Observation of Events with an Energetic Forward
Neutron in Deep Inelastic Scattering at HERA
ZEUS Collab oration
Abstract
In deep inelastic neutral current scattering of p ositrons and protons at the center
of mass energy of GeV we observe with the ZEUS detector events with a high
energy neutron pro duced at very small scattering angles with resp ect to the proton
direction The events constitute a xed fraction of the deep inelastic neutral current
event sample indep endent of Bjorken x and Q in the range x
BJ
and Q GeV
Intro duction
The general features of the hadronic nal state in deep inelastic lepton nucleon scattering
DIS are well describ ed by mo dels inspired by Quantum Chromo dynamics QCD In these
mo dels the struck quark and the colored proton remnant evolve into a system of partons
which fragments into hadrons Many of these mo dels neglect p eripheral pro cesses which
are characterized by leading baryons
A recent example of p eripheral pro cesses is the observation by ZEUS and H of
DIS events with large rapidity gaps These events are distinguished by the absence of color
ow b etween the nal state baryonic system and the fragments of the virtual photon and
they have b een interpreted as arising from di raction In the language of Regge tra jectories
a p omeron IP with the quantum numb ers of the vacuum is exchanged b etween the proton
and the virtual photon
Another example is provided by meson exchange which plays a ma jor
role in p eripheral hadronic scattering In this pro cess the incoming proton uctuates into
a baryon and a meson At HERA energies the lifetime of this state can b e su ciently
long that the lepton may interact with the meson In p p transitions the exchange of
neutral mesons o ccurs together with di ractive scattering These contributions may b e
separable by measuring the proton momentum distribution On the other hand p n
transitions signal events where charged meson exchange could dominate regardless
of the neutron momentum The pion b eing the lightest meson may provide the largest
contribution to the cross section Isolation of the one pion exchange contribution would
provide the opp ortunity to study virtual gamma pion interactions and thereby determine
the structure function of the pion
In order to study these issues we have installed a hadronic calorimeter to detect high
energy forward going neutrons pro duced in DIS ep en anything at HERA This pa
p er rep orts the rst observation of such events showing clear evidence of sizeable leading
neutron pro duction
Exp erimental setup
The data were collected with the ZEUS detector during while HERA collided ep
bunches of GeV p ositrons and GeV protons In addition unpaired bunches
of p ositrons and unpaired bunches of protons circulated p ermitting a measurement of
b eam asso ciated backgrounds The data sample used in this analysis corresp onds to an
integrated luminosity of pb
The present analysis makes use of a test Forward Neutron Calorimeter FNC I I
installed at the b eginning of in the HERA tunnel at degrees Z m
downstream of the interaction p oint The layout of the b eam line and calorimeter is shown
schematically in Fig FNC I I lo cated after the nal station of the ZEUS Leading Proton
Sp ectrometer LPS was an enlarged and improved version of the original test Forward
The ZEUS co ordinate system is de ned as right handed with the Z axis p ointing in the proton b eam
direction and the X axis horizontal p ointing towards the center of HERA
Neutron Calorimeter FNC I which op erated in The design construction and cali
bration of FNC II was similar to FNC I Both devices were iron scintillator sandwich
calorimeters read out with wavelength shifter light guides coupled to photomultiplier tub es
PMT The unit cell consisted of cm of iron followed by cm of SCSN scintillator
FNC II contained unit cells comprising a total depth of interaction lengths It was
cm wide and cm high divided vertically into three cm towers read out on b oth sides
There was no longitudinal sub division in the readout
The neutron calorimeter was situated downstream of the HERA dip oles which b end the
GeV proton b eam upwards Charged particles originating at the interaction p oint were
swept away from FNC I I The ap erture of the HERA magnets in front of FNC II limited
the geometric acceptance as shown in Figs c and d Between these magnets and
FNC II the neutrons encountered inactive material the thickness of which varied b etween
one and two interaction lengths Two scintillation veto counters preceded the calorimeter
one x x cm and one x x cm These counters were used o ine to identify
charged particles and thereby reject neutrons which interacted in the inactive material in
front of FNC I I The calorimeter was followed by two scintillation counters which were
used in coincidence with the front counters to identify b eam halo muons The resp onse of
the counters to minimum ionizing particles was determined with these muons
Energy dep osits in FNC II were read out using a system identical to that of the ZEUS
uranium scintillator calorimeter CAL In addition the rate of signals exceeding a threshold
of GeV was recorded The accumulated counts provide the average counting rate of
FNC II for each run
The other comp onents of ZEUS have b een describ ed elsewhere The CAL the
central tracking detectors CTD VXD the small angle rear tracking detector SRTD which
is a scintillator ho doscop e in front of the rear calorimeter close to the b eam pip e and
the luminosity monitor LUMI are the main comp onents used for the analysis of DIS
events
Kinematics of deep inelastic events
In the present analysis the two particle inclusive reaction ep en anything is compared
with the single particle inclusive reaction ep e anything In b oth cases the scattered
p ositron and part of the hadronic system denoted by X were detected in CAL Energetic
forward neutrons were detected in FNC I I The two particle inclusive events are sp eci ed
by four indep endent kinematical variables any two of x Q y and W for the scattered
BJ
lepton and any two of x p and t for the leading baryon see b elow
L T
Diagrams for one and two particle inclusive ep scattering are shown in Fig a and
b The conventional DIS kinematical variables describ e the scattered p ositron Q the
negative of the squared four momentum transfer carried by the virtual photon
0
Q q k k
0
where k and k are the four momentum vectors of the initial and nal state p ositron re
sp ectively y the energy transfer to the hadronic nal state
q P
y
k P
where P is the four momentum vector of the incoming proton x the Bjorken variable
BJ
Q Q
x
BJ
q P y s
where s is the center of mass c m energy squared of the ep system and W the c m
energy of the p system
Q x
BJ
M W q P
p
x
BJ
where M is the mass of the proton
p
The double angle metho d was used to determine x and Q In this metho d
BJ
event variables are derived from the scattering angle of the p ositron and the scattering angle
of the struck massless quark The latter angle is determined from the hadronic energy
H
ow measured in the main ZEUS detector
P P P
E p p p
Z Y X
i i i
cos
P P P
H
E p p p
Z Y X
i i i
where the sums run over all CAL cells i excluding those assigned to the scattered p ositron
and p p p p is the momentum vector assigned to each cell of energy E The
X Y Z
cell angles are calculated from the geometric center of the cell and the vertex p osition of
the event Final state particles pro duced close to the direction of the proton b eam give a
negligible contribution to cos since these particles have E p
H Z
In the double angle metho d in order that the hadronic system b e well measured it is
necessary to require a minimum hadronic energy in the CAL away from the b eam pip e A
suitable quantity for this purp ose is the hadronic estimator of the variable y de ned by
P
E p
Z
i
y
JB
E
e
where E is the electron b eam energy
e
The two indep endent kinematical variables describing the neutron tagged by FNC II
are taken to b e its energy E and transverse momentum p These quantities are related
n T
to the four momentum transfer squared b etween the proton and the neutron t by
x p
L T
M x M t
L
n p
x x
L L
where M is the mass of the neutron and x E E where E is the proton b eam energy
n L n p p
The geometry of FNC II and the HERA b eam line limited the angular acceptance of the
mrad and the threshold on energy dep osits in FNC II restricted scattered neutron to
x to x
L L
The invariant mass of the hadronic system detected in the calorimeter M can b e
X
determined from the cell information in CAL an approach similar to the double angle
metho d is applied to calculate M Given the energy E the momentum p and the
X H H
p olar angle of the hadronic system observed in the detector the following formulae
H
P P
pj where the sum runs over all calorimeter cells i p j determine M cos
Z X H
i i
excluding those assigned to the p ositron p Q y sin E E y p cos
H H e H H
H
q
M E p
X
H H
The identi cation of neutral current deep inelastic events uses the quantity de ned by
X
E p
Z
i
where the sum runs over all CAL cells i For fully contained neutral current DIS events
and neglecting CAL resolution e ects and initial state radiation E
e
We also use the variable which is de ned as the pseudorapidity
max
ln tan
of the calorimeter cluster with energy greater than MeV closest to the proton b eam
direction
Monte Carlo simulation and studies
The resp onse of FNC II was mo deled by a Monte Carlo MC simulation using the GEANT
program The mo del was inserted into the full simulation of the ZEUS detector and
b eam line For neutrons incident on the face of the calorimeter the predicted energy reso
p
lution is approximately E E with E in GeV The predicted energy resp onse
n n
n
of the calorimeter is linear to b etter than
To aid the study of energetic neutron pro duction b oth in b eam gas collisions and in DIS
a Monte Carlo generator was written for one pion exchange which gives a cross section
t 0
prop ortional to jtj x t see for example where t t m
L
0
is the pion tra jectory and GeV The co de uses as a framework the HERWIG
program Absorptive corrections to one pion exchange have b een widely discussed see
for example To estimate such e ects a simple prescription which replaces jtj
by jtj m in the numerator of the ab ove expression was used In addition to the one pion
exchange mo del the standard QCD inspired DIS mo dels ARIADNE HERWIG and
MEPS were used to predict the forward neutron pro duction
To compare data with the exp ectations of all these mo dels the MC events pro duced by
the generators were fed through the simulation of the ZEUS detector
Calibration and acceptance of FNC II
The relative gains of the PMTs were determined by scanning each tower with a Co gamma
source using the pro cedure develop ed for the ZEUS CAL This was done at the end of
the data taking p erio d Beam gas data taken in HERA were used for calibration These
data were obtained after the proton b eam was accelerated to GeV but b efore p ositrons
were injected To reject events where the neutrons had showered in material upstream of
FNC I I events were considered only when the energy dep osited in the veto counters was
b elow that of a minimum ionizing particle
The HERA b eam gas interactions o ccur at c m energies similar to those of p n data
measured at Fermilab and the ISR where neutron sp ectra were found to b e in go o d
agreement with the predictions of one pion exchange The energy scale of FNC II
was determined by tting the observed b eam gas sp ectrum ab ove GeV to that exp ected
from one pion exchange folded with the resp onse of FNC II as simulated by MC The error
in the energy scale is estimated as
Proton b eam gas data taken during a sp ecial run at proton energies of
and GeV showed that the energy resp onse of FNC II was linear to within
To correct for the drift in gains of the PMTs proton b eam gas data were taken with
an FNC trigger approximately every two weeks The mean resp onse of each tower showed
variations b etween calibration runs at the level of
The overall acceptance for neutrons A is indep endent of the acceptance of the
FNC
main detector To determine A the inactive material obscuring the ap erture had to b e
FNC
mo deled Ab out half of the inactive material was of simple geometric shap e and included in
the ZEUS detector simulation The remainder consisting mostly of iron b etween the b eam
line elements and FNC I I was mo deled by an iron plate The thickness of this plate was
adjusted so that the resulting MC energy sp ectrum of neutrons from b eam gas interactions
matched the observed sp ectrum Since the interaction of neutrons in the material leads
in general to the loss of energy either by absorption and or by particle emission outside
the acceptance of FNC I I the observed energy sp ectrum is very sensitive to the amount of
inactive material upstream Therefore in this study of inactive material events in which
the neutrons b egan showering upstream of FNC II were included in the sp ectrum that
is no cut was made on charged particles in the scintillator counters in front of FNC I I
The resulting thickness of the plate was cm Because of interactions in the inactive
material only ab out of neutrons with energy E GeV which pass through
n
the geometric ap erture reach FNC II and survive the scintillator cuts The acceptance is
constant within for neutrons with energy E GeV scattered at a xed
n
angle in the range to mrad
The overall acceptance assuming one pion exchange with the form describ ed in Section
is for neutrons with E GeV and jtj GeV The error quoted is
n
dominated by the systematic error in estimating the amount of inactive material in front of
FNC I I
To study the e ect of uncertainties in the theoretical form of the cross section for one
pion exchange the part of the acceptance due to the geometric ap erture as shown in
Fig d was calculated for several prop osed forms It was found to vary from
approximately to This part of the acceptance for exchange varies b etween
and dep ending on the mo del
Triggering and data selection
The selection was almost identical to that used for the measurement of the structure function
F
Events were ltered online by a three level trigger system At the rst level DIS
events were selected by requiring a minimum energy dep osition in the electromagnetic
section of the CAL The threshold dep ended on the p osition in the CAL and varied b etween
and GeV For events selected with the analysis cuts listed b elow this trigger was
more than e cient for p ositrons with energy greater than GeV as determined by
Monte Carlo studies
At the second level trigger SLT background was further reduced using the measured
times of energy dep osits and the summed energies from the calorimeter The events were
accepted if
X
E cos GeV E
i i S LT
i
where E and are the energies and p olar angles with resp ect to the primary vertex
i i
p osition of calorimeter cells and E is the energy dep osit measured in the LUMI photon
calorimeter For p erfect detector resolution and acceptance is twice the p ositron b eam
S LT
energy GeV for DIS events while for photopro duction events where the scattered
p ositron escap es down the b eam pip e p eaks at much lower values
S LT
The full event information was available at the third level trigger TLT Tighter timing
cuts as well as algorithms to remove b eam halo muons and cosmic muons were applied The
quantity was determined in the same manner as for The events were required to
T LT S LT
have GeV E Finally events were accepted as DIS candidates if a scattered
T LT
p ositron candidate of energy greater than GeV was found
In the analysis of the resulting data set further selection criteria were applied b oth to
ensure accurate reconstruction of the kinematical variables and to increase the purity of
the sample by eliminating background from photopro duction These cuts were
0
GeV E
e
y y
JB e
jX j cm or jY j cm
Z cm
vertex
GeV
0
where y is y evaluated from the scattered p ositron energy E and angle X and Y are
e
e
the impact p osition of the p ositron on the CAL as determined using the SRTD The cut on
jX j jY j is a ducial volume cut to avoid the region directly adjacent to the rear b eam pip e
Beam conditions sometimes resulted in a large FNC II counting rate from energy dep osits
ab ove the threshold of GeV Runs were rejected if the counting rate averaged over the
run was greater than kHz in order to reduce the probability of a b eam gas interaction
randomly overlapping a true DIS event Neutron tagged events were selected by requiring
that FNC II show an energy dep osit ab ove threshold and that the scintillation veto counters
show an energy dep osit b elow that of a minimum ionizing particle
This study is restricted to events with Q GeV After these selections k
events remain containing neutron tagged events constituting of the sample
Backgrounds
The counting rate of FNC II is predominantly due to protons interacting with residual
gas in the b eam pip e As a result the main background is due to the random overlap of
energetic neutrons from b eam gas interactions with genuine DIS events
The fraction of b eam gas triggers which survive the scintillation counter charged particle
veto was measured to b e The average raw counting rate of FNC II during the taking
of ep data was kHz leaving an e ective counting rate of Hz after the cuts With
proton bunches in HERA RF buckets and a crossing time of ns the overlap
Since neutrons are tagged in probability of a neutron with a random bunch was
of the events
signal
background
Thus only of the neutron tagged events result from random overlaps The same result
is obtained if the background is calculated on a run by run basis
The small random coincidence rate was con rmed by the rate of neutrons in non ep
background events cosmic rays and b eam halo muons and in a sample of random triggers
For the DIS selection the background from photopro duction was estimated to b e less
than overall A sample of photopro duction events was studied to rule out the p ossibility
that the observed rate of neutrons in DIS was due to an anomalously large pro duction rate
of neutrons in photopro duction A fractional rate in photopro duction comparable to that
in DIS was found verifying that the photopro duction background after the neutron tag
was also less than The same conclusion holds for the background from b eam gas
interactions
Characteristics of events with a leading neutron
The pro duction of neutron tagged events with neutron energy E GeV was studied
n
as a function of the lepton kinematical variables Figure c shows a scatter plot of Q
versus x for a sample of k DIS events which were not required to have a neutron tag
BJ
All events in the full sample with a neutron tag are shown in Fig d The neutron tagged
events follow the distribution of DIS events This is demonstrated quantitatively in Fig a
which shows the ratio r of tagged events to all events uncorrected for acceptance as a
unc
function of x Q and W Within the statistical accuracy r is consistent with b eing
BJ unc
constant This is also true if we take the ratio as a function of Q in bins of x not shown
BJ
Averaged over the x and Q region the value of the ratio is r
BJ unc
for E GeV The rst error is statistical and the second systematic The latter is
n
dominated by the neutron energy scale uncertainty
Further insight is gained by examining the scatter plot of M versus W shown in Fig e
X
for the sample of k events In this plot there is a concentration of events at low M
X
These events are found to have a large rapidity gap LRG The neutron
max
tagged events are distributed similarly to the full sample as seen in Fig f There is
a concentration of a few events with a rapidity gap at low M but most neutron tagged
X
events are ab ove the low M band
X
The distributions for all DIS events and for neutron tagged DIS events are similar
max
in shap e for Fig b showing an exp onential rise for Note that for
max max
the distributions are strongly a ected by limited acceptance towards the forward
max
b eam hole
For there are relatively fewer neutron tags in the LRG events by a factor of
max
ab out the small events represent of all DIS events but only of the neutron
max
tagged DIS events This is shown in the plot of r as a function of in Fig c
unc max
LRG events with a leading neutron are exp ected for instance from di ractive pro duction
of a baryonic system decaying to an energetic forward neutron and from double p eripheral
pro cesses where a p omeron is exchanged b etween the virtual photon and the virtual pion
emitted from the proton This e ect warrants further study
The measured fraction of DIS events with a leading neutron with E GeV r
n unc
can b e compared with the predictions of mo dels for DIS at HERA
ARIADNE which is a colour dip ole mo del including the b oson gluon fusion pro cess in
general gives a go o d description of the hadronic nal state in DIS at HERA The value of
Values of are an artifact of the clustering algorithm and may o ccur when particles are
max
distributed in contiguous cells around the b eam pip e
r predicted by ARIADNE is where the error is due to the uncertainty in
unc
the acceptance This is a factor of ab out less than that observed Figure a shows the
observed energy sp ectrum of neutrons tagged ab ove GeV by FNC I I The shap e of the
neutron energy distribution predicted by ARIADNE fails to describ e the data as seen from
the dashed histogram in Fig a The DIS mo dels MEPS and HERWIG predict a
higher rate of neutrons by ab out a factor of but still fail to repro duce the observed energy
sp ectrum
The result of the one pion exchange Monte Carlo calculation of the exp ected sp ectrum is
sup erimp osed on the energy sp ectrum in Fig a normalized to the total numb er of events
ab ove GeV There is reasonably go o d agreement b etween the Monte Carlo simulation
and the data at energies ab ove GeV At lower energies other exchanges such as the
may b ecome imp ortant The neutron energy distribution shows no indication of varying
with x or Q This is demonstrated in Fig b and c where the mean E and width
BJ AV
of the neutron energy distribution are shown as functions of x and Q
E BJ
If A as determined for one pion exchange is taken together with r as measured in
FNC unc
the data of DIS events have a neutron with energy E GeV and jtj
n
GeV The prescription for absorptive corrections discussed in section decreases this
fraction by ab out
Conclusions
We have observed energetic forward neutron pro duction in DIS at HERA The neutrons
are detected at very small scattering angles mrad and at high x E E x
L n p L
Within present statistics leading neutron pro duction is a constant fraction of DIS
indep endent of x and Q in the range x and Q GeV
BJ BJ
Furthermore the neutron energy sp ectrum shows no variation of its mean or width with x
BJ
and Q Neutrons with energy E GeV and jtj GeV account for a substantial
n
fraction at the level of of DIS events
Acknowledgments
We acknowledge helpful discussions with E Gotsman G Ingelman N Nikolaev F Schrempp
A Szczurek and P Zerwas We thank F Czempik A Kiang H Schult V Sturm and
K Westphal for their help with the design and construction of the calorimeter We also
thank the HERA machine sta for their forb earance during the op eration of the FNC We
esp ecially appreciate the strong supp ort provided by the DESY Directorate
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ZEUS
FNC
S6 S5 S4 S3 S2 S1 a
Photomultiplier Z Tube X Wavelength Shifter (WLS)
Forward Neutron Calorimeter
Muon Veto Veto
Counters Counter 2 Counter 1 b
(WLS) (WLS)
+
c d
Figure a Schematic layout of the proton b eam line viewed from the side with FNC
II at Z m b elow the b eam pip e and downstream of LPS stations S S b
Schematic drawing of FNC II viewed from the top c Front view of FNC II showing
the segmentation into three towers and the pro jected region of geometric ap erture allowed
by the HERA magnets The cross indicates the p osition of the zero degree line d
The geometric acceptance as a function of p olar angle scattering angle integrated over
azimuth ZEUS 1994
10 3 10 3
10 2 10 2
10 10 -3 -2 -3 -2 10 10 10 10 (c) (d) 100 100
50 50
0 0 0 100 200 300 0 100 200 300
(e) (f)
Figure a Diagram for the inclusive reaction ep e anything b for the two particle
inclusive reaction ep en anything a sp ecial case of a where the hadronic system of
mass W contains a forward neutron The part of the hadronic system detected by CAL is
denoted by X and has a mass M c A scatter plot of Q versus x for DIS events and
X BJ
d neutron tagged DIS events with E GeV corresp onding to c e A scatter plot
n
of M versus W for DIS events The events in the band at low M larger dots are the
X X
large rapidity gap events f A scatter plot of M versus W for neutron tagged DIS events
X
with E GeV The LRG events are plotted as squares n ZEUS 1994 1
0.75 10 2 0.5
0.25
10 -4 -3 -2 10 10 10
1 1 0.75 -2.5 0 2.5 5 7.5 0.5 (b) 0.25 1
0 20 40 60 80 100 0.8
1 0.6
0.75 0.4 0.5 0.2 0.25
0 0 0 100 200 300 -2.5 0 2.5 5 7.5
(a) (c)
Figure a The observed ratio of neutron tagged DIS events with E GeV to all
n
DIS events as a function of x Q and W b The data p oints show the distribution
BJ max
for tagged DIS events with E GeV The distribution for all DIS events multiplied
n
by is sup erimp osed as a histogram c The observed ratio of tagged DIS events
with E GeV to all DIS events as a function of
n max ZEUS 1994 100 80 60 40 20 0 400 600 800 1000 (a) 700 700 600 600 500 500
400 -4 -3 -2 400 10 10 10 0 20 40 60 80 100
300 300 200 200 100 100
0 -4 -3 -2 0 10 10 10 0 20 40 60 80 100
(b) (c)
Figure a The energy distribution of neutrons tagged by FNC I I uncorrected for accep
tance The solid p oints are data and the histogram is the result of a one pion exchange DIS
Monte Carlo calculation normalized to the numb er of events greater than GeV The
dashed histogram gives the prediction of ARIADNE normalized to the same luminosity as
the data b and c The variation of the mean E and width of the neutron energy
AV E
sp ectrum ab ove GeV as a function of x and Q BJ