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\noindent 

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%{\it {\large version of \today}} \\[.3em] 

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\begin{tabular}{llrr} 

%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http:// www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline  

Submitted to & & & 

\epsfig{file=H1logo_bw_small.epsi,width=2.cm} \\[.2em] \hline 

\multicolumn{4}{l}{{\bf 

International Europhysics 

Conference on High Energy Physics}, 

July~12,~2001,~Budapest} \\ 

{\bf EPS 2001:} 

& Abstract: & {\bf 816} &\\ 

& Parallel Sessions & {\bf 1, 2} &\\ 

%& Plenary Session & {\bf } &\\[.7em] 

\multicolumn{4}{l}{{\bf 

XX International Symposium on Lepton and Photon Interactions}, 

July~23,~2001,~Rome} \\ 

{\bf LP 2001:} & Abstract: & {\bf 508} &\\ 

%& Parallel Session & {\bf } &\\ 

& Plenary Session & {\bf S8} &\\ \hline 

&\multicolumn{3}{r}{\footnotesize{\it 

www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] 

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\vspace*{2cm}

{\par\centering \textbf{\large Comparison of Fragmentation Properties in Diffractive
and Non-Diffractive Deep-Inelastic scattering at HERA.}\large \par}

\vspace*{1cm}

{\par\centering H1 Collaboration\par}



\begin{abstract}
\noindent Fragmentation measurements are presented for diffractive and non-diffractive
deep inelastic \( ep \) scattering data in the Breit frame of reference. The
rapidity spectra for the diffractive event selection clearly shows the expected
suppression of tracks in the target hemisphere. The average charged multiplicity
in the current hemisphere, \( <n> \), is shown to compare well with DIS at
low \( \beta  \) and with \( e^{+}e^{-} \) at high \( \beta  \). The evolution
of the peak and width of the current hemisphere fragmentation functions for
charged particles is studied as a function of photon virtuality, \( Q \), and
is found to agree with results obtained in non-diffractive deep inelastic scattering.
Comparison with various models of diffraction are made with the resolved pomeron
model (H1 fit 2) providing the best description of the data.
\end{abstract}


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\pagestyle{plain}


\section{\label{sec:intro}Introduction}

Previous studies \cite{1,2,3,4} of Deep Inelastic \( ep \) Scattering (DIS)
in the Breit frame of reference \cite{5} have established the universality
of hadronic fragmentation properties and their energy dependence for quarks
ejected from a proton and for quarks produced from the vacuum in \( e^{+}e^{-} \)
annihilation experiments.

There exists a subclass of DIS events of distinctly separate properties, called
diffractive events. These events are identified by a gap in rapidity between
the observed hadronic system \( X \) , and the outgoing proton system \( Y \).
These events are evidence of a colourless exchange mechanism between the proton
and exchange boson, commonly referred to as pomeron (\( I\! \! P \)) exchange. 

It is a principal object of this paper to further test universal fragmentation
by examining the fragmentation properties of quarks thrown out of the pomeron
in diffraction when probed with the same highly virtual boson as used in \( ep \)
DIS scattering.

It is useful to recall some of the variables used in the description of DIS
in general and diffraction in particular. The total hadronic energy of the \( \gamma ^{*}p \)
system is \( W \), the magnitude of the four momentum transfer is \( Q \)
and \( M_{\mathrm{x}} \) is the mass of the observed hadronic final state in
the central detectors \( (\gamma ^{*}I\! \! P \) system). We also define the
Lorentz invariant dimensionless variables

\begin{equation}
\label{equ:t}
t=(p-p')^{2},
\end{equation}


\begin{equation}
\label{equ:beta}
\beta =\frac{Q^{2}}{2\left( p-p'\right) \cdot q}\simeq Q^{2}/(M^{2}_{\mathrm{x}}+Q^{2})
\end{equation}
 and

\begin{equation}
\label{equ:xip}
x_{I\! \! P}=\frac{\left( p-p'\right) \cdot q}{p\cdot q}\simeq (M^{2}_{\mathrm{x}}+Q^{2})/(W^{2}+Q^{2}),
\end{equation}
 

where the incoming proton four momentum is \( p \), the outgoing proton momentum
is \( p' \) and the four momentum of the exchange boson is \( q \). The squared
four momentum transferred at the proton vertex is \( t \). The proton mass
and momentum transfer \( t \) have been neglected in the approximation for
\( \beta  \) and \( x_{I\! \! P} \). In the infinite momentum frame, \( \beta  \)
is the fraction of momentum of the pomeron carried by the struck quark and \( x_{I\! \! P} \)
is the fraction of momentum of the initial state proton carried by the pomeron. 

Diffractive events are selected on the basis of an observed rapidity gap in
the forward region of the detector. Previous studies of diffractive phenomena
\cite{6} used selections requiring a laboratory pseudorapidity\footnote{%
Pseudorapidity \( \eta =-\ln (\tan (\theta /2)) \) where \( \theta  \) is
measured with respect to the proton beam direction.
} gap in the range \( 3.3<\eta <7.5 \). These requirements impose the approximate
constraint \( M_{Y}<1.6\: \mathrm{GeV} \), \( \left| t\right| <1.0\: \mathrm{GeV}^{2} \)
, \( x_{I\! \! P}<0.05 \) and \( 3.0<M_{x}<36\: \mathrm{GeV} \). Within this
analysis this is referred to as the DIFF selection. Previous DIS studies \cite{1,2}
excluded diffractive events since they were not generated by DIS Monte-Carlos
and could therefore not be corrected for. This required a minimum detected energy
flow in the forward region and this selection is referred to as the DIS selection. 

A particularly suitable frame of reference in which to study quark fragmentation
in \( ep \) scattering is the Breit Frame \cite{5}. 

In this frame and within the naive quark-parton model (\( QPM \)) the purely
space-like virtual photon has longitudinal momentum \( -Q \) and collides elastically
and head-on with a quark of longitudinal momentum \( Q/2 \). The struck quark
is scattered with an equal but opposite momentum while the proton remnant fragments
into the opposite hemisphere. Particles emerging from the interaction are assigned
to the current region (and associated with the struck quark) if they have negative
longitudinal momenta.

The energy scale for the current region, set by the virtual photon, is given
by \( Q/2 \), and is independent of the nature (diffractive or non-diffractive)
of the event. Unlike the hadronic center of mass system in DIS, or the center
of mass of system \( X \) in DIFF, the Breit frame is not a rest frame.

After a description of the relevant parts of the apparatus (section \ref{sec:h1})
and a discussion of the treatment of data (section \ref{sec:data}), we study
the rapidity spectra (section \ref{sec:rap}), the evolution of the fragmentation
function (section \ref{sec:pkw}) and the average charged multiplicity (section
\ref{sec:acm}) 


\section{\label{sec:h1}The H1 Detector}

The H1 detector is described in detail elsewhere \cite{7}. Here, we give only
a short description of the components more relevant to this analysis. We employ
a right-handed coordinate system with the positive (forward) \( z \) axis being
in the direction of the incoming proton. Polar angles are measured from this
direction.

In the central region of the apparatus momentum measurements of charged particles
are provided by two cylindrical and co-axial drift chambers \cite{8} which
are supplemented by two \( z \)-chambers. In the forward (proton) direction,
tracks are measured by the Forward Track Detector \cite{9} (FTD) which consists
of three Radial and three Planar drift chamber modules. All these track detectors
are inside a uniform \( 1.15\: \mathrm{T} \) magnetic field. Track segments
from all devices are combined to give efficient detection and momentum measurement
with \( \delta p/p^{2}<1\%/\mathrm{GeV} \) for most of the angular range used
in this analysis, (\( 10^{\circ }<\theta <160^{\circ } \)). 

In the polar range \( 4^{\circ }<\theta <154^{\circ } \), the trackers are
surrounded by a fine-grained liquid argon (LAr) sampling calorimeter \cite{10}
with lead and steel absorber in the electromagnetic and hadronic sections respectively.
A backward scintillating fibre calorimeter (SpaCal \cite{11}) covers the range
\( 153^{\circ }<\theta <177.8^{\circ } \) and provides identification and measurement
of the scattered positron. The SPACAL detector also gives time of flight information
for the efficient removal of beam related background for triggering purposes. 

Forward energy at small angles is observed in the outgoing proton beam direction
by the Forward Muon Detector (FMD) and the Proton Remnant Tagger (PRT). The
FMD covers the pseudo-rapidity range \( 1.9<\eta <3.7 \) directly but is also
sensitive to larger \( \eta  \) values (\( 3.5<\eta <6.5 \)) as a result of
secondary scattering off beam gas and the beam pipe. The PRT consists of scintillation
counters surrounding the beam pipe at \( z=24\mathrm{m} \), with an effective
sensitivity to energy flow in the range \( 6<\eta <8 \).


\section{\label{sec:data}Data Selection and Corrections}

The data are taken with \( 27.5\: \mathrm{GeV} \) positrons incident on \( 820\: \mathrm{GeV} \)
protons giving an \( ep \) centre of mass energy, \( \sqrt{\mathrm{s}} \),
of \( 300\: \mathrm{GeV} \). The trigger requires the identification of a large
electromagnetic energy deposited in the backward direction by the SpaCal detector.
The trigger is fully efficient (\( >99\% \)) and unbiased in both \( Q \)
and charged track multiplicity using the selection of low \( Q \) events described
below. The analysis begins with nearly two million events of which nearly half
a million survive basic fiducial cuts. This corresponds to an integrated luminosity
of about \( 7\: \mathrm{pb}^{-1} \). Event kinematic variables used in this
analysis are calculated using only the scattered lepton, which gives both good
resolution in the chosen region and explicit freedom from bias on the hadronic
system studied. Further cuts are made to ensure energy containment of the scattered
positron within the SpaCal. 

The events are explicitly selected to have an identified scattered positron
with an energy \( E_{e}>14\: \mathrm{GeV} \). The polar angle of the scattered
quark (\( \theta _{q} \)), calculated using four momentum conservation with
the scattered lepton and assuming the quark is massless, is required to be \( 10^{\circ }<\theta _{q}<150^{\circ } \).
This is inside the acceptance of the H1 track detectors and thus minimises corrections
at the cost of removing a further \( \sim 24\% \) of events. 

To reject beam associated background, we demand that there be no veto from the
time of flight system and that an event vertex be reconstructed within \( 35\: \mathrm{cm} \)
of the nominal vertex position. The dimensionless inelasticity variable, \( y=Q^{2}/xs \),
is required to be in the range \( 0.055<y<0.6 \) and the sum \( \sum _{i}\left( E^{i}-p_{z}^{i}\right)  \)
over all calorimeter energy deposits is required to be larger than \( 35\: \mathrm{GeV} \)
and smaller than \( 70\: \mathrm{GeV} \). Together, these conditions ensure
that contamination from mis-identified photoproduction events is below the \( 1\% \)
level and reduce QED radiative effects. 

There is a remaining source of error arising from initial state QED radiation.
This leads to an incorrect measurement of \( Q^{2} \) which affects the boost
to the Breit frame. The miscalculation of the boost results in a wrongly determined
Breit frame axis. In most cases this leads to a depleted (or even empty) region
of phase space where the scattered quark fragments are expected. To reduce the
size of the necessary QED corrections, this analysis reimposes the \( 0.055<y<0.6 \)
selection using hadronic system variables calculated with the Jaquet Blondel
method \cite{12}. 

Previous DIS studies \cite{1,2} included a further cut to remove events with
little forward energy flow by requiring that the total summed energy deposited
in the polar region \( 4^{\circ }<\theta <15^{\circ } \) to be greater than
\( 0.5\: \mathrm{GeV} \). The discovery of diffractive events with a hard scale
was a surprise and early DIS Monte--Carlos were incapable of their generation.
The cut was designed to remove these events and defines the DIS event selection.

The diffractive event selection, DIFF, requires the absence of hadronic activity
in the forward region. There must be no signal above noise levels in the FMD
and PRT detectors. The most forward hadronic energy cluster with \( E>400\: \mathrm{MeV} \)
must be at \( \eta <3.3 \). Non-diffractive contributions are further suppressed
by explicitly requiring \( x_{I\! \! P}<0.05 \). Contributions from light vector
meson production are excluded by requiring \( 3.0<M_{\mathrm{x}}<36\: \mathrm{GeV} \).
These cuts impose the approximate restrictions \( M_{Y}\leq 1.6\: \mathrm{GeV} \)
and \( \left| t\right| \leq 1\: \mathrm{GeV} \) on the reconstructed events.

Following all the selection procedures \( \sim 10^{5} \) events satisfy the
DIS selection and \( \sim 10^{4} \) events satisfy the DIFF selection.

In addition to these event selections there are also cuts made to reject badly
measured tracks. Any tracks in the central chambers with transverse momenta
below \( 150\: \mathrm{MeV} \) and those in the forward track detectors with
momentum below \( 500\: \mathrm{MeV} \) are removed. We also remove tracks
failing minimum requirements on the number of hits and the quality of the track
fit. In order to determine the primary multiplicity, cuts are also made to exclude
tracks not originating from the interaction vertex. There remains a small excess
contribution due to the decays of short-lived strange particles. 

To correct for this excess and for acceptance losses, we utilise the DJANGO
\cite{13} Monte-Carlo event generator for the DIS event selection. This combines
a leading order (LO) perturbative QCD matrix element calculation and the colour
dipole model with a calculation of QED radiative effects. For the DIFF selection
we use the RAPGAP \cite{14} Monte-Carlo. This combines a model of diffraction
as deep-inelastic scattering of a virtual photon off a pomeron or reggeon coupled
to the initial-state proton with the LEPTO \cite{15} Monte-Carlo.

Radiative effects remaining after our event selections have been corrected for
by comparing the results of Monte Carlo calculations with and without the inclusion
of QED radiative effects. The detector response is simulated using a program
based on the GEANT \cite{16} package and the simulated events are reconstructed
and selected using exactly the same analysis chain as with real data. No particle
identification is used in this analysis. We adopt the procedure throughout of
assuming that each charged particle is a pion and then using the same Monte
Carlo simulation procedure to correct for the \( \sim 12\% \) charged kaon
and \( \sim 5\% \) proton content. 

A large source of systematic error for this analysis originates in possible
calibration errors of \( \pm 1\% \) for the SPACAL electromagnetic calorimeter
energy scale since this directly affects the accuracy of Lorentz boosts and
translates into uncertainties on the number of tracks in the area of interest
of \( \pm 7\% \) throughout (in a highly correlated fashion). The systematic
error in the Monte-Carlo derived acceptance correction functions has been estimated
using two different generators \cite{13,15} and is \( \pm 7\% \). 

The full experimental details of how the corrected distributions of this analysis
are obtained from the data may be found in reference \cite{17}. 


\section{\label{sec:rap}Rapidity Spectra}

The rapidity, \( Y \), for a given hadron is defined as

\begin{equation}
\label{equ:Y}
Y=\frac{1}{2}\ln \left( \frac{E+p_{z}}{E-p_{z}}\right) 
\end{equation}
 where \( p_{z} \) is the longitudinal momentum of each track and the energy,
\( E \), is calculated assuming each charged hadron has the mass of a charged
pion ,\( m_{\pi } \). Corrections are made using Monte-Carlo to take admixture
of other particles into account.

For both event selections the total width of the \( Y \) distribution, the
longitudinal phase space, scales with energy and is typically given by \( 2\ln \left( W/m_{\pi }\right)  \),
while the width of the current hemisphere of the Breit frame is given by \( \ln \left( Q/m_{\pi }\right)  \).
For diffractive events the expected width of the observed \( \gamma ^{*}I\! \! P \)
system is given by \( 2\ln \left( M_{\mathrm{x}}/m_{\pi }\right)  \) with a
large rapidity gap separating it from the (unobserved) \( M_{Y} \) system in
the extreme forward region.


\begin{figure}
{\par\centering \resizebox*{!}{0.5\textheight}{\includegraphics{H1prelim-01-116.fig1.eps}} \par}


\caption{\label{fig:rapidity plots}Rapidity distribution in the Breit frame of reference.
(a)~Comparison of DIS and DIFF. (b)~Comparison of \protect\( \beta <0.2\protect \)
and \protect\( \beta >0.2\protect \) for DIFF selected events. The data is
compared with MEAR Monte-Carlo for DIS events and with RAPGAP using the resolved
\protect\( I\! \! P\protect \) model and the fit 2 parameterisation from H1
\cite{18}.}
\end{figure}


Figure~\ref{fig:rapidity plots}(a) shows the event normalised rapidity distribution
for DIS and DIFF event selections for all \( Q^{2} \). Compared with DIS, diffractive
events have a higher multiplicity in the current region. This is discussed in
detail in section \ref{sec:acm}. By definition, the multiplicity of diffractive
events must approach zero at the beginning of the rapidity gap as is clearly
seen in the DIFF selection. The distribution for the DIS selection, which has
no requirement for a rapidity gap, shows a plateau in the target region which
has been investigated elsewhere \cite{2}.

In \cite{18} the H1 collaboration interpreted the measurement of the diffractive
structure function, \( \mathrm{F}^{D(3)}_{2} \), in terms of a resolved pomeron
model incorporating a leading diffractive exchange and a subleading reggeon
contribution. Three different parameterisations were presented, a quark dominated
parameterisation (fit 1) and two gluon dominated parton distributions, a 'flat
gluon' (fit 2) and a 'peaked gluon (fit 3). Figure~\ref{fig:rapidity plots}
shows that (the generally preferred) fit 2 gives a good description of the DIFF
rapidity distribution.

In \cite{19} a parameterisation has been made of the diffractive DIS cross
section, the main feature of which is the decomposition of the \( \beta  \)
spectrum into three contributions: \( q\overline{q}g \) production (dominating
at low \( \beta  \) (\( \beta <\sim 0.2 \))) and transverse and longitudinal
\( q\overline{q} \) production (dominating at medium and high \( \beta  \)).
This motivates the subdivision of the DIFF selection into two different \( \beta  \)
regions. Figure~\ref{fig:rapidity plots}(b) shows that for \( \beta >0.2 \)
the rapidity distribution is symmetric about the Breit frame origin, consistent
with the back-to-back emission of a pair of quarks in either hemisphere. The
selection \( \beta <0.2 \) gives a broader and more asymmetric distribution
extending further into the target hemisphere of the Breit frame. This is consistent
with a \( q\overline{q}g \) system as claimed in \cite{19}. It also results
in higher total multiplicity which is also expected kinematically since lower
\( \beta  \) values correspond to higher values of \( M_{x} \).

It is noticeable that the \( \beta  \) dependence seen figure~\ref{fig:rapidity plots}(b)
is described by the resolved pomeron model. Other models of diffraction are
compared in Figures~\ref{fig:rap_rapgap} and \ref{fig:rap_lepto} and show
that fit2 and fit 3 cannot be differentiated and provide the best description
of the data. Fit 1 clearly does not describe the data and shows that the rapidity
distribution is sensitive to different models of diffraction.

Diffractive DIS can be treated (in the proton rest frame) by considering the
\( q\overline{q} \) and \( q\overline{q}g \) photon fluctuations as colour
dipoles \cite{19}. The saturation model by Golec-Biernat and Wusthoff \cite{21}
uses the colour dipole approach, with an ansatz for the dipole cross section
which interpolates between the perturbative and non-perturbative regimes of
the \( \gamma ^{*}p \) cross section. The model does not describe the data
as well as fits 2 and 3 of the resolved pomeron model, predicting a lower multiplicity
in the central region. 

In the soft colour interaction model (SCI), diffraction occurs through soft
colour rearrangements between the outgoing partons The original SCI model \cite{22}
used only one free parameter, the universal colour rearrangement probability,
fixed by a fit to \( \mathrm{F}^{D(3)}_{2} \). A recent refinement to the model
\cite{23} has been made by making the colour rearrangement probability proportional
to the normalised difference in the generalised area of the string configurations
before and after the rearrangement. 

SCI as implemented in LEPTO both in the original and refined forms together
with a version of LEPTO without SCI are compared with the data in figure~\ref{fig:rap_lepto}.
The new versions of SCI improves the description of the rapidity spectra for
DIS in the target region compared to the old version but still the version of
LEPTO without SCI gives a better description. Despite the significant changes
to the rapidity spectra for DIS the diffractive distributions show very little
effect of these changes. SCI describes the rapidity spectra at high \( \beta  \)
but underestimates the multiplicity in the target region at low \( \beta  \). 

All the models discussed are able to describe at least qualitatively the differences
between high and low \( \beta  \) indicating that they are mainly resulting
from phase space restrictions which are due to the correlation between \( \beta  \)
and \( M_{x} \).


\begin{figure}
{\par\centering \resizebox*{!}{0.5\textheight}{\includegraphics{H1prelim-01-116.fig2.eps}} \par}


\caption{\label{fig:rap_rapgap} Comparison of rapidity distributions with predictions
from a resolved pomeron model using three different parameterisations from H1\cite{18},
and the saturation model \cite{21}.}
\end{figure}



\begin{figure}
{\par\centering \resizebox*{!}{0.5\textheight}{\includegraphics{H1prelim-01-116.fig3.eps}} \par}


\caption{\label{fig:rap_lepto} Comparison of rapidity distributions with predictions
from the LEPTO Monte-Carlo with different implementations of Soft Colour Interactions
(SCI).}
\end{figure}



\section{\label{sec:pkw}Fragmentation Function}

The ratio of the momentum of any particular charged hadron to the energy scale
(\( Q/2 \)) of the current hemisphere of the Breit frame is \( x_{p}=p^{\pm }_{hadron}/(Q/2) \)
. It has been shown to be directly comparable to \( x_{p}=p^{\pm }_{hadron}/(E^{*}/2) \)
\cite{1} for one hemisphere of an \( e^{+}e^{-} \) experiment where \( \sqrt{s_{ee}}=E^{*}=Q \).
The event normalised charged track density,

\begin{equation}
\label{equ:Dxp}
D^{\pm }\left( x_{p}\right) =\left( \frac{1}{N}\right) \times dn_{tracks}^{\pm }/dx_{p}
\end{equation}
 is called the fragmentation function which characterises the complete process
of final state parton shower development and non-perturbative hadronisation.
The fragmentation function may be redefined to \begin{equation}
\label{equ:Dxi}
D^{\pm }\left( \xi \right) =\left( \frac{1}{N}\right) \times dn_{tracks}^{\pm }/d\xi 
\end{equation}
 by change of variable to \( \xi =\ln \left( \frac{1}{x_{p}}\right)  \), which
is used to expand the low momentum region.

The Modified Leading Log Approximation (MLLA) \cite{24} coupled together with
Local Parton Hadron Duality (LPHD) predicts that in the region of the peak of
the hadronic \( \xi  \) distribution, the shape is approximately Gaussian.
The MLLA also gives a prediction for the energy behaviour of the peak position
and width of this Gaussian (the first and second moments of the fragmentation
function respectively);

\begin{equation}
\label{equ:xipeek}
\xi _{peak}=0.5U+c_{2}\sqrt{U}+O(1)
\end{equation}


\begin{equation}
\label{equ:xiwidth}
\xi _{width}=\sqrt{\frac{U^{3/2}}{2c_{1}}}.
\end{equation}


Here \( U=\ln \left( Q/\Lambda _{eff}\right)  \), where \( \Lambda _{eff} \)
is an effective scale parameter, \( c_{1} \) and \( c_{2} \) are constants
dependent on the number of excited flavours and colours in QCD, and \( O(1) \)
is a slowly varying function of energy containing all QCD diagrams beyond leading
order. This term is assumed to be constant in this analysis.


\begin{figure}
{\par\centering \resizebox*{!}{0.5\textheight}{\includegraphics{H1prelim-01-116.fig4.eps}} \par}


\caption{\label{fig:pkw}The energy evolution of the (a) peak position and (b) width
of the fragmentation function for both DIS and DIFF selections. The solid (dashed)
line is the simultaneous fit of the MLLA parameterisation to the DIS (DIFF)
data.}
\end{figure}


Figure~\ref{fig:pkw} summarises the energy evolution of the fragmentation
function. The solid (dashed) line is the simultaneous fit to the peak position
and width of the MLLA parameterisation for the DIS (DIFF) data selection which
yields a result of \( \Lambda _{eff}=0.21\pm 0.04 \) (\( 0.19\pm 0.03 \))
and \( O(1)=-0.42\pm 0.12 \) (\( -0.49\pm 0.12 \)). 

Both DIS and DIFF distributions and parameters are compatible with each other,
thus lending further support to the concept of quark fragmentation universality.


\section{\label{sec:acm}Average Charged Multiplicity}

The area under the fragmentation function is the averaged charged multiplicity,
\( <\! n\! > \), also known as the zeroth moment of the fragmentation function.
Figure~\ref{fig:acm} compares the average charged multiplicity in the current
region between DIS and DIFF and the data is compared with MEAR Monte-Carlo for
DIS events and with RAPGAP using the resolved \( I\! \! P \) model and the
fit 2 parameterisation from H1 \cite{18}. In figure~\ref{fig:acm_sat} the
diffractive data is compared with predictions from the saturation model. The
DIFF selection is split into high and low \( \beta  \) samples and shown together
with a parameterisation \cite{25} of \( e^{+}e^{-} \) results for a single
hemisphere, where contributions from \( K^{0} \) and \( \Lambda  \) decays
have been subtracted, to be comparable with this data.


\begin{figure}
{\par\centering \resizebox*{!}{0.5\textheight}{\includegraphics{H1prelim-01-116.fig5.eps}} \par}


\caption{\label{fig:acm}The average charged multiplicities as a function of the energy
scale \protect\( Q\protect \). The error is dominated by a correlated systematic
error of about \protect\( \sim 7\%\protect \) associated with the energy uncertainty
of the scattered electron in the SpaCal. The solid curve is a fit to many \protect\( e^{+}e^{-}\protect \)
results as a function of the centre of mass energy \protect\( E^{*}\protect \)(\protect\( E^{*}=Q\protect \)),
the dashed line a prediction for the MEAR Monte-Carlo for DIS events and the
dotted and dashed-dotted lines comes from RAPGAP using the resolved \protect\( I\! \! P\protect \)
model and the fit 2 parameterisation from H1 \cite{18}.}
\end{figure}



\begin{figure}
{\par\centering \resizebox*{!}{0.5\textheight}{\includegraphics{H1prelim-01-116.fig6.eps}} \par}


\caption{\label{fig:acm_sat}The average charged multiplicities as a function of the
energy scale \protect\( Q\protect \). The data is compared with a prediction
of the saturation model.}
\end{figure}


In \cite{1}, the observation of a significant shortfall of \( <\! n\! > \)
for DIS compared to \( e^{+}e^{-} \) was explained by LO QCD processes present
in \( ep \) but absent in \( e^{+}e^{-} \) interactions. Such higher order
QCD processes lead to a depopulation of tracks in the current region (or even
an empty current region). This effect is also observed for the low \( \beta  \)
DIFF selection which is expected to be dominated by \( q\overline{q}g \) production.
The high \( \beta  \) DIFF selection which is expected to be dominated by \( q\overline{q} \)
production, compares well with the \( e^{+}e^{-} \) parameterisation and has
significantly fewer events with an empty current region\footnote{%
Note that for \( \mathrm{M}_{\mathrm{x}}<Q \) (\( \beta >0.5 \)) it is kinematically
forbidden to have an empty current region.
}. For \( 12<Q^{2}<15 \) \( (60<Q^{2}<80) \) \( \mathrm{GeV}^{2} \), 28\%
(10\%) of events in the DIS selection have an empty current region, compared
with 22\% (7\%) in the DIFF sample at low \( \beta  \) and 8\% (3\%) at high
\( \beta  \). As with the rapidity spectra both the resolved pomeron model
(H1 fit 2) and the saturation model are able to describe the \( \beta  \) dependence
and the \( Q^{2} \) evolution of the average charged multiplicity seen in the
data.


\section{\label{sec:conclusions}Conclusions}

The universality of quark fragmentation has been supported by comparing spectra
for quarks originating from the pomeron with those from quarks from the proton
and from quarks produced from the vacuum in \( e^{+}e^{-} \) annihilation experiments.

The \( \beta  \) dependence of diffractive DIS data is consistent with the
expectation for final states of \( q\overline{q}g \) at low \( \beta  \) and
for \( q\overline{q} \) at high \( \beta  \) but is also reproduced in models
where there is no explicit modeling of these final state configurations, strongly
suggesting that these effects are a result of restricting the phase space that
is implicit in making a selection of \( \beta  \).


\section*{Acknowledgments}

We are grateful to the HERA machine group whose outstanding efforts have made
and continue to make this experiment possible. We thank the engineers and technicians
for their work in constructing and now maintaining the H1 detector, our funding
agencies for financial support, the DESY technical staff for continual assistance,
and the DESY directorate for the hospitality which they extend to the non--DESY
members of the collaboration.

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