We present a new mechanism for the creation of large rapidity gaps in DIS
events at HERA. Soft colour interactions between perturbatively produced
partons and colour-charges in the proton remnant, modifies the colour structure
for hadronization giving colour singlet systems that are well separated in
rapidity. An explicit model is presented that, although the detailed results
depend on the initial state parton emission, can describe both the observed
rapidity gaps and, in addition, the forward energy flow in an inclusive event
sample.Comment: 4 pages Latex, 4 encapsulated Postscript figures, uses qcdparis.sty,
  tar-compressed and uuencoded with uufiles, Presented by GI at workshop `DIS
  and QCD', Paris, April 1995, minor Postscript problem fixe

Edin, A.

Ingelman, G.

Rathsman, J.

English

arXiv

We present a new mechanism for the creation of large rapidity gaps in DIS events at HERA. Soft colour interactions between perturbatively produced partons and colour-charges in the proton remnant, modifies the colour structure for hadronization giving colour singlet systems that are well separated in rapidity. An explicit model is presented that, although the detailed results depend on the initial state parton emission, can describe both the observed rapidity gaps and, in addition, the forward energy flow in an inclusive event sample

DESY

Rapidity gaps in DIS through soft color interactions

Edin, A

Ingelman, G

Rathsman, J

CERN Document Server

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1
Rapidity Gaps in DIS through Soft Colour Interactions
July 1995
A. Edin
1
, G. Ingelman
1;2
, J. Rathsman
1
1)
Dept. of Radiation Sciences, Uppsala University, Box 535, S-751 21 Uppsala, Sweden
2)
Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, D-22603 Hamburg, Germany
Abstract
We present a new mechanism for the creation of large rapidity gaps in DIS events at HERA.
Soft colour interactions between perturbatively produced partons and colour-charges in the proton
remnant, modies the colour structure for hadronization giving colour singlet systems that are well
separated in rapidity. An explicit model is presented that, although the detailed results depend
on the initial state parton emission, can describe both the observed rapidity gaps and, in addition,
the forward energy ow in an inclusive event sample.
Resume
A striking feature of deep inelastic scattering (DIS)
at the HERA ep collider is the relatively large fraction
( 10%) of events with a rapidity gap [1, 2], i.e. with no
particles or energy in a large rapidity region close to the
proton beam direction. These events can be interpreted
in terms of hard scattering on a pomeron (IP) [3], a
colour singlet object exchanged in a Regge description of
diractive interactions. Although explicit such models
(see e.g. [4, 5]) can describe the salient features of the
observations, there is no satisfactory understanding of
the pomeron and its interaction mechanism.
Here, we present a new and alternative way to
interprete the rapidity gap phenomenon, without using
the concept of a pomeron. Instead, our model is based
on normal DIS parton interactions, with perturbative
QCD (pQCD) corrections, complemented with the
new hypothesis that non-perturbative soft colour
interactions occur and change the colour structure such
that when normal hadronization models are applied
rapidity gaps may arise.
At small Bjorken-x (10
 4
  10
 2
), where the
rapidity gap events are observed, the boson-gluon-fusion
(BGF) process g ! qq (cf. Fig. 1) occurs frequently.

Presented by GI at workshop `DIS and QCD', Paris, April 1995
The cross section is calculable in rst order QCD,
with the conventional requirement m
2
ij
> y
cut
W
2
on
any pair ij of partons to avoid soft and collinear
divergences. Higher order pQCD emissions can be taken
into account approximately through parton shower
evolution from the nal partons and the incoming one
(as illustrated with one emitted gluon in Fig. 1). In
the following non-perturbative hadronization process
one usually considers the formation of colour singlet
systems (clusters, strings) that subsequently break up
into hadrons. In the conventional Lund model [6]
treatment, a BGF event gives two separate strings from
the q and q to the proton remnant spectator partons
(Fig. 1a), thereby causing particle production over the
whole rapidity region in between. This treatment is
implemented in the Monte Carlo LEPTO [7], which
describes most features of HERA DIS events.
This conventional treatment assumes that the colour
structure, i.e. the string topology, follows exactly
the perturbative phase with no further alternations.
Our main assumption here is that additional non-
perturbative soft colour interactions (SCI) may occur.
These have small momentum transfers, below the scale
Q
2
0
dening the limit of pQCD, and do not signicantly
Figure 1. The string conguration in a DIS boson-gluon-fusion
event: (a) conventional Lund string connection of partons, and
(b,c) after reconnection due to soft colour interactions.
change the momenta from the perturbative phase.
However, SCI will change the colour of the partons
involved and thereby change the colour topology as
represented by the strings. Thus, we propose that the
perturbatively produced quarks and gluons can interact
softly with the colour medium of the proton as they
propagate through it. This should be a natural part
of the processes in which `bare' perturbative partons
are `dressed' into non-pertubative quarks and gluons
and the formation of the conning colour ux tube in
between them.
Lacking a proper understanding of such non-
perturbative QCD processes, we construct a simple
model to describe and simulate these interactions.
All partons from the hard interaction (electroweak +
pQCD) plus the remaining quarks in the proton remnant
constitute a set of colour charges. Each pair of charges
can make a soft interaction changing only the colour
and not the momenta, which may be viewed as soft
non-perturbative gluon exchange. As the process is
non-perturbative the exchange probability cannot be
calculated so instead we describe it by a parameter R.
The number of soft exchanges will vary event-by-event
and change the colour topology of the events such that,
in some cases, colour singlet subsystems arise separated
in rapidity. In the Lund model this corresponds to a
modied string stretching as illustrated in Figs. 1bc,
where (b) can be seen as a switch of anticolour of
the antiquark and the diquark and (c) as a switch of
colour between the two quarks. This kind of colour
switches between the perturbatively produced partons
and the valence partons in the proton are of particular
importance for the gap formation.
Of relevance is also the modelling of the non-
perturbative proton remnant system, i.e. the proton
`minus' the parton entering the hard scattering process.
If that parton is a u or d quark, the remnant has
previously been modelled as a valence diquark which,
as a colour anti-triplet, will be an endpoint of a string.
Here we introduce a modied treatment of the remnant
three valence quarks, which are split into a quark and a
diquark in the conventional way [7], plus the partner
antiquark from the sea to conserve avour quantum
numbers. These three partons form two colour singlet
systems (strings) together with the scattered quark (and
extra gluons). This two-string conguration for sea-
quark-initiated processes provides a better continuity to
the two-string gluon-induced BGF events.
Rapidity gaps have been experimentally investigated
[1, 2] through the observable 
max
giving, in each event,
the maximum pseudo-rapidity in the detector where an
energy deposition is present. (With  =   ln tan =2
and  the angle relative to the proton beam,  > 0
is the proton hemisphere in the HERA lab frame.)
Fig. 2 shows the distribution of this quantity as obtained
from our model simulations for 7:5 < Q
2
< 70 and
0:03 < y < 0:7.
The maximum rapidity parton from the BGF matrix
element (Fig. 2a) can be central or even in the electron
beam hemisphere depending on the phase space allowed
by y
cut
. For y
cut
= 0:005, which has been shown
to be theoretically sound [8], about 10 % are BGF
events. The small y
cut
= 0:0001 results [7] in an
adjustment of the cut-o such that the total (Born)
cross section is saturated with 2 + 1-jet events, giving
 50% BGF events. The partons can here emerge with
a large rapidity gap relative to the spectator partons
at large  outside the detector coverage (beam pipe).
However, this gap does not survive to the hadron level
as shown by the large eects from parton showering
and hadronization. The introduction of soft colour
interactions have a large eect on the 
max
distribution,
as demonstrated in Fig. 2b. Still, our SCI model is
not very sensitive to the exact value of the parameter
R. In fact, increasing R above 0:5 gives almost no
eect. Once a colour exchange with the spectator has
occured additional exchanges among the partons need
not favour gaps and may even reduce them. In the
following we use R = 0:2, which can be seen as the
strong coupling 
s
(0:5GeV )=  0:2 at a typical small
momentum transfer representative for the region below
the perturbative cuto Q
2
0
 1GeV
2
.
One should note that the basic features of this
distribution, the height of the peak and the `plateau',
is in reasonable agreement with the data [1, 2]. (A
direct comparison requires taking detailed experimental
conditions into account.) Selecting events with rapidity
gaps similar to the H1 denition (i.e. no energy in
6:6 >  > 
max
where 
max
< 3:2) gives the full curve
in Fig. 2b, also in basic agreement with data [2].
The exact gap probability does, however, depend
on the details of the higher order parton emission
treatment. In particular, the cut-o Q
2
0
for the parton
3
Figure 2. Distribution of maximum pseudorapidity (
max
). (a) Partons from boson-gluon-fusion matrix element
(BGFME) with cut-o y
cut
, and hadrons (HAD) after parton showers and string hadronization (with improved
remnant sea quark treatment). (b) Hadron level after colour reconnection with probability parameter R for all
events and those satisfying the `gap' denition (full line). (c) Parton level (PS) and hadron level (HAD) for
dierent initial state parton shower cut-o values Q
2
0
.
Figure 3. Distributions for the selected rapidity gap events, i.e. with no energy in 6:6 >  > 
max
and

max
< 3:2: (a) squared momentum transfer t from incoming proton to remnant system R; (b,c) invariant
masses of the forward remnant system M
R
and of the produced central system M
X
(cf. Fig. 1).
shower is rather important. Chosing a value close the
hadronic mass scale  1 GeV
2
tends to produce too
much radiation at large rapidity such that the gaps
are partly destroyed. A value of 4 GeV
2
for the limit
of pQCD, as in many parton density parametrizations,
reduces such emissions and larger gaps thereby arise
after SCI (Fig. 2c).
In this context one should note that the leading
logarithm GLAP evolution need not be correct when
applied to the simulation of exclusive parton nal states
in a parton shower. It is derived for not-too-small x
and only for the inclusive case, i.e. for the evolution of
the parton density, and sums over all emissions such
that important cancellations can be exploited. It is
not clear whether this formalism is fully applicable also
to exclusive nal states. It seems likely that it gives
the correct mean behaviour, but it may not properly
estimate the uctuations that may occur in the emission
chain. Some events may therefore have less parton
radiation than estimated in this way and these would
favour the occurence of rapidity gaps.
Further features of our model are shown in Fig. 3,
4
Figure 4. Transverse energy ow versus  =    
q=QPM
,
i.e. lab pseudorapidity relative to the current direction in QPM
kinematics, for events with x < 10
 3
. The curves are from the
earlier Monte Carlo model (6.2), with improved parton shower
and sea quark treatment (6.3) and, in addition, with soft colour
interactions (6.3+SCI).
where the resulting distributions in momentum transfer
t and mass of the remainder system R and the
produced system X (cf. Fig. 1) are displayed for
the selected gap events. Although the model makes
no particular assumptions or requirements on these
quantities, their distributions are similar to those of
diractive interactions. This applies to the essentially
exponential t-dependence, 1=M
2
X
dependence and the
M
R
system being dominated by the proton with some
 resonance contribution. Thus, with a gap denition
suitable for selecting diractive interactions, our model
shows the same general behaviour as models based
on pomeron and other Regge exchanges. However,
the detailed behaviour depends on the gap denition.
Requirements of a large gap that extends very forward
in rapidity introduces a kinematical bias against large
values of t and M
R
. The 1=M
2
X
behaviour is explained
by the 1=s
qq
dependence of the BGF matrix elements,
but is distorted at large M
X
by requiring the gap to
extend into the central rapidity region. Thus, by varying
the gap denition or observing the forward-moving R-
system, one may nd observable dierences between the
two kinds of models.
The rate of gap events in the model is essentially
independent of the DIS kinematical variables x and
Q
2
. This is a natural consequence of the assumed
factorization of the SCI relative to the hard perturbative
interactions. Some small variation may still occur since
the parton shower details depends on x;Q
2
.
The observed quantity F
D
2
(;Q
2
) [2] can been
interpreted as the pomeron F
2
structure function [9]
with conventional QCD evolution of partons with
momentum fraction  in the pomeron [10]. Having no
pomeron in our model, one should instead consider the
ground for the models.
An observable which gives complementary informa-
tion relative to the rapidity gaps is the forward trans-
verse energy ow. Whereas substantial initial state par-
ton radiation spoils the rapidity gaps, it helps to de-
scribe the high level of the forward energy ow. It is
therefore a highly non-trivial test of any model that
both these observables can be accounted for. As shown
in Fig. 4, the E
T
-ow data [11] can be well described by
our new model. The two-string congurations from the
improved sea quark treatment contributes to enhancing
the energy ow. This is also the case for the SCI, which
can lead to congurations where the string goes `back
and forth' producing more energy per unit rapidity.
In conclusion, we have suggested a new mechanism
for the production of events with rapidity gaps. The
basic assumption is that soft colour interactions may
occur after the short space-time pertubative phase. This
modies the colour structure for hadronisation giving
colour singlet systems that are separated in rapidity. A
detailed model has features that are characteristic for
diractive scattering and can qualitatively account for
the rapidity gap events observed in DIS at HERA.
We are grateful to W. Buchmuller for interesting
discussions and to the Paris workshop organizers for a
stimulating meeting.
References
[1] ZEUS Coll., Phys. Lett. B315 (1993) 481; DESY 95-093
[2] H1 Collaboration, Nucl. Phys. B429 (1994) 477; Phys. Lett.
B348 (1995) 681
[3] G. Ingelman, P.E. Schlein, Phys. Lett. B152 (1985) 256
[4] G. Ingelman, J. Phys. G: Nucl. Part. Phys. 19 (1993) 1633
[5] P.V. Landsho, these proceedings
[6] B. Andersson et al., Phys. Rep. 97 (1983) 31
[7] G. Ingelman, proc. `Physics at HERA', DESY 1991, p. 1366
[8] G. Ingelman, J. Rathsman, Z. Phys. C63 (1994) 589
[9] G. Ingelman, K. Prytz, Z. Phys. C58 (1993) 285
[10] See contributions by H.G. Kohrs, A. Kaidalov, and
K. Golec-Biernat in these proceedings
[11] H1 Collaboration, I. Abt et al., Z. Phys. C63 (1994) 377
5


Rapidity gaps in DIS through soft colour interactions

Rapidity Gaps in DIS through Soft Colour Interactions

Rapidity Gaps in DIS through Soft Colour Interactions

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