Deep inelastic lepton-nucleus scattering

> x Nq N(X)~

(2°9)

where < pz2 > is the mean squared transverse momentum of a quark in the nucleon and Vd is the volume of the two-nucleon c o r r e l a t i o n m 4~/3.(1 fm)3° Using these numbers one gets f o r x = 0:2 F2Nex r2N

0:02 ~ F2N(X ) = 2%°

N a t u r a l l y also a s i m i l a r exchange c o n t r i b u t i o n

(2o10) e x i s t s f o r the pion in the nucleus

with Nq~N replaced by Nq/NONq/~, ioe: ex F2~ F2N

=

0o02 ~I F2~(x~ =

6%°

(2o11)

Therefore these simple c a l c u l a t i o n s show t h a t in the conventional nuclear p i c t u r e with nucleons and pions there are c o r r e c t i o n s at 0°2 < x < 0°6 which are of the order of several percent to the simple f o l d i n g model: Another argument against the use of ~ - c l u s t e r s in the nucleus has been given by J a f f e (1983) and J a f f e and others (i984): The l i f e t i m e of a ~ - c l u s t e r is given by 1

(2o12

which is the same order of magnitude as a nuclear i n t e r a c t i o n . Therefore the Quark d i s t r i b u t i o n in the c l u s t e r can be d i f f e r e n t from nucleus to nucleuso-A d i f f e r e n t approach is to s p l i t the d i s t r i b u t i o n f u n c t i o n of the Quark in the nucleus into 3q~ 6q and 9 q - c l u s t e r s etco Then the l i f e t i m e of these c l u s t e r s is i n v e r s e l y proportional to t h e i r e x c i t a t i o n energy £m ~ 0°3 - 0:6 GeV which may help to separate

Deep Inelastic Lepton-Nucleus

Scattering

38]

the internal c l u s t e r dynamics from the nuclear dynamics° However, i t is then unclear why such s h o r t - l i v e d high e x c i t a t i o n clusters should form a large part of the wavefunctiono The same c r i t i c i s m applies to combined QCD-radiation and cluster models° Jaffe and others (1984) give a p r o b a b i l i t y of 95% to have six (or higher) quark clusters in Au197o I t is d i f f i c u l t to imagine why normal nuclear properties have not t o t a l l y disappeared i f such a view holds° The ~ = p a r t i c ] e has been se= lected by Faissner and Kim (1983) as especially strongly bound and therefore being the origin of the EMC-datao We agree that the high density of t h e ~ - p a r t i c l e gives a higher p r o b a b i l i t y for larger quark clusters but we do not think i t is necessary to t r e a t t h e ~ - p a r t i c l e as a constituent of the n~c!eus without 6 and 9-quark ciustorso The quark c l u s t e r model (Pirner and Vary, 1981~ 1983) is d i f f e r e n t from an analysis of nuclear structure in terms of nuclear short-range c o r r e l a t i o n and/or high momentum components in the nuclear wavefunctiono We think the quark exchange from quark anti-symmetrization in two nearby nucleons should also be included in the six-quark c l u s t e r (see also Chemtob and Peschanski~ 1983)o Given a c r i t i c a l size parameter Rc of the nucleon we consider two nucleons forming a compound system of six quarks whenever t h e i r r e l a t i v e distance is smaller than 2Rco We remove the short-distance part of the two-nucieon wavefunction and replace i t by a multiquark cIuster~ which consists of p o i n t - l i k e quarks i n t e r a c t i n g with QCD~residual forces~ This approach is similar to QCD~motivated work on the NN~forceo Whereas strong i n t e r a c t i o n experiments l i k e NN~scattering can always be f i t t e d by e f f e c t i v e meson-nucleon dynamics~ tiqe el=ctromagn~tic probe at large Q2 w i l l see how impor~ ta~t hidden quark components are in the baryon number two system° An analysis of the He3 (Pirner and Vary~ 1981) system gives a best value f o r the c r i t i c a l radius Rc = 0°5 fmo The p r o b a b i l i t i e s to three, six and nine quark clusters are then P3 = 0o90~ P6 = 0oI0~ P 9 ! 0o01o The c l u s t e r expansion is rapidly convergingo The dependence of the Pi~s on Rc in He3 can be used to generate Pi'S for other nuclei° in the s p i r i t of the local density approximation only the average density PM is responsible f o r changes of the Pi in d i f f e r e n t nuclei° Normalizing the average density to the total nucleon number one can express i t with the average charge density pp as PM = ~A Pp°

(2o13)

This density defines the size RWS which a nucleon has available for i t s e l f nucleus 3

R

WS

3 = i__

#M

in the (2o14)

The radius RWS is called the Wigner-Seitz radius in solid state physics° Rescaling Rc with the ratios of the Nigner-Seitz cell we obtain the effective-RC=c f o r other nuclei A besides He3 (A = 3)

~(A)= L ~ ? aco

(2o15)

F r o m ~ one obtains the p r o b a b i l i t i e s Pi for other nuclei° Note in a former paper we have not c o r r e c t l y taken into account the increase of the average density with Ao %n Table I (Pirner and Vary, 1984) we give the c l u s t e r p r o b a b i l i t i e s Pi for a set of standard nuclei° i f one defines for He3 the percolation threshold as the s i t u a t i o n where the nine~ quark p r o b a b i l i t y x becomes larger than P3 and p6~ then percolation occurs for a c r i t i c a l nucleon size of about Rc = Ioi fmo This estimate agrees with similar comments before that a 7arge bag radius of Rc = Ioi fm would lead to percolation°

382

Hans Jo Pirner

TABLE 1 A

Cluster P r o b a b i l i t i e s for Various Nuclei (Rc = 0°5 fm) RWS [fm]

P3

P6

2°0

0.96

0°04

0

3He

1o55

0°89

0oi0

0o01

4He

1o20

0°76

0o19

0°05

9Be

Io48

0°87

0o12

0o01

27A!

Io27

0°78

0o18

0°04

40Ca

1o27

0°79

0o17

0°04

56Fe

io24

0°77

0o18

0°05

88Sr

1o21

0.76

0o19

0°05

208pb

1o19

0.74

0°20

0°06

d

P9

The inclusion of i-quark clusters into the nuclear structure function is a genera l i z a t i o n of the formula for nucleon (= 3-quark) clusters alone (eq. (2°4))° I t contains the structure functions Ni/A(Z ) for the. i-quark clusters in the nucleus folded with i t s c l u s t e r structure function F21: F2(x,A ) =

Adz i x Z f T F2 (~) Ni/A(Z) i=3~6~9 x

(2o16)

with F21(Y) • = ~ 3A Z ej2yoNq/i(y)o j=1

(2o17)

The d i s t r i b u t i o n function of the quark in the i-quark c l u s t e r is denoted by Nq/i(y ) Note y varies between 0 S Y ~ 1 but z varies between 0 < z < Ao The c l u s t e r probab i l i t i e s Pi to find a quark in an i-quark c l u s t e r are obtained by i n t e g r a t i o n A Pi = J dz Ni/A(z)o (2o18) 0 A simple approximation for Ni/A(Z ) is a Gaussian model with a mean < z > = i / 3 and a dispersion determined from the Fermi Gas Model ~. 2 I

=

<

z2

>

-

<

Z

>2

-

i k2 < (kz + Z~ o+k

~/3)2 >

(2.19)

( i / 3 1 ~ ~

For ~ we have ~ = i/5(kF2/m 2) and analogously f o r the higher clusters° In He3 the 6q-cluster has to carry the same momentum as the nucleon, and the 9q-c!uster is at rest° Eqo (2o19) neglects these f i n i t e A~effects I

Ni/A(Z) - ~i2#~-

e-(Z-i/3)2/2~i 2

(2°20)

Deep Inelastic Lepton-Nucleus Scattering

383

Note that the c l u s t e r motion is small compared to the width of the nucleon struc ture function i f one i d e n t i f i e s at low Q2 the d i f f e r e n c e between F2P - F2n as the s t r u c t u r e function of the valence quarks° Some papers have l e f t out the averaging and set Ni/A(Z) = ~(z - i / 3 ) o N a t u r a l l y the real r e s u l t f o r F2(Fe)/F2(d ) w i l l be a bigger r a t i o than the so obtain, ed t h e o r e t i c a l r e s u l t ° The s t r u c t u r e function of the higher m u l t i - q u a r k c l u s t e r s F21(x ) can be obtained f o r x ÷ i from counting rules ( S i v e r s , 19821 Sivers and others~ 1976) and f o r x-~ 0 from Regge behaviouro Analogously to the large Q2-behaviour of the e l a s t i c formfactor one can count the minimal number of energy denominators to create a very f a s t partonl then one has ( i - I ) g]uon exchanges and energy denominators° At each i n t e r a c t i o n the l o n g i tudinal momentum c of the ( i - i ) spectator quarks is t r a n s f e r r e d to the leading parton which then has the maximum f r a c t i o n of momentum " F21(x)dx

= x Nq/i(x)dx = x f d2k,~(x,k±)

dx

(x~ka) x

_

(2,21) = const o dx f d_~sII dk],(-~z )"2-i - 2 ~ ( x _ i &P

+ c - !)

kz 2 =

with

AP

sp+

°

Each "energy" denominator is proportional " x ÷ 1 F2](x ) ~ >

(1 -

x)2i-3

to I / ( 1 - x)o in t o t a l we obtain

o

(2°22)

For the nucleon the power i s 3~ e x p e r i m e n t a l l y at low Q2 the power varies between 2°7 and 3ol. For the higher c l u s t e r s because of more momentum sharing the decrease is f a s t e r ° For x = Q2/2mv ÷ 0 the photon is almost realo I t behaves l i k e a hadrono From consistency with Regge-behaviour one gets f o r small x F2i(x ) - ~

xi/2o

Combining these two l i m i t s we can estimate the l a r g e r c l u s t e r d i s t r i b u t i o n tions + F 2 i ( x ) = const o x l / 2 ( L = x)2i-3+21&Szl °

func(2°23)

The formula of eqo (2°23) only represents an educated guess based on the counting rules° Judging from the nucleon ( i = 3) i t s v a l i d i t y ~ however~ may be b e t t e r than its derivation° The sea quark and gluon d i s t r i b u t i o n of the multi-quark system has not y e t been determined° I t was estimated (Carlson and Havens, 1983) that the sharing of the energy between quarks and gluons is u n i v e r s a l l y 50%/50% as in the nucleon° But b e t t e r bag models should get a more precise number° In Fig° 2°4 one sees the r e s u l t of the c a l c u l a t i o n f o r He3 neglecting a l l f i n i t e mass corrections (M2He3/Q2 ÷ 0)o (These corrections amount to using the Nachtmann

+In the exponent As z = Sz(target ) - Sz(COnstituent ) presents a f i n e r d e t a i l due to nature of the exchanged gluon~ whether i t i982)o

is transverse or l o n g i t u d i n a l

(Sivers,

Hans J. Pirner

384

vW2 ~_.~

T

10-I ~ \

Tota~ \

lo -2 5 . \

8~" \ \

\ -\

10-3

\

9q'\ \

10-4 i

XX\

io-6 0

Fig° 2°4°

1

x

Quark c l u s t e r contributions to the structure function of He3 (Pirner and Vary, 1983)o

variable x = 2XB/(1 +~I + 4m2xB2/Q2) instead of x B = Q2/2Nbo) The curve shows the 3q-cluster d i s t r i b u t i o n declines sharply at x = Io0 and the 6q~clusters take over° The best f i t to the data with f i n i t e mass corrections is given in Fig° 2°5° I t corresponds to He3 being He3:

+ 86% nucleon + 13% 6pquark c l u s t e r +

i%

(2°24)

9-quark cluster

Note there is s t i l l some q u a s i - e l a s t i c peak at these energies° We have included i t a d d i t i v e l y with harmonic o s c i l l a t o r wavefunctions (Pirner and Vary~ !98!)o More recent calculations (Pirner and Vary: 1984) have been done using the "best" Fadeev calculations f o r the three-body nucleon wavefunction: One obtains a somewhat smaller percentage of six-quark clusters p= = 10% because part of the short-range NNcorrelations are taken into account b~ the wavefunctiono But note using correlated nucleon=basis functions does not change the parameter Rc, the e f f e c t i v e radius of l o c a l i z a t i o n of the valence quarks° I t stays at about Rc = 0°5 - 0°55 fmo This small radius may be contradictory to the charge of 0.8 fm mentioned at the beginningo In the c l u s t e r model i t is r e a l l y a dynamical quantity characterizing the two-nucleon system~ not one free nucleon° Even i f the t a i l s of the quark wavefunc ~ ~ns in two nucleons overlap, the i d e n t i t y of the nucleons is respected° This seems to be in agreement with the success of e f f e c t i v e meson exchange models of the nucleon-nucleon force° These can well be calculated to distances &R ~ i fm: below this range they are phenomenologically determined, The confinement region may well be larger than Rco In a dynamical theory of color in the nucleus (see l a s t chapter)

Deep Inelastic Lepton-Nucleus Scattering

.38

,27

.20

.15

.56

vW2 [ - -

385

.43

.34

,27

.22 ( ,18

I

I

I

t

1 j

vW2 1 - -

10-1

I0-1

10-2 t0-3

!0-2

/% / ; / 2~

2

'

I!

10-4.

10-3

//

!

I

I

.5

I

110

1.5

I.

20

t

•~0-5L] .5

v [GeV ]

Fig° 2°5°

L 1.0

I E--14.70 GeV f &3~
/__~° ,{

10-4 i

10-B L

/ '/'i t" / ,

q

J 1.5

L 2.0

J2.5

_L~ 3.0

v [GeV]

Results of the s t r u c t u r e function vW2 as a function of energy loss at 0 = 80° Theoretical curves ( P i r n e r and Vary~ 1981) are c a l c u l a t e d with Rc = O, 0o45, Oog fmo

the e f f e c t i v e extension of the color modes in the nucleon i s a Q2-dependent quant i t y ° We w i l l discuss i t there in more d e t a i l ° For the quark c l u s t e r model the real t e s t i n g ground is the region x > i of the nuclear s t r u c t u r e function° I d e a l l y the 1 < x < 2 region depends on the six-quark clusters~ 2 < x < 3 on the nine-quark c l u s t e r s and so on° For small x the e x i s t i n g sea quark estimates in a l l c l u s t e r models (Carlson and Havens: 1983; Chemtob and Peschanski: !983~ Cleymans~ 1983~ Date and Nakamura, !983~ Date and others, 1984; Dias de Deus~ 1983; Efremov and Bondarchenko~ !984; Faissner and Kim~ 1983; Jaffe~ !983; Krzywicki and Furmanski~ 1983; Pirner and Vary° !983; T i t o v , 1983) are rath~ er crude, therefore t h e i r p r e d i c t i v e power is l i m i t e d ° A simple understanding of the new SLAC-data can be obtained in the c l u s t e r model° Let the r a t i o p = F2(x,A,Q2)/ F2(x,d:Q2 ) be given by three and six-quark c o n t r i butions only (~5 = P6 ÷ P9 +°°°)° The s t r u c t u r e functions of these c l u s t e r s are given by eqo (2°23) P3(A)(l - x) 3 + p~5(A)olo20(1

- x/2) I0

p(x)~

(2°25)

P3(d)(1 - x)3~ + P6(d)olo20(1 - x/2) ~ where the c o e f f i c i e n t s are obtained by normalizing the valence quark d e n s i t i e s ° i t is easy to f i n d the minimum of p(X)o I t is given i n ~ @ n d e n t ~ , of P3~6(A)~ p3~6(d) at X = 0o6~

which approximately agrees with the SLAC-datao The value at the minimum is PIP M*

(2°26)

386

Hans Jo Pirner

p(x : 0°6) = I - OoSo(P6(A ) - P6(d))o P l o t t i n g t h i s value against mass number A one sees t h a t f o r Rc = 0o5~ i.eo with the Pi values of Table 1 one gets p = 0.87 instead of p = 0.80 experimentally° We i n t e r p r e t e t h i s as an i n d i c a t i o n t h a t the e f f e c t i v e c r i t i c a l radius parameter has to be increased when Q2 increases° A good f i t can be obtained with Rc : 0°65-0°7 fm, Then P3 + P6 = P~'6 in Pb equals 50% and P6 in the deuteron 10%o We t h i n k t h a t a Q2_ dependent c r i t i c a l radius i s the key to preserve low-energy nucleonic r e s u l t s but have at the same time a s i z a b l e admixture of deconfined quark states in the nucleus when the size of the e f f e c t i v e quarks 1/Q2 is diminished° We w i l l see a color d i e l e c t r i c model has these features° In low-energy nuclear physics i t would also be i n t e r e s t i n g to see how much of the weak and electromagnetic c o r r e c t i o n from exchange currents can be absorbed i n t o m u l t i - q u a r k configurations° T r a d i t i o n a l c a ] c u l a t i o n s are r a t h e r convincing f o r the one-pion exchange~ where the exchange current is given by low-energy theorems° They become doubtful the more numerous and more shortranged the meson exchanges become° DELOCALIZATION OF COLOR IN NUCLEi: THE GLUON STRUCTURE OF THE NUCLEUS Deep i n e l a s t i c electron s c a t t e r i n g determines t h a t 60% of the momentum of the proton are c a r r i e d by gluon f i e l d s (ego (io47)o In the low-energy p i c t u r e the confinement i s thought to be caused by gluonso Yet many models l i k e the c o n s t i t u e n t quark model and the MIT bag model can describe the s t a t i c p r o p e r t i e s of nucleons q u i t e well without them. How i s t h i s possible? On a length scale of (0°5 - 1) fm = I/AQc D the gluon degrees of freedom of t h i s length scale can be associated with the i n d i vidual quark converting i t i n t o a c o n s t i t u e n t quark or bagged quark° Therefore l e t us assume a model of the nucleon with quarks surrounded by ~luonic clouds or a quark core in a gluonic bag. Then at low Q2 deep i n e l a s t i c lepton-nucleus e x p e r i ments can be well described by nucleon s t r u c t u r e functions modified only s l i g h t l y due to the overlap of the quark f i e l d s ° Gluon r a d i a t i o n i s not very important~ In Q2/A2 is small° The gluonic cloud may be described by a mean color d i e l e c t r i c f i e l d X(X)o For a f r e e nucleon X = 1 i n s i d e the nucleon and × = 0 outside° No color degrees of freedom are allowed where the color d i e l e c t r i c constant e = X 4 i s zero° In a nucleus the color d i e l e c t r i c constant e becomes unequal zero outside of the nucleons° The nuclear medium allows quarks to leak outside of the nucleons in the nucleus° This leads to a softening of the nucleon s t r u c t u r e function° !n the l i m i t of large Q2 t o t a l color c o n d u c t i v i t y i s obtained as was discussed by Nachtmann and Pirner (1984a~ 1984b)o Nith several methods (Mack, 1984~ Nielsen and Patkos, 1982) i t has been shown how one can define an e f f e c t i v e theory of QCD, which has confinement properties° They define a new e f f e c t i v e gauge f i e l d Bu together with a scalar f i e l d X such t h a t l o cal gauge invariance can be obtained-by using the c o v a r i a n t d e r i v a t i v e X ~ - BUD X is the color s i n g l e t part of the averaged phase f a c t o r (Nc = numbe, of cOlD, s) 1 X(Xo) =-N~ c T r a v P exp(i / A (x)dx~ ) o xo B is the f i r s t - o r d e r d e r i v a t i v e : ]~ x 1 B~(Xo) = 3-~--x--av P exp(i / ~A (x)dx~)o ]~ x~

(3oi)

(3°2)

By i n t e g r a t i n g out the old gauge f i e l d s A over a b!ockspin c e l l they obtain the f o l l o w i n g Lagrangian

387

Deep Inelastic Lepton-Nucleus Scattering B~ L = i X 17yu (3# -X-->? -#T@ mq + av 2 ~ (SpX)2 1

- u(x) ~ x

4

~v

I~v

(3°3)

°

with r#v = (~p ~ ~ / X ) ~ / X - (~v - ~ / X ) ~ / X , and mq(Q2) as c u r r e n t quark mass and g2(Q 2) as the QCD-coupJing constant° U(X ) is a polynomial in X, which has the f o l l o w i n g l i m i t s : U ~ = 1) = B, the bag constant, and the vacuum value of U = 0 a t x = Oo N e a r x = 0 we can expand U(X ) and get U(×)

=1

2u,

2

~----~gXZ,x=O ° X

i

2 2 2

(3°4)

= ~mGB a v X ,

where mGB is the glue ball mass and a v the scale Of Xo Note in the s o l i t o n bag model of Friedberg, Lee and Wilets (1977, 1977, 1979, 1982) × has to be i d e n t i f i e d with X = ( ~ v ~ ) / a v o Therefore we associate av with the scale o f x . av can be related to the s t r i n a tension° T h e x 4 m u l t i p l y i n g the e f f e c t i v e color f i e l d tensor r~vF ~V in eqo (3.3) p]ays the role of color d i e l e c t r i c constant c =X4o I t is well known that the d i e l e c t r i c constant e =X 4 becoming zero in the vacuum does not allow c o l o r e l e c t r i c f i e l d s outside of hadronso By rescaling the fermion f i e l d s ~ the fermion Dart of the Lagrangian becomes without gauge f i e l d s L F = i ? y DU? -,#? mq/X°

(3°5)

We recognize the f a m i l i a r NIT bag mode7° In the l i m i t X + O, near the bag boundary, the quark mass becomes i n f i n i t e , and there is absolute confinement° Inside the bag X = 1, and the quark has i t s c u r r e n t quark mass° The energy of the MIT bag has the usual form 3x~°~ +]~- R3oB R

-

EBag -

(3°6)

with m < i because of center-of-mass corrections°

dEBag/dr = 0 determines the nu-

cleon mass mN = ~Xo/Ro Now when we embed t h i s bag in the nucleus, X w i l l

not be

zero outside of the bag° Quarks and gluons are suppressed, but may e x i s t ° In the Wigner-Seitz approximation we choose a c e l l of radius r o such that the nuclear density =

1

(3°7)

T - ws ° Inside t h i s Wigner ceil we place the nucleon with the boundary condition that X + ~N outside of the nucleon radius. We neglect a l l g r a d i e n t terms f o r a f i r s t ap proxlma~1on, a more accurate c a l c u l a t i o n has to include the f u l l U(X ), and the r dependence of Xo Then we get as boundary condition f o r the bag wavefunctions ~/~ - mq o J1(kR) =#m~-~ = m

+ mq

Jo(kR)

I

(1 +

• m o +~--~

2.v_22,.)

R~,m~o

(3°8)

where k2 + mq 2 = 2 and m o = mq/XNo We expand around m = xo/R = 2°04/R, for light quarks mq = ~ = I/2(m u + md) = 0

388

Hans Jo Pirner

m

.

XO (I 1=~____)

XO

R

R

.

.

.

2moR

(I -

X )o 2mqR

(3o9)

The i n t e r p r e t a t i o n of eqo (3°8) is simple: the quark wavefunction is allowed to spread beyond the normal nucleon bag because X = XN # 0 outside of the nucleon° This way each quark gets an energy m which is loweP than the c a v i t y eigenvalue xo/R of a quark in a f r e e nucleon° Consequently the whole nucleon f e e l s an a t t r a c t i v e p o t e n t i a l ° The force keeping X near i t s vacuum value is given by the s e l f i n t e r a c t i o n terms U(X) (eqo(3o3))o We combine the quark energies m with the energy of the vacuum e x c i t a t i o n which r e s u l t s from changing X from i t s vacuum value X = 0 to the value XN in a shell between the boundary RWS of the Wigner-Seitz c e l l and the bag boundary Ro We obtain 3mXo

E(X) = m N + W(X) = - - - + T R

4~

R3B -

3XoX ~

4~

3

I

2

2 2

~ - R3) X o ' "3-" (RWS T mGBav

(3o10)

q

The energy of the most stable state w i l l be given by the X f i e l d which minimizes E(X)o I t corresponds to a mean p o t e n t i a l energy W of the nucleon in the nucleus° In p r i n c i p l e the t o t a l energy consisting of E(X ) and the k i n e t i c energy of the nucleons in the nucleus should be minimized. But the d i f f e r e n c e between the two procedures is not s i g n i f i c a n t i f one neglects terms of order W2/mN2o We also varied the bag radius R but found very l i t t l e change of the minimal energy with respect to Ro We obtain f o r the minimum value of E(X ) at XN given by eqo (3o10) 3

mN

XN-- 4 2mqR(8~)(~ -"3KWS - K~ , J ~i rr'GBCv

o

(3oii)

l~ ~uu4 \vlxlt

t,

:

\N

0.2

Fig° 3olo

O.~

0.6

0,8

tO

1.2

I.~

t6

1.g

2.0

Components u ( r ) and v ( r ) of the quark wavefunction in the free nucleon (dashed l i n e ) and bound nucleon (R = 0°83 fm~ mo = 0°8 GeV)o

Deep Inelastic Lepton-Nucleus Scattering : 20 ~eV~ p = 0o17 fm-3o. VN = ~ Choosing gets f o r X~

R3 = 2°4 fm3~. 'G2B~vm 2

XN = 0°023° The r e s u l t i n g

potential

389

0°4 GeV4o one (3oi2)

W(XN) has the c o r r e c t magnitude (3.13)

~i(X N = -50 MeVo

Of course~ the above expression is only v a l i d f o r low nuclear matter density where (to/R) 3 = I/(poVN) > Lo At l a r g e r density a more accurate d e s c r i p t i o n of the t a i l s of the overlapping wavefunctions in d i f f e r e n t B- f i e l d s also become more important°

nucleons is necessary° The e f f e c t s of

F i n a l l y we want to look at the e f f e c t i v e b a r r i e r which the l i g h t quarks see in the nuc~euso m m =~ (3oi4) o XN Putting into t h i s equation the above numbers, we get that mo = °8 GeV at Q~ £ 1 GeV2 Increasing the resolution~ ~(Q2) w i l l evolve with the anomalous dimension d -

4 Ii-2/3f

where f is the number of f l a v o r s Q2 ~ and mo w i l l decrease°

mo(Q2) : mo(Q ) ° (

( f = 2)° We t h e r e f o r e expect t h a t with increasing

)do

(3oi5)

g~(Qo ~ ) Consequently~ at large Q2 : 100 GeV2 mo(Q2) is only 600 MeVo The nucleon w i l l t h e r e f o r e swell to a larger size f o r higher r e s o l u t i o n ° Note t h a t in t h i s color d i e l e c t r i c model of the nucleus there are only f i n i t e b a r r i e r s f o r quarks and gluons between d i f f e r e n t nucleons° Therefore also color modes may extend over the whole nucleus (Nachtmann and P i r n e r , 1984b)~ Fig° 3°2° Note the model we presented has two types of cut-offso A high-momentum scale Q2 2 2 which determines ~(Q2/i~rn)~ and g(Q /AQC~), and a low-momentum scale AQCD which can ~ 2~ mGB 2 "and ~ Bo A change in the high-momentum c u t - o f f ~2 w i l l a!so be tel ated to ~v influence the long distance p r o p e r t i e s of the quark wavefunctions in the nucleus via ~(Q2)o The model here gives a connection between the quark size L/Q 2 and the extension of quark wavefunctions confined in the x N - d i e l e c t r i c medium° I t provides an example f o r c o l o r c o n d u c t i v i t y of e f f e c t i v e quarks seen with high r e s o l u t i o n Q2 (Nachtmann and Pirner~ i984b)o At low Q2 the confinement size of the quark w i l l vary as a function of density P or of the size of the Wigner-Seitz cello We have calculated the e f f e c t i v e confinement size of quarks with e f f e c t i v e size L/Q 2 where Q2 = 1GeV 2 f o r various nuclei° They are shown in Table 2°

390

Hans J. Pirner

co

m2Zx,,

}

ao

4

IocaUzed I extended

-L/2

Fig° 3°2° TABLE 2

=~/2

+Z/2

+L/2

Localized and extended modes in a one-dimensional A = 2 nuclear system.

shows the size of the Wigner-Seitz cell which a nucleon has available for i t s e l f in d i f f e r e n t nuclei° < r 2 >1/2 is the romoSo radius of the quark d i s t r i b u t i o n °

A

RWS (Wigner-Seitz)[fm]

N

< r 2 >L/2[fm] 0o61

d

2.0

0o612

He3

1o55

0°62

Fe

1.25

0°66

Au

Io16

0°69

nuclear matter

1o12

0°72

We are s t i l l in the process to analyze this preasymptotic region and calculate the structure function of weakly deconfined quarks° Once color conductivity is established the QCD-scaling corrections discussed in the f i r s t chapter can be calculated (Nachtmann and Pirner ~ 1984a, 1984b)o We f i x the short-distance resolution I/Q2 but vary the long-range c u t - o f f which is now given by the nuclear size° We assume a series of isoscalar nuclei with radii RA < RA+2 < RA+4oo~ Due to the de-

Deep Inelastic Lepton-Nucleus Scattering

391

crease of the cut-off of transverse momenta from I/R A to I/RA+ 2 < I/R A new modes of the QCD fields can become occupied° The change in the gluon d i s t r i b u t i o n &NG can be calculated i~ an analogous way as before (eqo (1o51))o

ANG(x) = s,= PGq(X)In

R~+2 o

(3o16)

The PGq is the s p l i t t i n g function for a quark into a gluono For ~ two possible alternatives exist; (i)

~ = g(Q2), the running coupling constant determined by the resolution I/Q~

( i i ) ~ = const~ a l i m i t i n g value of the running coupling constant for low Q2o This l i m i t may be quite small despite confinement° Combining the evolution of the quarks and gluons one obtains an evolution equation similar to the A l t a r e l l i Parisi equation (eqo (Io53)) Ni(x~Q2,A+2) - Ni(x~Q2,A ) = ~2 - g

Q2R2 1 dy x in(~ '~+2)~ Z f m PiJ(~ ) NJ (y'Q2'A)°

-

j

(3o17)

x

0 i x ~ io Eqo (3o!7) neglects the t a i l s of the nuclear d i s t r i b u t i o n functions Ni(x,Q2~A) for x > 1o They are very small < 1% and do not effect the smaller xrange x ! 0o7~ For the region near x = i they would be important° The primordial cluster structure functions at low Q2 treated in the second chapter tend to a larger Nq(X,A) for x ÷ i when A is bigger due to the higher density of the heavier nuclei° The QCD-radiation is stronger for heavier nuclei with larger radii~ so the QCD-evolution w i l l reverse the ordering of structure functions at larger x > 0°8° ! t must be noted, however~ that the region x + l poses a d i f f i c u l t problem for the isolated nucleons because at the end of the kinematical region higher twist effects due to final state interactions are no longer suppressed by large Q2o in nuclei the kinematical region is O ! x ~ A~ so probably this problem does not occur° The main property of eqo (3o16) with ~ = g(Q2) can be obtained by comparing to the equiva ~ lent equation where the high momentum cut-off is varied (eqo (io51))o The comparison implies ~Ni(xoQ2~A) In R~

~Ni(xoQ2,A)

(3o18)

~ In Q2--

consequently, the d i s t r i b u t i o n functions are only functions of x and Q2R~o Also the structure functions F2(x,Q2~A ) s a t i s f y the scaling law

r2(xoQ2oA) = (xoQZoR )o

(3olg)

Any change in the nuclear radius at fixed Q2 can be related to a change in the resolving power for fixed radius° Me must~ however, emphasize that eqo (3,18) vio ~ fates the assumptions of the standard operator product expansion analysis in the f i r s t non-leading order of mso Comparing a heavy target nucleus (A) to deuterium (d) as has been done by the EHC we find g2 (x,Qm,A) : Fm(x,Q2R~/R~,d) = Fm(x:Q2,d) + 8F2(x'Q2'd)_-2--- l n ( ~ ) o In q Rd

(3°20)

392

Hans J° Pirner

b~P F

~

'

'

0.5 ~0.40,3 ~ 0.2 - # 03

,

-0.%

f

~

-0.2

I

-0.3

i

-0.5 0.2

0

0.~

O_g

X

In F# p Fig° 3°3°

I f we r e s t r i c t the EMC-ratio

The scaling v i o l a t i o n parameter bYP(x) (Aubert and others, 1980)o

ourselves to f i r s t - o r d e r

p(x)

3 1 n Q ~#

logarithmic scaling v i o l a t i o n s ,

we get for

2 Fz(x'Q2'A) bYd RA = F2(x,Q2 d) = i + oln R-~d ,

(3oZi) by d =

In F2(x,Q2~d ) In

Qg

Such a parameter b is sometimes used to describe scaling v i o l a t i o n s

(Fig° 3°3)° We

have used bYp (Aubert and others~ 1980), the parameter describing scaling v i o l a t i o n s of the proton, assuming that b does not depend on the target in leading order° With eqo (3o21), bYd m bYp, we calculate the r a t i o p of the iron and deuterium structure functions using the r.m°So radii Landolt-BSrnstein) In(

~)2

13o74 fm~2 = In~-TT7--## j = 1oi F2(x,Q2~Fe)

p(x) -

- i + bYP(x)ololo F2(x,~,d)

(3°22)

Deep inelas[ic Lepton-Nucleus Scattering

393

P 1,4 1,3 k

t,1 }~/~~)x~

x"

0,8 0

Fig° 3°4°

0.2

0o4

006

x

The EMC-ratio p = F2(x~Fe)/F2(x,d ) = 1 + bYPolol calculated in the model of color c o n d u c t i v i t y °

The r e s u l t i n g t h e o r e t i c a l p r e d i c t i o n is shown in Fig° 3°4° Considering the errors both on b and the EMC-ratio we see t h a t our eq° (3°20) is q u a l i t a t i v e l y supported by the data° E s p e c i a l l y the r a t i o p crosses p = 1 at x = 0o3~ where also the scaling v i o l a t i o n s vanish° For x + 1 and, of course~ f o r x = 1 we w i l l have to take i n t o account the t a i l s of the quark d i s t r i b u t i o n s in nuclei extending beyond x = 1, which we have neglected in eqo (3o21)o Q u a l i t a t i v e l y t h i s w i l l increase p again° We see the simple renormalizatien group argument may explain the 0 < x < i behaviour of the s t r u c t u r e functions of nuclei with d i f f e r e n t r a d i i ° Larger nuclei l i k e lead should show a mere d~amati¢ e f f e c t : since In(~)

2 = 2/3 in A : 2o7~

(3o23)

the r a t i o F2(x~Q2,A)/F2(x~Q2,Fe ) should increase l o g a r i t h m i c a l l y with nucleon numbore

PA/Fe(X) = I + bYFeo(2/3 in A - 2°7)°

(3°24)

Eqo (3°24) can be checked best by taking a series of nuclei as targets° Taking the option (b) with g as coupling constant (Nachtmann and Pirner~ 1984b) f o r low pz modes in nuclei we define

394

Hans Jo Pirner

~s = ~2/4~

(3025)

and obtain instead of eqo (3.18) Ni (x'Q2'A)

In-T-

~s

a Ni(x~Q2,A )

R:

Q7

In

(3°26)

Expanding around a nucleus Ao up to terms of f i r s t we find a r e s u l t s i m i l a r to eqo (3°20) Fm(x,Q2,A) F2(x ~

-

order in the scaling v i o l a t i o n s

R2 I A ~ s / ~ Q 2 j '' i + b(x,Q2,Ao ) In ~ j

(3°27)

RAo We have also compared the second formula to the EMC-ratio (unfortunately the SLACdata do not give b(x,Q2,A))° We use the scaling v i o l a t i o n parameter for b(x:Q2,Fe) (Rith)o We find for the ENC-ratio the linear curve of Fig° 3°5° The agreement is not perfect: I f we use the maximal systematic error of 7% and s h i f t the Fe/d data downward, the r e s u l t of Fig° 3.6 would obtain° We emphasize that the agreement should not be perfect. We are only considering an expansion to f i r s t order in scaling v i o l a t i o n s , and for large x we can expect the d i f f e r e n t kinematic boundaries for the deuteron (x = 2) and iron (x = 56) to play a role. We must also keep

i

i

~

i

c~

i

Fe/D I ~-b" 1.2

~o

'L3

+ 1,2

Q z~ LL "~

1.1

1 . 0 - -

z~

Q.9

O.B --I

Fig. 3.5.

OL.2

[

I O.4

~

I ~ 0,6

i

The EMC-data for F2(Fe)/F2(d ) as a function of x (Aubert and others, 1983) and the quantity 1 + b(x°Q2~Fe)olo2, where b = ~ In F2/~ In Q2 (eqso (3°26) and (3°27))° The data f o r b are from the EMC iron measurements.

Deep Inelastic Lepton-Nucleus Scattering

i

E

r

i

J

+

~

r

Fe/D

1'3i Z

i

395

1<.b'1.2

1.2

~.1 . , ~ . ~

Z~

1.o b~ Z~,d

0.g0.8 0.7t o

Fig° 3o8°

L

o+2

r

i

0.4

J

0.6

J

X

Same as Fig° 3:5 but the data f o r F2(Fe)/F2(d ) s h i f t e d downward by 7%°

in mind t h a t we have neglected in our discussion a l l heavy quarks° These w i l l con ~ t r i b u t e to the Q2-evolution° mostly at small x, but not to the nuclear evolution° I t is~ therefore~ q u i t e reasonable that the smallest x data point f o r 1 + b~ l i e s higher than the corresponding point f o r Fe/do We conclude that ~/ms(Q 2) = 1:1 ± 0o1 is s l i g h t l y preferred by the data° N a t u r a l l y also the gluon d i s t r i b u t i o n would evolve going from the deuteron to iron according to our equation (3o17)o I n d i c a t i o n s are in t h i s d i r e c t i o n from recent data on J/~ production by the EMC (C°fo Dr° Gabathuler~s t a l k in t h i s school)° Among the other models which have been proposed to explain the EMC-effect the model of Close: Roberts and Ross (1983) and of J a f f e and others (1984) is most s i m i l a r to the discussed QCD-radiation here~ The authors of these papers state that the e f f e c t i v e confinement radius increases f o r nucleons in the nucleus° They deduce from a c l u s t e r type model Ref f = (P3RN + P6R6) = RN(1 +[(R 6 - RN)/RN]oP6)° They get a 25% increase of Reff/R N f o r Au 197 by having R6/R N = 21/3o This corresponds to a P6 = 100%o For such a large p r o b a b i l i t y to have six-quark c l u s t e r s the system w i l l be already percolated° Our approach has been c r i t i c i z e d (Llewellyn Smith~ 1983) f o r i t s a p p l i c a t i o n on the deuteron° Commonly i t has been assumed that the r a t h e r weakly bound deuteron s t r u c t u r e functions are representing the sum of neutron and deuteron s t r u c t u r e functions rather accurately° One has deduced from the r a t i o (F2d

F2P)/F2P then the r e l a t i v e magnitude of the u/d quark d i s t r i b u t i o n

functions

396

Hans J .

Pirner

This r a t i o would show a dramatic x-dependence according to the new EMC-data (Drees and Montgomery, 1983; Rith, 1983). A d i r e c t measurement of ~ P and F~P reproduces up

to s-quark effects the same r a t i o ,

ioeo

F~n/F~ p = 1/4 + 5/24 FvP/FUPo

(3o28)

A combination (Drees and Montgomery° 1983) of EMC and SLAC experiments with the BEBC neutrino data gives a weaker deviation from the r a t i o of u/d = 0o5~ which corresponds to the uncorrelated r e s u l t of 2 u's and i d in the proton° Applying the color conductivity correction to the deuteron we can correct the deuteron data in such a way that the neutron and proton structure functions can be compared: ioeo if F2~d(x ) - F2PP(x ) R= , (3°29) c #P then the color conductivity corrected Rcorr is Rcorr = Ro(I - bYPoln(Rd2/Rp2)) - bYP°In(Rd2/Rp2)O

(3°3o)

The r e s u l t of Rcorr in Fig. 3°7 is not in contradiction with the neutrino measurements on the proton° We conclude at large Q2 even the deuteron shows effects of color conductivity.

1.0

1,0

-I

0.8

L~ ~'~ 0.8 >('4 L~ "¢ O4

016

0.6

0

u

-

LO +

0.2

0.4

-Q

0 0.2

o

Fig° 3,7°

0

0.2

0.4

0.8

0°8

1.0

X

The r a t i o R of quark d i s t r i b u t i o n functions d/u in the proton from combined ~p and ~p-data (Drees and Montgomery~ 1983) (small squares) and Rcorr from the color conductivity corrected F2~d and F2PP data (dots). The naive quark model gives d/u = !/2 f o r the proton wavefunction P = uudo

Deep Inelastic Lepton-Nucleus ScaEtering

397

Another application of the model is to the phenomenon of nuclear shadowing (Grammer~ jro and Sullivan~ 1978), which t e l l s us that in the l i m i t x ÷ 0 the nuclear structure function w i l l not be proportional to A but to A2/3o There is experimental evidence for t h i s effect in real photoproduction (Q2 = O) and in small Q2 electroproductiono We have made a simple ansatz for the nuclear structure function and parton densities per nucleon incorporating shadowing° We consider shadowing a leading t w i s t effect° F2(x,Q2 ,A) = F2(x:Q 2 oRA/Rd,d)o 2 2 f(X,Xc,A),

(3o3i

ioeo~ we assume for the quark and gluoin densities Nq~ NG 2 2 2 xN~(x~Q2~A)j = xNj(x~Q oRA/Rd,d;o f(x~x~,A)o~

(3°32

Most of the nuclear dependence is pet into rescaling Q2 as indicated in eqo (3°32 The function f ( x , x c , A ) takes care of shadowing in the small x ~ x c region, ioeo

f(X~Xc~A ) =

i

x [Tc+

A -i/3 (~) (z ~

)]

x<_x c

(3°33)

L

t

x >_ Xco

The x-value where shadowino disappears is Xco We insert eqso (3o3i: 3°32) into the sum rule MA/MN

I 0

,

,

dx x ~ N~[x~Q2~A) j J

MA

(3°34)

AoM

and replace MA/AM by the Bethe-Weizs~cker formula MA -

AoM

bv bs 1/3 I - - - + - - A= M M

(3°35)

I d e n t i f y i n g terms of the order A:1/3 on both sides of the sum rule we get a relation between b s and Xc; bs- = X~c~xo~ 2 2 M 2 ' j N.(x 'j ,Q2 RA/Rd~dZr, °21/3 ix= 0

(3°36)

and between bs, bv and the binding energy of the deuteron c B = 2 MeV: ms = (b v - ~-~B)o21/3o 2

(3°37)

We find bs = 18o2 MeV which agrees with the experimental value for bs within 6%° Setting the gluon density at small equal to the quark densities x ~ Nj(x,Q 2~d) m 2°~ --~8 F2(O,Q~2,d)~ J we get ×c = 0o0!5o

(3°38)

398

Hans J° Pirner

The conventional p i c t u r e would give shadowing when the conversion length of the photon into a p-meson before the nucleus is longer than the mean f r e e path of a p-meson in the nucleuso i : e ° v ~ > >

L - - =

2 fmo

P~N

p

(3°39)

For Q2 >> m 2 t h i s gives Q2/2M~ = 0°04° p We have also discussed various other problems which are a f f e c t e d by a d e l o c a l i zation of color in nuclei° I enumerate them here and r e f e r f o r d e t a i l s to Nachtmann and Pirner (1984b)o (1 (2 (3

Test of Wilson's operator product expansion with nuclei° Harder fragmentation f u n c t i o n D(Z~A) in l a r g e r nuclei i f there is no rescatter. ingo Softer p z - d i s t r i b u t i o n in l a r g e r nuc]eio

With color c o n d u c t i v i t y the EMC-effect is r e l a t e d to a ~L1obal property of the nucleus; i t s size° This is in c o n t r a s t to other models l i k e enhanced T-meson e f f e c t s or p a r t i a l c l u s t e r i n g in nuclei or swelling of the nucleons which r e f e r only to local p r o p e r t i e s of the nucleus° We propose a c r u c i a l t e s t to d i s t i n g u i s h between these two classes of models: deep i n e l a s t i c muon s c a t t e r i n g on a deformed nucleus. Depending+on the o r i e n t a t i o n of the deformed nucleus r e l a t i v e to the photon threemomentum q we should see d i f f e r e n t s t r u c t u r e functions i f our model is correct° This comes about since the low PT QCD-radiation which we discuss depends on the radius of the nucleus transverse to the photon momentum° A good candidate to study may be Ho165~ which has an i n t r i n s i c quadrupole moment (Powers and others~ 1976) of 7.53 ± 0°07 fm2° The contour l i n e of 50% charge dens i t y shows a cigar-shaped nucleus with a long semi-axis of RI = 7°04 fm and short semi-axes of R2 = 5o12 fmo Let us now consider deep i n e l a s t i c muon s c a t t e r i n g on t h i s deformed nucleus in two o r i e n t a t i o n s (Cfo Fig° 3°8): e i t h e r with the long nuclear axis or with the short nuclear axis aligned along the photon momentum d i r e c t i o n s r e s p e c t i v e l y ° We denote the corresponding s t r u c t u r e functions by F~ and F~° The transverse area of the nucleus seen by the v i r t u a l photon in the ca~es (a) ~and (b) is d i f f e r e n t . According to our philosophy t h i s means t h a t in going from case (a) to case (b) a c e r t a i n number of low PT modes is thawed° Taking eqo (3°25) f o r the coupling parameter of these modes~ we f i n d from a simple c a l c u l a t i o n F2 b(x~Q2) - F2a(x:Q2)

~s

F2a(x,Q2 )

= ms-~)

I = In (

2R1

a In F2a(x,Q2 ) !n QT-=-- ° I,

(3°4o)

)2

R1 + R2 (x~q 2) - F2a(x,Q2) ~ =-0.065°

The d i f f e r e n c e between the two o r i e n t a t i o n s

is t h e r e f o r e 6%°

(3o4L)

Deep Inelastic Lepton-Nucleus Scattering

y.(~)

399

Z

(a)

Z

(

(b) Fig° 3°8°

Schematic view of the v i r t u a l photon scattering o f f a deformed nucleus in parallel (a) and perpendicular (b) d i r e c t i o n to the photon momentum:

F i n a l l y we would l i k e to stress the importance of understanding the color dielect r i c properties of nuclei° Only a successful application of color d i e l e c t r i c theory also to the low Q2-phenomena of nuclear physics~ l i k e the saturation of nuclear matter~ w i l l make f u l l use of the new ideas created by the new deep i n e l a s t i c lepton scatterings done at CERN and SLACo

ACKNOWLEDGEMENT I would l i k e to thank my collaborators on this work: Otto Nachtmann: Guy Chanfray, and James Vary° I am grateful to Sonja Bartsch for typing the manuscript°

400

Hans Jo Pirner

REFERENCES A l t a r e l l i ~ Go~ and Go Parisi (1977)o Asymptotic freedom in parton language° Nuclo Physo B~ 126, 298° Arnold, Ro Go~ and others (1984)o Measurement of the A dependence of deep-inelastic electron scattering from nuclei° Phys. Revo Letto~ 529 727° Aubert~ Oo Jo~ and others (1981)o European Muon Collaboration (EMC): Measurement of the proton structure function F2 in muon hydrogene interactions at 120 and 280 GeVo Physo Lotto, 105B~ 315o Aubert, Jo Jo~ and others (1983)o European Muon Collaboration (EMC): The r a t i o of the nucleon structure functions F2N For iron and deuterium° Physo Lotto, 123B, 123o Berger, Eo Lo~ Fo Coester, and Ro Bo Wiringa (1984)o Pion Density in nuclei and deep i n e l a s t i c lepton scattering° Physo Revo D~ 29~ 398° Bjorken~ Jo Do (1969)o Asymptotic sum rules at i n f i n i t e momentum° Physo Revo, Z79~ 1547o Bjorken~ Jo Do~ and So D. Drell (1964)o R e l a t i v i s t i c Quantum Mechanics° McGraw Hillo Bloom~ Eo Do (1975)o Deep hadronic structure and the new particles° SLAC Summer I n s t i t u t e on Particle Physics~ po 25° Bodek~ Ao~ and others (1983)o Electron scattering from nuclear targets and quark d i s t r i b u t i o n s in nuclei° Phys: Revo Letto: 50~ 1431o Brodsky~ So Jo (1982)o In Do Co Fries, and Bo Z e i t n i t z (EdSo)~ Quantum Chromodynamics at Nuclear Dimensions in Quarks and Nuclear Forces~ Springer Tracts i00o Buras, Ao Jo (1981)o A tour of perturbative QCDo PrOCo Lepton Photon Conference~ Bonn (Germany)° Carlson, Co Eo~ and To Jo Havens (1983)o Quark d i s t r i b u t i o n s in nuclei° Physo Revo Letto~ 51~ 261o Chemtob, Mo (1980)o Scaling laws in high-energy electron nuclear scattering° Nuclo Physo A~ 336~ 299° Chemtob, Mo~ and Ro Peschanski (1984)o Clustering and quark distributions° To appear in Jo Physo Go Chodoso Ao, Ro Lo Jaffe, Ko Johnson~ Co Bo Thorn~ and Vo Fo Weisskopf (i974)o New extended model of hadronso Physo Revo D, 9~ 3471o Cleymans~ Jo (1983)o The nucleus as one quark bag° Bielefeld preprinto Close~ Fo Eo (1979)o An introduction to quarks and partonso Acad~ Press~ London° Close~ Fo Eo~ Ro Go Roberts~ and Go Go Ross (1983)o The effect of confinement size on nuclear structure functions° Physo Letto~ 129B~ 346° Date, So, and Ao Nakamura (1983)o Mass number dependence of large transverse momentum production and massive lepton pair production° Progr. Theoo Physo, 69~ 565° Date~ So, Ko Saito, Ho Sumiyoshi~ and Ho Tezuka (1984)o New scaling phenomena in nuclear structure functions° Waseda University preprint WU-HEP-84-1o Day~ Do~ Jo So McCarthy, Io Sick~ Ro Go Arnold~ Bo To Chertok~ So Rock~ ZoMo Szalata: Fo Martin~ Bo Ao Mocking, and Go Tamas (1979)o Inclusive electron scattering from He3o Physo Revo Letto~ 43, 1143o Dias de Deus~ Jo (1983)o Mu!tiquark clusters in nuclei and the EMC-effecto MPI-PAE/PTh 61/83o Dias de Deus, Jo: Mo Pimenta~ and Jo Vareia (1984)o Structure functions in nuclei: quark clusters and size effects° CFMC-E-1/84~ Lisboao Dominguez, Co Ao, Po Do Morley~ and !o Ao Schmidt (1984)o R e l a t i v i s t i c nuclear wave functions: off-mass shell nucleon structure functions and the EMC-effecto USM-TH-19, Valparaiso~ Chile° Donnelly, To Wo~ and Jo Do Walecka (1975)o Electron scattering and nuclear structure. Ann° Revo of NUClo Science~ 25~ 329° Drees~ Jo, and Ho E. Montgomery (1983)o Muon scattering° Ann° Revo NUC]o Part° Scio~ 33~ 383° Efremov, Ao Vo, and Eo Ao Bondarchenko (1984)o Multiquark states in nuclei and the deep inelastic scattering° Dubna preprint~ submitted to Jadernaya Physicao

Deep inelastic Lepton-Nucleus Scattering

401

Ericson, Mo~ and Ao Wo Thomas (1983)o Pionic corrections and the EMC-enhancement of the sea in iron° Physo Letto~ 128B~ 112o Faissner, Ho~ and Bo Ro Kim (1983)o The influence of m-clusters on deep inelastic lepton nucleus scattering° Physo Letto, 130B, 321o Frankfurt~ Lo Lo~ and Ho Io Strikman (1981)o High energy phenomena, short range nuclear structure and QCDo Physo Repo C~ 76, 216= Frankfurt, Lo Lo~ and Mo Io Strikman (1984a)o EMC-effect and p o i n t - l i k e components in hadronSo Leningrad preprint 929° 7rankfurt~ Lo Lo~ and Mo Io Strikman (!984b)o Proceedings of the Dubna meeting on Hultiquark Phenomena° Dubnao Friedman, Jo Io, and Ho No Kenda] (1972)o Deep inelastic electron scattering° Ann° Revo Nuclo Scio, 22, 203° Grammer, j r ° , Go, and Jo Do Sullivan (1978)o Nuclear shadowing of electromagnetic processes° In Ao Donnachie~ and Go Shaw (EdSo)~ Electromagnetic Interactions of Hadrons, VO]o 2~ po 195o Goldflam, Ro~ and Lo Wilets (1982)o Soliton bag model° Physo Revo D~ 25~ 1951o GUttner~ Fo~ Go Chanfray~ Ho Jo Pirner~ and Bo Povh (1984)o Analysis of pion electroproduction data in terms of a pion d i s t r i b u t i o n function of the proton° MPI-H-1984-V14~ to be published in Nucio Physo Hofstadter, Ro (1963)o Nuclear and nucleon structure° In Benjo incorpo (Edo)~ New York° Jaffe, Ro Lo (1983a)o Quark d i s t r i b u t i o n s in nuclei° Physo Revo Letto, 50~ 228° Jaffe, Ro Lo (1983b)o The EMC-effect: looking at the quarks in the nuc]euso Preprint CTP-1120: MZTo Jaffe~ Ro Lo~ Fo Eo Close~ Ro Go Roberts~ and Go Go Ross (1984)o On the nuclear dependence of electroproductiono Physo Letto~ 134Bo 449° Kahana, So~ Go Ripka~ and Vo Soni (1984)o Soliton with valence quarks in the chirai invariant q-modelo NUCio Physo A~ 415~ 351o Kogut, Jo (1982)o Lectures on Lattice Gauge Theory° Proceedings of the Carg@se Summer School° Kogut, Jo, and Lo Susskind (i973)o The parton picture of elementary particles° Physo Repo C~ 8~ 76° IKrzywicki~ Aoo and Wo Furmanski (1983)~ Anomalous behaviour of nuclear structure functions revisited° Proceedings of the 6th High Energy Heavy Ion Study: Berkeley° Landolt-BSrnstein (1967)o In Ho Schopper (Edo), Zahlenwerte und Funktion aus Naturwissenschaften und Technik~ Bdo 2, Kernradien~ Berlin° Llewe]lyn Smith, Co Ho (1983a)o A possible explanation of the difference between the structure functions of iron a~d deuterium° Physo Letto, 128B, 107o L!ewellyn Smith~ Co Ho (1983b)o Nuclear effects in deep inelastic structure functions° Invited talk at the DESY meeting about HERA~ Amsterdam° Lee~ To Do (1977~ 1977~ 1979)o Fermion-field nontopological solitonso Physo Revo D~ !5~ 1694, 16~ I096~ 19~ 1802o Mack, Go (1984)o Dielectric l a t t i c e gauge theory° Nuc]o Physo B~ 235, [FS11] , 197o Moniz, Eo Jo~ and others (197i)o Nuclear Fermi momenta from quasielastic electron scattering° Physo Revo Letto~ 26, 445 Nachtmann~ Oo (1980)o The classical tests of Quantum Chromodynamicso Acta Physo Austriaca~ Supplo XXI!, 101 (Schladming Lecture Notes)° Nachtmann, 0o~ and Ho Jo Pirner (1984a)o Color conductivity in nuclei and the EMC~ effect° Zo Physo C: 21, 277° Nachtmann, 0o~ and Ho Jo Pirner (1984b)o Color conductivity at high resolution: a new phenomenon of muclear physics° Heidelberg preprint HD-THEP-84-7~ submitted to NUC!o ?hyso Nielsen~ Ho Bo, and Ao Patkos (1982)o Effective d i e l e c t r i c theory from QCDo Nucio Physo B, 195, i37 Pennington~ Mo Ro (i983)o Cornerstones of QCDo Repo on Progro in Physics~ 46° 393° ?irner, Ho Jo (!984)o Deep inelastic lepton-nucleus scattering° MPI-H-L984-V12o to be published in International Review of Nuclear Physics, VOlo 11o

402

Hans Jo Pirner

Pirner, Ho Joo Go Chanfray, and Oo Nachtmann (1984)o A color d i e l e c t r i c model for the nucleus° Submitted to Phys. Letto Pirner, H. Jo, and J~ Po Vary (1981)o Deed i n e l a s t i c electron scattering and the quark structure of SHe° Physo Revo Letto, 46, 1376o Pirner~ H. Jo, and J. Po Vary (1983)o Deep i n e l a s t i c lepton scattering and the quark structure of nuclei° Proceedings of the 6th High Energy Heavy Ion Study~ Berkeley° Pirner, Ho Jo, and Jo P° Vary (1984). The quark cluster model of nuclei and i t s application to deep i n e l a s t i c electron scattering° To be published° Powers~ Ro Jo~ and others (1976). Muonic X-ray study of the charge d i s t r i b u t i o n of 165Hoo Nucl. Physo A, 262~ 493° Reya, Eo (1981). Perturbative Quantum Chromodynamicso Phys. Repo C~ 69, 257° Rith, Ko (1983). Invited talk at the International Europhysics Conference on High Energy Physics, Brighton (UK)o In Jo Guy, and Co Costain (Eds~): po 80° Rith, Ko Private communication° Sivers, Do (1982). What can we count on? Ann° Revo Part° Scio, 32~ 149-175o Sivers, D, So Jo Brodsky, and Ro Blankenbecler (1976)o Large transverse momentum processes. Phys. Rep. C, 23, io Szwed~ Jo (1983)o Structure functions of nucleons inside nuclei° Physo L e t t . , 128B~ 245~ T~Hooft (1980)o The topological mechanism for permanent quark confinement in QCDo Proceedings of the 21 Scott° Univ. Summer School in Physics° Thomas, Ao Wo (1982). Chiral symmetry and the bag model: a new starting point for nuclear physics° In Jo Negele, and Eo Vogt (EdSo), Advo Nucl. Physo~ Volo 13o Titov, Ao Io (1983). Multiquark states in deep i n e l a s t i c muon-nucleus scattering. Dubna preprint B2-83-72o West, Go Bo (1983)o Understanding the structure function of iron. Preprint Los Alamoso Wilczek, Fo (1982)o Quantum Chromodynamics: the modern theory of the strong i n t e r action° Ann° Revo of Nuclo and Part° Science° 32°