x

IgLWlmnP'_,~,i~-"Z'I,,"][II,,~"J PROCEEDINGS SUPPLEMENTS

Nuclear Physics B (Proc. SuppL) 25B (!992) 152-166 North-Holland

POMERON PHYSICS IN DIFFRACTIVE DEEP INELASTIC SCAIWER!NG AT LARGE !/x Nikolai N.Nikolaev * Branch of L.D.Landau Institute at ISl Foundation, vl. Settimio Severo 65,1-10125 Torino, Italy and Dipartimento di Fisica Teorica, Universi~ di Torino, and lstituto Nazionale di Fisica Nucleate, Sezione di Todno Via P. Giuria 1,1-10125 Torino, Italy I review recent progress in the perturbative QCD approach to pomeron physics in deep inelastic scattering (DIS) at large l/x.(refs.l-4), I discuss the crucial role the color transparency plays in a diffractive DIS, and how it can be quantified in terms of the wave function (WF) of (panonic) hadronic fluctuations of photons and universal, flavour independent, q~ pair interaction cross section. Different DIS processes probe this unversal cross section at different sizes. The emerging WF formalism greatly simplifies the involved calculations. I present quantitative predictions for the nuclear shadowing and the diffraction dissociation (DD) rate in DIS, and the valence and sea quark distributions in a QCD Pomeron. I point out a dramatic difference of sea densities in a nucleon as probed by muons and neutrinos and flavour dependence of the pomeron couplings in DD and conclude that perturbative QCD pomeron does not factorize. I emphasize a numerical importance of shadowing in deuterium for tests of the Gotffried sum rule.

1. INTRODUCTION At high energies, photoabsorption can be viewed as mediated by virtual hadronic fluctuations of photon X of mass Mx, formed at large distance upstream the target

- ,IP

nucleon (nucleus): Az - 2W(Q2+ M~ ) .~ I/mblx >- RN(RA) (hereafter x = Q2/2p.q is the Bjorken variable, p and q are the proton's and photon's 4-momenta Q2 = _ q 2 , W 2 _2p.q - Q2). Henceforth, at

x <~

! RAmN

(1)

photons are expected to have diffractive interactions similar to that of hadrons. The pomeron (P), exchange by which in the t-channel describes diffractive : :.ttering (Fig.l), remains one of the most mysterious o~+.cts in high energy physics. Since DIS is tractable in QCD, there are much expectations of unravelling the structure of pomerons in the dedicated large 1/x-DIS experiments at HERA.5 The issues involved are: What is the pomeron in QCD? What are hadronic fluctuations of photons and how do they couple to the QCD

a)

b)

FIGURE 1 The pomeron (wavy line) exchange contribution to the elastic scattering (a) and diffraction dissociation (b) amplitudes. pomeron? What are factorization properties of the QCD pomeron? What is flavour dependence of pomeron couplings? What are scaling properties of diffractive DIS? What is a total rate of diffractive DIS and is it ob~rvable? In this talk I shall mostly review the recent work done in collaboration with E.Barone, M.Genovese, E.Predazzi and B.G.Zakharov. t -4

*Permanent address:L.D.Landau Institute for Theoretical Physics, 117940 G SP-I, ul.Kosygina 2, Moscow V-334, USSR

N.N. Nikoiaev / Pomeron [~bysics i~ di_."reactivedeep #m!.~.st;.csca~,,'ering 2, WHAT IS THE POMERON ~N QCD?

J. W ~ A I

the rightmost even-signature singularity at j = ~ ( t ) = i + A

an¢| rnntrn|~

th~ flcvmntntie

h,~,h~tvaiatav r t f the, ¢ a t ~ ; o~¢xee

section (s = W2),

153

I:AL~RON|~: FLUCTUAT|ONS Ob

A~

To the lowest order in perturbative QCD, photons , a ~,~ ~

J,~,~

sls I patna.

~

vtltu~; ut

~;q.~,tJ, a t r a n s v e g s e

size of the pair, ~, and partition of photon's longitudinal momentum between quark and antiquark, (x ( the Sudakov Otot *¢ s a

(2)

or the light cone variable I I), are the adiabatic, diagonal, papameters of the scattering process. For a q~ pair of size

If pomeron is an isolated pole in the j-plane, then the

the total cross section is universal for all flavors and does not depend on ¢z: JI

pomeron exchange satisfies the factorization properties typical of the panicle exchange. Despite the considerable progress 6, a full QCD theory of the pomeron is still lacking. None the less, a viable phenomenology of diffractive DIS can be built, in which properties of the pomeron and fundamental color transparency property of QCD 7 prove to be strongly interrelated. The driving term of the color-singlet, pertu:'hative QCD pomeron is the two-gluon exchange (Low-Nussinov approximationS). Since gluons have spin 1, this produces the constant cross section, which experimentally is a dominant feature of all cross sections up to moderately high energies, E ~ 102 - 103GeV/c. To the higher orders in perturbative QCD, one finds rising contributions to otot. To

l~ 2/d2EV~ll-exp{£.~]

c~...,

(k2~2~ 2

P' = - - ' ~

(3)

t/ where (Xs is the slrong coupling. The effective mass of a gluon lag introduced to not have color forces propagate beyond the confinemer~t radius Re: PG = R~~ = g~. T h e GGNN vertex function equals

V(k) = l- G2 (k -- k)

(4)

where G2(kl, k2) = (N I exp(i ~l " El+ i ~2 • ki) I N) is the two-quark form factor of the nucleon. The vertex function

all orders in perturbative QCD pomeron proves to he a

(4) vanishes at ~2 < l/R2: colorless nucleons decouple

series of poles accumulating at j = 1, with the rightmost pole having A >_ 0 . 3 - 0.5 (ref.6). The Froissart bound requires A = 0; still a local growth with energy, eq.(2), is

from gluons with the wavelength ~.g > RN.

consistent with asymptotic theorems. Assuming small

Then, if WF of q~ fluctuations, V((~, ~), is known, computing the total photoabsorption cross section and inclusive forward DD cross .¢ection is straightforward2:

relative normalization of the rightmost pole contribution,

= j' d,

which is the higher order effect, one finds very viable

(5)

phenomenology of the p(~)p total cross sections and cosmic ray data on ultrahigh energy pAir absorption cross sections.9 In DIS Otot(T*N) = 4n2~temF2(x,Q2)/Q2 and structure functions are indeed constant at least up to l/x ~ 102-10 3 (ref.10). Constant otot(Y*N) has always been behind the f,~milar *~l/x sea partoa densities. Hence, at meuderately high energies and modcratley high I/x of prime interest for the planned HERA experiments5, the principal properties of the QCD pomeron can well be understood in the LowNussinov approximation.

dt

'L=o

: 16~

(6)

By definition, in DD proton changes its longitudinal momentum a little, ApL/pL = AXL ¢~ ! in the y*p c.m.s, or PfL" mN in the laboratory frame, and is separated from the hadronic debris of the photon by a large rapidity gap. The usual cutoff is AXL < 0.05 - 0.1. In (6), t is a square of the momentum transfer to the recoil proton.

154

N.N. Nikolaev/ Porneron physics in diffractive deep inelastic scattering

The W~'s ...~ ~: ~,~,~ ~e~:, j transverse and (L) iongitudina::

NI

~)

N!

20 where £2 = Ot(l-O0Q2 + m~

(9) I

and Kv(x) is the Bessel function of the imaginary argument. A striking simplicity of eqs.(5,6) is due to a remarkable diagonalization of the diffractive scattering matrix in the mixed (p, a ) representation. The Feynman diagram representation of the same quantities, in particular of the forward DD cross section, is nearly intractable.13A saliem feature of the cross secdon (3) is its color transparency propc~;77:

o(p) ,= (Z2sp2

(lO)

for the small-size q~ pairs, ~2 < R 2. For the large-size q~ pairs, ~2 ~ R 2 the cross section (3) saturates (Fig.2),

o(p) = Rc2

(II)

Obviously, both the color transparency property (I0), which is basically a manifesfation of the gauge invariance, and the saturation propcrey (11), do only use the most fundamental properties of QCD being the gauge theory and :he confinement property, and are protected against.the higher order QCD corrections. Different deep inelastic interactions probe different parts of this universal curve for

o(p). We take three flavors, AQCD = 0.2(GeVlc), and the

0

I

2

3

.p, FIGURE 2 Total (qq-)-nucleon cross section as a function of a Iransverse size of the a pair.

We take effective quark masses mu,d = i 34MeV/c 2 ffi m~, ms = 300MeV/c 2 ( ~ 15OMeV/c 2 strange-nonstrange mass splitting assumed) and mc = 1.5GeV/c 2 . The last choice is obvious, the former provides natural cutoff of u~, dd fluctuations of wansvese size p ~ 1~ and gives otot(l~l) ll01.tb for the real photons, Q2 = 0 (ref.12), and o(y--~cc~ = 1. lgb for photoproduction of open charml3, in a very good agreement with experiment. At large Q2 an exact value of mu,d.s is obviously unimportant. The subsequent numerical predictions for diffractive DIS are parameterfree. 4. COLOR TRANSPARENCY SCALING 1,2.

AND

BJORKEN

If hadronic fluctuations of photons have the hadronic cross section,then

single-loop, freezing strong coupling: %(q2) = %(q~, at OT(y~N)

o~

O~mOmt(hN)

02)

q2 < q02,where q0 = .44(GeWc) (r~f.3) is fixed using as a normalization Otot(~N) = 26rob calculated from generalization of e,q.(9) to pions.

which grossly violates the Bjorken scaling (the BjorkenGribov disasterl4). It is very instructive to see. how the

N.N. Nikolaev / Pomeron physics in diffractive deep inelastic scattering B'orken scaling a~- large I/x derive; from ~he -e~or traaspm~nCyo

P'" ~ " ~ '

Fog excita~ien of charm in ~e~::~i~o ia~eractioas, -he un~Nrl,/ing subprecess is the W-g!uon lesion: vv

u,~ ~ , , , , ~ r ~ , u u - in (5),

(13) j o -~ With the p2 law (!0) we find the scaling, I/Q 2, photoabsorption cross section times the Iog(Q2) scaling violation factor, the latter coming from the small size partonic fluctuations of photons, p2 _ I/Q2 Without the color transparency, with o ( p ) ~ R 2 one runs into the Bjorken-Gribov disater, eq.(l 2). Hence, scaling violations ~* small x probe smail-p behaviour of O(p), but large-p contribution is still there and controls a magnitude of the cross section (13) at moderate Q2. Calculations using (5) do nicely reproduce F2N(X, Q2) (ref.10) from very small to moderate values of Q2 (refs.2,3).

5. NONUNIVERSALITY OF SEA DENSITIES PROBED BY NEUTRINOS AND MUONS 3. From (13) one easily finds a flavonr dependence of the pomeron couplings to the sea

155

, 6--T~TO

I suJ

which can be understood either as excitation of charm on the strange sea, if c-quark is produced in the W-hoson hemisphere, or as an excitation of ~ on the anticharmed quark, if i is produced in the W-bcnon hemisphere. Excitation of charm is absolutely inseparable from simultaneous excitation of (anti)strangeness, which suggests that in neutrino interactions (a lepton probe index is attached for clarity to a panm density)

~,,(x, Q2) = ~v(x, Q2)

(17)

Next, Wg and T*g fusion have different threshold masses, 2ms < ms + mc < 2me. Henceforth, a sequenceof inequalities

~,(x,Q2) << ~v(x, Q2). ev(x, Q2) < ~(x, Q2) < ~,(x, Q2), ~(x, Q2) (is) With allowance for the Csbibho suppressed transitions, even the light quark sea distributions will depend on the lepton probe. Correct treatment of neutrino interactions requires cc'~bined sea densities CSv(x,Q2). USv(x.Q2), cdv(x, Q2), and ndv(X, Q2).

(15)

At very large Q2 ~, 4m~ the flavour symmetry will be restored, but at moderate Q 2 . 4 m ~ cq.(15) explains a suppression of the charmed and strange sea in nucleons, which persists under further QCD evolution in a broad range of Q2. At finite x the heavy flavour suppression is much stronger. Namely, since x = Q2/(Q2 + w 2 _ m~) and

This nonunivesality of parton densities, eq.(IS), leads to a numerically very large effects and very distinct xdependence of 2~E6 + d), 2~/(-6 + d) ratios: at x = 0 we find ~ 30% vtolation of SU(3) symmetry, at larger x flavour symmetry is broken badly. Remarkably, one finds (FigA) very good quantitative agreement with the c h ~ excitation datalS, 16 assuming a dominance of lt*g and Wg fusion and negligible intrinsic charm and .qrangeness (for more detailes ref.3). At x --* 0 excitation of charm and strangeness in

m~¢).

neutrino interactions can also be treated by Eq.(5) and generalization of WF (7) to W-boson fluctuations into unequal mass system. Here one pmhes o(p) at p -l/me.

Numerically, for the charmed sea, Xmax- 0.1, 0.25, 0.5 at Q2 = 1, 3, lO(GeV/c)2, respectively.

The classical quark-charge ~uared test of the panon model 17 is most instructive, in Fig.5 we show Rv/tt =

W is bounded from below, W > 2m I, the 6jq f sea vanishes kinematically at x > Xmax = Q2/(Q2 + 4m~ -

5F~lVJ(x,Q2)]181d~) (x, Q2) for the textbook formula

N.N. "~'ikolaev/Pomeron physics in diffracHve deep inelastic scattering

t 56

I

n__

,, ....

~

1

o nuuIr ,i~.. -,; ",,

D

0.050 tl

2e/(u+d)'l~"" . .

tO

x

0.05

i.J

n

9;~ !5.0 ~.~n,~ lJ.u

v

77--

e

iE5 1

m

0 0

24.3 28.6

t •

0.2

0.25

i

1_ _5, 7 19.2 21.6

\ \\

0.010

\\

0 005

t

Q~=10 GeV8

,, \

,. t

0.01

,

,

O.Ot

,

..... 0.05

I O.I

,

,,

....

.

0

0.5

I ....

/~..

0.05

O. 15

O. 1

0.3

x

X

FIGURE 3 Strange-to-Nonstrange and Charmed-to-Nonstrange sea p a t t o n d e n s i t y ratios in m u o p r o d u e t ; o , : a n d neutrinoproduction vs. x at Q2 = i(~(GcV/c)2.

FIGURE 4 A comparison of the perturbative-evolution calculation of the strange sea as measured in (anti)neutrinoproduetion with the CCFR 16 data, for various Q2 (in (GeV/c)2). Starling from below, the curves correspond to Q2 = I, 2, 3, 4.1,8, 16, 32 (Gev/c) 2, respectively.

1.3

Off

:L t~

r,_ ~O

qe=!

.

.

.

.

,

, , , |

•

,

•

•

•

,.,,

x=O.OI5

0 GeV e 05

n EMC, Ca o CDHSW,Fe

=t

r~

r~

co u~

I.I

I).4

i

~~}

o.:l

:1. t~ 1) 2

II, I

1.0 •

10-3

•

.

,

,,,,I

10-2

I

I0-I

I0 0

X

FIGURE 5 A comparison of the neutrino structure functions computed from the muoproduction patton densities, eq.(2) (dashed line), and with correct treatment of the mass corrections, eq.(ll) (solid line), vs.: z at Q2 = IO(GeV/¢)2.

0.1

,

,

0.5

i

, i , (

i

i

I

I

~

5

,

,,j

IU

qZ (Gev/c)2 FIGURE 6 A comparison of the EMC I0 and C D | I S W 18 data on the nucleon structure functions at : x = 0.015 vs. Q2.

N.N. Nikolaev / l'omeron physics in diffractive deep itwlastic scattering ~t',

t X . V J - j = th, ~X°k*-~ +- U . i X . k t - i ~ ~ . t x_.k_~%' + d . ~ × ~ O ~ i

do ~o::_ e×piicitiy appear in F i ( x , Q 2 ) .

157

After ~.his

rei~erpreta~ic..m, >'.roag mas~ dependence ~_~f~he Bethe--e---:-----ercross $ee--o~ propaga>:-: -rite s.re~g m~ss (19)

dependence of the sea parton aensttJes. l ne at)ore m~ss

and the full QCD calculation with threshold corrections

effects are in the leading twist structure functions and

explicitly included:

persist numerically in a broad range of Q 2. As an accuracy of the structure function measurements is approaching a

o2)

2 UOv(X, I --.4COSO~ Q2) + 4cosO~2 CSv(X, Q 2) .

2

.

2

the sea distributions is credible, and the whole

+ 4smO: USv(X,Q2) + 4smOc cdv(x, Q2) + Fll'~i,ltx, Q2)

few per cent level, none of the current 'definitive' sets of

(20)

Tbe principal difference between (19) and (20) is that 2csv(x, Q2) is larger than ~(x, Q2) + Cl~(X,Q2) at x ~ 0.2, and smaller at x _> 0.2. Henceforth, at small x we predict Rv/l~ by =10% larger than given by the textbook formula (19) and decreasing with x, but not quite below unity even at x > 0.2, since the valence is somewhat less evolved in neutrino case 4 (Fig.5). A comparison of the Iow-x EMC (ref.10) and CDHSW (ref. 18) structure functions supports

phenomenology of patton densities and of dilepton production in neutrino interactions must be redone. 6. DD RATE IN DIS IS HIGH, QCD POMERON DOES NOT FACTORIZE4. After the a integration in (6) we find the inclusive forward DD cross .section:

do DD)/ ~-

J

(a~-d~ ~ ° ( p ) 2

(22)

~=o - ~)2 1,j_ '

this prediction (Fig.6), hut is inconclusive because of the familar problem of systematic errors.

which is completely dominated by large size, p - I/ml, q~

The conventional patton model phcnomcnology is universally done neglecting excitation of (anti)strangeness

fluctuations of photons. Hence the total DD rate, dominated by excitation of light flavors, probes o ( p ) a t the

on charmed sea altogether 16, which is quite wrong. The

confincmcnt scale, whcreas diffracllon excitation of beavy flavours probes thc small-p part of o(p).

corresponding final states do necessarily contain slow charmed particles, and contribute to the dimuon events. In precision tests of the standard model like a comparison of

Since a slope bDD of the t-dependencc of the recoil proma distribution is controlled by tbe target proum size,

the neutral current and charged current total cross sections,

bDD = RZN= R~, then o(DD) ~ R~2(do(DD)/dt)~-_.o, Then

one must use the correct formula ¢20).

cq.(22) gives lhc .scaling, and strongly flavour dependent, DD cross section

The above lepton probe-dependence of .,;ca densities does not invalidate the patton model, and comes from the very heart of the panon model and notion of the Q2 evolution. Namely, the virtual photoabsorF-tion cross

1

Q2

I 2 2 Rcm!

(23)

which differs drastically from the flavour mass dependence of the total cross section, eq.(15). Becau~ of the oc2(i-a) 2

section c:,n be decomposed as ff't"h (x,Q 2) = £ o¥*i (x,Q 2, M 2) @ fi/h (x, M2) i

OTtDD~

(21)

factor in eq.(8), OL(PD) is dominated by p ~ I/Q, and Vrobes short-distance behaviour of o(p):

wbece the summation is made over the patton species: i = q,

% ~UD~,~ I I • 2 2 2 Q RcQ

(24)

~4, g. in the standard patton model approach one always reinterprets the Bethe-Heitler subprocesses "lf~g--+q q and W g -.~ c g as interaction with quarks and antiquarks

in the total DIS rate both OT and OL do scale, which tits the

radiatively generated by gluons, so that gluon distributions

vector dominance motivated intuition, and this intuition

158

N.N. Nikolaev / Pomeron physics in diffractive deep inelastic scattering ~9

_ ~mn!v

~he

~-~CD

n,-.mo-~

dries

M~

factorize, dc:es nc;t

neff

clearly originate from the c o i o u r transparency. Here we

k~+ -2

=

f/3|

'":

As we have seen above, lor transverse photons the leading onnteihlltirln

lrl

;"i['~

l',rtlcc

cpoti~n

o/~rno,~

~'rclm

I¢~

--

I ;Ini~

disagree with a treatment of a pomeron as a vector particle exchanged 19.

m~, so that M 2 - m}/o~ (I - oO ~ m}/o~ . Then, in eq.(6)

In Fig.7 we present our numerical predictions for the

one can substitute d a = dM 2 m//Mx,2 4 and ¢2 ~. m~(l +

total DD activity. We find that DD makes - 15% of the total

Q2/M~). After d2~ integratior,

in

(6)

DIS rote. A relative fraction of different flavour excitation which is diffractive is shown in Fig.& We conclude that

'

DD of virtual photons is observable at HERA and our

OT(DD ) ~ R~2

prediction of strong suppression of diffractive excitation of heavy flavours can also easily be checked at HERA 20.

and

L

[(x2 +(I- a}2]e2 +m}

dot

e6

(26)

M dOT{DD) ,~ 1 1 [const + Mi2 ] dM{ R~ m} (Mi + Q2)2 [ {Mi + Q2}J

(27)

V~/DD

whcre const ~ i. Similarly, fi)r the longitudinal photons, •

. . . . . .

-..

. . . • . . . .....

"

totoi

"

de*, IDOl "~, , ~

ui. -t- ~

dml

,

...t_

Q2

_L

(28)

S~ {ml + 02P ml

More detailed calculations show that to a good r

approximation c~x

-2 "C

10

...... / / " -

/

i

/:

S~

',

•

,

,+ii

~0

,

2

,i

;0:

~ e V / C /

M~

= E Do

dtdM, ]t-O I

i

dox<~)I

(29)

{Q2 + M~)3

with normalization EDD(UU+ dd) = (40-50)p.b, EDD(SS) = (4 5-5)p.b and EDD(CE) = ll,tb in the region of M 2x - Q2 which contributes most to the total DD rate. By virtue of eq.(25), DD is dominated by excitation of very asymmetric

FIGURE 7 A total traction of diffractive DIS at x = 0.{X)25 tncluding our estimation of the triple-pomeron contribution to excitation of light flavours. Shown separatel,v are contributions of diffraction excitation of q~4 pairs o f different flavors.

7. DIFFRACTION DISSOCIATION OF VIRTUAL PHOTONS' MASS SPECTRUM4. Gross features of the DD mass spectrum can most easily be derived directly fmr~ eq.(6). Notice that (mass) 2 of the ¢~,cited state equals

q~ pairs with m2 a - ~

(30)

Q2

Unlike the total DD rate (6), which only depends on gross featur,-s of o(p) at large p, the DD mass spectrum (27,29) uses a specific partonic structure of the large-p fluctuations of photons. 8. T R I P L E - POMERON SCA'I'TERING4.

IN

DEEP

INELASTIC

A rapid decrease of the DD mass spectrum (27-29) can be traced back to quarks having spin !/2. An outstanding

N.N. Nikolaev / Pomeron physics in difl'ractive deep inelastic scattering

159

_f-canute • of DD of ha~rol~s a.--~d-'_hereal phobc,~s, Q2 = 0, i_~;

uy virtue of (32) upqg . . . . - I d qg ~- =,,u --~ we find IPM~ m a s s

k..

(31) o,o, (hPll dtdM~ It=0

M2

"

spectrum. The combined mass spectrum takes the form:

x

dOT~D) I ="Ym with the triple-pomemn coupling A31t == 0.10(GeV/c) 2 (ref.21). In 1984 I have emphasized that l/M2component must be present in DIS too, and despite being the dimensional constant, A3lr could only deper.d logarithmically on Q2 (ref.22). Generation of the I/M~ component in perturbativ¢ QCD requires spin-I exchange in 7*P scattering, i.e., diffractive excitation of q~g fluctuations of photons. Since

M~ = mq2+kq + ctq

+

s ctg

(z~

2

M~

(Q'+-ll3

i,=0

(35)

492 OtemA3lvF2p(X==O' Q2) MI ] where, with ~ (5-10yGeV/c) 2, 4R 2 ¢.ZemA3IP F2p (x--0,Q 2) = O. 15 F2p (x = 0,Q 2}

(36)

(32) From (35,36) it follows that q~ excitation will dominate up

excitation of large masses, M2x ,, Q2, requires ctg ,, I and/or large kg. The qclg fluctuation is generated from colorless qq by radiaton of gluons. Because of the color cancellations, gluons should have the (transverse) wavelength ~.g ~_ pq~ SO that 130(q )g ~'g ~ Pqq" Then, for M2x* Q2 of interest, the three-panicle wave function takes the factorized form 2

2

(33)

to M2x <. 10Q2. Work on the perturbative QCD evaluation of A31¢ is in progress 24. Our formalism is infrared finite, we reproduce well omt(¥N), and as a crude test of our model we calculate a mass spectrum in DD of real photons, Q2 = O. We obviously cannot reproduce the resonance structure, but on average an agreement between the data21 and pcrturbativ¢ QCD calculation is remarkable (Fig 9 ). 9. STRUCTURE FUNCTION OF THE POMERON 4. Treating pomerou as a paruclc, one may reinterpret DD of photons in terms of the photon-pomeron interaction

The interaction cross section of q~g system will be controlled by a size of the primary qq fluctuations, i.e., dominated by fluctuations of hadronic size I/my. Hence A31t will be strongly fl.wour dependent, very much alike aT(DD), and one cannot introduce a universal triple-

cross section a~(y*lP, M2,) (ref.25):

pomeron constant like in Gribov's rcggcon calculus23, This

This allows an operational definiti.n of the pomeron

is a direct consequence of the colour transparency. The driving term of the large-mass spectrum will DD of

structure function26:

(anti)quarks: q ~ q + g. Since, at ~ 2

,, I/m~

°t°c(T*lP'M~)= o,o~pp)

F2, (z,Q2) -

dtdM~

Q2 o,N ('t*IP.M~) 41t2ot.:m

{,:0

(37)

(38)

160

N.N. Nikolaev / Pomeron physics in diffractive deep inelastic scattering

0,28

T

a L

L~.£a

O~=O.O

=,=(75- ~¢8)C-ev

2

2L L

10" r i

~

u& ~8

0.16

r

o

o

0

> ..Q

0.~2 c S x 10 0.08 0.04. 0

s,~ r

-

L .....

,~,t

i

i il;'!

1

I ",i,;

10

I

I

i

i i ,lllJ

10 -I

10:

C: (GeV,/c) 2

,

1

,

. , i,'.'"2%

10 M," (GeV/c)"

FIGURE 8 A relative contribution of the diffraction dissociation into excitation of given flavour in DIS.

FIGURE 9 The perturbativc QCD prediction (solid curve) for the diffraction excitation mass spectrum in real photoproduction (Q2 = O) in comparison with the photoproduction data 21. The triple-ptmeron contribution is shown separately (dashed curve).

with the Sjorken variable z = Q2/(Q2 + M2). In Fig.lO we

Scattering on valence dominates at z ~ O. 1-O.2, i.e., at M 2

plot the pomeron structure function which follows from the

_< 10Q2. Our pomeron structure function is by an order in

mass spectrum (35). Excitation ofq~ fluctuations gives

magnitude smaller than the proton structure function, see

F~tp(z,

Q2).

0.25zCl - ~2

(39)

eq.(40) and Fig.l(). It corresponds to quarks carrying ---IO% of pomeron's momentum, Fig.I I, and very small

We may dubb it valence as it vanishes towards small z . The mass spectrom (35) and the structure function (39) are a direct consequence of an accurate treatment of the color transparency property. Donnachie and Landshoff suggested the z ( l - z ) structure function t9. Notice the threshold effect

number of the valence quarks in a pomeron, Fig. 12. Notice a difference from Bjorken's conjecture of equal proton and Ix)memn structure functions 27, Previously, DIS on pomerons was discussed with

in excitation of heavy flavours, very much similar to

conflicting conclusions on the quark or gluon dominated pomeron structure functionlg.26. 28. Pomeron is often

discussed in Section 5.

treated as a particle, so that gluons and quarks carry

The iow-z pomeron structure function is dominated by

altogether iiXI% of pomeron's momentum26, 28. To my opinion, at least in the perturbative QCD framework, there

the triple Pomeron term:

are no reasons for the momentum sum rule to hold, very

~l(z

-

much similarly to the photon structure f~l~ction. It is not at

0, Q2) =

all obvious, that definition (38) is more than just

---- 161IA3,p F21~ g ,,, O,Q2 ) ,, 0.08.F2p (x = 0,Q2) O,ol(pp)

(40)

operational, and that one can ascribe to pomeron a structure function which obeys the QCD-evolution equations (see more discussion in inf.5).

N.N. Nikolaev / Pomeron physics in dilfractive deep inelastic scattering

161

-i

iO QCD evoi. -I

... -•"

-2

!0

.'

..- . . . . . . . . ."

Voience

7 .'

'-. "-.

cnor,~,

x ~0

"~

~

A

1

\ % - ~ ''-

........

LOI.O!

--

u~ + da

r

x~

V

s~

I

\ \

¢3 0

0.2

0.-~

3.6

10

0.8

'

.......

10

30

..."-..

]

,,,,,i

•

I ilIlal

10

I

10z

O" (Gevyc)'

Z F I G U R E 10

The flavour and valenceh)cean(pomeron) decomposition of the pomeron structure function F2~(z, Q2). For the u~+dd contribution we show separately the valence component. The valence strange quark contribution (not shown} makes ~10% of the ufi + dd contribution. The valence charm contribution is .scaled up by a factor of I0.

FIGURE ! 1 A fraction of pon-eron's momentum < xa > carried by all quarks and different flavours separately/Also shown is a Q2-dependence of < Xq > dictated by the QCD evolution, if the momentum carded by gluons and quarks adds up to 100%. 10.DIFFRACTIVE FEATURES OF THE PHOTONPOMERON COLLISIONS AND JETS 5.

-1

lO

Regarding a treatment of the pomeron as a particle, a

.........................................

uO, da

A

quantity of particular interest is an angular distribution of jets in the photon-pomeron annihilation 7* + IP -..9 q + ~. One can easily reconstruct the jet axis and the corresponting

V

momentum transfer .squared kilt, = 2k~(i - cos0), where

c E x 10 -2

10

44

-

4m.

Our perturbati,,e QCD pomeron is an exchange by the two seemingly uncerrelated

s~

gluons, still angular

distribution of jets exhibits a diffraction peak typical of the hadmnic reactions. For the light quarks at small k i ! ~ (0.3-0.5) (GeV/c) 2 we find a typical hadronic diffraction slope:

-3

10 1

10

10z

0 ~ (OeV/c) ~

FIGURE 12 Number of valence q~ pairs in a pomeron < nq > for different flavours vs Q2.

bqm = / (9.0- III.0)(C~V/c)-2. 0~ +rid [ (6.0- 6.5)(G~V/c)-~ . s~

(41'

For the open charm produc6on the diffraction peak ¢xlends up to kid -< (I - 2)(GeV/c)2 whith the slope

162

N.N, Nikolaev/ Pomeron physics in diffractive deep inelastic scattering

b.,~ = ¢! ¢. - 9 a'~/,q.~.V'~-2

\~z.- l

2 og

This__ s!ope ~,~-~--o..ig related t_o .-:.~_--~*'at ~ p -- t/mf, but

nA~,D,

z),

where nA{r/ zs the.. nUClear matter density,

Tb-J., ~;~;'-~ .:oeq (5),

non._ton annihi|an'~; d~__~_.~,es be.rim-.,,n,4~-~..~.,~__,_'ng. For the wide-angle jets of transverse momentum k, i n

orj. {Y'A}= ]0i da f d2 ~PT, L (a,P" ~ OA(P)

(45)

the practically interesting region o f ~ - Mxz ~ Q2 we found •

-4

+

2

~4.

2.-1/2

t-N1

(43)

In eq.(43) there is a familiar Jacobian-peak, l/cos(0), singularity for the 0 ---90°jets. One finds the same 1/k4 law (up to logarithmic factors) in a region of the moderately high-~ jets, M~ ~ Q2, too ( see also ref.29). This law is

Expand OA(p) in v-fold scattering terms. The impulse upproximation term, v = 1, gives ora.(~A) = AOT.L(T*N). It exhibits the conventinal scaling violations. The double scattering term, v = 2, a driving term of shadowing, is proportional to , and produces the scaling shadowing in o r and nonscaling shadowing ~ I/Q2, in OL. For the cr) transverse photons, the nuclear shadowing is a probe of large-p behaviour of o(p) and, hence, probes

specific for the permrbartive QCD pomeron and its check at HERA is of great interest. At large k2 one probes p2 ~ l/k 2 part of o(p). If pomeron was a spin-I particle, then one would have found l/k 2 law,

QCD near the confinement scale. In the large-size q~fluctuations, dominating the shadowing in OT, (anti)quarks have small transverse

In the triple pomcron region of M~ ,) Q2 too, the

diffractive scattering comes from M~ - Q2, the momentum

dominant feature of final states will be the two hadronic jets aligned along the photon-pomeron collision axis, with the parent patton of the forward (respective to the photon direction) jet being a quark, the second (anti)quark being held back to the central region, and gluon being the parent parton of the backward jet in the pomeron direction. Considerations of Sect.3 on the spatial size ordering in the q~g fluctuations of photons suggest the following emergence of the three-jet final states in the triple-

partition in such pairs is very asymmetric: ec - m~/Q2, see

pomeron region of M~ - Q2: The forward hadronic jet, originating from (anti)quark. remains aligned in the photon direction. The gluon jet, produced in the pomeron hemisphere, recoils from the central region (anti)quark jet. 1i. NUCLEAR SHADOWING IN DIS 1,2. Calculation of the nuclear shadowing in the W F formalism is a trivial task. For a q~ pair of size p the nuclear cross section equals30Jl:

momentum,

k -

mr. Since the dominant contribution to

eq.(30), as was advocated already in 197532. The q~ fluctuations dominate a shadowing at x > 10-2. Because of the different scaling violations in Or and Or(DD) a q~ pair contribution to shadowing decreases - l/log(Q2), as was first suggested in ref.22. Shadowing decreases towards large x when the longitudinal momentum transfer kL = mNx(! + M~/Q2) becomes big, i.e., kLRA ~ 1 , compare with eq.(l). A shape of the shadowing curve here depends on the DD mass spectrum and the nuclear form factor. At smaller values of x significant contribution will come from the triple-pomeron component of diffraction dissociation, which leads to - log(l/x) rise of the shadowing. The scaling violations of the triple-pomeron are not known yet. In Fig.13 we show our typical prediction for shadowing. An overall agreement is good, but at low-x there is a -10% theoretical uncertainty related to a poorly understood low-x manifestations of the nuclear EMC effect33.3.

163

N.N. Nikolaev / Pomeron physics in diffractive deep inelastic scattering

"

I

t . aJ,~t ~,'

.~.,:A) ,-

~_rq~ :,ii

!~-d.~,

~.

0.7

0.5

-

~)#

*

%.-

FdO) .

o.

i

0.1

"'.7

a Cu.le

it

w .

.

.

.

.

.

.

,If

oo,.

! 10-2

'

'

. . . . . .

'

'

~J'~

,~

t

~* '

10 - ! X

FIGURE 13 Theoretical estimation of nuclear shadowing in pCa DIS (solid curve) vs. the EMC data tO (for references to other data see ref.10).

0.05

........

10.3

J

,

J,,,,,

10"2

"'j 10"!

x

12.NUCLEAR SHADOWING IN DEUTERON AND THE ~31TFRIED SUM RULE3a,35. There was a universal ignorance about shadowing in deuterium, despite early theoretical warning the effect must be quite large22. To get quick estimations, shadowing in He4 makes about 3/4 of that in carbon, and shadowing in deuterium is just !/4 of that in heluim-4 (ref.36). Hence one should expect (3-4)% effect in deuterium and it is quite illegitimate to neglect it. In Fig.14 we show the EMC/NMC data on a difference ,~2"n(x,Q 2) -- 21~2(x,Q2) - FD(x,Q2), which is very uncritically regarded as FP(x,Q2) _ l~2(x,Q2) (ref.37). The true proton-neutron difference is rather

FIGURE 14 Difference between the proton and neutron structure

functions, F~(x,Q2)-F~(x,Q 2) (.solid curve), derived from the pD and pp data aftre applying the shadwoing correction (solid curve). The data points are the NMC data37 on the difference AFP'n(x,Q2) -- 2F~(x,Q2) - F~(x, Q2), which is equal to the above only if the shadowing is neglected. The shadowing contribution is a difference between the solid curve and the broken curve drawn through the data points to guide the eye. Expected Regge decrease below the crossover point is indicated. < 1 8 G e V (re£3g), Otot(yn) - otm(YP) = -(18.3 + 6.Ipb GeVI/2)/,~.

Above

the crossover point w e expect

Otot(¥n) > Otot(YP) by - 5%, followed by the Regge

Fp (x,Q2)- ~ (x,Q2) = AF~" (x,Q2)- LxF~2"{x,Q2), (46) and is s h o w n in Fig.14 by a solid line. A difference

between the data points and the solid line is the shadowing contribution Al~2 "a(x, Q2), evaluated in 34.35. Them arc two striking consequences of a correct treatment of the deuteron structure functions: i) At large x, l~2(x,Q2) < F~(x,Q 2) and we predict

crossover at x ,, 0.02 and l~2(x,Q2) > F~(x,Q 2) at smaller x. A common lore is that this difference should vanish ~ 4g as x .-~ 0. which is indicaL~_ in Fig.14. Assuming weak Q2 dcpendencc, we predict similar crossover of otot(yn) and Oux('tP) at Ey> (50-100)OeV, since at lower energies. E1,

convergence at higher ener[ es. This conclusion about

crossover hangs on assuming correct absolute normalization of the deuterium and proton structure functions 37, since calculations of shadowing are reliable and agree with experiment j0. It can not be excluded that otodYn) -> Otot(YP)already at Ey~ 10GeV, since the shadowing in yD scattering assumed in38 seems to be

understimated. Most regretfully, no deuterium data were taken in the Fennilab tagged photuproduction experiment 3g. ii) The NMC collaboration had estimated 37

so--

l

fdO~AF"(.Qi=o.z4-+O.Ol7

(47)

164

.Y.3,. 2"~;,~,-,.+~tev/ Pomeron pL5 ~ics in diffractive doc,~ inelastic scatt~ ,'ing

With aiiowanc¢ fi'~r ~.~'~:"~'+~'

A~,,~ts~

ihe m~e va!e~ of SG is

= O.(_mO_(x> O+_nOn_ ) 4. 0.028(x < 0.004~')

(48)

so that S t j ( ; r u o - O. 15 - a very dramatic deviation from "he canonical valve I;3 (ref.40). Flavour asymmetry of the nucleon sea, whach leads to F~(x,Q 2) > F~(x,Q2), was reccntly discussed by ~orte41. 13.NUCLEAR SHADOWING:

THE PARTON

FIGURE 15 v-fold scattering cont ibution to the photon-n,,cleus total cross s¢ctiofl.

RECOMBINATION VINDICATED23'32. The typical QCD perturbation ~hc.,3rydiagram for v-fold 7*A interaction, shown in Fig.15, irr.~ies that the quark struck by the virtual photon, belongs to 011 v nucleons

amplitude of forw:/rd product!on on a proton is siren by

involved in an interaction. This precisely corresponds to the

sizes probed are l/me < V ~ Rjpp. The same holds for the

panon-recombination mechanism of shadowing p:'~posed

quasielastic production off h ,clei too However, in n sclt.~

by V.I.Zakharov and myself in 1975 0ef.32): in the Breit

there is important interferen,-, bet~veen the dire'tly produced and absorbed J,/W and ¥ - ~ ~P' -->JPP transitions

frame, in which q =- (0,0,0, - ~

), the stru,:k quark i~a.+

a momentum kz = 'VQZ/2 and longitudinal localization 8z ~ l/kz Nucleons have a momentum p = kz/x and the Lt~rentz factor l" = p/m N. if the Lorentz contracted size of a nucleus,

eq.(5) with LP2 substituted by ~P'~Lpjpp. Hence the ypical

(higher mass intermediate states do also c¢atribute), whi :h obscures straightforward interpretation ol ~hc observed J / u

RA/I", becomes smaller than 5z, i.e., x < I/RAmN, then in

attenuation in terms of pure absorption at cert+in dominar, t size p Similar transitions ~-.> JPP --> ~P' lead tt

view of the spatial overlap partons can recombine, reducing

antishado,ving ([) in photoproduction of Lp, on nuclei.

their density, and cannot be attributed t<~separate nucleons. Notice, we have rederived the shadowing condition, eq.(l). In terms of the patton recombination l':ctur~, shadowing of

15. CONC'.USIONS. Diffractiv~ int~::~ctions of real and virtual photons are

the q~ fluctuations can be reinterpreted as a fusion of the

controlled by the colour transparency property of QCD. The emerging QCD pomeron does not factorize and can nol b¢

sea quarks with gluons, whereas shadowing of q~g ~uctuations will have a component correspondin,g to recombimttion of gluons from different nucleons and then

treated as a particle. Pon,cro~ couplings to a sea of aeavy quarks exhibit striking flavouc dependence, whk:h persists

radiatively generating a sea. Notice that recombining

up to very large Q2 Sea distribut,,ns in the neutral cun'en~

panons have small transvers ; momenta k - mr.

and charged current DIS of neut, inos are different+

14. COLOR TRANSPARENCY IN PHOTOPRODUCTION o F JPP (ref.42).

numerically the effect is very impc)rtant ,,nd was hithe-t.J illegitimately ignored. DD of photons at HERA will make ~ 15% of the total DIS rate and is observable. QC~ pomcTon

I met~tion it here just for the sake of completeness, see the talk by Boris Kopeliovich42 for more details. One compares quasidastic photoproduction on protons, ¥ + p --+ JPP + p, and qu~sielastic diffractive production on nuclei, ~/+ A --+JPP * A*, followed by a break-up of a nucleus but without multiple production. At high energy an

predicts very strong flavour dependence of DD rate, v.'rich can be checked at HERA. Measurements of the argular distributions of jet,; in the photon-pomeron annihilaaon and of triplepomeron asywptotics of the DD mass spectrum at HERA are of particular imerest. The forthcoming data from the dedicated ZEUS experime0t5 should contribute much to

N..v, Ni~:olaev/ Pomero~ physics in diffractive deep inelastic sca~terit~g

!65

~n~i i-"s sc?!i~-g }¢operfie~ are ,~,H! .~ b~{~-~ i~ 0 C 9 . ,..,,u~u,-*.~

:,: u~.uv..:~u.,

:H,~a

~.,-'*~a~

iii

X '< ]G--'= - - ] 0 - ' ~

llOQl~ AIA.

phenomenology of parton densities needs a drastic overhaul.

2.

N.N. Nikolaev and B.G. Zakharov. Z.Phys. C49 (1991) 607.

The color transparency property of DIS can be quantifieai in terms of the universal, flavour-independent cross section o(p), eq.(3) and Fig.2. Different deep

3.

E. Baronc, M. Genovese, N.N. Nikolaev, E. Prcdazzi and B.G. Zakharov. Univ. of Torino prcprint DI~T19/91, submitted to Phys.Lcn.B;

4.

N.N. Nikolaev and B.G. Zakharov. Univ. of Torino prcprint DFTT-5/91, submitted to Z.phys.C;

5.

M. Arneodo and C. Peroni. Suppl.) 12 (1990) 149.

5.

L.N. Lipatov. Sov.Phys.JETP 63 (1986) 904. L.N. Lipatov, these proceedings. V.S.Fadin, these proceedings.

inelastic processes probe different parts of this universal curve, in Fig.16 we summarize the principal conclusions reached in this talk.

~(~) (~b)

""

"

SCALING VIOLATIONS

I-=

.~,/-~-,Jv_

o,Jv

NucI.Phys. B (Proc.

7. A.B. Zamolodchikov, B.Z. Kopeliovich and L.I. Lapidas. Pisma v ZhETF 33 (1981) 612; G. Bertsch, S.J. Brodsky, A.S. Goldhaber and J. Gunion. Phys.Rev.Lett. 47 ( 1981 ) 267. 8.

F.E. Low. Phys.Rev. DI2.(1975) 163; S. Nussinov. Pkys.Rev.Lelt. 34 (1975) 12~6; J.F. Gunion and D.E. Soper. Phys.Rev. DIS (1977) 2617.

9.

B.Z. Kopeliovich, N.N. Nikolaev and Potashnikova. Phys.Rev. D39 (1989)769.

I.K.

I0. M. Arnetxlo et al. Nucl.Phys. B333 (1990) I.

R

~

/ ~

F,.,

"'"

SHADOWING

~J.(7N), o,o,(DD) I

I

"

! I. V.V. Sndakov. ZhI-TF 3(1 (1956) 187. 12. D.O. Caldwell el al., Phys.Rev.i.etl. 40 (1978) 1222. 13. T. Sloan, G. Smadja and R. Voss. Phys.Rep. 162 (1988) 45. 14. V.N. Gribov .Soy.Phys./ETP bf 29 (1969) 483; J.D. Bjorken and J. Kogul. Phys. Roy D8 (1973) 1341.

FIGURE 16 Which region of sizes p of the universal cross section of Fig.2 is probed in some typical deep inealstic and real photon interactions,

ACKNOWLEDGEMENTS: Thanks are due to V.Barone, M.Genovese, E.Predazzi and B.G.Zakharov for a pleasure of collaboration and much insight, in preparing this talk I benefited from sti nulating discussions with M.Arnet~lo, J.Bjorken,/.Ellis, S.Forte, C.Mariotti, M.Peskin, C.Pertmi. A.Solano and V.RZoller.

15. G.D. Gollin et al. Phys.Rev. D24 (1981) 559. J.J. Aubert el al. Nucl.Phys. B213 (1983) 31. 16. H. Abramowicz el al. Z.Phys. C!5 (1982) 19. C. Foudas el al. Phys.Rev.Lett. 64 (199(I) 1207. M. Shaevitz. Invited talk at Neutrino-90 Conference and private commumcalion. 17. C.H. Llewellyn .~mith. Nucl.Phys. BI7 (1970) 277. 18. P. Berge et al. Z.ph/s. C49 (1991) 187. 19. A. Donnachie and P.V. Landshoff. Nucl. Phys. B267 (1985) 69{); NucLPhys. B~)3 (1988) 6.'L~. 20. A. S~lano, these Pnwccedings.

166

~i.~V. Nikolaev / Pomeron physics in diffractive deep inelastic scattering

2i+ T+J+Chapin et ai. Phys+Rev D3i (i985) i7. ~~ N.N. =~;v,+.... c~v¢~,,~+~; . . . . . . . ;"' 58/84 :me ~. A!=~ in: }.~u]~iquark ia~eractions and © .... +;+~ Chmmc~¥n~miC$: Pro¢: V~g g~+cr~o Scmiear o ~ .~.eb!ems of High I::. . . . . . Physics, m_9~ w.... ~aga i iI irln~l

32. N.N. Nikolaev ,and V.i. Zakharo:,.Phys.Lett. B55 (i975) 397; V.L Zakharov and N.N. Niko::aev. Juv.o,l~u~l..

~ IU:,.

~ 177.~/

.c.z. ¢ .

33+ N+N+ Nik-+!aev. U~iv. of Tgk--o r - , ~ a

r

------~q~:~:-

i i ~t ~t i~

34. N.N. Nikolaev, unpublished. 23. V.N. Gfibov. Sov.Phys: JEPT 53 (1967) 654.

35. V.R. Zoller. Moscos preprint ITEP-58-91 (1991). 24. E. Barone, N.N. Nikolaev, E. Predazzi and B.G. Zakharov, paper in preparation.

36. L.G. Dakhno and N.N. Nikolaev. NucI.Phys. A436 (1985) 653.

25. A.B. Kaidalov and K.A. T¢r-Martimsyan. Nucl.Phys. B75 (1974) 471.

37. NMC Collaboration. P.Amaudruz et ai.Preprint CERN-PPE/91-05 (i 991).

26. G. Ingelman and P.E. Shl¢in. Phys.Lctt. B152 (1985) 256; H. Fritzsch and K.H. Streng. Phys.Lett. B164 (1985) 391.

38. D.O. Caidwell et al. Phys.Rev.Lett. 23 (1969);

27. J.D. Bjorken, these Proceedings.

39. D.O. Caldwell et ai. Phys.Rev.Lett. 40 (1978) 1222;

28. E. Berger et al. Nucl.Phys. B286 (1987) 704. 29. M.G. Ryskin. Yadernaya Fizika 52 (1990) 828. 30. R.J. Giauber. In:Lectures in Theoretical Physics, v.i, ed.W.E. Brittin and L.G. Dunham. Interscience Publ., N.Y., 1959. 31. V.N. Gribov. Soy. Phys. JETP 30 (t07~) 709.

Phys.Rev. D7 (1973) 1362. 42 (1979) 553.

40. K. Gottfried. Phys.Rev.Lett. 18 (1967) 1174; J.D. Bjorken and E.A. Paschos. Phys. Rev. 185 (1969) 1975. 41. S. Forte. Univ. of Torino preprint DFIT-91/23 (1991) 42. B.Z. Kopeliovich, these proceedings.