreliable, are shifted to larger Xvis when part of the final state is missed by the detector (xvis = Q ~ / ( Q ~ + w ~ ~ ~ ~ ) ) . The un- fold procedure will always have some inherent model dependence. This can be avoided by detecting both scattered beam electrons, but event yields are then reduced.

4. Conclusions

-

I would like to conclude by noting that photon-photon physics has become a standard feature of the elementary particle physics landscape. The topics included in this talk are quite divergent in character, yet center on our under- standing of the strong interaction and hadronic structure. Study of the spectrum of resonant states produced by yy collisions is by now an old game, but always with new and useful results. It also seems clear that, when viewed as a particle in its own right, the photon displays a structure that is remarkably point-like even at modest Q ~ . We should expect, then, that PEP and PETRA will continue to be excellent places to study this physics.

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[3] KESSLER (P.), contributed paper 0761 to this conference.

C41 WEDEIlEYER (R. J.), Proceeding of the 1981 Symposium on Lepton and Photon Interactions at High Energies, ed. W. Pfeil.

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ACHASOV (N. N.), DEVYANIN (S. A.), SHESTAKOV (G. N.)

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~hys. Lett., 1982, 108B, 134.

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PARTICLE DATA GROUP, Phys. Lett., 1982,

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G. Cochard and P. Kessler.

BARTEL (W.) et al., JADE Collaboration, Phys. Lett., 1982,

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BEHREND (H. J.) et al., CELLO Collaboration, DESY 82-008, and talk at this conference.

C!jANOWITZ (M. S.), Phys. Rev. Lett., 1980, 44, 59.

LUKE (D.), TASSO Collaboration, presentation at this conference.

EDWARDS (C.) et al., Phys. Rev. Lett., 1982, 48, 458.

FRANKLIN (M.E.B.) et al., Bull. Am. Phys. Soc., 1982,

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See also BLOOM (E.), raporteur at this conference.

BEHREM) (H. J.), CELLO Collaboration, presentation at this conference, and contributed papers 0562, 0739, and 0740.

HEINZELMANN (G.), JADE Collaboration, presentation at this conference.

ROSNER (J. L.), University of Minnesota preprint, July 1982.

BRANDELIK (R.) et al., TASSO Collaboration, Phys. Lett., 1980,

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For a good summary of the formalism of deep inelastic ey scattering see PETERSON (C.)

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^~ALSH (T. F.)

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ZERWAS (P. M.)

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Nucl. Phys. B, 1980,

174,

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Discussion

P. -WSSLER (ColZBge de France)

.-

^I would l i k e t o s t r e s s one fact which has been correctly observed by t h e CELLO people, but seems t o have completely escaped t o the PLUTO and JADE peopZe : mmely t h a t t h e partonmode2 prediction, used correctly

(i. e. with Zn

I&

instead of In Q ~ ) , i s practicaZly the same as t h e leading order QCD prediction ( a t moderate Q~ values). Thus present experiments cannot be conside- red as a Oest of leading-order QCD us. the parton model. On t h e other hand, they might be considered a t e s t for next-to-leading order corrections, but here every- body knows there are considerable theoretical d i f f i c u l t i e s .

D.L. B U R K E .

-

This does. seem t o be the case. I t should be pointed out, however, t h a t , f o r a given QCD calculation

,

the value of ~ 2 Y i s

a

s e n s i t i v e measure of the scale parameter A

.

^If i t tan be shown t h a t the perturbative s e r i e s converges i n t h e same region of X, then F2y may be t h e best measure of A.