UCR/9517
MSUNPI/9530/394
August 1995

ELECTROWEAK TOP QUARK PRODUCTION
AT THE FERMILAB TEVATRON*


A.P. HEINSON
Department of Physics, University of California,
Riverside, CA 925210413, USA

A.S. BELYAEV and E.E. BOOS
Nuclear Physics Institute, Moscow State University,
RU119899 Moscow, Russia


ABSTRACT

Top quarks can be produced from the electroweak Wtb coupling, leading to a
single top or antitop in the final state. We examine single top quark production at the
Fermilab Tevatron and calculate the cross section as a function of top quark mass,
for each of three separate production processes. We give details of the interferences
between Feynman diagrams in W-gluon fusion and then study the effects of an
anomalous (V+A) term in the Wtb coupling. Using predictions for the next Tevatron
run, we estimate the experimental sensitivity to the CKM matrix element Vtb as a
function of the strength of the anomalous coupling.


1. Introduction

The top quark has recently been discovered by the D1 and CDF2 collaborations at
the Fermilab Tevatron. Measurements of its mass are 199  30 GeV and 176  13 GeV
from D and CDF in the lepton+jets decay modes and 14532 GeV in the dilepton decay
mode from D3. Because the top quark is so heavy, electroweak production of single top
quarks from a Wtb vertex becomes competitive with strong production of tt pairs from a
gtt vertex. The resummed next-to-leading order cross section for tt production4 is
 12 Sep 1995 2 26 0
+ .26
. 0.17 pb at s = 1.8 TeV when the top quark mass m = 200 GeV. A recent
t
calculation to O( 2
)for single top production5 gives the cross section for the principal
s
single top process (for t and t combined) as 1.7 pb, which is 75% of the total tt rate.
Therefore, the possibility exists for an experimental measurement of single top production
at the Tevatron with the current ~100 pb1 data set.
We have examined the processes for single top production, and calculated the
corresponding cross sections, at the current Tevatron energy of s = 1.8 TeV. In addition,
we have started to prepare for the large numbers of single top events predicted for the next
Tevatron run at s = 2.0 TeV, when there should be twenty times as much data as exists
now. We have examined the effects of an anomalous right-handed (V+A) coupling at the
Wtb vertex from which single top quarks are produced. The single top quark system is the
only place to study this coupling, and to measure the CKM matrix element V .
tb
There is an extensive literature on single top physics at hadron colliders5,6, although
few papers use the current Tevatron energy with modern parton distributions. How to
study the Wtb coupling and what can be learnt have also featured in the literature7.


* Presented by Ann Heinson at the Workshop on Physics of the Top Quark, IITAP, Iowa State
University, Ames, Iowa, May 2526th 1995. Heinson@ucrph0.ucr.edu

1


2. Single Top Quark Cross Section

2.1 Single Top Processes

We have calculated the tree level cross sections for the following processes:

1. pp tb + X
2. pp tq + X
3. pp tW - + X

where X represents additional final state particles other than gluons. In process 1. the final
state t and b are produced from an extremely off-shell s-channel W boson. Process 2.
occurs via a t-channel W boson. Process three has several types of Feynman diagrams. We
have included the following subprocesses in our calculations:

1.1 q' q tb 1.2 q' g tb q
2.1 q'b tq 2.2 q' g tqb
3.1 bg tW 3.2 qq tWb 3.3 gg tWb

where q is a valence or sea u or d quark. Subprocess 2.2 q'g tqb is known as Wgluon
fusion. Although 1.2 and 2.2 look superficially the same, in fact they each have two
Feynman diagrams which form separate gauge invariant sets, and the diagrams are
calculated in pairs as higher order corrections to the 22 processes with tb and tq in the
final state. Feynman diagrams for these processes are shown in Fig. 1.
In our calculations, we have omitted subprocesses with strange or charm sea quarks
in the initial state for simplicity. These would boost the total cross section by ~23%. We
have included diagrams with intermediate state photons or Z bosons where appropriate (3.2
and 3.3) but the contributions are not significant. For subprocesses 3.2 and 3.3, we have
omitted diagrams with strong tt production, where the t has decayed to a Wb . We have
included diagrams with off-diagonal CKM matrix elements.
The subprocesses we have included in our calculations comprise all the significant
ones with two or three vertices, except those with a gluon in the final state, which are
significant but have not yet been fully treated. Subprocesses with an extra quark in the final
state, for instance bg tqq' and qb tWq, although they have several Feynman
diagrams, do not contribute more than ~12% to the total cross section. This also applies to
the subprocess bb tWb , despite its large number of Feynman diagrams, including one
with electroweak tt production.


2.2 Calculation Details

We have calculated the production cross section for each of the subprocesses
mentioned above. We used the computer program CompHEP8 to do the tree level symbolic
calculations and to generate optimized FORTRAN code for the squared matrix elements. We
used the BASES9 package to integrate over all phase space using parton distribution
functions, and a CompHEPBASES interface10 to generate the event kinematics with





2


u d t
u W
u b
W u
d b
b

W
d t
d
g t g

(a) 1.1 ud tb 1.2 ug tbd



d u d
u u d



W
W W
t b
b t


b t g g
b t


(b) 2.1 ub td 2.2 ug tdb



b W b W

b t

g
t
g t



(c) 3.1 bg tW



Fig.1 Representative Feynman diagrams for the significant subprocesses included in
our calculation for single top quark production at the Tevatron: (a) W boson s-
channel production pp tb + X ; (b) W boson t-channel production
pp tq + X and (c) pp tW  + X .


smoothing of singular variables. For parton distributions, we have used the CTEQ3M11 and
MRS(A')12 fits, which are representative next-to-leading-order sets in the MS
renormalization scheme.
The following Standard Model parameters have been used in our calculations: m =
Z
91.19 GeV, m = 5.0 GeV, = 1/128, sin2 = 0.225 and CKM matrix elements V =
b W ud
0.975 and V = 0.999. All results have been obtained in the unitarity gauge and the
tb
't HooftFeynman gauge, as a check of the calculations. Differences between calculations
in the two gauges are less than 0.1%.
We have chosen to use m2 as the QCD evolution parameter or scale
t Q2. A typical x
value is 0.1, where x is the fraction of the proton or antiproton momentum carried by each
initial state parton. At a scale Q2 = (180 GeV)2, the value of is 0.104.
s



2.3 Combining Cross Sections

Care must be taken when combining some single top subprocesses to avoid double
counting. Subprocesses 2.1 ( q'b tq ) and 2.2 ( q'g tqb : W-gluon fusion) have a
considerable region of overlap when the g bb is on-shell, so that the b quark which
fuses with the W boson is the same as the initial state b sea quark in subprocess 2.1. A
technique has been developed13 which takes care of this double counting whilst being




3


consistent with the definition of the b sea quark in the parton distributions. It involves
summing the cross sections calculated for each of the two subprocesses, and then
subtracting the gluon splitting rate convoluted with subprocess 2.1. We have adopted this
technique here.
The subtracted term is not a small correction. For example, using CTEQ3M and m =
t
180 GeV, the 22 subprocess q'b tq gives a cross section of 0.750 pb before
subtraction, W-gluon fusion q'g tqb gives 0.293 pb and the correction is 0.536 pb,
giving a total rate for pp tq + X of 0.507 pb. The subtraction term forms just over half
of the raw total rate. Alternatively, if the 22 subprocess and the subtraction term are just
ignored, then the remaining cross section from only the W-gluon fusion subprocess is less
than 60% of the total pp tq + X rate.


2.4 Cross Section Versus Top Quark Mass

Our results are shown in Fig. 2 as a function of the top quark mass m , at
t s =
1.8 TeV. The solid curves are from the calculations with CTEQ3M and the dot-dash curves
are from MRS(A'). With m = 180 GeV, we find the total cross section for top to be
t
0.834 pb (CTEQ3M), with contributions of 0.247 pb from subprocess 1.1, 0.032 pb from
1.2, 0.215 pb from 2.1 after correction, 0.293 pb from 2.2 (W-gluon fusion), 0.042 pb
from 3.1, and 0.005 from subprocesses 3.2 and 3.3 combined.


] ]
b b
2 CTEQ3M gbb CTEQ3M
ppt+X 1
[p [p
MRS(A') diagram s = 1.8 TeV
n n
io s = 1.8 TeV io
ct 1.5 ct q'gtqb
e e
S S total
0.5
ss pptq+X ss
ro ro
C 1 C
gtt
pptb+X diagram
0
0.5
interference
pptW+X

0 -0.5
100 140 180 220 100 140 180 220

Top Quark Mass m [GeV] Top Quark Mass m [GeV]
t t

Fig.2 Electroweak single top quark production Fig.3 Interference between the Feynman diagrams
cross section from pp interactions. of the W-gluon fusion subprocess q' g tqb .


3. A Closer Look at W-Gluon Fusion

We have studied the contributions to the production rate from the two Feynman
diagrams in subprocess 2.2, W-gluon fusion: q'g tqb . These calculations were done in
the unitarity gauge with the CTEQ3M parton distributions. The Feynman diagram in which
the initial state gluon produces a bb pair contributes 145% to the total rate, whereas the
diagram in which the gluon splits to a tt pair contributes only 5%. Although this diagram




4


contributes so little to the total, the destructive interference between the two diagrams is
very significant, at 50%. Figure 3 shows the contributions to the total W-gluon fusion
cross section from each diagram and from the interference between them as a function of
the top quark mass.


4. Wtb Coupling and Vtb

We have investigated the effect of an anomalous contribution to the Wtb coupling, in
the form of a right-handed (V+A) structure, specified by a parameter A . In the unitarity
r
gauge, the Wtb coupling is given by:

= eVtb [  1(- 
5 ) + A 1
( )
r + 5 ]
2 2 sinW

where e is the electronic charge, sin = 0.474 and
W  and 5 are Dirac matrices.
The dependence of the total single top cross section on the parameter A is shown in
r
Fig. 4 for the upgraded Tevatron energy of s = 2.0 TeV and V = 0.999. Here
tb
(t + t ) = (tb ) + (tb) + (tq) + (tq ) + (tW - ) + (tW +
( )) . The cross section rises from the SM value
of 2.37 pb to 4.60 pb when A = +1.
r



5 1
]b m = 180 GeV CTEQ3M tb
t V
[p s = 2.0 TeV
V = 0.999 t
tb n 0.9
n e
io m
ct 4 le
e E
S 0.8
trix
ss a
ro MM
t C 0.7
K
3 C
t +

0.6



2 0.5
-1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
(V+A)/(VA) Coupling Strength A (V+A)/(VA) Coupling Strength A
r r

Fig.4 Total single top quark production cross Fig.5 Region of sensitivity at the 95% C.L. in the
section in pp interactions as a function of ( V ,
tb A ) plane, for an experiment with 2 fb1
r
the right-handed (V+A) coupling parameter A . of data, S:B = 1:2, 10% efficiency and m =
r t
180 GeV.


We have estimated the experimental sensitivity in the (V plane from the next
tb , Ar )
Tevatron collider run. The parameters used in our estimate are that the collider will operate
at 2.0 TeV, there will be a 2 fb1 data set, the top quark has a mass of 180 GeV, and the
search will take place in the electron+jets and muon+jets decay modes with 10% overall
efficiency. We assume the branching fraction will remain constant at 2/9 and that the
signal-to-background ratio will be 1:2, based on a study for the TeV-2000 project14. If the
Wtb coupling has SM form and there are only three quark families (i.e.
0 9988
. V at the 90% CL15),
tb 0 9995
.



5


then there should be approximately 105 fully reconstructed b tagged events. Assuming that
315 events are seen (105 signal and 210 background), limits can be placed on V as a
tb
function of any anomalous coupling as parametrized by A . These 95% CL limits are
r
shown in Fig. 5. If the W coupling is purely left-handed, then the limits on V are
tb tb
0 817
. V . For = 0.5, 0 735
. V , and if = 1.0, then 0 586
. V .
tb 0 826
.
tb 1
tb 1 A A
r r



5. Acknowledgements

We would like to thank P. Baringer, P. Ermolov, P. Grannis, A. Klatchko, W.-K.
Tung, S. Willenbrock and C.-P. Yuan for useful discussions, and the Moscow State
University CompHEP group, especially S. Ilyin and A. Pukhov for their valuable help.
This paper is an abridged version of a more detailed one in preparation16.


6. References

1. S. Abachi et al. (The D Collaboration), Phys. Rev. Lett. 74 (1995) 2632.
2. F. Abe et al. (The CDF Collaboration), Phys. Rev. Lett. 74 (1995) 2626.
3. S. Abachi et al. (The D Collaboration), to appear in the Proceedings of the European
Physical Society Conference, Brussels (1995).
4. E. Laenen, J. Smith and W.L. van Neerven, Phys Lett B321 (1994) 254.
5. G. Bordes and B. van Eijk, Nucl. Phys. B435 (1995) 23.
6. S. Dawson, Nucl. Phys. B249 (1985) 42; S.S.D. Willenbrock and D.A. Dicus, Phys. Rev. D 34
(1986) 155; S. Dawson and S.S.D. Willenbrock, Nucl. Phys. B284 (1987) 449; T. Moers, R.
Priem, D. Rein and H. Reitler, in Proceedings of the Large Hadron Collider Workshop, Aachen
(1990) 418; S. Cortese and R. Petronzio, Phys. Lett. B253 (1991) 494; R.K. Ellis and S.
Parke, Phys. Rev. D 46 (1992) 3785; G. Bordes and B. van Eijk, Z. Phys. C57 (1993) 81; D.O.
Carlson and C.-P. Yuan, Phys. Lett. B306 (1993) 386; D.O. Carlson and C.-P. Yuan,
MSUHEP-40903 (March 1995); T. Stelzer and S. Willenbrock, DTP/95/40, ILL-(TH)-95-30
7. (May 1995).
C.-P. Yuan, Phys. Rev. D 41 (1990) 42; G.V. Jikia and S.R. Slabospitsky, Phys. Lett. B295
(1992) 136; D.O. Carlson, E. Malkawi and C.-P. Yuan, Phys. Lett. B337 (1994) 145;
E. Malkawi and C.-P. Yuan, Phys. Rev. D 50 (1994) 4462; C.-P. Yuan, Mod. Phys. Lett. A10
(1995) 627.
8 E.E. Boos et al., in Proceedings of the XXVIth Rencontre de Moriond, ed. J. Tran Than Van,
(Edition Frontiers, 1991) 501; E.E. Boos et al., in Proceedings of the Second International
Workshop on Software Engineering, ed. D. Perret-Gallix, (World Scientific, 1992) 665.
9. S. Kawabata, Comp. Phys. Commun. 41 (1986) 127.
10. V.A. Ilyin, D.N. Kovalenko and A.E. Pukhov, INP MSU Preprint-95-2/366, Moscow State
University (1995).
11. H.L. Lai et al., Phys. Rev. D 51 (1995) 4763.
12. A.D. Martin, R.G. Roberts and W.J. Stirling, RAL-95-021 (February 1995).
13. R.M. Barnett, H.E. Haber and D.E. Soper, Nucl. Phys. B306 (1988) 697; F.I. Olness and
W.-K. Tung, Nucl. Phys. B308 (1988) 813.
14. P. Baringer and A.P. Heinson, "Single Top Physics with a High Luminosity Tevatron",
D Note 2600 (June 1995); D. Amidei et al., in preparation for submission to Phys. Rev. D.
15. "Review of Particle Properties", Phys. Rev. D 50 (1994) 1315.
16. A.P. Heinson, A.S. Belyaev and E.E. Boos, "Single Top Quarks at the Fermilab Tevatron", in
preparation.





6



