Search for exclusive events using the dijet mass fraction at the
  Tevatron
Search for exclusive events using the dijet mass fraction at the Tevatron
O. Kepka∗
DAPNIA/Service de physique des particules, CEA/Saclay, 91191 Gif-sur-Yvette cedex, France
IPNP, Faculty of Mathematics and Physics, Charles University, Prague and
Center for Particle Physics, Institute of Physics, Academy of Science, Prague
C. Royon†
DAPNIA/Service de physique des particules, CEA/Saclay, 91191 Gif-sur-Yvette cedex, France
In this paper, we discuss the observation of exclusive events using the dijet mass fraction as
measured by the CDF collaboration at the Tevatron. We compare the data to pomeron exchange
inspired models as well as Soft color interaction ones. We also provide the prediction on dijet mass
fraction at the LHC using both exclusive and inclusive diffractive events.
I. INTRODUCTION
Double pomeron exchange (DPE) processes are expected to extend the physics program at the LHC not only due
to the possible Higgs boson detection but also because of the possibility to study broader range of QCD physics and
diffraction [1, 2, 3, 4, 5, 6, 7, 8]. The processes are theoreticaly characterized by large rapidity gap regions devoid of
particles between centrally produced heavy object and the scattered hadrons which leave the interaction intact. This
is attributed to the exchange of a colorless object, the pomeron (or the reggeon). In the LHC environment, however,
the rapidity gap signature will not appear because of the high number of multiple interactions occuring at the same
time, and the diffractive events will be identified tagging the escaping protons in the beam pipe.
One generally considers two classes of DPE processes, namely, exclusive DPE events if the central object is produced
alone carrying away the total available diffractive energy and inclusive events when the total energy is used to produce
the central object and in addition the pomeron remnants. Exclusive events allow a precise reconstruction of the mass
and kinematical properties of the central object using the central detector or even more precisely using very forward
detectors installed far downstream from the interaction point. The most appealing exclusive process to be studied at
the LHC is the Higgs boson production but since it cannot be observed at the Tevatron due to the low production
cross section, one should find other ways to look for exclusive events at the Tevatron, for example in dijet, diphoton
channels. It is needed to mention that until recently, there was not a decisive measurement that would provide enough
evidence for the existence of exclusive production.
Although exclusive production yields kinematically well constrained final state objects, their experimental detection
is non-trivial due to the overlap with the inclusive DPE events. In those events, the colliding pomerons are usualy
viewed as an object with partonic sub-structure. A parton emitted from the pomeron takes part in the hard interaction
and pomeron remnants accompanying the central object are distributed uniformly in rapidity. Exclusive events usually
appear as a small deviation from the inclusive model predictions which need to be studied precisely before accepting
a new kind of production. In particular, the structure of the pomeron as obtained from HERA is not precisely known
at high momentum fraction, and specifically, the gluon in the pomeron is not well constrained. It is not clear if such
uncertainty could not lead to mis-identifying observed processes as exclusive. This would for instance preclude the
spin analysis of the produced object.
In this paper, we aim to investigate the observation of exclusive production at the Tevatron. Indeed, we use the dijet
mass fraction distribution measured by the CDF collaboration and show that even taking into account uncertainties
associated with the pomeron structure, one is unable to give a satisfactory description of the data without the
existence of exclusive events. We also include other approach to explain diffraction in our study, the so called Soft
color interaction model (the properties of all the models are discussed later). As an outlook, we apply current models
for the DPE production for LHC energies and demonstrate the possible appereance of exclusive events through the
dijet mass fraction.
The paper is organized as follows: in the second section we give a brief description of the inclusive, exclusive, and
Soft color interaction models. The third section discusses how well the various models can explain the preliminary
∗Electronic address: kepkao@fzu.cz
†Electronic address: royon@hep.saclay.cea.fr
http://arxiv.org/abs/0704.1956v1
mailto:kepkao@fzu.cz
mailto:royon@hep.saclay.cea.fr
Tevatron dijet mass fraction data and the constraints implied by data on the current models. In the fourth part,
we foreshadow an application of the dijet mass fraction distribution as a tool to observe exclusive events at LHC
energies. Finally, we discuss issues concerning the dijet mass fraction reconstruction and fast detector simulation in
the Appendix.
II. THEORETICAL MODELS
Inclusive and exclusive DPE models used in this paper are implemented in the Monte Carlo program DPEMC [9].
The Soft color interaction model is embeded in the PYTHIA program [18]. The survey of the different models follows.
A. Inclusive Models
The first inclusive model to be mentioned is the so called “Factorized model”. It is an Ingelman-Schlein type of
model [10] describing the diffractive double pomeron process as a scattering of two pomerons emitted from the proton,
assuming a factorization of the cross section into a regge flux convoluted with the pomeron structure functions. For ep
single diffraction, it is necessary to introduce secondary reggeon trajectory to describe the observed single diffractive
non-factorable cross section. In the case of the Tevatron, the pomeron trajectory alone is sufficient to describe present
data and the cross section is factorable as it was advocated in [11]. Factorization breaking between HERA and
Tevatron comes only through the survival probability factor, denoting the probability that there is no additional
soft interaction which would destroy the diffractively scattered protons. In other word, the probability to destroy
the rapidity gap does not depend on the hard interaction. At Tevatron energies, the factor was measured to be
approximately 0.1, and calculation suggested the value of 0.03 for the LHC. Pomeron structure functions, reggeon
and pomeron fluxes are determined from the DIS ep collisions fitting the diffractive structure function FD
at HERA.
For one of the most recent published diffractive structure function analysis see e.g [12].
On the other hand, the Bialas-Landshoff (BL) inclusive model [8], is a purely non-perturbative calculation utilising
only the shape of the pomeron structure function and leaving the overall normalization to be determined from the
experiment; one can for example confront the prediction of DPE cross section with the observed rate at the Tevatron
[11] and obtain the missing normalization factor 1.
Both models use the pomeron structure measured at HERA which is gluon dominated. In this paper, we use the
results of the QCD fits to the most recent Pomeron structure function data measured by the H1 collaboration [12].
The new gluon density in the Pomeron is found to be slightly smaller than the previous ones, and it is interesting
to see the effect of the new PDFs with respect to the Tevatron measurements. However, the gluon density at high
β, where β denotes the fraction of the particular parton in the pomeron, is not well constrained from the QCD fits
performed at HERA. To study this uncertainty, we multiply the gluon distribution by the factor (1 − β)ν as shown
in Fig. 1. QCD fits to the H1 data lead to the uncertainty on the ν parameter ν = 0.0± 0.5 [12]. We will see in the
following how this parameter influences the results on dijet mass fraction as measured at the Tevatron.
B. Exclusive Models
Bialas-Landsoff exclusive model [13] is based on an exchange of two “non-perturbative” gluons between a pair of
colliding hadrons which connect to the hard subprocess. Reggeization is employed in order to recover the pomeron
parameters which successfully described soft diffractive phenomena, e.g. total cross section at low energies. A
calculation of qq̄ and gg production and more details can be found in [13] and [14], respectively.
On the contrary, the Khoze, Martin, Ryskin (KMR) [15] model is purely a perturbative approach. The interaction
is obtained by an exchange of two gluons directly coupled to the colliding hadrons (no pomeron picture is introduced).
While one gluon takes part in the creation of the central object, the other serves to screen the color flow across the
rapidity gap. If the outgoing protons remain intact and scatter at small angles, the exchanged di-gluon system, in
1 One more remark is in order. In the BL inclusive model, the partonic content of the pomeron is expressed in terms of the distribution
functions as fi/P(βi) ≡ βiGi/P(βi), where the Gi/P(βi) are the true parton densities as measured by the HERA collaboration, and
βi denotes the momentum fraction of the parton i in the pomeron. The integral of fi/P(βi) is normalized to 1, so that in the limit
fi/P(βi) → δ(βi) the exclusive cross section is recovered [9].
FIG. 1: Uncertainty of the gluon density at high β (here β ≡ z). The gluon density is multiplied by the factor (1− β)ν where
ν=-1., -0.5, 0.5, 1. The default value ν = 0 is the gluon density in the pomeron determined directly by a fit to the H1 FD2 data
with an uncertainty of about 0.5.
both models, must obey the selection rules JZ = 0, C-even, P-even. Such constrains are also applied to the hard
subprocesses for the production of the central object.
The two models show a completely different pT dependence of the DPE cross section. The energy dependence of
the BL model is found to be weaker since the Pomeron is assumed to be soft whereas it is not the case for the KMR
model.
C. Soft Color Interaction Model
The Soft color interaction model (SCI) [17, 18] assumes that diffraction is not due to a colorless exchange at the hard
vertex but rather to a string rearrangement in the final state during hadronisation. This model gives a probability (to
be determined by the experiment) that there is no string connection, and so no color exchange, between the partons
in the proton and the scattered quark produced during the hard interaction. Since the model does not imply the
existence of a pomeron, there is no need of a concept like survival probability and a correct normalisation is found
between single diffraction Tevatron and HERA data without any new parameter, which is one of the big successes of
this model.
III. DIJET MASS FRACTION AT THE TEVATRON
Dijet mass fraction (DMF) turns out to be a very appropriate observable for identifying the exclusive production.
It is defined as a ratio RJJ = MJJ/MX of the dijet system invariant mass MJJ to the total mass of the final state
system MX (excluding the intact beam (anti)protons). If the jet algorithm has such properties that the outside-cone
effects are small, the presence of an exclusive production would manifest itself as an excess of the events towards
RJJ ∼ 1; for exclusive events, the dijet mass is essentially equal to the mass of the central system because no pomeron
remnant is present. The advantage of DMF is that one can focus on the shape of the distribution; the observation
of exclusive events does not rely on the overall normalization which might be strongly dependent on the detector
simulation and acceptance of the roman pot detector.
In the following analysis, we closely follow the measurement performed by the CDF Collaboration. One can find
more information about the measurement and the detector setup in a note discussing preliminary results [16]. In
this paragraph, we will mention only the different cuts which are relevant for our analysis. To simulate the CDF
detector, we use a fast simulation interface [19], which performs a smearing of the deposited cell energy above a
0.5GeV threshold and reconstructs jets using a cone algorithm. Properties of the event such as the rapidity gap size
were evaluated at the generator particle level.
CDF uses a roman pot detector to tag the antiprotons on one side (corresponding to ηp̄ < 0). For the DMF
reconstruction, we require the antiprotons to have the longitudinal momentum loss in the range 0.01 < ξp̄ < 0.12 and
we apply the roman pot acceptance obtained from the CDF Collaboration (the real acceptance is greater than 0.5 for
0.035 < ξp̄ < 0.095). On the proton side, where no such device is present, a rapidity gap of the size 3.6 < ηgap < 5.9 is
required. In the analysis, further cuts are applied: two leading jets with a transverse momentum above the threshold
pjet1,jet2 > 10GeV or p
jet1,jet2
T > 25GeV in the central region |ηjet1,jet2 | < 2.5, a third jet veto cut (p
T < 5GeV) as
well as an additional gap on the antiproton side of the size −5.9 < ηgap < −3.6. For the sake of brevity, the threshold
for the transverse momentum of the two leading jets will be in the following denoted as pminT , if needed.
The dijet mass is computed using the jet momenta for all events passing the above mentioned cuts. In order to
follow as much as possible the method used by the CDF collaboration, the mass of the diffractive system MX is
calculated from the longitudinal antiproton momentum loss ξp̄ within the roman pot acceptance, and the longitudinal
momentum loss of the proton ξpartp is determined from the particles in the central detector (−4 <∼ ηpart <∼ 4), such
that:
sξp̄ξ
p , (1)
ξpartp =
particles
pT exp
η, (2)
summing over the particles with energies higher than 0.5GeV in the final state at generator level. To reconstruct the
diffractive mass, ξpartp was multiplied by a factor 1.1, obtained by fitting the correlation plot between the momentum
loss of the proton at generator level ξp and ξ
p at particle level with a straight line.
The DMF reconstruction is deeply dependent on the accuracy of the detector simulation. Since we are unable to
employ the complete simulation in our analysis, we discuss possible effects due to the various definitions of DMF on
the generator and the particle level in the Appendix.
A. Inclusive model prediction
We present first the dijet mass fraction calculated with FM and BL inclusive models. As stated in a previous
section, we want to explore the impact of the high β gluon uncertainty in the pomeron. To do this, we multiply the
gluon density by a factor (1− β)ν , for diverse values of ν = −1,−0.5, 0, 0.5, 1. The impact of the parameter is shown
in Fig. 2 and Fig. 3 for jets with pT > 10GeV and pT > 25GeV, respectively. The computed distributions were
normalized in shape, since there was no luminosity determination, implying no cross section estimation, in the CDF
measurement. The interesting possible exclusive region at high RJJ is enhanced for ν = −1, however, not in such
extent that would lead to a fair description of the observed distributions. As a consequence, the tail of the measured
dijet mass fraction at high RJJ cannot be explained by enhancing the gluon distribution at high β, and an another
contribution such as exclusive events is required.
A particular property seems to disfavour the BL inclusive model at the Tevatron. Indeed, the dijet mass fraction
is dumped at low values of RJJ , especially for jets pT > 10GeV. Since the cross section is obtained as a convolution
of the hard matrix element and the distribution functions, the dumping effect is a direct consequence of the use of a
multiplicative factor β in the parton density functions in the pomeron (see footnote 1). We will come back on this
point when we discuss the possibility of a revised version of the BL inclusive model in the following.
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
=0.5ν
=-0.5ν
FM INC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
=0.5ν
=-0.5ν
BL INC
FIG. 2: Dijet mass fraction for jets pT > 10GeV. FM (left) and BL (right) models, inclusive contribution. The uncertainty
of the gluon density at high β is obtained by multiplying the gluon distribution by (1− β)ν for different values of ν (non-solid
lines).
As we have seen, inclusive models are not sufficient to describe well the measured CDF distributions. Thus, it
opens an area to introduce different types of proceses/models which give a significant contribution at high RJJ .
B. Exclusive models predictions
In this section, we will study the enhancement of the dijet mass distribution using exclusive DPE processes, with
the aim to describe the CDF dijet mass fraction data. We examine three possibilities of the interplay of inclusive plus
exclusive contributions, specifically:
1. FM + KMR
2. FM + BL exclusive
3. BL inclusive + BL exclusive
The full contribution is obtained by fitting the inclusive and exclusive distribution to the CDF data, leaving the
overall normalization N and the relative normalization between the two contributions rEXC/INC free. More precisely,
the DMF distribution is obtained with the fit as N(σINC(RJJ )+ r
EXC/INCσEXC(RJJ )). The fit was done for jets with
pminT = 10GeV and p
T = 25GeV, separately.
The overall normalization factor cannot be studied since the CDF collaboration did not determine the luminosity
for the measurement. On the other hand, the relative normalization between the inclusive and exclusive production
is a useful information. The relative normalization allows to make predictions for higher pT jets or for LHC energies
for instance. For this sake, the relative normalizations rEXC/INC should not vary much between the two pminT mea-
surements. Results are summarized in Table I. We give the inclusive and σINC and the exclusive cross sections σEXC,
obtained directly from the models, and the relative scale factor needed to describe the CDF data to be applied to the
exclusive contribution only. Whereas the relative normalization changes as a function pminT by an order of magnitude
for the exclusive BL model, it tends to be rather stable for the KMR model (the uncertainty on the factor 2.5 might
be relatively large since we do not have a full simulation interface and the simulation effects tend to be higher at low
jet transverse momentum). Finally, in Fig. 4 and 5, the fitted distributions are depicted for pminT = 10, 25GeV jets,
respectively.
The Tevatron data are well described by the combination of FM and KMR model. We attribute the departure
from the smooth distribution of the data to the imperfection of our fast simulation interface. On the contrary, the
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
=0.5ν
=-0.5ν
FM INC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
=0.5ν
=-0.5ν
BL INC
FIG. 3: Dijet mass fraction for jets pT > 25GeV. FM (left) and BL (right) models, inclusive contribution. The uncertainty
of the gluon density at high β is obtained by multiplying the gluon distribution by (1− β)ν for different values of ν (non-solid
lines).
contributions rEXC/INC(10) σINC(10)[pb] σEXC(10)[pb] rEXC/INC(25) σINC(25)[pb] σEXC(25)[pb]
FM + KMR 2.50 1249 238 1.0 7.39 3.95
FM + BL exc 0.35 1249 1950 0.038 7.39 108
BL inc + BL exc 0.46 2000 1950 0.017 40.6 108
TABLE I: Cross sections for inclusive diffractive production σINC, exclusive cross section σEXC to be rescaled with a relative
additional normalization between inclusive and exclusive events rEXC/INC for pT > 10GeV and pT > 25GeV jets and for
different models (see text). Note that the fit to the data is parametriezed as N(σINC(RJJ ) + r
EXC/INC
EXC(RJJ )).
BL inclusive model is disfavoured because it fails to describe the low RJJ region. It is due to the βi factor in the
parton density fi/P(βi) used by the BL inclusive model (see footnote 1 where the variables are defined) that the RJJ
distribution is shifted towards higher values. This factor was introduced to maintain the correspondence between the
inclusive and exclusive model in the limit fi/P(xi) → δ(xi). On the contrary, this assumption leads to properties in
contradiction with CDF data. Using the BL inclusive model without this additional normalization factor leads to a
DMF which is in fair agreement with data. Indeed, we show in Fig. 6 the predictions of the “modified” model (i.e.
defined as fi/P(βi) ≡ Gi/P(βi)) for pT > 10GeV and pT > 25GeV jets. We see that the low RJJ region is described
well and that fitting the prediction of the exclusive KMR model with the BL inclusive model yields roughly the same
amount of exclusive events as using the factorable models. The BL inclusive model will be revised to take these effects
into account. We will not mention further this ”modified” version of the BL inclusive model since it gives similar
results as the factorable models.
The exclusive BL model leads to a quite reasonable description of the DMF shape for both pminT cuts in combination
with FM, however, it fails to grasp the shape of the exclusive cross section measured as a function of the jet minimal
transverse momentum pminT . To illustrate this, we present the CDF data for exclusive cross section corrected for
detector effects compared with the predictions of both exclusive models after applying the same cuts as in the CDF
measurement, namely: p
jet1,2
T > p
T , |ηjet1,2| < 2.5, 3.6 < ηgap < 5.9, 0.03 < ξp̄ < 0.08. The BL exclusive model
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
preliminary
DPE data (stat.)
exclusive contribution
FM INC + KMR EXC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
exclusive contribution
BL INC + BL EXC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
exclusive contribution
FM INC + BL EXC
FIG. 4: Dijet mass fraction for jets pT > 10GeV. FM + KMR (left), BL + BL (right), FM + BL (bottom) models. We notice
that the exclusive contribution allows to describe the tails at high RJJ .
shows a much weaker pT dependence than the KMR model and is in disagreement with data.
2 Let us note that the cross section of exclusive events measured by the CDF collaboration is an indirect measurement since it was
obtained by subtracting the inclusive contribution using an older version of the gluon density in the pomeron measured at HERA. In
that sense, the contribution of exclusive events using the newest gluon density from HERA might change those results. However, as
we noticed, modifying the gluon density even greatly at high β by multiplying the gluon distribution by (1 − β)ν does not change the
amount of exclusive events by a large factor, and thus does not modify the indirect measurement performed by the CDF collaboration
much.
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
exclusive contribution
FM INC + KMR EXC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
exclusive contribution
BL INC + BL EXC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
exclusive contribution
FM INC + BL EXC
FIG. 5: Dijet mass fraction for jets pT > 25GeV. FM + KMR (left), BL + BL (right), FM + BL (bottom) models. We note
that the exclusive contribution allows to describe the tails at high RJJ .
To finish the discussion about the pomeron like models, it is worth mentioning that these results assume that the
survival probability has no strong dependence on β and ξ. If this is not the case, we cannot assume that the shape
of the gluon distribution as measured at HERA could be used to make predictions at the Tevatron. However, this
is a reasonable assumption since the survival probability is related to soft phenomena occuring during hadronisation
effects which occur at a much longer time scale than the hard interaction. In other words, it is natural to suppose
that the soft phenomenon will not be influenced by the hard interaction.
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
exclusive contribution
BL INC modified + KMR EXC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
exclusive contribution
 + KMR EXC
BL INC modified
FIG. 6: Dijet mass distribution at the Tevatron calculated with the ”modified” parton densities (see text) for 10GeV (left)
and 25 GeV (right) jets, KMR exclusive model included.
(GeV)min
10 15 20 25 30 35
Bialas-Landshoff
CDF preliminary
FIG. 7: Exclusive cross section as a function of the minimal transverse jet momentum pminT measured by the CDF collaboration
and compared to the prediction of the KMR and BL exclusive models. We note that the BL model overshoots the CDF
measurement while the KMR model is in good agreement.
C. Prospects of future measurements at the Tevatron
In this section, we list some examples of observables which could be used to identify better the exclusive contribution
in DMF measurements at the Tevatron. We present the prediction as a function of the minimal transverse momentum
of the two leading jets pminT . Since the BL inclusive model does not describe the DMF at low RJJ , we choose to show
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
-1Luminosity 200pb
 >10GeV
 >50GeV
exclusive contribution
IS INC+ KMR EXC
FIG. 8: Dijet mass fraction for two values of minimal transverse jet momentum pminT . We note that the relative exclusive
contribution is higher at high pminT .
(GeV)
0 10 20 30 40 50 60 70 80
= 0.5ν
=-0.5ν
IS + BL
IS + KMR
-1Number of jet events for 200pb
(GeV)
0 10 20 30 40 50 60 70 80
= 0.5ν
=-0.5ν
IS + KMR
Mean value of dijet mass fraction
FIG. 9: Number of jet events and mean of the dijet mass fraction as a function of the minimal jet pminT . We note that the ideal
value of pminT to enhance the exclusive contribution is of the order of 30-40 GeV which leads to a high enough production cross
section as well as a large effect of the exclusive contribution on the dijet mass fraction.
only the FM prediction in combination with both, KMR and BL exclusive models.
The same roman pot acceptance and restriction cuts as in the CDF measurement were used, specifically, 0.01 <
ξp̄ < 0.12, p
jet1,2
T > p
T , |ηjet1,2| < 2.5, 3.6 < |ηgap| < 5.9. Moreover, we adopted a normalization between inclusive
and exclusive events as obtained for the pT > 25GeV analysis in the previous section because we are less sensitive
to the imperfections of the fast simulation interface for higher pT jets. Fig. 8 illustrates the appearance of DMF for
two separate values of minimum jet pminT . The character of the distribution is clearly governed by exclusive events at
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
preliminary
DPE data (stat.only)
Soft color interaction
-10 -5 0 5 10
FIG. 10: Dijet mass fraction at the Tevatron for jets pT > 10GeV (left) and the η distribution of produced particles (right)
for the Soft color interaction model.
high pminT .
Fig. 9 shows the rate of DPE events. In addition to the curves denoting inclusive contribution with the varied
gluon density for ν = −0.5, 0, 0.5, the full contribution for both exclusive models is shown. For the FM model which
is in better consistency with accessible data, the measurement of the DPE rate does not provide an evident separation
of exclusive contribution from the effects due to the pomeron uncertainty since the noticable difference appears when
the cross sections are too low to be observable. It is possible, however, to examine the mean of the DMF distribution.
As seen in Fig. 9, this observable disentangles well the exclusive production with the highest effect between 30 and
40GeV.
It needs to be stressed that even though we obtain a hint in understanding the exclusive production phenomena
at the Tevatron, the final picture cannot be drawn before precisely measuring the structure of the pomeron. For
this purpose the DMF or the DPE rate are not suitable at the Tevatron. In the former, there is no sensitivity to
the high β gluon variation, whereas in the latter, the gluon variation and the exclusive contribution cannot be easily
separated. The way out is to perform QCD fits of the pomeron structure in gluon and quark for data at low RJJ where
the exclusive contribution is negligible. Another possibility is to perform silmutaneously the global fits of pomeron
structure functions using DGLAP evolution and of the exclusive production.
A final important remark is that this study was assuming pomeron like models for inclusive diffraction. It is worth
studying other models like Soft color interaction processes and find out if they also lead to the same conclusion
concerning the existence of exclusive events.
D. Soft color interaction model
The Soft color interaction model uses different approach to explain diffractive events. In this model, diffraction is
due to special color rearrangement in the final state as we mentionned earlier. It is worth noticing that in this model,
the CDF data are dominated by events with tagged antiproton on the p̄ (ηp̄ < 0) side and a rapidity gap on the p
side. In other words, in most of the events, there is only one single antiproton in the final state accompanied by a
bunch of particles (mainly pions) flowing into the beam pipe. This is illustrated in Fig. 10 right which shows the
rapidity distribution of produced particles and we notice the tail of the distribution at high rapidity. We should not
omit to mention that on the other hand, the probability to get two protons intact (which is important for the double
tagged events) is in SCI model extremly small.
After applying all CDF cuts mentioned above, the comparison between SCI and CDF data on RJJ is shown in
Figs. 10 (left) and 12. Whereas it is not possible to describe the full dijet mass fraction for a jet with pT > 10GeV,
Jet1η
-4 -2 0 2 4
Jet2η
-4 -2 0 2 4
FIG. 11: Rapidity distribution of a leading jet (left) and a second leading jet (right) in the SCI model when calculating dijet
mass fraction.
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
preliminary
DPE data (stat.only)
Soft color interaction
exclusive contribution
SCI + KMR EXC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
preliminary
DPE data (stat.only)
Soft color interaction
FIG. 12: Dijet mass fraction at the Tevatron for jets pT > 10GeV for the SCI model and KMR exclusive model (left), and for
jets pT > 25GeV for the SCI model only (right).
it is noticeable that the exclusive contribution is found to be lower than in the case of the pomeron inspired models.
Indeed, performing the same independent fit of SCI and KMR exlusive contribution one finds that only 70% of the
exclusive contribution needed in case of pomeron inspired models is necessary to describe the data. For jets with
pT > 25GeV, no additional exclusive contribution is needed to describe the measurement which can be seen in Fig. 12.
Since most events are asymmetric in the sense that only the antiproton is strictly intact and on the other side, there
is a flow of particles in the beam pipe, it is worth studying the rapidity distribution of jets for this model. The results
are shown in Fig. 11. We note that the rapidity distribution is boosted towards high values of rapidity and not
centered around zero like for pomeron inspired models and CDF data. Moreover, the cross section for pT > 10GeV
jets is in the SCI model σSCI = 167 pb, about only 13% of the cross section predicted by the pomeron inspired models
which however give a correct prediction of a large range of observables including DPE cross sections. Therefore, such
properties disfavour the SCI model. However, it would be worth studying and modifying the SCI model since the
probability to observe two protons in the final state (and/or two gaps) should be higher than the square probability
of observing one proton (and/or one gap) only (single diffraction) as it was seen by the CDF collaboration [21]. The
model needs to be adjusted to take this into account and than it would be interesting to see the impact on the dijet
mass fraction and the existence of exclusive events.
IV. DIJET MASS FRACTION AT THE LHC
It was suggested that exclusive production at the LHC could be used to study the properties of a specific class of
centrally produced objects like Higgs bosons. However, it relies on many subtleties such as a good understanding
of the inclusive production. The perturbative nature of the diffractive processes results in the factorization of the
cross section to a regge flux and pomeron structure functions, while factorization breaking appears via the survival
probability only. The gluon density in the pomeron is of most important matter, since its value at high momentum
fraction will control the background to exclusive DPE, and the pomeron flux and the survival probability factor will
have to be measured at the LHC to make reliable predictions.
The flux depends on the pomeron intercept αP whose impact on the DMF distribution for LHC energies is shown
in Fig. 13. The pomeron intercept is parametrized as αP = 1 + ǫ and the prediction is made for four values of
ǫ = 0.5, 0.2, 0.12, 0.08. The updated HERA pomeron structure function analysis [12] suggests that the “hard pomeron”
intercept value is close to αP = 1.12. Nevertheless, new QCD fits using single diffractive or double pomeron exchange
data will have to be performed to fully constrain the parton densities and the pomeron flux at the LHC.
FIG. 13: Sensitivity of the dijet mass fraction to different values of the pomeron intercept αP = 1 + ǫ.
We also give the dependence of the DMF on jet pT at the LHC. DPE events in this analysis were selected ap-
plying the roman pot acceptance on both sides from the interaction point, and using a fast simulation of the
CMS detector [20] (the results would be similar using the ATLAS simulation) and asking two leading jets with
pT >= 100, 200, 300, 400GeV. We have disfavored the predictions of the BL exclusive model at the Tevatron. The
BL exclusive shows weak pT dependence which makes the model unphysical for LHC energies since it predicts cross
sections even higher than the inclusive ones. We therefore focus on the predictions of FM and KMR models, only. As
in the previous sections, we also include a study of the uncertainty on the gluon density enhancing the high β gluon
with a factor (1− β)ν .
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FIG. 14: Dijet mass fraction at the LHC as a function of jet minimal transverse momentum pminT , FM inclusive model.
FIG. 15: Dijet mass fraction at the LHC for jets pT > 200GeV and pT > 400GeV, respectively, FM inclusive + KMR exclusive
models.
100 150 200 250 300 350 400
FIG. 16: Number of DPE events at the LHC as a function of minimal transverse momentum pminT of two leading jets. FM
inclusive + KMR exclusive models. The gluon variation is displayed for different ν values.
100 150 200 250 300 350 400
FIG. 17: Average value of the dijet mass fraction as a function of minimal transverse momentum pminT of the leading jets.
Exclusive contribution and different values of ν are shown. FM + KMR models.
The dijet mass fraction as a function of different pT is visible in Fig. 14. The exclusive contribution manifests
itself as an increase in the tail of the distribution which can be seen for 200GeV jets (left) and 400GeV jets (right),
respectively in Fig. 15. Exclusive production slowly turns on with the increase of the jet pT which is demonstrated
in Fig. 16 where the number of expected DPE events is shown. However, with respect to the uncertainty on the
gluon density this appearance is almost negligiable. One can use the average position of the DMF as a function of
the minimal jet transverse momentum pminT to study the presence of the exclusive contribution, see Fig. 17. This is
true especially for high pT jets.
The exclusive production at the LHC plays a minor role for low pT jets. Therefore, measurements e.g for pT <
200GeV where the inclusive production is dominant could be used to constrain the gluon density in the pomeron.
Afterwards, one can look in the high pT jet region to extract the exclusive contribution from the tail of the DMF.
V. CONCLUSION
The aim of this paper was to investigate whether we can explain the excess of events at the high dijet mass fraction
measured at the Tevatron without the exclusive production. The result is actually two fold.
Concerning the pomeron induced models (”Factorized model” and Bialas-Landshoff inclusive models) we found
that the uncertainty on the high β gluon density in the Pomeron has a small impact at high RJJ . Therefore, an
additional contribution is needed to describe the CDF data with these models. We examined the exclusive KMR model
and Bialas-Landshoff exclusive model predictions for the role of the additional contribution and found that the best
descriprion of data is achieved by the combination of the Factorized inclusive model (or the modified inclusive Bialas-
Landshoff one) and the KMR exclusive model. The exclusive contribution at the Tevatron can be magnified requesting
higher pT jets and studying specific observables like a mean of the dijet mass fraction, for example. Though, one of
the limitations of using high pT jets is due to the rate of DPE events which falls logarithmicaly allowing measurements
for jets up to approximately 40GeV. The Bialas-Landshoff exclusive model seems to be disfavoured by Tevatron data
since it shows a softer jet pT dependance and predicts unphysically large DPE rates at LHC energies.
In the case of the Soft color interaction model which is not based on pomeron exchanges, the need to introduce an
additional exclusive production is less obvious. For low pT jets the amount of exclusive events to describe the data is
smaller than in case of Factorized model, but for high pT jets no additional contribution is necessary. This draws a
new question: whether the double pomeron exchange events could be explained by a special rearrangement of color
only? The CDF data are in this model dominated by single diffractive events. The probability of tagging two protons
in the final state within this model is very small, contradicting the CDF observation. So even though the SCI model
is not applicable for DPE events in the current state it would be worth adjusting this model to correctly predict the
rate of double tagged events and study the model prediction of dijet mass fraction and other DPE induced processes.
Dijet mass fraction at the LHC could be used to select the exclusive events. Indeed, it is possible to study jets with
pT > 200GeV for instance, and to focus on events with DMF above 0.8 which is dominated by exclusive production
(see Fig. 15). However, as it was advocated earlier, a complete QCD analysis consisting of measuring the gluon density
in the Pomeron (especially at high β) and study the QCD evolution of exclusive events as a function of jet pT is needed
to fully understand the observables, and make predictions for diffractive Higgs production and its background at the
LHC as an example.
Acknowledgments
The authors want to thank M. Boonekamp, R. Enberg, D. Goulianos, G. Ingelman, R. Pechanski and K. Tereashi
for useful discussions and for providing them the CDF data and roman pot acceptance.
VI. APPENDIX
Throughout the paper, we have purpously omitted a discussion of imperfections concerning the dijet mass fraction
reconstruction within our framework, postponing it to this section. In this appendix, all calculations are done for jets
with pT > 10GeV.
• In our analysis, we define the dijet mass fraction as a ratio of the two leading jet invariant mass MJJ to the
central diffractive mass MX . The latter was determined using the momentum loss ξp̄ measured in a roman pot
on the antiproton side and the ξpartp obtained from particles on the generator level, such as MX = (sξp̄ξ
In this case, we must ensure that all of the produced diffractive energy MX is deposited into the central detector.
If this is not the case, our MX at generator level might be sensibly larger than the one measured by the CDF
collaboration. The energy flow of the particles on the generator level as a function of rapidity is shown in Fig.
18, upper plot. The middle plot shows the energy flow weighted by the transverse momentum of the particle
ET . We see that most of the energy is deposited in the calorimeter region, i.e. for |η| < 4. In p̄ tagged events,
protons most frequently loose a smaller momentum fraction (roughly ξp ∼ 0.025) than the tagged antiproton
for which the acceptance turns on for ξp̄ > 0.035. This can be seen from the ξp population plot in the bottom of
Fig. 18. Thus, a collision of more energetic pomeron from the antiproton side with a pomeron from the proton
side is boosted towards the p̄ as it is seen on the energy flow distributions.
• A comparison between the proton momentum loss obtained from particles ξpartp calculated using formula (2)
and the proton momentum loss at generator level ξp leads to the factor 1.1 mentionned in a previous section.
The dependance is displayed in Fig. 19.
• The size of the rapidity gap runs as a function of the momentum loss ξ like ∆η ∼ log 1/ξ. The size of the gap
which increases with decreasing ξ for inclusive models can be seen in Fig. 20. Regions of high rapidity show
the p̄ hits whereas the low rapidity region is due to the produced particles detected in the central detector; they
are well separated by a rapidity gap. For exclusive events, the size of a rapidity gap is larger and does not show
such a strong ξ dependance as for inclusive models.
• The simulation interface plays a significant role in the determination of the exclusive contribution. As previously
stated, we cannot profit from having access to the full simulation interface and having under control all the
effects of the detector. In order to eliminate some effects of the simulation we plot the dijet mass distribution
RJJ using the information from the generator and check whether the need of exclusive events to describe the
data is still valid. Specifically, we require the same cuts as in Section III but the diffractive mass MRP is
evaluted using the true (anti)protons momentum loss (ξp̄)ξp at generator level
MRPX =
sξp̄ξp. (3)
The dijet mass fraction calculated with MRP is shown in Fig. 21. We see that the distribution is shifted to
lower values of RJJ , requesting slightly more exclusive events to describe the CDF data. The description of the
data is also quite good.
• The role of the simulation interface to reconstruct jets can be illustrated by comparing the above distributins
to DMF calculated at generator level defined as
RJJ =
sξp̄ξpβ1β2
sξp̄ξp
β1β2, (4)
where β1, β2 denote the fraction of the pomeron carried by the interacting parton. As can be seen, in Fig. 21
(right), the DMF distribution at pure generator level shows a completely different shape not compatible with
CDF data and shows the importance of jet reconstruction.
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http://arxiv.org/abs/hep-ph/0702213
http://arxiv.org/abs/hep-ph/0609291
http://www.isv.uu.se/thep/MC/scigal/
-8 -6 -4 -2 0 2 4 6 8
-8 -6 -4 -2 0 2 4 6 8
-8 -6 -4 -2 0 2 4 6 8
-8 -6 -4 -2 0 2 4 6 8
0 0.02 0.04 0.06 0.08 0.1
0 0.02 0.04 0.06 0.08 0.1
FIG. 18: Upper and medium plots: Rapidity and ET weighted rapidity distributions of all particles produced (except the
protons); Lower plot: momentum loss of the proton in double pomeron exchange events ξp for FM (left) and BL (right)
inclusive models.
0 0.02 0.04 0.06 0.08 0.1
0 0.02 0.04 0.06 0.08 0.1
FIG. 19: Comparision of the proton momentum loss ξpartp calculated with formula (2) and the proton momentum loss ξp at
generator level.
0 0.02 0.04 0.06 0.08 0.1
0 0.02 0.04 0.06 0.08 0.1
0 0.02 0.04 0.06 0.08 0.1
0 0.02 0.04 0.06 0.08 0.1
FIG. 20: Rapidity of particles on the p̄ side vs. p̄ momentum loss: inclusive models (top) for FM (left) and BL (right); exlusive
models (bottom) for KMR (left) and BL (right). Hits of scattered p̄ are included.
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
exclusive contribution
FM INC + KMR EXC
x/Mjj=MjjR
0 0.2 0.4 0.6 0.8 1
DPE data (stat.)
preliminary
FM INC
FIG. 21: Dijet mass fraction for jets pT > 10GeV: FM + KMR (left), and at generator level calculated according to (4).
	Introduction
	Theoretical Models
	Inclusive Models
	Exclusive Models
	Soft Color Interaction Model
	Dijet mass fraction at the Tevatron
	Inclusive model prediction
	Exclusive models predictions
	Prospects of future measurements at the Tevatron
	Soft color interaction model
	Dijet mass fraction at the LHC
	Conclusion
	Acknowledgments
	Appendix
	References
