I

.-

SLAC-PUB-5616 March 1992

T/E

Rapidity Gaps and Jets as a New Physics Signature

in Very High Energy Hadron-Hadron Collisions*

J. D. BJORKEN

Stanford Linear Accelerator Center

Stanford University, Stanford, California 94309

Submitted to Physica. Review II

* Work supported by the Department of Energy, contract DE-AC03-76SF00515.

I :

1. Introduction

At SSC/LHC energies there emerges a new class of processes which are of

importance in the attempt to push beyond the standard-model phenomenology.

These reactions are characterized by the presence of virtual electroweak bosons in

the hard subprocesses. The most familiar-and perha.ps important-of these [l] is

the two-body scattering of W’s and Z’s, with the W’s a,nd Z’s treated as partons of

the incoming proton bea.ms (Fig. la.). Closely rela.ted is the production of a Higgs

boson (or other new elect,rowea.k/Higgs-sector pa.rticle) via IV-W fusion (Fig. lb).

(b)

P

Figure 1. Basic mechanism for producing W-N’ int,eraction processes in high-energy pp col- lisions, with the presence of a rapidit.y-gap in the final state.

At the naive, “fa.ctorized,” level depicted in Fig. 1, the event-structure is atyp-

2

- ical. For example, in the W-W scattering example, let the W’s decay leptonically.

Then there will be a large “rapidity-gap,” i.e. a region of (pseudo-) rapidity in

which no hadrons are found, separating the bea.m-jets containing the fragments of

the left-moving and right-moving projectiles.

This is the event morphology characteristic of double-diffraction, which has a

large cross-section. The presence of isolated leptons, however, largely suppresses

this. And if la.rge transverse momentum is excha.nged between left and right movers

in the process, this double-diffra.ction background will itself be highly suppressed.

As will be discussed further in Section 2, the signal event, as shown in Fig. 2, has

the characteristic feature of “tagging-jets” at the edge of the ra.pidity-gap [2]. These

are simply the ha.dronization products of the init,ia.l-sta.te quarks that emitted the

W’S.

“.‘A t-;-j I;T””

Figure 2. Even morphology in lego variables for the processes depicted in Fig. 1. The tagging jets are the hadronization products of the quarks, while for large Higgs masses, almost a.11 of the W-decay product.s lie within the dashed circles. The remaining region, marked gap, contains on avera.ge no more than 2 or 3 hadrons.

The combination of ra.pidity-ga.ps, tagging-jets, a.nd leptons within the gap

would seem to be a strong signature for this process. Indeed even if one allows

hadronic decays of the W’s, the signatures still look quite good. Therefore we

3

believe that the possibility of using this “underlying-event” structure should be

studied seriously by theorists, phenomenologists, and experimentalists. The ba-

sic idea of utilizing the rapidity-gap signature is due to Dokshitzer, Troyan and

Khoze [3]. But up to now not much has been done in developing it [4]. There are

many difficult issues involved. They include the following:

1. How big must the ra,pidity-gaps be in order that multiplicity fluctuations do

not mimic their effect?

2. How big are strong-intera.ction (Pomeron-exchange) backgrounds and how

do they scale with energy a.nd pi?

3. What fraction of a given electroweak-boson exchange process, as defined at

the parton level, rea.lly leads to a final state conta.ining the rapidity-gap. Most

of the time specta.tor intera.ctions will fill in the ga.p present at the naive level

considered above. We estimate in Section 3 tl1a.t the survival probability of

the rapidity gap is of order 5%, but there are serious theoretical issues here

which need further explora.tion.

To make a complete feasibility study of this stra.tegy requires a considerable

amount of serious hflonte-Carlo simulation work. It is not the purpose of this paper

to provide any of t,ha.t. While such work is necessa.ry, it is not sufficient. There

are several fundamental theoretical issues, most ha.ving to do with the physics

of rapidity-ga.p crea.tion in strong processes (“Pomeron physics”), which need to

be a.ddressed before one can really a.ssess whet.her the inputs to a Monte-Carlo

simulation are realistic. It is the purpose of this paper to look at some of these

underlying issues, and discuss how they might be a.ddressed, both from the point

of view of funda.mental theory a.s well as from experiment.

In Section 2 we survey semi-quantita.tively some typical electroweak-boson ex-

4

- change processes in order to get some feel for the pra.cticality of the strategy,

and how they are calculated. In Section 3 we look at the physics underlying the

“survival of the rapidity gap,” i.e. what fraction of events retain the factorized

structure containing the rapidity-gap. Section 4 considers potential backgrounds

from “hard diffraction” processes, i.e. high-pl double or multiple diffraction. A

conclusion from tha.t section is that it is arguable that these corrections will be

large. If so, these strong-interaction processes may be able to be utilized for new-

physics as well. Section 5 is devoted to concluding comments, and enumeration of

suggestions for further experimental and theoretica. work.

2. Hard Collisions with Electroweak-Boson Exchange

Processes involving electroweak-boson exchanges have by now been considered

at great length in connection with the high-energy ha.dron collider programs such

as SSC and LHC. It is not our purpose t,o repea.t any of that work here [5], but

only to describe the revisions needed if one is to utilize the ra.pidity-gap signa.ture.

The processes we consider here are as follows:

a) Exchange of a single 7, IV, or 2.

b) Two-boson nonresonant processes, in particu1a.r yy -+ pspL-, and yy + X

or w+w- + .x.

c) Resona,nt production of the Higgs boson aad elastic scattering of TV’s and/or

Z’S.

a,) Single-boson exchange:

We begin with a description of the photon-excha,nge process described in Fig.

3, with final-state interactions of specta.tor partons temporarily disregarded. If q”

5

2x I I I 0.. l

. . l

. + . l

.

l . . , et -+ cl e l , :‘* ; l . y

. . l *- . 5

-@?j. .

n ’ 1 . . I I I I

u-a -4 0 4 a

3-92 Jl 7112A3

Figure 3. Event morphology for virtual photon exchange between two protons at large q2, with survival of the rapidity gap assumed.

is large, then the event-topology in the lego plot is as shown in Fig. 3. The jets are

created by the hadronization products of the scattered quarks. A “rapidity-gap”

lies between these jets (provided it is not filled in by absorption effects). It is

not hard to estimate the amount of leakage into the gap [6]. For this purpose we

suggest the following candidate definition of the boundary of the gap:

1. Define the ta,gging jets as the cont,ents of the lego plot within a circle of

radius 0.7 enveloping the jet core.

2. Define the boundary of the rapidity ga,p a.s the tangents to these circles as

shown in Figs. 2-3.

Because the part,icle distribut,ions of the beam jets are essentially known from

deep-inelastic lepton-ha.dron phenomenology, it is stiaightforward to estimate the

leaka.ge into the gap. Only the frame of reference is non-standard (from a fixed-

target, not HERA, perspective). A simple kinema.tic exercise [6] leads to the esti-

mate for the leakage per edge:

-“R 2 0.5 (2.1)

with R = 0.7 the ra.dius of the circle enveloping the jet. So for the signal we

I .

.-

- typically expect no more than one hadron in the ga.p. Since at SSC/LHC energies

-8-10 (2.2)

(for charged + neutral hadrons), a gap width of 3 units appears quite sufficient to

reduce Poisson-like multiplicity fluctuations to a, negligible level.

However, multiplicity distributions at these energies are non-Poissonian. There

are large long-range rapidity correlations in the local multiplicity density dN/dq,

so that it is reasona,ble to simply argue that only the low-multiplicity tail of the

total “nega.tive-binomial” distribution is releva.nt. However, for minimum bias

event,s this component is less likely to have high-pt jet’s in the final sta.te. Likewise

ordinary hadron-hadron events conta.ining high llt jets a.re less likely to have a low-

multiplicity component in their associa,ted-multiplicity distribution. I therefore find

little help from direct experimental informa.tion in estimating what an appropriate

minimum A7 should be, although 3 does seem a. reasonable value.

It might be interesting to scrutinize extant sa.mples of da.ta on e+e- -t hadrons

to see how often rapidity-ga.ps this wide do appear, since there are no diffractive

mechanisms availa.ble in such processes to crea.te gaps: only fluctuations are avail-

able. Indeed, this gives rise to a rough estima.te for the ga,p proba.bility. Suppose

there is a certain fra.ction of eSe- -+ hadron events containing a rapidity gap of

width 07 or la.rger. Then assume this fraction does not depend strongly on the

eSe- ems energy fi. If this is true, then we may reduce s until the process is

quasi-elastic, i.e. to

s - so N (1 GeV’) en7 . (2.3)

But this qua.si-elastic fra.ction is of order lFx(so)/2, where F, is the elastic form

7

I .

.-

- factor for e+e- --t x+7r-, namely

2 2

IF~(S())12 N % ( > N t eb2*q . (2.4)

This leads to the estimate, at any energy s >> so

Fraction of events with gaps with width Aq z e-(2A9’1.4) . (2.5)

For Aq N 3, the fra.ction would be no more than 10s3. A more careful exami-

nation lowers this number by orders of magnitude [7]. In any case it is important

to study the issues experimentally.

Returning to the process of interest, we now estimate the cross-section for

the photon-exchange process, differential in q’ = -Q’ a.nd the positions of the

tagging-jets in the lego plot. This 1la.s the simple form

da dql drj:! dQ’

= F F2(xl, Q’) F&, Q”) (IS12) (2.6)

with F2 the fa.miliar structure function and (IS]‘) the a.bsorption correction, dis-

cussed in Section 3. We have defined the tagging-jet rapidities’ to be

01 71 = -en tan F > 0 72 = en tan $ < 0 .

The parton fractions ~1 a.nd x2 are related to t.hese ra.pidities as follows:

rll g ell ..L = ell 2E1 = 01 Q

en 2ElX] - = 411. e + !n x1

Q Q

(2.7)

(2.8)

1 Hereafter we do not distinguish between true rapidit,y y aud pseudbrapidity 17.

8

We see that

71 - 172 = .!?n ~1x2s - en Q2 = en -?- Q"

where J” ’ h s 1s t e ems energy of the qq system undergoing the hard subprocess. A

necessary condition tha.t there be a. rapidity gap between the two tagging jets is

771 - 72 = A7 + 2(U) , (2.10)

with the rapidity-ga.p A7 ;2 3. This implies a subenergy for the q?j process bounded

below by

; ;2 Q” ,@v+W 2 so Q” . (2.11)

This is not much of a constraint for these processes but will be a considerably

larger one for two-boson exchange processes to be discussed later.

By themselves, we do not know how interesting this class of processes would

be to study. As discussed in Section 4, there proba.bly is a large hard-diffraction

background, difficult to eliminate. And the struct,ure-function physics in general

requires precision. S ffi u ciently a.ccurate determination of Q2 and of the size of

absorption corrections to attain that precision might be problematic. However the

values of Q2 a.nd W2 ava.ilable a.t SSC/LHC energies exceeds by far what will have

been studied a.t HERA. This follows form the observation that, according to Eq.

(2.6), the elementa.ry parton-level cross-sections a.t Q” N lo5 GeV” are of order

10-35~m2. With a 5% survival probability for the rapidit,y gap, as discussed in

Section 3, this lea.ds to a respectable event sa.mple for any integra.ted luminosity in

excess of 1038cm-’ ‘. Note that at Q” N lo5 GeV”, TV and 2 exchange predominate

over photon exchange.

9

. .

- b) Two-boson processes:

There are many processes of considera,ble interest, but we shall begin with a

quite mundane one, namely yy + c~+,u-. Our reasons for this are that it is a sim-

ple prototype rea.ction and most importa.ntly, it appears to be an excellent reaction

for experimentally determining the absorption corrections, i.e. the “survival prob-

ability of the ra.pidity-gap.” The event-structure is shown in Fig. 4 and is similar

to the previous ca.se. In calculating the cross-section for this kind of process, it is

convenient to consider the hard subprocess to be

q+q+q+q+p++p- (2.12)

and compare the yield with given gap parameters to the total yield.

Figure 4. Event structure for dilepton-plus-rapidity-gap production in pp collisions.

To determine the yield when the kinematics is constrained to allow a rapidity-

ga,p, with each muon isolated within the gap, it is convenient to view the process

at first in the collinear frame for which the photoproduced dimuon system ha.s

zero longitudinal momentum; this is essentially the ems system of the dimuon. In

10

. .

- this frame we make a cut on the dimuon angular distribution about 90”; more

specifically we only allow a limited rapidity separation between p+ and /.L-:

117-t - 77-l < A77PP * (2.13)

A value AqPP of 2 already covers most of “47r”: I cos 81 < 0.75.

We now require tha.t the edges of the rapidity-ga.ps, created by the tagging-

quark jets, are at least distances Aq1, AQ from the dimuons (cf. Fig. 4). This

requires

As in the previous case, the distance in the lego-plot between the tagging-jets,

together with their transverse momenta qt, determines the ems energy of the qij

system:

2E1 ql - q2 = ell - 2E2 + ell - 91 92

= en Z - ell qtl - en qt2 . (2.15)

To get a feel for numbers, take

Qt1 - cltz - 20GeV (2.16)

And for the dimuon constraints, ta.ke

(2.17)

AQ,~ = 2 .

This gives a minimal tagging-jet separa.tion of

A17jj E 5.4

11

(2.18)

I .

.-

- and a minimum qq ems energy of

& = qtei*“l-’ M 14qt - 300 GeV . (2.19)

Note that the typical laboratory angles of the tagging jets in the dimuon ems frame

do not exceed, for this choice of qt,

8 2% max z - N J-

50mrad . (2.20)

This implies that in any frame, at least one tagging jet will have a production

angle smaller than this amount; equivalently at least one tagging jet has a rapidity

exceeding qmin N 3.7. The minimum angle a tagging-jet can possess is, for the

SSC, roughly

0. N mm (5 _ 14dTe\i) N 2 - 4mra,d (2.21)

or qmax 5 7.

Let us now turn to an estima.tion of the cross section. The usual Weiszacker-

Williams method is eminently suitable, given the kinematics sketched above, which

leaves the longitudinal fraction of the photon momentum relative to the parent

quark small compa.red to unity (in order to create the rapidity-gaps).

The cross section is

da = 2 F(q) F(r2) 3 $$ + $ dql dip&‘, Av,J (ISI?) (2.22) 2

with the photon longitudinal fractions given by

h k-2 Yl = -

El y2=-.

E2 (3.23)

The I;i a.nd E; are photon and quark energies respectively in, say, the dimuon rest

12

.

. -

- f rame. T h e s q u a r e d yy e m s e n e r g y is

s’ = Y l Y 2 : = Y l Y 2 ( W 2 4 (2 .24)

a n d A q P c l is th e m a x i m u m d i m u o n rapid i ty s e p a .rat ion a l l owed by th e restr icted

in tegra t ion o f e m s d i m u o n a n g l e s .

A c o n v e n i e n t way to cast th e a b o v e cross-sect ion fo r m u l a is in te r m s o f s’ a n d

7 , th e m e a n rapid i ty o f th e d i m u o n system. This m e a n s e l imina t ing y1 a n d y2 in

te r m s o f s’ a n d ii. In th e yy rest f rame, ii van ishes a n d lir = k2. T h e n

E ; 4 7 1 y2 - e n yl = e n E ’ .

n

B u t f rom E q . ( 2 .8 ) a n d E q . ( 2 .1 .5 )

7 ; + rl; = e la - - pl,, 3 E ’ & I = e T 2 1 - e n , - 2 E ;

Q l Q 2 E ; Q :!

7 ; - 7 ; = e la 2 - - el l . q l q 2 .

(2 .25)

(2 .26)

This a l lows us to d e te r m i n e 7 7 ; a n d 7 .: in th e yy rest f r ame a n d th e r e b y a l low 7 to

b e re la ted to th e m ( a .n d th e y’s):

T h u s w e h a v e th e superb ly sim p le Jac0b ia .n

dv ds’ = d Y l d Y 2 SI Yl Y ’ *

(2 .27)

( 2 .2s)

1 3

I .

.-

The cross section is

(2.29)

Expressed in these varia.bles, it depends upon almost nothing except kinematic

limits. Again, analogous to Eq. (2.8), we have

fi vl =elz-+enx, G &I

-q2 =e~--+e~~~ . Q2

(2.30)

The yield as a function of 71 a.nd 72 is in proportion to the product of parton den-

sities F(zl, QT)F(xz, Qz). Th is is plotted in Fig. 5 for a few choices of transverse

momenta q;; q1 = q:! is assumed for simplicity. Also shown is the kinematic re-

striction for a rapidity gap, Eq. (2.15). Note that the cross-section formula breaks

down when the rapidity-gap closes up too much, in pa.rticu1a.r when the approxi-

mation ~1, y2 << 1 breaks down. This ca.se requires a better calculation, but one

can expect a diminishing yield where it occurs.

For fixed Qf, s’, and 7, one has some idea of how much yield one gets after

integrating over t,he tagging-jet locations (~1, ~2) by inspection of Fig. 5. Since

uyy - (.A-‘)-~, th e s’ int,egration is dominated by the threshold region. The 11 range

of integration is again straightforward, a.s is, more or less, the range in log q”.

The dimuon yield is loW, but mea.sura.ble, with choices of q and n in the tens

of GeV. The issue will be backgrounds, not rate. These are controlled in terms of

high-pi triple-diffra.ction processes. These are very uncertain to estimate, but are

discussed in Section 4. Alternatively one may reduce Q2 to l-10 GeV2 and gain

in rate, but a.t the price of a more difficult ba.ckground problem.

14

. .

11 8

1 o.ooc

(4

1 0.001

72

/ 0.1 7- 1

x2

0.01

0.1

-81 I I I I 0.001 0.01 0.1

Xl

rll

Figure 5. Estimate of the parton luminosity L, defined as

L = FZ(ZI, Q:, F2(22, Q;,

for 0 = 100 GeV and fi = 40 TeV (SSC), as a funchon of the ta.gging-jet rapidities 771 and q2: (a) Q: = Q”, = 100 GeV2; (b) QT = Q; = lo3 GeV’. Up to a factor ens/Q” in uy-,, .C is proportional to the different.ial dilepton yield, Eq. (2.29).

15

.

. -

T h e h a d r o n i c , q q fina l sta tes p r o d u c e d in yy col l is ions a r e desc r i bed by th e s a m e

express ion as u s e d fo r th e d i m u o n s . H o w e v e r , th e s e p rocesses a r e p r o b a b l y o b s c u r e d

by th e a fo r e m e n tio n e d b a c k g r o u n d s . If o n e w ishes to stu d y such c o n fig u r a tio n s , it

is p r o b a b l y b e s t to u til ize h a r d di f f ract ion p rocesses to p r o d u c e th e m .

H o w e v e r , th e r e m a y b e “n e w physics” wh ich is m o r e a .ccessible. P romis ing

c a n d i d a tes w o u l d inc lude pa i r - p roduc tio n o f c h a r g e d , co lor -s ing le t systems (heavy

lep tons o r s leptons, fo r e x a m p l e 2 ) fo r wh ich th e a b s e n c e o f a n unde r l y i ng e v e n t

m ight c rea te a rela.t ively c lean s ignature . A n o th e r class m ight b e p a r ticles wi th

signi f icant p a r tia l -wid th fo r decay into yy. W e d o n o t exp lo re th e s e h e r e , b u t tu r n

to sim ilar, p e r h a p s m o r e p romis ing cases, u ti l izing W - W col l is ions.

c) H iggs P r o d u c tio n in W - W ’ Coll is ions:

T h e two- IV p rocesses a r e a c e n tral subject o f S S C /L H C physics, a n d h a v e

b e e n extensively stu d i e d . H e r e w e very br ief ly sketch a sim p le a n d m o s t interest-

i ng case- that o f 1 4 7 ~ - W ’L ann ih i la t ion in to a H iggs -boson r e s o n a n t sta te . T h e

a n a l o g o u s W e isza.cker-Wi l l iams cross-sect ion is easi ly constructed. Fo r th e p rocess

qi j t q q H (v ia T V L - IV L annih i la t ion) , w e fin d

(2 .31)

H e r e w e h a v e u s e d th e resul ts o f C h a n o w i tz a n d G a i l lard [S ], in p a r ticu la r the i r

E q s . ( 4 .1 ) a n d ( 4 .4 ) . T h e p a r a m e ters v (H iggs rapid i ty) a n d q ( m e a n ta g g i n g jet

rapid i ty) a r e d iscussed in m o r e d e tai l in w h a t fo l lows. W h e n th e e m s qua rk -qua rk

e n e r g y & is m u c h la . rger th a n th e H iggs mass ? n H , th e e n e r g i e s o f th e seconda ry

qua rks a r e essen tial ly th e sa .me as th e p r imary e n e r g i e s . T h u s th e rapid i t ies o f th e

2- I thank G o r d o n K a n e for this suggest ion.

1 6

.-

_ secondary-quark tagging jets are determined by their transverse momenta, which

have the distribution (for longitudinal-W emission)

dN - dPf (pf + mh)? *

(2.32)

.iables vi, this leads to the distribution Upon changing to the ra.pidity vaI

co

qq’) = l 2 cosh2 7 ’ J d+D(q’) = 1 (2.33)

--oo

where 77’ is the fluctua.tion about the mean rapidity q of the tagging-jets, given by

the expression

& T= logtan -

naw (2.34)

which occurs for pt, = mw. For q?j ems energies of 1 to 10 TeV, the mean separation

A7 of the tagging-jets in the lego plot va,ries as follows:

J- A@2+2log -=

7.0 &= 1TeV rl2 it’ 9.6 &= 10TeV *

(2.35)

The separation a.t & = 1 TeV is alrea.dy just about sufficient for a rapidity-gap

signature, while the size of the gap at & = 10 TeV is clearly more than enough.

In any case, we see that the criterion for creating a large rapidity-gap has

little to do with the properties of the Higgs-boson, a.nd much more to do with the

ems energy of the qij system. Remarkably this is true for the cross-section, Eq.

(2.31), as well, which shows no dependence on Higgs mass a.t all! Actually the

mass-dependence is buried in the dependence of the cross-section on 7, the mean

rapi.dity of the decay products of the Higgs. (The kinematics, here is the same as

17

I .

.-

- that of the previous subsection for yy + CL~, and the conclusions are similar.) The

total cross-section is, according to Chanowitz and Gaillard [S],

(2.36)

with

(Av) = (1 +x)&r 1 - 2(1 - 2) + (2.37) 2

and

x=,,g 2 *

(2.38)

In accordance with the discussion in the previous subsection, the kinematic re-

striction on the cross-section for producing a. mpidity-ga,p of width A7 (we expect

A7 ;2 3 to be a reasonable cut) is

ql -rj2 >Arj+1.4. (2.39)

In addition we should require (cf. Fig. 2)

171 =; $ - 1.4 (2.40)

in order that most of the time the decay products of the Higgs boson land within

the rapidity-gap. Thus

lql 5 ; (‘I’ - Tjz) - 2.1 = F+ f (77; + 17;) - 2.1 . (2.41)

The typical values of 11; and 71 a.re of order f 1; a, safe limit for 7 should be

]~]5~-3++-3. (2.42) mlv

This leads to a crude estimate for the cross-section for Higgs production with decay

18

.

. -

- p r o d u c ts g o i n g in to th e rapid i ty g a p

(2 .43)

In Fig. 6 , th e s - d e p e n d e n c e o f th e factor e n - -& - 6 , wh ich c o n trols th e cross-sect ion

b e h a v i o r wi th g a p s ignature , is c o m p a r e d with th a t o f (Av), th e p a r a m e te r wh ich

c o n trols th e to ta l cross-sect ion e n e r g y d e p e n d e n c e .

6 I I I I I I

0 2 6 8

3 - 9 2 7 1 1 2 M

F igure G . Approx ima te d e p e n d e n c e of t .he H iggs-produc t ion cross-sect ion, wi th the II iggs- part ic le l and ing wi th in the g a p ( d a s h e d curve), u p o n the e m s ene rgy & of the init iat, ing q q system. A lso s h o w n (sol id curves) is the & d e p e n d e n c e of the total q q + q q H cross-sect ion (cf. Eqs. (2 .36) a n d (2.43)) .

It a p p e a r s f rom th a t fig u r e th a t o n c e th e H iggs mass exceeds a b o u t 5 0 0 G e V ,

th e decay p r o d u c ts o f th e H iggs r e s o n a .n c e a lmos t a .lwa.ys a u to m a ticnl ly fal l wi th in

th e fiduc ia l r a ,pidi ty g a p . T h e r e fo r e th e e fficiency o f th e g a p s igna tu re is c o n tro l led

by .th e m a g n itu d e o f th e a b s o r p tio n cor rec t ion (IS I’).

1 9

The fact that the gap cross-section is essentially independent of Higgs mass,

and that the gap-signature is efficient for Higgs mass above 500 GeV allows us to

finesse the question of convolution over parton distributions. For any Higgs mass,

we have

Ogap(S) g Otot( s, nzH = 500 GeV) ( lS12) (2.44)

Z (3 X 10e3’cm2) (lS12) .

Assuming no large ba,ckground sources from QCD or other processes, and that the

absorption factor (ISI’) is N 5%, this provides an ample yield of bosons because

all Higgs decay modes should be accessible.

As will be discussed further in Section IV, we have not identified any ob-

vious sources of background for this signal other than the nonresonant and not

uninteresting W-W two-body sca.ttering processes themselves. The experimental

procedure for isola.ting a signal should be stra.ight,forwa.rd no ma,tter what is the

decay mode. Th e most problematic ca.se is when both final-state intermediate-

bosons decay ha,dronically. This is the only case we discuss in detail here. In fact,

we shall further restrict our attention to the case of a very henvy Higgs (0.5-l TeV)

because that signature is the cleanest and ea.siest to consider. This occurs because

the dijet decay products of the W are boosted into a cone of small opening angle

as a consequence of the la.rge value of yt = pt/nzbv N 3 - 6. The event topology for

the signal is shown in Fig. 7. We have used the concept of extended lego-plot [6]

to describe the internal structure of this dijet system. Also shown is the lego-plot

of the event when the z-axis is chosen to be the thrust axis for the products of the

decaying Higgs-boson. Either way, one sees the existence of a transverse rapidity-

gap in addition to the usual longitudinal one. The width of this gap A71 is, for

20

.

. -

s y m m e tric decays, a n d a 1 T e V H iggs-mass

A q t N 2 m H O n G - 0 .7 I

N 3 .5

l a rge e n o u g h to b e o f u s e .

(a)

(b) ,B e a m Jet

3-92

l . IIT e t

. l .

.

. e t

2x I I I 1

l .

. ’ .

l .

c p . * . _ G a p _ *

0 I I I

- 4 o \ 4 T B e a m Jet ,,

8

l 1 2 A 7

(2 .45)

Figure 7. Event - topo logy for the H iggs process for a 1 T e V H iggs part icle: (a) the event structure as s e e n in ex tended p h a s e space (po lar coord ina tes u s e d ins ide the circles of rad ius 0 .7 a re t ranscr ibed into a n e w lego plot); (b) tl re event as s e e n in l ego var ia.b les wi th z-axis taken a l ong the thrust axis of the Higgs-par t ic le decay products in the H iggs rest f rame.

T o isolate th is s igna l wi th a fu l l -a ,cceptance d e tector [9 ], o n e m a y , fo r th e al l -

h a .d ron ic decay m o d e s ,

2 1

.-

1. Select 4-jet events, with Et k. Etmin _ > 300 GeV, say, and pt of each jet

> Ptmin 2 20 GeV. The jets are defined as all hadrons within appropriately

chosen circles-of-radius-O.7 in the lego plot.

2. Define the fiducial rapidity gap Aq as usual (Fig. 2); cut on Aq 2 Aqmin N 3.

3. Measure the total multiplicity ngap within the gap-but exterior to the two

jets within the gap. Then cut on ngap 5 nmax, with nmax m 3, say.

4. Construct the extended lego plots for the interior jets; demand in each a

two-jet system with n2 E nzw.

5. Define, if possible, a transverse rapidity gap and make an additional multi-

plicity cut on it.

We expect this idealized procedure is in fact overkill. The event topology is an

experimentalist’s dream: the primary signal is two well collima.ted coplanar “jets”

with total Et in the 500-1000 GeV range, and absolutely nothing else in the re-

mainder of a typical central detector. In addition ea.ch “jet” will consist of a jet

pair with A7 - A+ separation N 0.2, which in principle precisely reconstructs to

the intermediate-boson mass.

And this a,na.lysis is worst-case; about ha.lf the time one of the TV’s decays

leptonically, leaving a very isola,ted high pt tra.ck. Thus if the ra.pidity-gap signature

does exist (i.e. (IS/‘) is not too small) and if there is no ba.ckground (something

not easy to concoct), it ma.y well be tl1a.t a rela.tively simple detector, certainly no

more sophistica.ted than Fermilab’s CDF or D@), could suffice to find the high-mass

Higgs at the SSC-and in all its decay modes. However, a good deal of additional

study and simula.tion will be necessary to back this assertion up.

Evidently this strategy is applicable to many other processes, in particular to

22

.-

continuum two-body scattering processes involving W’s, Z’s, and photons. Discus-

sion of these, as well a further discussion of the Higgs process, seems unwarranted

in the absence of Monte Carlo simulations of real events. We urge that the appro-

priate studies be carried out.

Figure 8. A candidat,e background process for the Higgs product,ion

The question of QCD b&grounds to the ra.pidity-gap signature is a difficult

one. The biggest ca.ndida.te that comes to mind is the tree-level process shown

in Fig. 8. It is of order c$, and 3 sets of color-singlet gluon-pairs (as shown

by the dashed lines) are required to provide, via, conventional color-transparency

arguments [lo], the rapidity-gaps a.t t,he perturba.tive level. In order of ma.gnitude,

we guess for this process

2 (4 x lo-3”c172z) x ($ x (;)3 2 10-42cn~2 (2.46)

where we have taken the color singlet suppression fact.ors C to be statistical. This

23

should be compared with the parton-level q?j cross-section, Eq. (2.43)

4v a,q - - 2 16m& (ISI > f-w 1.5 x 10-38cm2 (2.47)

The above estimate, albeit very crude, does lend encouragement to the possibility

that the backgrounds will indeed be small, especially since we have not found other

background mechanisms with a smaller power of cys. But more critical examination

of this point is most appropriate.

3. Survival oft he Rapidity Gap

The claims in the previous section depend in an essential way on the estimate

that the fraction of events for which spectator inbera,ctions do not fill in the rapidity

gaps of interest is sizeable, of order 5%. This fraction was called (IS]‘), and is

estimated most naively as follows.

3-92 7112A8

Figure 9. Convolut.ion of parton densihes in impact. plane.

The hard collision of interest is initiated by a close collision of two partons,

one.from each beam. It therefore is a convolution of parton densities (cf. Fig. 9)

24

.-

_ in the transverse impact plane.

aHard g 00 J

d2Bd2hp(b)p(B - b) f orJ J

d2BF(B) . (34

The simplest estimate of survival probability of the ga.p, i.e. that no other inter-

actions occur except the ha.rd collisions of interest, is simply to multiply the above

integrand by IS(B)]‘, the probability tha.t the two projectiles pass through each

other without any interaction when they arrive with impact parameter B. This

estimate will be rea.sonable if the relevant pa.rton densities are uncorrelated in the

transverse, “impact-plane” coordina.tes. Whether this assumption itself is reason-

able can be questioned, and will be discussed a little more later on. But setting

that issue aside for the moment, we then can write for the survival probability of

the ga.p the expression

(pq2) = s d2B w>lw>12 j?BF(B)

which justifies the notat,ion.

A traditional estima.te of IS]” is given by the eikonal picture [ll]

IS(B = exp -vx(B)

where x is itself a convolution of parton densities, and is chosen such that

x(0) = 1 .

(3.2)

(3.3)

(3.4)

For simplicity, suppose that both the function x and the hard-collision convolution

F, are chosen to be Ga.ussian. Then the exponential can be expanded and the

25

.

. -

- in tegra ls p e r fo r m e d . T h e a n s w e r is sim p le

-B'/G w n ( 3 .5 )

n = O 4 1 + ww2) ) - 0

This in tu r n c a n b e s u m m e d , fo r e x a m p l e by construct ing th e di f ferent ia l e q u a tio n

th is s u m satisfies a n d th e n so lv ing it:

(ISI”) = a ” ( ju g - - l e -u c r (a + 1 ) u a J u a

( u > 1 )

0

(3 .6 )

w h e r e

R" Ci=7 j .

% W )

A crucia l p a , rameter is th e c e n tral a .b s o r p tio n V . E v e n m o r e crucia l is th e r a tio

o f th e in teract ion a . rea T R Y fo r th e h a r d p a r to n - p a r to n col l is ion to th a t o f th e

soft col l is ions, xR ', c o n trol l ing th e to ta l cross sect ion. W e m a y k e e p th e fo r m e r

rad ius fixe d by cons ide r ing th e p rocess fo r d i f fer ing c e n te r - o f-mass e n e r g i e s , b u t

a lways a t th e sa .me z1 a n d x:! o f th e qua rks (i.e. w e k e e p th e f ract ion o f e n e r g y in

th e qua rk -qua rk subsys tem fixe d ) . B u t th e r a .d ius a .ssocia. ted wi th th e to ta l cross

sect ion b e h a v i o r clea.r ly r ises wi th e n e r g y , a n d s h o u l d b e r e g a , rded as s o m e w h a t

l a rge r th a n th e hard-co l l i s ion rad ius.

W e m a y a lso q u e s tio n w h e th e r th e resul t d e p e n d s sensit ively o n th e cho ice o f

G a u s s i a n distr ibut ions. R e p e a .t o f th e ca lcu la t ion wi th e x p o n e n tia l d is t r ibut ions

l eads to th e resul t

(lS l2) = Jy g $ ,-W R = g 1 2 !(1 , (-v 0

+ ( n R /Ro) )’

” 3 8 1 -a-- J

( ju lp- l e -u q a + 1 ) = - M 8 a u a u a

0

( 34

n l o g u - + ] . a

2 6

.

. .

- W e a g a i n s e e a sim i lar b e h a v i o r , b u t wi th a s o m e w h a t l a rge r survival p robab i l -

ity. Th is is p r o b a b l y a . c o n s e q u e n c e o f th e l o n g e r tai l o f th e d is t r ibut ion a t l a rge

impac t p a r a m e ters, l e a d i n g to m o r e per iphera l i ty . W e conc lude th a t th e survival

probabi l i ty ( lS12 ) d p d e e n s o n th e c e n tral a b s o r p tio n Y in p p col l is ions rough ly as

a n inverse p o w e r , wi th th e e x p o n e n t p r o b a b l y b e tween 1 a n d 2 , a n d with s o m e

sensitivity to th e a s s u m e d s h a p e s o f th e distr ibut ions.

I I I

F(b) (arbi t rary scale) _

.o o 1 2 3 b ( fermi)

4 - I I I I I

0 2 4 6 3-92 b* (f*> 7 1 1 2 A 9

F igure 10. (a) T h e quant i ty vx(B) = - l og IS ( B as a funct ion of impact pa ramete r B for eIastic p p scat ter ing at fi = 4 0 Tel/. Also s h o w n is t ,he funct ion F(B) def in ing the impact- pa ramete r d e p e n d e n c e of ha.rd-col l is ion luminosi ty. (b) This is rep lo t ted versus b 2 , a long with Jvwwl;, ,~ T h e curves a re taken f rom the analys is of B lock e l al. (Ref. 12) .

2 7

Another way to estimate (]S12), perhaps the most reasonable, is to use the

absorption fa.ctor determined experimentally from pp elastic scattering data. These

are provided in a convenient form by Block et al. [12] We use for the hard collision

impact-parameter distribution a shape distribution which fits the total cross section

data for vx(b) at moderate energies, before the rise in total cross section sets in

and the elastic scattering distribution shows significant shrinkage. [Actually, as

one can see from Fig. lOa, the shape changes very little with energy.] The central

absorption v is estimated as 3-4 at ISR energies, about 5 at fi = 2 TeV and nearly

10 at fi = 40 GeV. The results are exhibited in Fig. lob and lead to an estimate,

via numerical calculation, of

(I$) = 0.10 . P-9)

There is an additional uncerta,int,y stemming from the a.ssumption of uncor-

related parton distributions in the impa.ct plane. It may be tha,t there is more

probability of absorption in a hard collision than the estimates above because of

clustering of the distributions of the relevant partons a.round the valence quarks.

We may consider an extreme ca.se of this in terms of the additive quark model. We

consider the constituent quarks to be small, ra,ther black structures with a radius

of order 0.2-0.3 fermi, chosen to give the a.pproximate relation

In this picture, close collisions of these constituent qua.rks are supposed to con-

tribute a sizeable fraction of the total proton-proton cross section. But, these

collisions cannot alone produce the expected large value of the central absorption

v at SSC energies. There must be a. big contribution from the clouds around these

28

quarks as well, one which is growing with energy. However, none of these consider-

ations precludes the possibility of a large value of absorption in a central collision

(zero impa.ct parameter) of two constituent quarks. And a.gain the preceding dis-

cussion can be carried over to this case. We may write, ignoring the shadowing of

one constituent quark by another [13],

(IS/“) E s d2B F(B)lSpp(B)12 Jd2b’o~d(b’)lSqq(b’)~2

J&B F(B) j-d2b’a,fFd(b’) (3.11)

= (l~12)pp * (PI”) qq *

It is not at all c1ea.r what to take for the a.dditional QQ survival proba,bility, which

is a simple multiplier (in this simplified case) to the previous estima.te. We here

only note tha.t the expectation from perturbative QCD is that the quark-quark

interaction, a,t any fixed scale of momentum transfer t, is expected to become

strong as s tends to infinity [14]. Th erefore a. significant a.dditional diminution

to the overall survival probability from this source must be considered seriously.

However, in the light of our previous estima.tes it seems unreasona.ble to assess

more than an order of ma.gnitude loss from this source.

Hereafter, I take for the estima.te of (IS]“)

(ISI’) 26 0.05 (3.12)

with a factor 3 uncertainty in either direction. I can only conclude that this

unhappy situation needs a lot more expertise and detailed consideration than I

can here provide.

The best answer to this problem is to determine the survival probability ex-

perimentally. The yy + p+pL- process discussed in the previous section is an ideal

29

- way to do this. Another may be highly inelastic double diffraction at large t, if

the theoretical estimates of the underlying hard subprocess can be made precise

enough. This will be discussed in the next subsection.

4. Jets and Gaps in Strong Interactions

As we have alrea.dy mentioned, there is reason to believe that there are also

strong interaction mechanisms which can lead to event topologies containing both

jets and rapidity gaps [15]. Th e simplest mechanism is just two gluon exchange

between partons, with the restriction tha.t the pair of gluons be in a color singlet

state, and that the physics is short-distance dominated. The consideration of this

physics has been in the lore for a long time [16]. In th e interest of being reasonably

self-contained, we review the calculations as simply as possible in the following.

To begin, consider qua.rk-quark scattering at the parton level via photon ex-

change. The amplitude is

e2 TQED(q) = ” (2~~) - (2p3)QQ’ = y QQ’ , (4.1)

where Q and Q’ are the charges of the relevant pa.rtons. Our normalizations are

such that da -=- dt 16: ITI

2 s 2

(4.2)

ImT= j&J IT12di + inela.st,ic contributions .

We work in the high energy limit at fixed but large momentum transfer. Helicity

is conserved, and there will be absolutely no complica.tions due to spin. We will be

int,erested in the next order, two-photon exchange cont8ribution. In QED, this leads

30

.

. .

- m a inly to acquis i t ion o f a C o u l o m b p h a s e , b e s t s e e n by work ing in th e impac t-

p l a n e , i.e . m a k i n g a Four ie r t ransform in th e t r ansve rse -momen tu m var iab les.

T h e canon ica l ly c o n j u g a te impac t - p a r a m e te r var iab les a r e in fact constants o f th e

m o tio n ( a n g u l a r m o m e n ta ) . W ith

T(q) = J

d 2 b e ’q?(b ) (4 .3 )

w e fin d

f& o ( b ) = J d ”q R 2 - (27 r )Z e

- iq .b z 2 a s Q Q log b 2 ( b2 < R2 ) ( 4 .4 )

In rea l life th e in f ra . red d i ve rgence in th is express ion is r e m o v e d by sc reen ing con -

t r ibut ions p r o v i d e d o n e h a s n e u tral pro ject i le co l l id ing wi th e a c h o th e r . T h e ful l

a m p litu d e wil l h a v e th e fo r m

T Q E D ( b ) = J

d 2 b l . . . d 2 b ,p(b l . . . b ,)@ (Eb i )d’b ; . . . d 2 b ;Sc2) (Cb; )p(b ; . . . b :)

X 32 .3 c Q iQ jlo g (b _ /j? + ,Z+ ! ij E 3

(4 .5 ) which e l iminates in pr inc ip le th e d e p e n d e n c e o f th e cutoff R ’. If on ly o n e p a ,ir o f

p a r to n s { io, js} h a v e a c lose col l is ion, w e recover th e sim p lifie d fo r m o f E q . ( 4 .4 ) .

H e r e a fte r w e d o n o t i nc lude th e nicet ies, b u t sim p ly cut o ff th e d i ve rgence a t

a sca le a p p r o p r i a te to h a d r o n i c size.

T h e unitar i ty cond i t ion in i m p a .ct s p a .ce is d ia .gona l

Im p ( b ) = ; IT(

a n d p rov ides a n instant est imate o f th e d o m i n a n t, imag ina ry p a .rt o f th e two-

3 1

.-

- photon-exchange amplitude

R2 S&rD(b) = ict2s QQ’ log2 b2

or

I .

(4.7)

(4.8)

In QED, the contribution we have calcula.ted exponentiates in higher orders to a

phase factor, leaving the lowest order cross section unmodified. However in QCD

this cannot occur. The color-singlet-exchange contribution first occurs in the two-

gluon-exchange amplitude, hence cannot be a harmless additional phase on the

lowest order amplitude. To be sure, higher orders can be significant, and the

problems this presents will be mentioned again below.

The modification of the above estima.te in the case of QCD is now a matter of

inclusion of the color factors. We write

2 8 i;,co(b) = 3 -ass log + c T, . T,’ .

n=l

The imaginary part of the two-gluon excha.nge amplitude is

ImTQco(b) = (c&slog2 ;) & (TaTb) . (Ta’T;) .

The color singlet piece is extra.cted using the identity

1 TaTb = - 6,bl -I- Octet

6

leading to

5 (TaTb) * (Ta?‘d = ; a,b=l

(4.9)

(4.10)

(4.11)

(4.12)

32

.

. -

- a n d

Im F(b)Q co 2 R 2 = - 9

scr; l o g 2 - . 1 c h a n n e l s ing le t b 2 (4 .13)

W e n o w c a n est imate th e r a tio o f th e o n e - p h o to n - e x c h a n g e a m p litu d e to th e two-

g l u o n - e x c h a n g e , co lor -s ing le t a m p litu d e

T Q E D ( b )

Im % jcD (b) = Q Q ' (o ; lo g ;;2 ,b 2 ) -

This g ives fo r th e cross-sect ion r a tio

(4 .14)

(4 .15)

T o g e t a fee l fo r th e n u m b e r s , let us r e m o v e th e logar i thm in th e Q C D a m p litu d e

by us ing th e r u n n i n g o f th e Q C D coup l i ng constant

2 1 N 3 3 - 2n j - cl 3 1 2 T

l og Q . A ’

(4 .16)

A s s u m i n g th a t th is logar i thm a n d th e two -g luon -excha ,nge logar i thm a r e th e s a m e ,

s o m e th i n g th a t b e c o m e s m o r e a n d m o r e a ,ccurate a t h i g h e r m o m e n tu m transfers,

w e g e t

(4 .17)

P u ttin g in

.n ,j = 3 2 ( Q > = 0 .2 5 (4 .18)

gives th e b o tto m l ine

(4 .19)

It is a lso in terest ing to no rma l i ze th is to th e s ing le -g luon e x c h a n g e cross-sect ion,

3 3

.

. -

which is

(4 .20)

T h u s fo r e a c h gene r i c two jet fina l sta te g e n e r a te d by a qua rk -qua rk col l is ion, w e

expec t rough ly th e f ract ion

aJet

OJe t = ; ( 33 :2 n ,)” (IS I”) z 0 .1 ( lS12 ) ( 4 .2 1 )

to c o n ta in a rap id i ty -ga.p s ignature . N o te th a t h e r e w e m u s t a lso inc lude th e factor

( lS/2) fo r th e surv iva l -probabi l i ty o f th e rapid i ty g a .p . T h e fract ion o f th e g a p

e v e n ts wh ich a r e p h o to n - e x c h a n g e a r e h e r e es t imated to b e

O G a p c2 - d u o n ) ~ 2 .6 a G a P ( p h o to n )

’ - l o -2 _ l o -3 . (4 .22)

T h e s a m e exerc ise c a n b e r e p e a te d fo r q u a r k - g l u o n a n d g l u o n - g l u o n col l is ions; th e

on ly c h a n g e is th e c o m p u ta tio n o f th e co lor factors. T h e resul t is

S ince th e o n e - g l u o n - e x c h a n g e cross-sect ions o b e y th e s a m e cond i t ions

(4 .23)

(4 .24)

it fo l lows th a t th e f ract ion o f two- jet e v e n ts c o n ta in ing g a p s s h o u l d n o t d e p e n d o n

w h e th e r th e ini t iat ing p a r to n s a r e qua rks o r g l u o n s .

In th e a b o v e cons idera t ions, w e h a v e uncri t ical ly a .ssumed th a t h i g h e r o rde rs

in & d o n o t signif icant ly c h a n g e th is result . Th is is n a .ive , a n d a . p r o p e r est imate

3 4

.

. -

\ / >

3 - 9 2 7 1 1 2 A l O

Figure 11. Impor t .ant correct ions to the na ive two-g luon e x c h a n g e ampl i tude at very la rge s.

s h o u l d inc lude a t th e least th e l adde rs o f e x c h a n g e d g l u o n s (Fig. ll), soft r ad ia tio n

th e r e from, a ,n d v i r t ,ual - loop correct ions wh ich c rea te d a m p ing o f th e t ree c o n tri-

b u tio n s . Th is is m o r e p roper l y desc r i bed by th e B F K L evo lu t ion e q u a tio n [1 7 ], a

subject b e y o n d th e scope o f th is p a p e r a n d th e c o m p e te n c e o f its a u th o r . Q u a l-

ita tively, th e resul t o f th e s e a d d i tio n a l c o n tr ibut ions is a n inc rease in s t rength o f

th e q q in teract ion a .t very l a rge s, as wel l as a n inc rease in th e re lat ive i m p o r ta n c e

o f th e co lor -s ing le t e x c h a n g e c o n tr ibut ion. T h e in terested r e a .d e r is e n c o u r a g e d to

consul t th e p a p e r o f M u e l ler a n d Nave le t [1 8 ] a n d r e fe rences th e r e i n fo r a n overv iew

o f th is p h e n o m e n o n .

W ith respect to th e cons idera . t ions h e r e , it w o u l d b e reassur ing to s e e th a t th e

a d d i tio n o f so f t -g luon e m ission to th e t w o - g l u o n - e x c h a n g e , co lor s inglet a m p litu d e

(Fig. 1 2 ) is s u p p r e s s e d if th e r a .pidi ty o f th e g l u o n is in th e g a ,p r e g i o n , a n d

u n s u p p r e s s e d in th e r e m a i n i n g b e a m - j e t reg ions . If a sim p le d e m o n s tra.t ion o f th is

exists in th e lite r a tu r e , th is a u th o r w o u l d l ike to k n o w a b o u t it.

In a n y case, th e est ima.te w e h a .ve m a d e , E q . ( 4 .2 1 ) , is l a rge . S o m e w h e r e

b e tween 0 .1 % a .n d 1 % o f two-jet e v e n ts s h o u l d c o n ta .in a rapid i ty g a p b e tween

3 5

(a)

Bi q

Octet 9

Singlet q’

04

Figure 12. Amplitude for emission (a) of a soft, gluon into the rapidity gap (b). This process should be highly suppressed.

them. This should be amena.ble to experimental tests without much difficulty. We

urge that such studies be carried out.

IrEi q

Singlet Cl 9’

Singlet q’

Z-92 7112A12

Figure 13. Hard triple diffraction, induced by two-gluon, color-singlet exchanges.

If the above considerations are reliable, clearly one photon exchange and even

single-W exchange amplitudes will be swamped by the above QCD process in all

circumstances. Of more interest a.re the two-photon and two-IV processes discussed

in Section 2. The strong-interaction analogue is triple hard diffraction (Fig. 13).

It seems reasonable that the process as shown in Fig. 14 should be estima.ted via

36

Figure 14. Lego plot for the triple hard diffraction process shown in Fig. 13.

a “factorization” ansatz. The production of the right-hand gap R can be viewed

in a frame where zero eta is located in the middle of that ga.p. In that frame,

the dynamics associated with production of the left-hand gap L appears to be

irrelevant to the estimate, via. unit,arity, we previously made. That allowed the two

exchanged gluons to be viewed as a single quasi-photon being exchanged instead.

By boosting into a fra.me in which zero eta is located in the middle of the left-hand

gap, the same consideration can then be applied to the left-hand exchange as well,

leading to the desired result.

9 Singlet

9

E

g 9 H

Singlet q

3-92 7112A14

Figure 15. Higgs product.ion via a triple hard diffraction mechanism. Again the gluon pairs are required to be color singlet.

More subtle is t,he ca.se of Higgs production via gg annihilation plus an extra

gluon exchange, as shown in Fig 15. This ca.se has already been discussed in the

literature quite a bit [19]. The simple unitarity approach we have used is no longer

37

I .

so simple. This can be appreciated by going to the frame where the Higgs particle

is at rest. A mix of transverse gluons and Coulomb gluons are present, something

which seems to be the case in any frame of reference one might entertain. This

distinguishes this situation from the ones which were discussed above. Therefore,

despite its importance, we do not try to analyze this ca.se further here, although

we hope to return to it in the future.

5. Concluding Remarks

The physics which might be accessed using the signature of rapidity gaps, jets,

and isolated leptons is unquestiona.bly superb. But rea,l event simulations and

careful creation of optimal event selection algorithms are an essential next step in

order to be ready to assess candida,te background processes. For the “flagship”

processes of 2-body electrowea.k-boson interactions a.t Ecms rS 1 TeV, I find it hard

to come up with a. competitive background. But every effort must be made to find

and evaluate the best ca,ndidates for such background.

The candidate background processes probably will emerge from hard-diffra,c-

tion physics. The phenomenology and even fundamenta.1 theory for this subject

is in a primitive condit,ion. There are at least two distinct lines which need to be

followed, both theoretically and experimentally. The first is the Ingelman-Schlein

program [20] of determina.tion of the “structure function of the Pomeron,” both in

hadron-hadron collisions and lepton-hadron collisions. The second is the study of

the frequency of rapidity ga.ps (in the lego plot) between coplana,r jets, as discussed

in Section 4. Both these test the issue of what range of momentum transfers t (if

any) in hard diffraction are describable in terms of two-gluon exchange, with or

without BFKL enhancements.

38

.-

The survival-probability of the rapidity gap (lS12) is not well understood, and

the best answer is data. The processes mentioned above are sensitive to this,

provided the underlying hard subprocess can be understood, at least semiquan-

titatively. Perhaps a large enough data set would be sufficient to create enough

confidence in the phenomenology to allow (IS/‘) to be extracted. In the absence

of that option, a safe but more infrequent process is the production of dileptons

which lie within a “hard-diffraction” rapidity ga,p.

It is very likely that hard-diffra,ction processes do exist and, as emphasized by

h4ueller and Navelet, are enhanced by orders of magnitude from the most naive two-

gluon-exchange mechanisms when the initial-stat,e parton-parton center-of-mass

momentum is sufficiently high, sar of order l-10 TeV. If the hard-diffraction pro-

duction mechanisms do indeed exist, they ca.n be utilized for new-physics processes,

with improved signa.tures in comparison to the normal situation.

It is therefore ha.rd to avoid the conclusion that the physics of rapidity-gaps

and jets should be of great importance in the coming decades.

ACKNOWLEDGh4ENTS

This work was largely stimulated by the initiative [9] for providing a full-

acceptance detector (FAD) at the SSC. I thank all my collea,gues in the FAD

working group, too numerous to mention here, for valuable contributions and stim-

ulation. I also especially thank M. Block, S. Brodsky, V. Del Duca, L. Frankfurt,

V. Gribov, H. Haber, F. Halzen, G. I<a.ne, P. La.ndshoff, B. Margolis, A. Mueller, N.

Nikolaev, F. Paige, M. Peskin, E. Predazzi, J. Pumplin, P. Schlein, M. Strikman,

and R. Vega, for much encouragement and assista.nce.

39

I .

REFERENCES

[l] See J. Gunion, H. Haber, G. Kane, and S. Dawson, “The Higgs Hunters

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[2] R. Cahn et al., Phys. Rev. m, 1626 (1987).

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[4] There has been some simulation work by Y. Dokshitzer, V. Khoze and

T. Sjostrand (Durha,m preprint DTP91-66), but apparently not with much

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[la] M. Block, F. H 1 a zen, and B. Margolis, Northwestern University preprint

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