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Available on CMS information server CMS NOTE 2000/065
The Compact Muon Solenoid Experiment
Mailing address: CMS CERN, CH­1211 GENEVA 23, Switzerland
CMS Note
``SingleTop'' ­ an event generator for the
single top quark production at the LHC.
Part 1.
E.E. Boos a) , L.V. Dudko b) , and V.I. Savrin c)
Institute of Nuclear Physics, Moscow State University
Abstract
We present the first version of the event generator SingleTop, which is based on the complete
tree­level diagram calculations by means of the CompHEP program. A special attention
is paid to a proper matching of the 2 ! 3 W ­gluon fusion contribution to the relevant
2 ! 2 process, which includes the b­quark in the initial state. The latter process is simulated
by means of the PYTHIA program. The matching of two contributions allows to simulate
correctly events in the entire kinematical region avoiding the double counting and the events
with negative weights.
a) boos@theory.npi.msu.su
b) dudko@npi.msu.su
c) savrin@theory.npi.msu.su

1 Introduction.
After the top quark discovery at the Tevatron collider and the measurement of its mass the main problem
of top quark physics is the detailed study of the top quark properties like couplings, widths etc. The
exploration of couplings acquires a special interest because the top quark is very heavy, and therefore one
can more likely expect some deviations from the Standard Model structure in the top quark sector.
The top quark has been discovered in the strong QCD pair production mode. The single top production
at hadron colliders is the additional electroweak source of top quarks. It has been stressed in a number
of studies that the reactions with a single top quark could be very sensitive to probe top quark couplings,
in particular, the structure of the important W tb coupling, which is responsible for the most of the top
decay rate and which is proportional to the CKM matrix element V tb in the SM . The reason for the high
sensitivity is that in contrast to the top pair production the single top rate is directly proportional to the
W tb vertex.
The total cross section of the single top production at the LHC is about 300 pb, what is comparable to
the cross section of the top quark pair production (about 800 pb). Due to such a large rate the single top
production will be the important source of background to many other expected processes, especially to
the SM and MSSM Higgs bosons production, and therefore it is needed to know the detailed kinematical
properties of the single top quark. For the physics analysis we need an accurate simulation of the processes
of single top quark production and relevant backgrounds.
Single top production at hadron colliders has been studied by a number of authors (cf. [1] and references
therein). So far, the most complete set of SM processes contributing to the single top rate was studied
in [3, 4] and the most accurate NLO calculations of main processes were presented in [2]. In papers [4, 6]
the complete Monte Carlo (MC) analysis of the single top signal versus the backgrounds was presented.
The Feynman diagrams for all processes contributing to the single top production rate were shown
previously (cf. e. g. [4]) and included the s­channel exchange of virtual W , W ­gluon fusion and W + top
production. The first process is the simplest 2 ! 2 reaction, while the W ­gluon process includes the
2 ! 3 parton diagrams. In order to resume the large QCD corrections to the diagram of the g ! b ¯ b
splitting in the latter, they are combined with the 2 ! 2 process involving the b­quark in the initial
state [1, 2, 3], and the corresponding first term of the g ! b ¯ b splitting function is subtracted to avoid the
double counting. The s­channel W exchange and W ­gluon fusion processes have been included in the
first version of the SingleTop generator.
The W + top production process gives the large contribution (62 pb at the QCD scale Q 2 = M 2
t [5]) to
the total single top production at the LHC. But this process has sufficiently different signature which is
similar to the top quark pair production signature. The process will be included in the SingleTop later
on.
Several MC generators (ONETOP and the generators based on MADGRAPH, PYTHIA and CompHEP,
see [4, 6, 8]) were developed in the past in order to simulate single top events. However, one should stress
that none of the generators has solved all the problems mentioned below.
1) The direct implementation of the subtraction procedure in the W ­gluon fusion part of the generator
leads to the problem that some events have negative weights. This can be improved by subtraction of
the first g ! b ¯ b splitting term from the b­quark distribution function with the further use of the modified
function as it has been done in [4]. In this way one removes all events with negative weights. However,
it remains problematic to include the initial state radiation in the manner like it is realized in PYTHIA
with the use of the standard PDF distributions. As we shall show, however, the ISR is an important
source of the forward b­jets, which can be detected at the LHC and therefore should be simulated in a
reasonable way.
2) The same diagrams depending on the kinematical region contribute to the different mechanisms of the
single top production. For instance, the process pp ! tbg +X represents a part of the NLO corrections
to the ''s­channel W \Lambda '' if the additional gluon jet is rather soft and cannot be resolved as a separate jet.
However, if the gluon jet is rather hard and one requires a detection of the jet, the contribution should
be added to the ''W­gluon fusion'' part. It is necessary to take a special care in order to account all the
contributions properly and to solve the problem of correct matching of the LO and NLO calculations.
3) As it has been already stressed many times the top quark in the single top production processes is
produced highly polarised as a result of the (V­A) structure of the W tb vertex in the Standard Model.
2

This fact leads to the spin correlations between the top production and the top decay [7] what should be
implemented in the generator.
4) It has been shown in [9], where all the spin correlations have been explicitly taken into account, that
the cross section of the single top production at LHC is very sensitive to anomalous W tb structure, and
in order to measure it the corresponding anomalous operators should be included into the generator as
well. One also might add other anomalous contributions like FCNC etc.
5) At the LHC the single top and single antitop production have significantly different rates. The
corresponding asymmetries in the rates and distributions could be useful to reduce systematic uncertainties
in the measurements of the top parameters [9]. Therefore it makes sense to keep separately the single
top and antitop parts in the generator.
In this note we present the first version of the generator SingleTop 1.0 as a step forward in resolving
the above problems for generators. All matrix element calculations for the complete set of Feynman
diagrams are done by means of the computer package CompHEP 41.10 [10], and the events generated by
CompHEP at the parton level for final particles are included in a form of ''new process'' to the program
PYTHIA [11]. In this way the subsequent top and W ­boson decays as well as the jet fragmentation are
taken into account in a way as it is done in PYTHIA. Therefore, at the first step the spin correlations
are not taken into account. For the next SingleTop version the complete set of diagrams including decays
will be calculated, and the corresponding events will be generated by means of CompHEP. The correct
spin structure and, therefore, all the spin correlations will be taken into account. The resulting events
can be used in PYTHIA as a ''new process'', and only the fragmentation of final light and b­quarks into
jets will be simulated by means of PYTHIA itself. However, one should stress that it makes sense to use
and keep both versions of the SingleTop generator because a comparison of distributions obtained using
both of them would show explicitly the influence of spin correlations.
For the ''W ­gluon'' fusion process we present for various distributions the results of comparison between
the calculation of the complete set of matrix elements by means of CompHEP and the simple usage of
the gluon splitting approximation in PYTHIA. This comparison allows us to find a reasonable matching
of contributions from different kinematical regions.
2 The main subprocesses and cross sections.
We start from the ''W­gluon'' fusion part, which at the LHC energies gives the main contribution to the
single top rate of about 245 pb at the NLO level. An important part of the large rate is coming from the
soft kinematical regions for the b­quark jets.
We begin with rather hard kinematical range P b
T
?
¸ 10 GeV, P q
T
?
¸ 20 GeV (2 ! 3 process) and the
distance in the '; j parameter space \DeltaR(j; j0) =
p
\Delta' 2 + \Deltaj 2 ? 0:5, where one can compute the
complete set of tree­level diagrams.
Under that condition we carry out the calculation of four processes and the relevant subprocesses with
the rates as indicated below:
pp ! t ¯ b + jet +X 73:8pb (1)
Subprocesses :
ug ! dt ¯ b ug ! st ¯ b ¯
dg ! ¯ ct ¯ b u ¯
d ! gt ¯ b
gu ! dt ¯ b gu ! st ¯ b g ¯
d ! ¯ ct ¯ b u¯s ! gt ¯ b
cg ! dt ¯ b cg ! st ¯ b ¯
sg ! ¯ ct ¯ b ¯
dc ! gt ¯ b
gc ! dt ¯ b gc ! st ¯ b g¯s ! ¯ ct ¯ b ¯
sc ! gt ¯ b
¯
dg ! ¯
ut ¯ b ¯
du ! gt ¯ b
g ¯
d ! ¯
ut ¯ b ¯
su ! gt ¯ b
¯
sg ! ¯ ut ¯ b c ¯
d ! gt ¯ b
g¯s ! ¯ ut ¯ b c¯s ! gt ¯ b
59:7 pb 6:6 pb 5:4 pb 2:2 pb
3

pp ! ¯ tb + jet +X 46:2pb (2)
Subprocesses :
¯
ug ! ¯
d ¯ tb ¯ ug ! ¯
s ¯ tb dg ! c ¯
tb ¯
ud ! g ¯
tb
g¯u ! ¯
d ¯ tb g¯u ! ¯
s ¯ tb gd ! c ¯
tb ¯
us ! g ¯
tb
¯ cg ! ¯
d ¯ tb ¯
cg ! ¯
s ¯ tb sg ! c ¯ tb d¯c ! g ¯
tb
g¯c ! ¯
d ¯ tb g¯c ! ¯
s ¯ tb gs ! c ¯ tb s¯c ! g ¯
tb
dg ! u ¯ tb d¯u ! g ¯
tb
gd ! u ¯ tb s¯u ! g ¯
tb
sg ! u ¯ tb ¯
cd ! g ¯
tb
gs ! u ¯ tb ¯ cs ! g ¯
tb
34:4 pb 4:4 pb 6:2 pb 1:3 pb
and
pp ! t ¯ b +X 4:9pb (3)
Subprocesses :
¯
du ! t ¯ b u ¯
d ! t ¯ b ¯
dc ! t ¯ b c ¯
d ! t ¯ b
¯ su ! t ¯ b u¯s ! t ¯ b ¯
sc ! t ¯ b c¯s ! t ¯ b
pp ! ¯ tb +X 3:1pb (4)
Subprocesses :
d¯u ! ¯ tb ¯
ud ! ¯ tb ¯ cd ! ¯ tb s¯c ! ¯
tb
s¯u ! ¯ tb ¯
us ! ¯ tb d¯c ! ¯ tb ¯ cs ! ¯
tb
It will be clear later on why we have chosen such a set of initial cuts for the event samples. First, one
should point out that contrary to the Tevatron the rates for top and antitop quarks at the LHC are
different [9], and these rates are shown and included separately in the generator. In our calculations
m t = 175 GeV and the CTEQ5M [12] set of parton structure functions have been used. A value for the
QCD factorisation scale has been chosen in such a way that the results of LO calculations would be as
close as possible to the NLO results [2]. This procedure leads to the factorisation scale Q 2 ú (M t =2) 2
for the W ­gluon fusion process and to Q 2 ú (M t ) 2 for the s­channel W \Lambda exchange process [9]. The
CompHEP weighted events have been generated for the all above subprocesses on the parton level. Then
we have passed on the events to the standard CompHEP -- PYTHIA interface [13] for reweighting and
mixing the subprocesses. Several files have been prepared. The first one ''tb—events'' has 50000 reweighted
events for the process 3. The second one ''Tb—events'' has 50000 reweighted events for the process 4. The
third file ''tb+Tb—events—tot'' includes 81000 events for the both processes. The same structure is for
the qtb processes. There are 61000 events of the process 1 in the file ''qtb—events'', 67000 events of the
process 2 in the file ''qTb—events'' and 100000 properly mixed events for the both processes in the file
''qtb+qTb—events—tot''. With the help of the CompHEP -- PYTHIA interface these files become ready for
processing as external processes in PYTHIA for a further analysis. The symmetrization of initial states
is done automatically in the interface. The generated events represent the first version of the SingleTop
1.0 generator, and it is available at the CMS Event Data Base [14].
However we didn't consider the region of very soft b­quarks which might be needed for some physics
studies. In order to do that it makes sense to compare results of event generation by means of CompHEP
for all tree 2 ! 3 diagrams with PYHTIA for 2 ! 2 process where an additional b­quark is coming from
the initial and final state radiation.
3 Comparison of CompHEP and PYTHIA for the
pp ! tb + jet +X event generation.
The CompHEP calculations presented above are the exact tree­level calculations for the complete set
of diagrams for all reactions where the top quark is produced in association with the additional b­quark
and the light parton. However, there are other ways to simulate the same final state for the single top
production process. The most commonly used way is to run the PYTHIA 2 ! 2 top production process
with the b­quark in the initial state and to select the additional b­quark jet from the initial and final state
gluon radiation with its splitting into the b ¯ b quark pair.
4

The problem here is that the both ways of simulation are srictly speaking incorrect. The complete 2 ! 3
tree level computation does not include the most important part of the QCD corrections which comes
from the splitting of the gluon to the b ¯ b quark pair. The corrections are taken into account by introducing
the b­quark as the initial particle. However, it means that such a simulation, when the additional b­quark
is radiated off, works only in the rather ''soft'' P t region for the b­quark, and it does not work correctly in
the ''hard'' kinematical region. In the hard kinematical region one has to take into account the complete
set of 2 ! 3 diagrams.
In order to find these soft and hard kinematical regions for the produced b­quark we compare the rates
and distributions from the SingleTop generator and the generator based on the above mentioned splitting
approximation using PYTHIA . In the latter case one starts the PYTHIA process pp ! tq +X (MSUB
switch -- 83) with the initial/final state radiations turned on. One selects events with the top, light
quark and one additional b­quark production, which as mentioned is a result of splitting of the initial
(or radiated) gluon into the b ¯ b quark pair. For comparison the same model parameters, PDFs and QCD
scales have been used. In order to see better a difference the comparison has been done on the parton
level for final particles. The rates for these calculations without any initial cuts are 235 pb from PYTHIA
and 224 pb from CompHEP . Therefore the agreement in the production cross section is about 5%.
CompHEP and Pythia for the tqb process, without cuts (Rs ­
= 14 TeV)
0
0.02
0.04
0.06
0 50 100 150 200
P T (t), [GeV]
1/N
dN/dP
T
(t)
0
0.01
0.02
0.03
­5 ­2.5 0 2.5 5
y t
1/N
dN/dy t
0
0.02
0.04
0.06
50 100 150
P T (q), [GeV]
1/N
dN/dP
T
(q)
0
0.01
0.02
0.03
­5 ­2.5 0 2.5 5
y q
1/N
dN/dy
q
0
0.1
0.2
0.3
0 20 40 60 80
P T (b), [GeV]
1/N
dN/dP
T
(b)
0
0.01
0.02
0.03
­5 ­2.5 0 2.5 5
y b
1/N
dN/dy
b
,
Figure 1: Comparison of the CompHEP and PYTHIA momentum transfer P T and rapidity y distributions
for the processes (1, 2) without applying any cuts and with the rates normalized to unit.
In Fig. 1 a number of distributions normalized to unit are shown for the SingleTop (CompHEP) and
PYTHIA simulations. The P T and rapidity distributions for the top and light quark production are
similar. However the distributions for the b­quark are significantly different. The P T spectrum from the
PYTHIA splitting approximation as one might expect is much softer, and the y b distribution is peaked
in the forward region, while the complete tree­level matrix element calculations lead to more central
b­quarks.
The question could be which distributions are more correct, and the answer would be that both of
them are, strictly speaking, incorrect in the whole kinematical region. Indeed, the complete tree­
5

CompHEP and Pythia for the tqb process, P T b>20 GeV (Rs ­
= 14 TeV)
0
1
2
3
4
0 50 100 150 200
P T (t), [GeV]
ds/dP
T
(t)
0
1
2
3
­5 ­2.5 0 2.5 5
y t
ds/dy t
0
2
4
50 100 150
P T (q), [GeV]
ds/dP
T
(q)
0
1
2
­5 ­2.5 0 2.5 5
y q
ds/dy q
0
2.5
5
7.5
10
20 40 60 80 100
P T (b), [GeV]
ds/dP
T
(b)
0
1
2
3
4
­5 ­2.5 0 2.5 5
y b
ds/dy
b
,
Figure 2: The CompHEP and PYTHIA distributions for the processes (1, 2) with the P b
T – 20 GeV and
P q
T – 20 GeV cuts.
level calculation works in the ''hard'' kinematical region. If we apply the cut P b
T ? 20 GeV the rate
from the complete calculations (116 pb) is several times larger than the rate from PYTHIA (25.4 pb).
The corresponding distributions are shown in Fig. 2, from which one can clearly see that the splitting
approximation from PYTHIA gives significantly lower values in the hard region, and as it is expected it
does not reproduce the complete calculation. From the other hand the complete tree­level computation
does not take into account the large QCD corrections from the soft b­quarks. As it was mentioned in
Introduction they could be included by evaluating the process with the b­quark in the initial state. And
this has been done by means of PYTHIA . So, in order to reproduce the correct kinematical properties
and to avoid the double counting it is necessary to properly combine the two calculations.
The main contribution to the NLO corrections comes from the ``soft'' region which is available. The NLO
rate for the W ­gluon fusion process is equal to 245 pb [2]. To incorporate the known NLO results we
take the following normalization for the ``soft'' region :
oe 2!2 (PYTHIA) = oe(NLO) \Gamma oe 2!3 (CompHEP)j P b
T ?cut(P b
T )
where, for instance,
oe 2!3 (CompHEP)j P b
T ?20GeV;P q
T ?20GeV
ú 88:7 pb
and
oe 2!3 (CompHEP)j P b
T ?10GeV;P q
T ?20GeV
ú 124 pb:
The idea is to take the events generated in the ``hard'' region P b
T ? cut(P b
T ) from the SingleTop generator
and the events generated in the ``soft'' region P b
T ! cut(P b
T ) from PYTHIA as it has been explained
above, and to find such value of cut(P b
T ) that the common P b
T distribution would be smooth in the entire
kinematical region.
6

CompHEP (tqb+ISR) and Pythia (tq+ISR) processes, P T b cut = 20 GeV
0
5
10
0 50 100 150 200
P T (t), [GeV]
ds/dP
T
(t),
[pb/GeV]
0
2
4
6
­5 ­2.5 0 2.5 5
y t
ds/dy t
,
[pb]
0
5
10
15
50 100 150
P T (q), [GeV]
ds/dP
T
(q),
[pb/GeV]
0
2
4
6
­5 ­2.5 0 2.5 5
y q
ds/dy
q
,
[pb]
1
10
0 20 40 60
P T (b), [GeV]
ds/dP
T
(b),
[pb/GeV]
0
2
4
­5 ­2.5 0 2.5 5
y b
ds/dy b
,
[pb]
Figure 3: The result of combining the CompHEP and PYTHIA events with cut(P b
T ) = 20 GeV and
P q
T – 20 GeV.
In Fig. 3 the results are shown for the cut(P b
T ) = 20 GeV. One can see the large bump in the P b
T
distribution. After some play with the cut we found that the cut of about 10 GeV satisfies the above
requirement. The corresponding distributions are shown in the Fig. 4. The combined P b
T distribution is
smooth enough, and therefore the reasonable matching of the ``hard'' and ``soft'' regions can be got.
4 Conclusion.
The first version of the SingleTop generator has been prepared. The events for the two main processes of
the single top quark production at the LHC are available in the CMS processes data base PEVLIB [14].
The events are collected separately for the top and antitop quarks in the following files:
ffl pp ! t ¯ b + jet +X (1) -- 61000 events in the file ''qtb—events''
ffl pp ! ¯ tb + jet +X (2) -- 67000 events in the file ''qTb—events''
ffl pp ! t( ¯ t) ¯ b(b) + jet +X (1,2) -- 100000 events in the file ''qtb+qTb—events—tot''
ffl pp ! t ¯ b +X (3) -- 50000 events in the file ''tb—events''
ffl pp ! ¯ tb +X (4) -- 50000 events in the file ''Tb—events
ffl pp ! t( ¯ t) ¯ b(b) +X (3,4) -- 81000 events in the file ''tb+Tb—events—tot''
Comparison between CompHEP and PYTHIA simulation methods has been done. We can conclude that
P b
T = 10 GeV is the approximate boundary between the ``soft'' and ``hard'' kinematical regions in the
simulation of the W ­gluon fusion process. Using this boundary one can describe the whole phase space
of the process by taking the events from the SingleTop generator in the region of P b
T ? 10 GeV and
7

CompHEP (tqb+ISR) and Pythia (tq+ISR) processes, P T b cut = 10 GeV
0
5
10
0 50 100 150 200
P T (t), [GeV]
ds/dP
T
(t),
[pb/GeV]
0
2
4
6
­5 ­2.5 0 2.5 5
y t
ds/dy t
,
[pb]
0
5
10
50 100 150
P T (q), [GeV]
ds/dP
T
(q),
[pb/GeV]
0
2
4
6
­5 ­2.5 0 2.5 5
y q
ds/dy
q
,
[pb]
1
10
0 20 40 60
P T (b), [GeV]
ds/dP
T
(b),
[pb/GeV]
0
2
4
6
­5 ­2.5 0 2.5 5
y b
ds/dy b
,
[pb]
Figure 4: The result of combining the CompHEP and PYTHIA events with cut(P b
T ) = 10 GeV and
P q
T – 20 GeV.
the events generated by PYTHIA, in the region of P b
T ! 10 GeV. Specific kinematical properties of the
single top events will be used for separating the signal and backgrounds as well as in the analysis. In
particular, one should stress that the light quark and, therefore, the corresponding jet distribution has
the clear maxima in the forward­backward regions at y q ú \Sigma2:5. The top quark rapidity has the maxima
at slightly lower values of y t ú \Sigma2.
Acknowledgements
This work was partially supported by the CERN­INTAS 99­377, RFBR­DFG 99­02­04011, RFBR 00­01­
00704 grants, by the Russian Ministry of Science and Technologies and by the program ``University of
Russia'' (grant 990588).
References
[1] D. Dicus and S. Willenbrock, Phys. Rev. D34, 155 (1986); C.­P. Yuan, Phys. Rev. D41, 42 (1990);
G. V. Jikia and S. R. Slabospitsky, Phys. Lett. B295, 136 (1992); R. K. Ellis and S. Parke, Phys. Rev.
D46, 3785 (1992); G. Bordes and B. van Eijk, Z. Phys. C57, 81 (1993); D. O. Carlson and C.­P. Yuan,
Phys. Lett. B306, 386 (1993); G. Bordes and B. van Eijk, Nucl. Phys. B435, 23 (1995); S. Cortese
and R. Petronzio, Phys. Lett. B253, 494 (1991); D.O. Carlson, E. Malkawi, and C.­P. Yuan, Phys.
Lett. B337, 145 (1994); T. Stelzer and S. Willenbrock, Phys. Lett. B357, 125 (1995); R. Pittau, Phys.
Lett. B386, 397 (1996); M. Smith and S. Willenbrock, Phys. Rev. D54, 6696 (1996); D. Atwood,
S. Bar­Shalom, G. Eilam, and A. Soni, Phys. Rev. D54, 5412 (1996); C. S. Li, R. J. Oakes, and
J. M. Yang, Phys. Rev. D55, 1672 (1997); C. S. Li, R. J. Oakes, and J. M. Yang, Phys. Rev. D55,
5780 (1997); G. Mahlon, S. Parke, Phys. Rev. D55, 7249 (1997); A. P. Heinson, A. S. Belyaev, and
E. E. Boos, Phys. Rev. D56, 3114 (1997); T. Stelzer, Z. Sullivan, and S. Willenbrock, Phys. Rev. D56,
8

5919 (1997); T. Tait and C.­P. Yuan, MSUHEP­71015, hep­ph/9710372; D. Atwood, S. Bar­Shalom,
G. Eilam, and A. Soni, Phys. Rev. D57, 2957 (1998); T. Stelzer, Z. Sullivan, and S. Willenbrock,
Phys. Rev. D58 094021 (1998); A. Belyaev, E. Boos, and L. Dudko, Phys. Rev. D59, 075001 (1999),
hep­ph/9806332.
[2] M. Smith and S. Willenbrock, Phys. Rev. D54, 6696 (1996); T. Stelzer, Z. Sullivan, and
S. Willenbrock, Phys. Rev. D56, 5919 (1997).
[3] A. P. Heinson, A. S. Belyaev, E. E. Boos, Phys. Rev. D56, 3114 (1997).
[4] A. Belyaev, E. Boos, and L. Dudko, Phys. Rev. D59, 075001 (1999), hep­ph/9806332.
[5] A. Belyaev, E. Boos, hep­ph/0003260
[6] T. Stelzer, Z. Sullivan, and S. Willenbrock, Phys. Rev. D58 09402 (1998).
[7] ``Top Quark Physics'', hep­ph/0003033
[8] D.O. Carlson and C.­P. Yuan, ``Studying the Top Quark via the W­Gluon Fusion Process'', Phys.
Lett. B306, 386 (1993).
[9] E. Boos, L. Dudko, and T.Ohl, Eur.Phys.J. C 11, (1999) 473­484
[10] E. E. Boos, M. N. Dubinin, V. A. Ilyin, A. E. Pukhov, and V.I. Savrin, INP MSU 94­36/358 and
SNUTP­94­116, hep­ph/9503280; P. Baikov et al., in Proc. of the Xth Int. Workshop on High Energy
Physics and Quantum Field Theory, QFTHEP­95, ed. by B. Levtchenko and V. Savrin, (Moscow,
1995), p. 101.
[11] T. Sj¨ostrand, Comp.Phys.Comm. 82, 74 (1994)
[12] CTEQ Collaboration, H. Lai, J. Huston, S. Kuhlmann, F. Olness, J. Owens, D. Soper, W.­K. Tung,
and H. Weerts, Phys. Rev. D55, 1280 (1997).
[13] V. Ilyin et al. ''CompHEP -- PYTHIA interface'' (to appear as CMS Note)
[14] /afs/cern.ch/cms/physics/PEVLIB/singleT/
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