We show that the production rate of the single-top quark event from the
$W$-gluon fusion process is sensitive to new physics which strongly modifies
the interactions of the top quark. The measurement of its production rate gives
the partial decay width of the top quark which combined with the branching
ratio measurement from the $t \bar t$ pair event determines the lifetime of the
top quark.Comment: 7 pages, uuencoded PS file. Talk given by C.-P. Yuan at the Workshop
  on Physics of the Top Quark, IITAP, Iowa State University, Ames, Iowa, May 25
  \& 26, 199

Carlson, Douglas O.

Yuan, C. -P.

English

arXiv

We show that the production rate of the single-top quark event from the W-gluon fusion process is sensitive to new physics which strongly modifies the interactions of the top quark. The measurement of its production rate gives the partial decay width of the top quark which combined with the branching ratio measurement from the t \bar t pair event determines the lifetime of the top quark

Carlson, D O

Yuan, C P

CERN Document Server

he
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95
MSUHEP-50823
August 1995
Probing New Physics from the Single-Top Production
a
Douglas O. Carlson and C.{P. Yuan
Department of Physics and Astronomy
East Lansing, MI 48824 , USA
We show that the production rate of the single-top quark event from the W -gluon
fusion process is sensitive to new physics which strongly modies the interactions
of the top quark. The measurement of its production rate gives the partial decay
width of the top quark which combined with the branching ratio measurement
from the t

t pair event determines the lifetime of the top quark.
1 Introduction
From the direct search at the Tevatron, the top quark has been discovered
and found to have mass of m
t
= 176  8 (stat:)  10(sys:)GeV from CDF
data, and m
t
= 199
+29
 21
(stat:)  22(sys:)GeV from D data. For a heavy
top quark, m
t
is of the order of the electroweak symmetry breaking scale v =
(
p
2G
F
)
 1=2
= 246GeV. (v=
p
2 = 175GeV.) It is likely that the generation of
fermion mass is closely related to the electroweak symmetry breaking, eects
from new physics would be more apparent in the top quark sector than any
other light sector of the electroweak theory. Thus, the top quark system may
be used to probe the symmetry breaking sector. A few examples are discussed
in Ref. [1] to illustrate that dierent models of electroweak symmetry breaking
mechanism will induce dierent interactions among the top quark and the W -
and Z-bosons. These interactions may strongly modify the production and/or
the decay of the top quark. It is therefore important to test whether it is a
Standard Model (SM) top quark.
In this work we will concentrate on the single-top quark event produced
from the W -gluon fusion processes q
0
g(W
+
g)! qt

b or q
0
b! qt.
a
Talk given by C.{P. Yuan at the Workshop on Physics of the Top Quark, IITAP, Iowa
State University, Ames, Iowa, May 25 & 26, 1995.
1
Table 1: Cross sections (in pb) of various processes for m
t
= 180(140)GeV. (Branching
ratios are not included.) For the single-top rates we only include single-t production.
p
S(TeV) qq; gg ! t

t W -gluon q
0
q ! W

! t

b gb! W
 
t
fusion
2 (pp) 4.5(16) 1(2) 0.3(0.8) 0.1(0.3)
14 (pp) 430(1300) 100(140) 4.6(11) 3.6(8.8)
2 The Single-Top Production Mechanism
In this section we consider the production rate of a single-top quark at
hadron colliders. In referring to single-top production, unless stated otherwise,
we will concentrate only on the positive charge mode (i.e. only including single-
t, but not single-

t). The colliders we consider are the Tevatron (a pp collider)
with the Main Injector (Run-II) at
p
S = 2TeV and the LHC (a pp collider)
at
p
S = 14TeV.
A single-top quark signal can be produced from theW -gluon fusion process
q
0
g(W
+
g)! qt

b (or q
0
b! qt) [2], the Drell-Yan type process q
0
q ! W

! t

b
(also known as \W

" production) [3], orWt production via gb! W
 
t [4]. For
later reference in this paper, we show the total cross sections of these processes
at the Tevatron and the LHC in Table 1, for m
t
= 180(140)GeV. For the
single-top rates we only include t production. To include the production rates
for both single-t and single-

t events at pp colliders, a factor of 2 should be
multiplied to the single-t production rates because the parton luminosity for
single-

t production is the same as that for single-t. At the LHC the rates should
be multiplied by  2 because the relevant parton luminosities for producing
single-t and single-

t events in high energy collisions are dominated by the sea
quarks.
The single-top quark produced from the W -gluon fusion process involves
a very important and not yet well-developed technique of handling the kine-
matics of a heavy b parton inside a hadron. Thus the kinematics of the top
quark produced from this process cannot yet be accurately calculated. How-
ever, the total event rate for single-top quark production via this process can
be estimated using the method proposed in Ref. [5]. The total rate for the
W -gluon fusion process involves the O(
2
) (2 ! 2) process q
0
b ! qt plus
the O(
2

s
) (2 ! 3) process q
0
g(W
+
g) ! qt

b (where the gluon splits to b

b)
minus the splitting piece g ! b

b 
 q
0
b ! qt in which b

b are nearly collinear.
These processes are shown diagrammatically in Fig. 1. The splitting piece is
2


	
q
t
g
b
b
g
q
q
q
q
q
b t
t
W
+
W
+
W
+
0
0
0
b
b
b


Figure 1: Feynman diagrams illustrating the subtraction procedure for calculating the total
rate for W -gluon fusion: q
0
b! qt  q
0
g(W
+
g)! qt

b 	 (g ! b

b 
 q
0
b! qt).
subtracted to avoid double counting the regime in which the b propagator in
the (2 ! 3) process is close to on-shell. This procedure is to resum the large
logarithm 
s
ln(m
2
t
=m
2
b
) in the W -gluon fusion process to all orders in 
s
and
include part of the higher order O(
2

s
) corrections to its production rate.
(m
b
is the mass of the bottom quark.) We note that to obtain the complete
O(
2

s
) corrections beyond just the leading log contributions one should also
include virtual corrections to the (2 ! 2) process, but we shall ignore these
non-leading contributions here.
b
Using the prescription described as above we
found that the total rate of theW -gluon fusion process is about 25% less than
that from the (2! 2) process for m
t
= 180 (140) GeV regardless of the energy
or the type (i.e. pp or pp) of the machine. To estimate the uncertainty in
the production rate due to the choice of the scale Q in evaluating the strong
coupling constant 
s
and the parton distribution function (PDF), we have per-
formed a detailed study in Ref. [7]. Although the individual rate from either
(2 ! 2), (2 ! 3) or the splitting piece is relatively sensitive to the choice of
the scale, the total rate as dened by (2 ! 2) + (2 ! 3)   (splitting piece)
only varies by about 30% and 10% for M
W
=2 < Q < 2m
t
at the Tevatron and
the LHC, respectively. We note that in the (2! 2) process the b quark distri-
bution eectively contains sums to order [
s
ln(Q=m
b
)]
n
from n-fold collinear
gluon emission, whereas the subtraction term (namely, the splitting piece) con-
tains only rst order in 
s
ln(Q=m
b
). As Q ! m
b
, the (2 ! 2) process picks
up only the leading order in 
s
ln(Q=m
b
) and so is largely cancelled by the
b
A complete next-to-leading-order calculation for this process was recently done in Ref. [6]
in which the large logs were not properly resummed.
3
splitting piece in calculating the total rate. Consequently, the total rate is
about the same as the (2 ! 3) rate for Q ! m
b
. We also note that when
Q ' M
W
=2, the (2 ! 2) and (2 ! 3) processes have about the same rate.
As Q increases the (2 ! 2) rate gradually increases while the (2 ! 3) rate
decreases such that the total rate is not sensitive to the scale Q. Furthermore,
based upon the factorization theorem in the QCD theory, we conclude that the
total rates calculated via this prescription will not be sensitive to the choice of
PDF although each individual piece will vary with a dierent set of PDF.
Another single-top quark productionmechanism is the Drell-Yan type pro-
cess q
0
q ! W

! t

b. As shown in Table 1, for top quarks with mass on the
order of 180GeV, the rate for W

production is about one third that of W -
gluon fusion at
p
S = 2TeV. TheW

process becomes much less important for
a heavier top quark. This is because at higher invariant masses
p
s^ (for pro-
ducing a heavier top quark) of the t

b system, W

production suers the usual
1=s^ suppression in the constituent cross section. However, in the W -gluon fu-
sion process the constituent cross section does not fall o as 1=s^ but attens
out asymptotically to 1=M
2
W
. Therefore, for colliders with higher energies, the
W

production mechanism for heavy top quarks becomes much less impor-
tant. However, the kinematics of the top quarks produced from this process
are dierent from those in the W -gluon fusion events [7, 8].
3 Measuring the Lifetime of the Top Quark
As shown in Ref. [9], the intrinsic width of the top quark cannot be mea-
sured at hadron colliders, such as the Tevatron and the LHC, through re-
constructing the invariant mass of the jets from the decay of the top quark
produced from the usual QCD processes (qq; gg ! t

t) because of the nite
resolution of the jet energy measured by the detector. For a 180GeV SM top
quark, its decay width is about 1.6GeV, however the measured width from
the invariant mass distribution of the top quark is unlikely to be better than
10GeV [10]. Is there a way to measure the top quark width  (t ! bW
+
) to
within a factor of 2 or better, at hadron colliders? The answer is yes. It can
be measured from the single-top events.
The width  (t! bW
+
) can be measured by counting the production rate
of top quark from the W -b fusion process which is equivalent to the W -gluon
fusion process by properly treating the bottom quark and the W boson as
partons inside the hadron. In the previous section, we have discussed how to
correctly treat the b-quark as a parton inside the proton to properly resum
all the large logs to all orders in 
s
. Here, we illustrate how to treat the W -
boson as a parton inside the proton. Consider the q
0
b! qt process. It can be
4
viewed as the production of an on-shell W -boson which then rescatters with
the b-quark to produce the top quark. This factorization is exactly the same
as that in the deep-inelastic scattering processes. The analytic expression for
the ux (f

(x)) of the incomingW

-boson ( = 0;+;  for longitudinal, right-
handed, or left-handed polarization) to rescatter with the b-quark can be found
in Ref. [11]. The constituent cross section of ub! dt is given by
^(ub! dt) =
X
=0;+; 
f


x =
m
2
t
s^

"
16
2
m
3
t
s^(m
2
t
 M
2
W
)
2
#
 (t! bW
+

) ;
where M
W
is the mass of W
+
-boson and
p
s^ is the invariant mass of the
hard part process. Since the scattering rate of Wb ! t is proportional to the
decay rate of t ! Wb, the production rate of single-top event from the W -
gluon fusion process measures the partial decay width of the top quark  (t!
bW
+
). Furthermore, the branching ratio of t!Wb can be measured from the
ratio of the numbers of double-b-tagged versus single-b-tagged t

t events [10].
Combining this model-independent measurement of the branching ratio for
t ! Wb with the measurement of the partial decay width  (t ! bW
+
) from
the single-top production rate, one can determine the total decay width of the
top quark, i.e. the lifetime of the top quark. At the Run-II of the Tevatron
(with an integrated luminosity of 2 fb
 1
), we expect that the lifetime of the
top quark would be known to about 20%  30%. Here, we have assumed that
the branching ratio for  (t ! bW
+
) can be measured to about 10% and the
cross section for W -gluon fusion process is known to about 15%  20%.
4 Probing New Physics via Single-Top Production Rate
The most general operators for the t-b-W coupling are [12]:
g
p
2

W
 


b

(f
L
1
P
 
+ f
R
1
P
+
)t 
1
M
W
@

W
 


b

(f
L
2
P
 
+ f
R
2
P
+
)t

+
g
p
2

W
+


t

(f
L
1

P
 
+ f
R
1

P
+
)b 
1
M
W
@

W
+


t

(f
R
2

P
 
+ f
L
2

P
+
)b

+ @

W
 


b(f
L
3
P
 
+ f
R
3
P
+
)t+ @

W
+


t(f
R
3

P
 
+ f
L
3

P
+
)b ;
where P

=
1
2
(1  
5
), i

=  
1
2
[

; 

] and the superscript  denotes the
complex conjugate. In the SM, the only nonvanishing form factor at the tree
level is f
L
1
= 1. These form factors would have dierent values if new physics
exists. Nevertheless, the conclusion that the production rate of the W -gluon
5
fusion event is proportional to the decay of t ! Wb holds irrespective of the
specic forms of the f 's. Hence, measuring the single-top event rate from
the W -gluon fusion process is an inclusive method for detecting eects of new
physics which might produce large modications to the interactions of the
top quark. Strictly speaking, from the production rate of single-top events,
one measures the sum of all the possible partial decay widths, such as  (t !
bW
+
) +  (t ! sW
+
) +  (t ! dW
+
) +   , therefore, this measurement is
really measuring the width of  (t ! XW
+
) where X can be more than one
particle state as long as it originates from the partons inside the proton (or anti-
proton). If new physics strongly enhances the avor-changing-neutral-current
t-c-Z, then the single-top production rate would also be enhanced from the
Z-c fusion process qc! qt.
Therefore, we conclude that measuring the production rate of the single-
top quark event from the W -gluon fusion process can probe new physics in an
inclusive way. This does not require knowing the specic form of the t-b-W form
factors prior to the analysis, in contrast to many other studies (either for the
t

t or the W

events) which usually require assuming some kind of t-b-W form
factors from the very beginning of the analyses.
Acknowledgments
This work is supported in part by the NSF under grant no. PHY-9309902.
References
1. Ehab Malkawi and C.{P. Yuan, Phys. Rev. D50, 4462 (1994); and the
references therein.
2. S. Dawson, Nucl. Phys. B249, 42 (1985);
D.O. Carlson and C.{P. Yuan, Phys. Lett. B306, 386 (1993); and the
references therein.
3. S. Cortese and R. Petronzio, Phys. Lett. B253, 494 (1991).
4. G.A. Ladinsky and C.{P. Yuan, Phys. Rev. D43, 789 (1991).
5. M. Aivazis, J.C. Collins, F. Olness and Wu-Ki Tung, Phys. Rev. D50,
3102 (1994); and the references therein.
6. G. Bordes and B. Van Eijk, Nucl. Phys. B435, 23 (1995).
7. D.O. Carlson, Ph.D. thesis, Michigan State University, MSUHEP-
050727, August 1995.
8. T. Stelzer and S. Willenbrock, hep-ph/9505433, 1995.
9. S. Mrenna and C.{P. Yuan, Phys. Rev. D46, 1007 (1992).
6
10. Dan Amidei and Chip Brock, \Report of the TeV 2000 Study Group on
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(1987); and the references therein.
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(1992).
7


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