# The “Top Priority” at the LHC

Tao Han111email<EMAIL_ADDRESS>Department of Physics, University of
Wisconsin, Madison, WI 53706
KITP, University of California, Santa Barbara, CA 93107

###### Abstract

The LHC will be a top-quark factory. With 80 million pairs of top quarks and
an additional 34 million single tops produced annually at the designed high
luminosity, the properties of this particle will be studied to a great
accuracy. The fact that the top quark is the heaviest elementary particle in
the Standard Model with a mass right at the electroweak scale makes it
tempting to contemplate its role in electroweak symmetry breaking, as well as
its potential as a window to unknown new physics at the TeV scale. We
summarize the expectations for top-quark physics at the LHC, and outline new
physics scenarios in which the top quark is crucially involved.

To be published as a chapter in the book of “Perspectives on the LHC”, edited
by G. Kane and A. Pierce, by World Scientific Publishing Co., 2008.

††preprint: MADPH–08–1509, NSF–KITP–08–55

##  I Brief Introduction

The top quark plays a special role in the Standard Model (SM) and holds great
promise in revealing the secret of new physics beyond the SM. The theoretical
considerations include the following:

  * •

With the largest Yukawa coupling $y_{t}\sim 1$ among the SM fermions, and a
mass at the electroweak scale $m_{t}\sim v/\sqrt{2}$ (the vacuum expectation
value of the Higgs field), the top quark is naturally related to electroweak
symmetry breaking (EWSB), and may reveal new strong dynamics Hill:2002ap .

  * •

The largest contribution to the quadratic divergence of the SM Higgs mass
comes from the top-quark loop, which implies the immediate need for new
physics at the Terascale for a natural EW theory Giudice:2008bi , with SUSY
and Little Higgs as prominent examples.

  * •

Its heavy mass opens up a larger phase space for its decay to heavy states
$Wb,\ Zq,\ H^{0,\pm}q$, etc.

  * •

Its prompt decay much shorter than the QCD scale offers the opportunity to
explore the properties of a “bare quark”, such as its spin, mass, and
couplings.

Top quarks will be copiously produced at the LHC. The production and decay are
well understood in the SM. Therefore, detailed studies of the top-quark
physics can be rewarding for both testing the SM and searching for new physics
Quadt:2006jk .

##  II Top Quark in The Standard Model

In the SM, the top quark and its interactions can be described by

$\displaystyle-{\cal L}_{SM}$ $\displaystyle=$ $\displaystyle
m_{t}\bar{t}t+{m_{t}\over
v}H\bar{t}t+g_{s}\bar{t}\gamma^{\mu}T^{a}tG_{\mu}^{a}+eQ_{t}\bar{t}\gamma^{\mu}tA_{\mu}$
$\displaystyle+$
$\displaystyle{g\over\cos\theta_{w}}\bar{t}\gamma^{\mu}(g_{V}+g_{A}\gamma^{5})tZ_{\mu}+{g\over\sqrt{2}}\sum_{q}^{d,s,b}V_{tq}\bar{t}\gamma^{\mu}P_{L}qW^{-}_{\mu}+h.c.\
\ \ \ $

Besides the well-determined gauge couplings at the electroweak scale, the
other measured parameters of the top quark are listed in Table 1.

Table 1: Experimental values for the top quark parameters pdg . $m_{t}$ (pole) | $|V_{tb}|$ | $|V_{ts}|$ | $|V_{td}|$
---|---|---|---
(172.7 $\pm$ 2.8) GeV | $>0.78$ | $(40.6\pm 2.6)\times 10^{-3}$ | $(7.4\pm 0.8)\times 10^{-3}$

The large top-quark mass is important since it contributes significantly to
the electroweak radiative corrections. For instance, the one-loop corrections
to the electroweak gauge boson mass can be cast in the form

$\Delta r=-{3G_{F}m_{t}^{2}\over
8\sqrt{2}\pi^{2}\tan^{2}\theta_{W}}+{3G_{F}M_{W}^{2}\over
8\sqrt{2}\pi^{2}}\left(\ln{m_{H}^{2}\over M_{Z}^{2}}-{5\over 6}\right).$ (2)

With the $m_{t}$ value in Table 1, the best global fit in the SM yields a
Higgs mass $m_{H}=89^{+38}_{-28}$ GeV pdg . The recent combined result from
CDF and D0 at the Tevatron Run II gave the new value Brubaker:2006xn

$m_{t}=171.4\pm 2.1\ {\rm GeV}.$ (3)

The expected accuracy of $m_{t}$ measurement at the LHC is better than 1 GeV
Etienvre:2006ph , with errors dominated by the systematics.

To directly determine the left-handed $V$-$A$ gauge coupling of the top quark
in the weak charged current, leptonic angular distributions and $W$
polarization information would be needed gordy . No direct measurements are
available yet for the electroweak neutral current couplings,
$g_{V}^{t}=T_{3}/2-Q_{t}\sin^{2}\theta_{W},\ g_{A}^{t}=-T_{3}/2$ and
$Q_{t}=+2/3$, although there are proposals to study them via the associated
production processes $t\bar{t}\gamma,\ t\bar{t}Z$ Baur:2001si . The indirect
global fits however indicate the consistency with these SM predictions pdg .

###  II.1 Top-Quark Decay in the SM

Due to the absence of the flavor-changing neutral currents at tree level in
the SM (the Glashow-Iliopoulos-Maiani mechanism), the dominant decay channels
for a top quark will be through the weak charged-currents, with the partial
width given by twidth

$\Gamma(t\to W^{+}q)={|V_{tq}|^{2}m_{t}^{3}\over 16\pi
v^{2}}(1-r_{W})^{2}(1+2r_{W})\left[1-{2\alpha_{s}\over 3\pi}({2\pi^{2}\over
3}-{5\over 2})\right],$ (4)

where $r_{W}=M_{W}^{2}/m_{t}^{2}$. The subsequent decay of $W$ to the final
state leptons and light quarks is well understood. Two important features are
noted:

  * •

Since $|V_{tb}|\gg|V_{td}|,|V_{ts}|$, a top quark will predominantly decay
into a $b$ quark. While $V_{ts},\ V_{td}$ may not be practically measured via
the top-decay processes, effective $b$-tagging at the Tevatron experiments has
served to put a bound on the ratio

${B(t\to Wb)\over B(t\to
Wq)}={|V_{tb}|^{2}\over{|V_{td}|^{2}+|V_{ts}|^{2}+|V_{tb}|^{2}}},$ (5)

that leads to the lower bound for $|V_{tb}|$ in Table 1.

  * •

Perhaps the most significant aspect of Eq. (4) is the numerics:

$\Gamma(t\to W^{+}q)\approx 1.5\ {\rm GeV}\approx{1\over 0.5\times 10^{-24}\
{\rm s}}>\Lambda_{QCD}\sim 200\ {\rm MeV}.$

This implies that a top quark will promptly decay via weak interaction before
QCD sets in for hadronization tlife . So no hadronic bound states (such as
$\bar{t}t,\bar{t}q$, etc.) would be observed. The properties of a “bare quark”
may be accessible for scrutiny.

It is interesting to note that in the top-quark rest frame, the longitudinal
polarization of the $W$ is the dominant mode. The ratio between the two
available modes is

${\Gamma(t\to b_{L}\ W_{\lambda=0})\over\Gamma(t\to b_{L}\
W_{\lambda=-1})}={m_{t}^{2}\over 2M_{W}^{2}}.$ (6)

###  II.2 Top-Quark Production in the SM

####  II.2.1 $t\bar{t}$ production via QCD

Historically, quarks were discovered via their hadronic bound states, most
notably for the charm quark via $J/\psi(\bar{c}c)$ and bottom quark via
$\Upsilon(\bar{b}b)$. Due to the prompt decay of the top quark, its production
mechanisms and search strategy are quite different from the traditional one.

Figure 1: Top-quark pair production in hadronic collisions via QCD
interaction. This figure is taken from Ref. Willenbrock:2002ta .

The leading processes are the open flavor pair production from the QCD strong
interaction, as depicted in Fig. 1. The contributing subprocesses are from

$q\bar{q},\ gg\to t\bar{t}.$ (7)

The cross sections have been calculated rather reliably to the next-to-leading
order Nason:1987xz  and including the threshold resummations Laenen:1993xr ;
Bonciani:1998vc , as given in Table 2.

Table 2:  Cross sections, at next-to-leading-order in QCD, for top-quark production via the strong interaction at the Tevatron and the LHC Bonciani:1998vc . Also shown is the percentage of the total cross section from the quark-antiquark-annihilation and gluon-fusion subprocesses. |  $\sigma_{\rm NLO}$ (pb) | $q\bar{q}\to t\bar{t}$ | $gg\to t\bar{t}$
---|---|---|---
Tevatron ($\sqrt{s}=1.8$ TeV $p\bar{p}$) | $4.87\pm 10\%$ | $90\%$ | $10\%$
Tevatron ($\sqrt{s}=2.0$ TeV $p\bar{p}$) | $6.70\pm 10\%$ | $85\%$ | $15\%$
LHC ($\sqrt{s}=14$ TeV $pp$) | $803\pm 15\%$ | $10\%$ | $90\%$

Largely due to the substantial gluon luminosity at higher energies, the
$t\bar{t}$ production rate is increased by more than a factor of 100 from the
Tevatron to the LHC. Assuming an annual luminosity at the LHC of $10^{34}$
cm-2 s${}^{-1}\Rightarrow 100$ fb${}^{-1}/$year, one expects to have 80
million top pairs produced. It is truly a “top factory”. In Fig. 2(a), we plot
the invariant mass distribution, which is important to understand when
searching for new physics in the $t\bar{t}$ channel. Although the majority of
the events are produced near the threshold $m(t\bar{t})\sim 2m_{t}$, there is
still a substantial cross section even above $m(t\bar{t})\sim$ 1 TeV, about 5
pb. This is illustrated in Fig. 2(b), where the integrated cross section is
given versus a minimal cutoff on $m(t\bar{t})$ and decay branching fractions
of one top decaying hadronically and the other leptonically have been
included.

,

Figure 2:  (a) Invariant mass distribution of $t\bar{t}$ at the LHC and (b)
integrated cross section versus a minimal cutoff on $m(t\bar{t})$. Decay
branching fractions of one top decaying hadronically and the other
leptonically ($e,\mu$) have been included.

It should be noted that the forward-backward charge asymmetry of the
$t\bar{t}$ events can be generated by higher order corrections, reaching
$10-15\%$ at the partonic level from QCD Kuhn:1998jr  and $1\%$ from the
electroweak Bernreuther:2005is .

####  II.2.2 Single top production via weak interaction

As discussed in the last section, the charged-current weak interaction is
responsible for the rapid decay of the top quark. In fact, it also
participates significantly in the production of the top quark as well
Willenbrock:cr . The three classes of production processes, $s$-channel Drell-
Yan, $t$-channel $Wb$ fusion, and associated $Wt$ diagrams, are plotted in
Fig. 3. Two remarks are in order:

  * •

The single top production is proportional to the quark mixing element
$|V_{tb}|^{2}$ and thus provides the direct measurement for it, currently
Abazov:2006gd  $0.68<|V_{tb}|\leq 1$ at the $95\%$ C.L.

  * •

The $s$-channel and $t$-channel can be complementary in the search for new
physics such as a $W^{\prime}$ exchange Cao:2007ea .

For the production rates Smith:1996ij ; Stelzer:1997ns ; Zhu:uj ;
Kidonakis:2006bu ; Kidonakis:2007ej , the largest of all is the $t$-channel
$Wb$ fusion. It is nearly one third of the QCD production of the $t\bar{t}$
pair. Once again, it is mainly from the enhancement of the longitudinally
polarized $W$. The total cross sections for these processes at Tevatron
Kidonakis:2006bu  and LHC energies Kidonakis:2007ej  are listed in Table 3
Smith:1996ij ; Stelzer:1997ns ; Zhu:uj . We see the typical change of the
production rate from the Tevatron to the LHC: A valence-induced process (DY-
type) is increased by about an order of magnitude; while the gluon- or
$b$-induced processes are enhanced by about a factor of 100.

Figure 3: Single top-quark production in hadronic collisions via the charged-current weak interaction. This figure is taken from Ref. Willenbrock:2002ta .  Table 3:  Cross sections, at next-to-leading-order in QCD, for top-quark production via the charged current weak interaction at the Tevatron and the LHC. $\sigma({\rm pb})$ |  $s$-channel |  $t$-channel | $Wt$
---|---|---|---
Tevatron ($\sqrt{s}=2.0$ TeV $p\bar{p}$) | $0.90\pm 5\%$ | $2.1\pm 5\%$ | $0.1\pm 10\%$
LHC ($\sqrt{s}=14$ TeV $pp$) | $10.6\pm 5\%$ | $250\pm 5\%$ | $75\pm 10\%$

####  II.2.3 Top quark and Higgs associated production

Of fundamental importance is the measurement of the top-quark Yukawa coupling.
The direct probe to it at the LHC is via the processes Marciano:1991qq

$q\bar{q},\ gg\to t\bar{t}H.$ (8)

The cross section has been calculated to the next-to-leading-order (NLO) in
QCD Beenakker:2001rj ; Dawson:2003zu  and the numerics are given in Table 4.
The cross section ranges are estimated from the uncertainty of the QCD scale.

Table 4: Total cross section at the NLO in QCD for top-quark and Higgs associated production at the LHC Dawson:2003zu .  $m_{H}$ (GeV) | 120 | 150 | 180
---|---|---|---
$\sigma$ (fb) | 634$-$719 | 334$-$381 | 194$-$222

The production rate at the LHC seems quite feasible for the signal
observation. It was claimed Desch:2004kf  that a $15\%$ accuracy for the
Yukawa coupling measurement may be achievable with a luminosity of 300 fb-1.
Indeed, the decay channel $H\to\gamma\gamma$ should be useful for the search
and study in the mass range of $100<m_{H}<150$ GeV unknown:1999fr ;
Zhou:1993at . However, the potentially large backgounds and the complex event
topology, in particular the demand on the detector performance, make the study
of the leading decay $H\to b\bar{b}$ very challenging Benedetti:2007sn .

##  III New Physics in Top-quark Decay

The high production rate for the top quarks at the LHC provides a great
opportunity to seek out top-quark rare decays and search for new physics
Beyond the Standard Model (BSM). Given the annual yield of 80 million
$t\bar{t}$ events plus $34$ million single-top events, one may hope to search
for rare decays with a branching fraction as small as $10^{-6}$.

###  III.1 Charged Current Decay: BSM

The most prominent examples for top-quark decay beyond the SM via charged-
currents may be the charged Higgs in SUSY or with an extended Higgs sector,
and charged technicolor particles

$t\to H^{+}b,\ \ \pi^{+}_{T}b.$ (9)

Experimental searches have been conducted at the Tevatron Abazov:2001md , and
some simulations are performed for the LHC as well Hashemi:2006qg ;
Quadt:2006jk . It is obvious that as long as those channels are kinematically
accessible and have a sizable branching fraction, the observation should be
straightforward. In fact, the top decay to a charged Higgs may well be the
leading channel for $H^{\pm}$ production.

More subtle new physics scenarios may not show up with the above easy signals.
It may be desirable to take a phenomenological approach to parameterize the
top-quark interactions beyond the SM gordy ; Tait:2000sh , and experimentally
search for the deviations from the SM. Those “anomalous couplings” can be
determined in a given theoretical framework, either from loop-induced
processes or from a new flavor structure. One can write the interaction terms
as

$\displaystyle{\cal L}_{CC}={g\over\sqrt{2}}\left(\
\bar{t}(1+\delta_{L})\gamma^{\mu}P_{L}qW^{-}_{\mu}+\bar{t}\delta_{R}\gamma^{\mu}P_{R}qW^{-}_{\mu}\right)+h.c.$
(10)

The expected accuracy of the measurements on $\delta_{L,R}$ is about $1\%$
Tait:2000sh ; Quadt:2006jk , thus testing the top-quark chiral coupling.

###  III.2 Neutral Current Decay: BSM

Although there are no Flavor-Changing Neutral Currents (FCNC) at tree level in
the SM, theories beyond the SM quite often have new flavor structure, most
notably for SUSY and technicolor models. New symmetries or some alignment
mechanisms will have to be utilized in order to avoid excessive FCNC. It is
nevertheless prudent to keep in mind the possible new decay modes of the top
quark such as the SUSY decay channel

$t\to\tilde{t}\tilde{\chi}^{0}.$ (11)

Generically, FCNCs can always be generated at loop level. It has been shown
that the interesting decay modes

$t\to Zc,\ \ Hc,\ \ \gamma c,\ \ gc$ (12)

are highly suppressed Eilam:1990zc ; Cao:2007dk  with branching fractions
typically $10^{-13}-10^{-10}$ in the SM, and $10^{-7}-10^{-5}$ in the MSSM. It
has been shown that the branching fractions can be enhanced significantly in
theories beyond the SM and MSSM, reaching above $10^{-5}$ and even as high as
$1\%$ AguilarSaavedra:2004wm .

One may again take the effective operator approach to parameterize the
interactions. After the electroweak symmetry breaking, one can write them as
Peccei:1989kr ; Han:1998tp ; Han:1996ep

$\displaystyle{\cal L}_{NC}$ $\displaystyle=$ $\displaystyle{g\over
2\cos\theta_{w}}\sum_{\tau=\pm,q=c,u}\kappa_{\tau}\bar{t}\gamma^{\mu}P_{\tau}qZ_{\mu}+h.c.$
(13) $\displaystyle+$ $\displaystyle
g_{s}\sum_{q=c,u}{\kappa^{g}_{q}\over\Lambda}\bar{t}\sigma^{\mu\nu}T^{a}tG_{\mu\nu}^{a}+eQ_{t}\sum_{q=c,u}{\kappa^{\gamma}_{q}\over\Lambda}\bar{t}\sigma^{\mu\nu}tA_{\mu\nu}+h.c.$
(14)

The sensitivities for the anomalous couplings have been studied at the LHC by
the ATLAS Collaboration Carvalho:2007yi , as listed in Table 5

Table 5: $95\%$ C.L. sensitivity of the branching fractions for the top-quark decays via FCNC couplings at the LHC Carvalho:2007yi .  Channel | 10 $\rm fb^{-1}$ | 100 $\rm fb^{-1}$
---|---|---
$t\to Zq$ | $3.1\times 10^{-4}$ | $6.1\times 10^{-5}$
$t\to\gamma q$ | $4.1\times 10^{-5}$ | $1.2\times 10^{-5}$
$t\to gq$ | $1.3\times 10^{-3}$ | $4.2\times 10^{-4}$

##  IV Top Quarks in Resonant Production

The most striking signal of new physics in the top-quark sector is the
resonant production via a heavy intermediate state $X$. With some proper
treatment to identify the top decay products, it is possible to reconstruct
the resonant kinematics. One may thus envision fully exploring its properties
in the c.m. frame.

###  IV.1 $X\to t\bar{t},\ t\bar{b}$

Immediate examples of the resonant states include Higgs bosons He:1998ie , new
gauge bosons Agashe:2007ki , Kaluza-Klein excitations of gluons Lillie:2007ve
and gravitons Fitzpatrick:2007qr , Technicolor-like dynamical states
Hill:2002ap ; Quadt:2006jk ; Choudhury:2007ux  etc.

The signal can be generically written as

$\displaystyle\sigma(pp\to X\to t\bar{t})$ $\displaystyle=$
$\displaystyle\sum_{ij}\int
dx_{1}dx_{2}f_{i}(M_{X}^{2},x_{1})f_{j}(M_{X}^{2},x_{2})$ (15)
$\displaystyle\times$ $\displaystyle{4\pi^{2}(2J+1)\over s}{\Gamma(X\to
ij)B(X\to t\bar{t})\over M_{X}}.$

Thus the observation of this class of signals depends on the branching
fraction of $X\to t\bar{t}$ as well as its coupling to the initial state
partons. Figure 4 quantifies the observability for a bosonic resonance (spin
0,1,2) for a mass up to 2 TeV at the LHC Barger:2006hm  via $q\bar{q},gg\to
X\to t\bar{t}$. The vertical axis gives the normalization factors ($\omega$)
for the cross section rates needed to reach a $5\sigma$ signal with a
luminosity of 10 fb-1. The normalization $\omega=1$ defines the benchmark for
the spin 0, 1 and 2 resonances. They correspond to the SM-like Higgs boson, a
$Z^{\prime}$ with electroweak coupling strength and left (L) or right (R)
chiral couplings to SM fermions, and the Randall-Sundrum graviton $\tilde{h}$
with the couplings scaled with a cutoff scale as $\Lambda^{-1}$ for
$\tilde{h}q\bar{q}$, and $(\Lambda\ln(M^{*}_{pl}/\Lambda))^{-1}$ for
$\tilde{h}gg$, respectively. We see that a $Z^{\prime}$ or a graviton should
be easy to observe, but a Higgs-like broad scalar will be difficult to
identify in the $t\bar{t}$ channel.

Figure 4: Normalization factor versus the resonance mass for the scalar
(dashed) with a width-mass ratio of $20\%$, vector (dot-dashed) with 5%, and
graviton (solid) 2%, respectively. The region above each curve represents
values of $\omega$ that give 5$\sigma$ or greater statistical significance
with 10 fb-1 integrated luminosity.

It is of critical importance to reconstruct the c.m. frame of the resonant
particle, where the fundamental properties of the particle can be best
studied. It was demonstrated Barger:2006hm  that with the semi-leptonic decays
of the two top quarks, one can effectively reconstruct the events in the c.m.
frame. This relies on using the $M_{W}$ constraint to determine the missing
neutrino momentum, while it is necessary to also make use of $m_{t}$ to break
the two-fold ambiguity for two possible $p_{z}(\nu)$ solutions. Parity and CP
asymmetries Atwood:2000tu  can be studied.

Top-quark pair events at the high invariant mass are obviously important to
search for and study new physics. In this new territory there comes a new
complication: When the top quark is very energetic, $\gamma=E/m_{t}\sim 10$,
its decay products may be too collimated to be individually resolved by the
detector $-$ recall that the granularity of the hadronic calorimeter at the
LHC is roughly $\Delta\eta\times\Delta\phi\sim 0.1\times 0.1$. This is a
generic problem relevant to any fast-moving top quarks from heavy particle
decays Lillie:2007ve ; Barger:2006hm ; Skiba:2007fw  (see the next sections).
The interesting questions to be addressed may include:

  * •

To what extent can we tell a “fat top-jet” from a massive QCD jet due to
showering?

  * •

To what extent can we tell a “fat $W$-jet” from a massive QCD jet?

  * •

Can we make use of a non-isolated lepton inside the top-jet ($b\ell\nu$) for
the top-quark identification and reconstruction?

  * •

Can we do $b$-tagging for the highly boosted top events?

These practical issues would become critical to understand the events and thus
for new physics searches. Detailed studies including the detector effects will
be needed to reach quantitative conclusions.

###  IV.2 $T\to tZ,\ tH,\ bW$

In many theories beyond the SM, there is a top-quark partner. These are
commonly motivated by the “naturalness” argument, the need to cancel the
quadratic divergence in the Higgs mass radiative correction, most severely
from the top-quark loop. Besides the scalar top quark in SUSY, the most
notable example is the Little Higgs theory Schmaltz:2005ky . If there is no
discrete symmetry, the top partner $T$ will decay to SM particles in the final
state, leading to fully a reconstructable fermionic resonance.

Figure 5: Production of the top-quark partner $T$ in pair and singly at the
LHC versus its mass. The Yukawa coupling ratio $\lambda_{1}/\lambda_{2}$ has
been taken to be 2 (upper dotted curve) 1 (solid) and 1/2 (lower dotted),
respectively. The $T\bar{T}$ pair production via QCD includes an NLO
$K$-factor (dashed curve).

It was pointed out Han:2003wu  that the single $T$ production via the weak
charged-current may surpass the pair production via the QCD interaction due to
the longitudinal gauge boson enhancement for the former and the phase space
suppression for the latter. This is shown in Fig. 5. Subsequent simulations
Azuelos:2004dm  performed by the ATLAS collaboration demonstrated the clear
observability for the signals above the backgrounds at the LHC for $T\to tZ,\
bW$ with a mass $M_{T}=1$ TeV, as seen in Fig. 6.

Figure 6: Observability for the decays (a) $T\to tZ$ and (b) $T\to bW$ at the
ATLAS Azuelos:2004dm .

##  V Top-rich Events for New Physics

Although the top-quark partner is strongly motivated for a natural electroweak
theory, it often results in excessively large corrections to the low energy
electroweak observables. In order to better fit the low energy measurements, a
discrete symmetry is often introduced, such as the R-parity in SUSY, KK-parity
in UED, and T-parity in LH Cheng:2003ju . The immediate consequence for
collider phenomenology is the appearance of a new stable particle that may
provide the cold dark matter candidate, and results in missing energy in
collider experiments.222Alternatively, the breaking of the R-parity
Barbier:2004ez  or the T-parity Hill:2007nz  would lead to different collider
phenomenology Barger:2007df .

###  V.1 $T\bar{T}$ pair production

The top partner has similar quantum numbers to the top quark, and thus is
commonly assigned as a color triplet. This leads to their production in QCD

$q\bar{q},\ gg\to T\bar{T}.$ (16)

The production cross section is shown in Fig. 7 for both spin-0 and spin-1/2
top partners. Although there is a difference of a factor of 8 or so (4 from
spin state counting and the rest from threshold effects) in the cross
sections, it is still challenging to tell a scalar and a fermionic partner
apart us ; Cheng:2005as ; Meade:2006dw  due to the lack of definitive
features.

Due to the additional discrete symmetry, the top partner cannot decay to a SM
particle alone. Consequently, $T\to tA^{0}$, leading to $t\bar{t}$ pair
production plus large mixing energy. The crucial parameter to characterize the
kinematical features is the mass difference $\Delta M_{TA}=m_{T}-m_{A}$. For
$\Delta M_{TA}\gg m_{t}$, the top quark as a decay product will be energetic
and qualitatively different from the SM background. But if $\Delta
M_{TA}\approx m_{t}$, then the two will have very little difference, making
the signal difficult to separate out. Depending on the top-quark decay, we
present two classes of signals.

Figure 7: Leading order total cross section for the top partner $T\bar{T}$
production at the LHC versus its mass us . Both spin-0 and spin-1/2 top
partners are included. The QCD $t\bar{t}$ and the SM $t\bar{t}Z$ backgrounds
are indicated by the horizontal lines.

####  V.1.1 $t\bar{t}$ pure hadronic decay

For both $t\bar{t}$ to decay hadronically Meade:2006dw ; Matsumoto:2006ws ,
the signal will be 6 jets plus missing energy. While it has the largest decay
rate, the backgrounds would be substantial as well. With judicious acceptance
cuts, the signal observability for $\Delta M_{TA}>200$ GeV was established, as
seen in Fig. 8. Possible measurements of the absolute mass scale and its spin
of the top partner were considered us ; Meade:2006dw , but the determination
remains difficult.

Figure 8: Contour in $m_{\tilde{t}}-m_{N}$ for $\tilde{t}\to tN$ for the
statistical significance of a scalar $\tilde{t}$ at the LHC with an integrated
luminosity of 100 fb-1. Purely hadronic decays are considered.

####  V.1.2 $t\bar{t}$ semi-leptonic decay

If one of the $t\bar{t}$ decays hadronically and the other decays
leptonically, the signal may be cleaner. It turns out that if the mass
difference $\Delta M_{TA}$ is sizable, then requiring large missing transverse
energy may be sufficient to suppress the background. However, if $\Delta
M_{TA}\sim m_{t}$, then the $E\\!\\!\\!\\!/_{T}$ for the signal is not much
different from the background. On the other hand, the fact that the $t\bar{t}$
kinematics can be fully reconstructed in the SM implies that the
reconstruction for the signal events would be distinctive due to the large
missing mass. Indeed, the reconstructed $m^{r}_{t}$ based on the
$E\\!\\!\\!\\!/_{T}$ will be far away from the true $m_{t}$, and mostly result
in an unphysical value. If we impose

$|m_{t}-m_{t}^{r}|>110\ {\rm GeV},$ (17)

we can reach optimal signal identification. The summary plot for the
statistical significance (the number of $\sigma$) is given in Fig. 9 at the
LHC with an integrated luminosity of 100 fb-1, where the left panel is for a
fermionic $T$, and the right is a scalar $\tilde{t}$, both decaying to $t+$ a
missing particle.

Figure 9: Contour in $m_{T}-m_{A}$ for $T\to tA$ for the statistical
significance at the LHC with an integrated luminosity of 100 fb-1. Left panel
is for a fermionic $T$, and the right is a scalar $\tilde{t}$, both decaying
to a top plus a missing particle.

###  V.2 Exotic top signatures

Searching for exotic events related to the top quark can be rewarding. First,
there exists a variety of natural electroweak models with distinctive top
partners that should not be overlooked for collider phenomenology. Second,
potentially large couplings of the top quark to new physics may result in
multiple top quarks from new particle decays. Finally, the exotic events have
less SM background contamination, and thus may stand out for discovery even at
the early phase of the LHC. We briefly list a few recent examples.

  * •

Multiple top quarks and $b$-quarks in the final state may help to search for
new heavy particles in the electroweak sector and can be distinctive from the
SM backgrounds Han:2004zh .

  * •

Heavy top partners and other KK fermions in the RS model may lead to unique
top-quark and $W$-boson signatures Contino:2008hi .

  * •

New exotic colored states may predominantly couple to heavy quarks and thus
lead to multiple top quarks in the final state Gerbush:2007fe .

  * •

Composite models for the right-handed top-quark may lead to $t\bar{t}t\bar{t}$
signals at the LHC Lillie:2007hd .

  * •

Like-sign top quark pairs may indicate new dynamics Cao:2004wd .

##  VI Summary and Outlook

The LHC will be a true top-quark factory. With 80 million top-quark pairs plus
34 million single tops produced annually at the designed high luminosity, the
properties of this particle will be studied to a great accuracy and the deep
questions related to the top quark at the Terascale will be explored to an
unprecedented level. Theoretical arguments indicate that it is highly likely
that new physics associated with the top quark beyond the SM will show up at
the LHC. This article only touches upon the surface of the rich top quark
physics, and is focused on possible new physics beyond the SM in the top-quark
sector. The layout of this article has been largely motivated by experimental
signatures for the LHC. Interesting signatures covered here include

  * •

Rare decays of the top quark to new light states, or to SM particles via the
charged and neutral currents through virtual effects of new physics.

  * •

Top quark pair production via the decay of a new heavy resonance, resulting in
fully reconstructable kinematics for detailed studies.

  * •

Top quark pair production via the decay of pairly produced top partners,
usually associated with two other missing particles, making the signal
identification and the property studies challenging.

  * •

Multiple top quarks, $b$ quarks, and $W^{\pm}$’s coming from theories of
electroweak symmetry breaking or an extended top-quark sector.

The physics associated with top quarks is rich, far-reaching, and exciting. It
opens up golden opportunities for new physics searches, while brings in new
challenges as well. It should be of high priority in the LHC program for both
theorists and experimentalists.

## Acknowledgments

I thank Gordy Kane and Aaron Pierce for inviting me to write on this subject,
which I consider a very important and exciting part of the LHC physics
program. I would also like to thank Vernon Barger, Tim Tait and Lian-Tao Wang
for reading and commenting on the draft. This work was supported in part by
the US DOE under contract No. DE-FG02-95ER40896 and in part by the Wisconsin
Alumni Research Foundation. The work at the KITP was supported by the National
Science Foundation under Grant No. PHY05-51164.

## References

  * (1) For a review on new strong dynamics related to the top quark, see e.g., C. T. Hill and E. H. Simmons, Strong dynamics and electroweak symmetry breaking, _Phys. Rept._ 381, 235 (2003) [Erratum-ibid. 390, 553 (2004)] [arXiv:hep-ph/0203079]; and references therein.
  * (2) For a general discussion on the “naturalness”, see e.g., G. F. Giudice, Naturally Speaking: The Naturalness Criterion and Physics at the LHC, arXiv:0801.2562 [hep-ph].
  * (3) For recent reviews on top-quark physics, see, e.g., D. Chakraborty, J. Konigsberg and D. L. Rainwater, Review of top quark physics, Ann. Rev. Nucl. Part. Sci. 53, 301 (2003) [arXiv:hep-ph/0303092]; A. Quadt, Top quark physics at hadron colliders, _Eur. Phys. J. C_ 48 (2006) 835, and references therein.
  * (4) Particle Data Group, W.-M. Yao et al., _J. Phys. G_ 33, 1 (2006).
  * (5) E. Brubaker et al. [Tevatron Electroweak Working Group], Combination of CDF and D0 Results on the Mass of the Top Quark, arXiv:hep-ex/0608032.
  * (6) A. I. Etienvre, Top mass measurement at LHC, PoS TOP2006 (2006) 023.
  * (7) G. L. Kane, G. A. Ladinsky and C. P. Yuan, Using the top quark for testing standard model polarization and CP predictions, _Phys. Rev. D_ 45, 124 (1992).
  * (8) U. Baur, M. Buice and L. H. Orr, Direct measurement of the top quark charge at hadron colliders, _Phys. Rev. D_ 64, 094019 (2001) [arXiv:hep-ph/0106341]; U. Baur, A. Juste, L. H. Orr and D. Rainwater, Probing electroweak top quark couplings at hadron colliders, _Phys. Rev. D_ 71, 054013 (2005) [arXiv:hep-ph/0412021].
  * (9) M. Jezabek and J. H. Kuhn, QCD Corrections to Semileptonic Decays of Heavy Quarks, _Nucl. Phys. B_ 314, 1 (1989).
  * (10) I. I. Y. Bigi, Y. L. Dokshitzer, V. A. Khoze, J. H. Kuhn and P. M. Zerwas, Production and Decay Properties of Ultraheavy Quarks, _Phys. Lett. B_ 181, 157 (1986).
  * (11) S. Willenbrock, The standard model and the top quark, arXiv:hep-ph/0211067.
  * (12) P. Nason, S. Dawson and R. K. Ellis, The Total Cross-Section for the Production of Heavy Quarks in Hadronic Collisions, _Nucl. Phys. B_ 303, 607 (1988); W. Beenakker, H. Kuijf, W. L. van Neerven and J. Smith, QCD Corrections to Heavy Quark Production in p anti-p Collisions, _Phys. Rev. D_ 40, 54 (1989); N. Kidonakis and R. Vogt, Next-to-next-to-leading order soft-gluon corrections in top quark hadroproduction, _Phys. Rev. D_ 68, 114014 (2003) [arXiv:hep-ph/0308222].
  * (13) E. Laenen, J. Smith and W. L. van Neerven, Top Quark Production Cross-Section, _Phys. Lett. B_ 321, 254 (1994) [arXiv:hep-ph/9310233]; E. L. Berger and H. Contopanagos, The Perturbative Resummed Series for Top Quark Production in Hadron Reactions, _Phys. Rev. D_ 54, 3085 (1996) [arXiv:hep-ph/9603326];
  * (14) R. Bonciani, S. Catani, M. L. Mangano and P. Nason, NLL resummation of the heavy-quark hadroproduction cross-section, _Nucl. Phys. B_ 529, 424 (1998) [arXiv:hep-ph/9801375]; and references therein.
  * (15) J. H. Kuhn and G. Rodrigo, Charge asymmetry in hadroproduction of heavy quarks, _Phys. Rev. Lett._ 81, 49 (1998) [arXiv:hep-ph/9802268].
  * (16) W. Bernreuther, M. Fuecker and Z. G. Si, Mixed QCD and weak corrections to top quark pair production at hadron colliders, _Phys. Lett. B_ 633, 54 (2006) [arXiv:hep-ph/0508091]; W. Bernreuther, M. Fuecker and Z. G. Si, Weak interaction corrections to hadronic top quark pair production, _Phys. Rev. D_ 74, 113005 (2006) [arXiv:hep-ph/0610334].
  * (17) S. S. Willenbrock and D. A. Dicus, Production Of Heavy Quarks From $W$-Gluon Fusion,  _Phys. Rev. D_ 34, 155 (1986); C. P. Yuan, A New Method to Detect a Heavy Top Quark at the Tevatron, _Phys. Rev. D_ 41, 42 (1990); T. Stelzer, Z. Sullivan and S. Willenbrock, Single top quark production at hadron colliders, _Phys. Rev. D_ 58, 094021 (1998) [arXiv:hep-ph/9807340]; Z. Sullivan, Understanding single-top-quark production and jets at hadron colliders, _Phys. Rev. D_ 70, 114012 (2004) [arXiv:hep-ph/0408049].
  * (18) V. M. Abazov et al. [D0 Collaboration], Evidence for production of single top quarks and first direct measurement of $|V(tb)|$, _Phys. Rev. Lett._ 98, 181802 (2007) [arXiv:hep-ex/0612052].
  * (19) Q. H. Cao, J. Wudka and C. P. Yuan, Search for New Physics via Single Top Production at the LHC, _Phys. Lett. B_ 658, 50 (2007) [arXiv:0704.2809 [hep-ph]].
  * (20) M. C. Smith and S. Willenbrock, QCD and Yukawa Corrections to Single-Top-Quark Production via $q\bar{q}\to t\bar{b}$,  _Phys. Rev. D_ 54, 6696 (1996) [arXiv:hep-ph/9604223].
  * (21) T. Stelzer, Z. Sullivan and S. Willenbrock, Single-top-quark production via $W$-gluon fusion at next-to-leading order, _Phys. Rev. D_ 56, 5919 (1997) [arXiv:hep-ph/9705398].
  * (22) S. Zhu, Next-To-Leading Order QCD Corrections to $bg\to tW^{-}$ at the CERN Large Hadron Collider,  _Phys. Lett. B_ 524, 283 (2002) [Erratum-ibid. B 537, 351 (2002)].
  * (23) Q. H. Cao, R. Schwienhorst and C. P. Yuan, Next-to-leading order corrections to single top quark production and decay at Tevatron. I: s-channel process, _Phys. Rev. D_ 71, 054023 (2005) [arXiv:hep-ph/0409040]; N. Kidonakis, Single top production at the Tevatron: Threshold resummation and finite-order soft gluon corrections, _Phys. Rev. D_ 74, 114012 (2006) [arXiv:hep-ph/0609287].
  * (24) Q. H. Cao and C. P. Yuan, Single top quark production and decay at next-to-leading order in hadron collision, _Phys. Rev. D_ 71, 054022 (2005) [arXiv:hep-ph/0408180]; N. Kidonakis, Higher-order soft gluon corrections in single top quark production at the LHC, _Phys. Rev. D_ 75, 071501 (2007) [arXiv:hep-ph/0701080].
  * (25) W. J. Marciano and F. E. Paige, Phys. Rev. Lett. 66, 2433 (1991); J. F. Gunion, Phys. Lett. B 261, 510 (1991).
  * (26) W. Beenakker, S. Dittmaier, M. Kramer, B. Plumper, M. Spira and P. M. Zerwas, Higgs radiation off top quarks at the Tevatron and the LHC, _Phys. Rev. Lett._ 87, 201805 (2001) [arXiv:hep-ph/0107081]; W. Beenakker, S. Dittmaier, M. Kramer, B. Plumper, M. Spira and P. M. Zerwas, NLO QCD corrections to t anti-t H production in hadron collisions, _Nucl. Phys. B_ 653, 151 (2003) [arXiv:hep-ph/0211352].
  * (27) S. Dawson, L. H. Orr, L. Reina and D. Wackeroth, Associated top quark Higgs boson production at the LHC, _Phys. Rev. D_ 67, 071503 (2003) [arXiv:hep-ph/0211438]; S. Dawson, C. Jackson, L. H. Orr, L. Reina and D. Wackeroth, Associated Higgs production with top quarks at the Large Hadron Collider: NLO QCD corrections, _Phys. Rev. D_ 68, 034022 (2003) [arXiv:hep-ph/0305087].
  * (28) K. Desch and M. Schumacher, Model independent determination of the top Yukawa coupling from LHC and LC, _Eur. Phys. J. C_ 46, 527 (2006) [arXiv:hep-ph/0407159].
  * (29) ALTAS TDR: ATLAS detector and physics performance. Technical design report. Vol. 2, CERN-LHCC-99-15; CMS TDR: CMS Physics: Technical Design Report V.2: Physics Performance, CERN-LHCC-2006-021.
  * (30) H. Y. Zhou and Y. P. Kuang, Difficulties of detecting the intermediate mass Higgs boson in the associate production channel p p $\to t\bar{t}HX$, Phys. Rev. D 47, 3680 (1993).
  * (31) D. Benedetti et al., Observability Of Higgs Produced With Top Quarks And Decaying To Bottom Quarks, _J. Phys. G_ 34 (2007) N221.
  * (32) V. M. Abazov et al. [D0 Collaboration], Direct search for charged Higgs bosons in decays of top quarks, _Phys. Rev. Lett._ 88, 151803 (2002) [arXiv:hep-ex/0102039].
  * (33) M. Hashemi, Search for the light charged Higgs in CMS, In the Proceedings of IPM School and Conference on Lepton and Hadron Physics (IPM-LHP06), Tehran, Iran, 15-20 May 2006, pp 0018 [arXiv:hep-ph/0612104].
  * (34) T. Tait and C. P. Yuan, Single top quark production as a window to physics beyond the Standard Model, _Phys. Rev. D_ 63, 014018 (2001) [arXiv:hep-ph/0007298]; C. R. Chen, F. Larios and C. P. Yuan, General analysis of single top production and W helicity in top decay, _Phys. Lett. B_ 631, 126 (2005), [arXiv:hep-ph/0503040].
  * (35) G. Eilam, J. L. Hewett and A. Soni, Rare decays of the top quark in the standard and two Higgs doublet models, _Phys. Rev. D_ 44, 1473 (1991) [Erratum-ibid. D 59, 039901 (1999)]; B. Mele, S. Petrarca and A. Soddu, A new evaluation of the t $\rightarrow$ c H decay width in the standard model, _Phys. Lett. B_ 435, 401 (1998) [arXiv:hep-ph/9805498].
  * (36) J. J. Cao, G. Eilam, M. Frank, K. Hikasa, G. L. Liu, I. Turan and J. M. Yang, SUSY-induced FCNC top-quark processes at the Large Hadron Collider, _Phys. Rev. D_ 75, 075021 (2007) [arXiv:hep-ph/0702264].
  * (37) J. L. Diaz-Cruz, H. J. He and C. P. Yuan, Soft SUSY breaking, stop-scharm mixing and Higgs signatures, _Phys. Lett. B_ 530, 179 (2002) [arXiv:hep-ph/0103178]; J. A. Aguilar-Saavedra, Top flavour-changing neutral interactions: Theoretical expectations and experimental detection, _Acta Phys. Polon. B_ 35, 2695 (2004) [arXiv:hep-ph/0409342]; G. Eilam, A. Gemintern, T. Han, J. M. Yang and X. Zhang, Top quark rare decay t $\rightarrow$ c h in R-parity-violating SUSY, _Phys. Lett. B_ 510, 227 (2001) [arXiv:hep-ph/0102037]; F. Larios, R. Martinez and M. A. Perez, New physics effects in the flavor-changing neutral couplings of the top quark, _Int. J. Mod. Phys. A_ 21, 3473 (2006) [arXiv:hep-ph/0605003]; K. Agashe, G. Perez and A. Soni, Collider signals of top quark flavor violation from a warped extra dimension, _Phys. Rev. D_ 75, 015002 (2007) [arXiv:hep-ph/0606293]; For a review on FCNC processes of top decay, see e.g., J. M. Yang, arXiv:0801.0210 [hep-ph].
  * (38) R. D. Peccei and X. Zhang, Dynamical Symmetry Breaking and Universality Breakdown, _Nucl. Phys. B_ 337, 269 (1990); T. Han, R. D. Peccei and X. Zhang, Top Quark Decay Via Flavor Changing Neutral Currents At Hadron Colliders, _Nucl. Phys. B_ 454, 527 (1995) [arXiv:hep-ph/9506461].
  * (39) T. Han, M. Hosch, K. Whisnant, B. L. Young and X. Zhang, Single top quark production via FCNC couplings at hadron colliders, _Phys. Rev. D_ 58, 073008 (1998) [arXiv:hep-ph/9806486].
  * (40) T. Han, K. Whisnant, B. L. Young and X. Zhang, Top-Quark Decay Via the Anomalous Coupling $\bar{t}c\gamma$ at Hadron Colliders, _Phys. Rev. D_ 55, 7241 (1997) [arXiv:hep-ph/9603247].
  * (41) J. Carvalho et al. [ATLAS Collaboration], Study of ATLAS sensitivity to FCNC top decays, _Eur. Phys. J. C_ 52, 999 (2007) [arXiv:0712.1127 [hep-ex].
  * (42) H. J. He and C. P. Yuan, New method for detecting charged (pseudo-)scalars at colliders, _Phys. Rev. Lett._ 83, 28 (1999) [arXiv:hep-ph/9810367]; C. Balazs, H. J. He and C. P. Yuan, QCD corrections to scalar production via heavy quark fusion at hadron colliders, _Phys. Rev. D_ 60, 114001 (1999) [arXiv:hep-ph/9812263].
  * (43) K. Agashe et al., LHC Signals for Warped Electroweak Neutral Gauge Bosons, _Phys. Rev. D_ 76, 115015 (2007) [arXiv:0709.0007 [hep-ph]].
  * (44) K. Agashe, A. Belyaev, T. Krupovnickas, G. Perez and J. Virzi, LHC signals from warped extra dimensions, _Phys. Rev. D_ 77, 015003 (2008) [arXiv:hep-ph/0612015]; B. Lillie, L. Randall and L. T. Wang, The Bulk RS KK-gluon at the LHC, _JHEP_ 0709, 074 (2007) [arXiv:hep-ph/0701166]; B. Lillie, J. Shu and T. M. P. Tait, Kaluza-Klein Gluons as a Diagnostic of Warped Models, _Phys. Rev. D_ 76, 115016 (2007) [arXiv:0706.3960 [hep-ph]].
  * (45) A. L. Fitzpatrick, J. Kaplan, L. Randall and L. T. Wang, Searching for the Kaluza-Klein graviton in bulk RS models, _JHEP_ 0709, 013 (2007) [arXiv:hep-ph/0701150].
  * (46) C. T. Hill and S. J. Parke, Top production: Sensitivity to new physics, _Phys. Rev. D_ 49, 4454 (1994) [arXiv:hep-ph/9312324]; C. X. Yue, H. Y. Zhou, Y. P. Kuang and G. R. Lu, $t\bar{t}$ production rates at the Tevatron and the LHC in topcolor-assisted multiscale technicolor models, _Phys. Rev. D_ 55, 5541 (1997) [arXiv:hep-ph/9608294]; T. Han, D. L. Rainwater and G. Valencia, TeV resonances in top physics at the LHC, _Phys. Rev. D_ 68, 015003 (2003) [arXiv:hep-ph/0301039]; D. Choudhury, R. M. Godbole, R. K. Singh and K. Wagh, Top production at the Tevatron / LHC and nonstandard, strongly interacting spin one particles, _Phys. Lett. B_ 657, 69 (2007) [arXiv:0705.1499 [hep-ph]].
  * (47) V. Barger, T. Han and D. G. E. Walker, Top Quark Pairs at High Invariant Mass - A Model-Independent Discriminator of New Physics at the LHC, _Phys. Rev. Lett._ 100, 031801 (2008) [arXiv:hep-ph/0612016].
  * (48) D. Atwood, S. Bar-Shalom, G. Eilam and A. Soni, CP violation in top physics, _Phys. Rept._ 347, 1 (2001) [arXiv:hep-ph/0006032]; G. Valencia and Y. Wang, New CP-odd observable in H $\rightarrow t\bar{t}$, _Phys. Rev. D_ 73, 053009 (2006) [arXiv:hep-ph/0512127].
  * (49) W. Skiba and D. Tucker-Smith, Using jet mass to discover vector quarks at the LHC, _Phys. Rev. D_ 75, 115010 (2007) [arXiv:hep-ph/0701247]; U. Baur and L. H. Orr, High $p_{T}$ Top Quarks at the Large Hadron Collider, _Phys. Rev. D_ 76, 094012 (2007) [arXiv:0707.2066 [hep-ph]]; R. Frederix and F. Maltoni, Top pair invariant mass distribution: a window on new physics, arXiv:0712.2355 [hep-ph].
  * (50) For a review, see e.g., M. Schmaltz and D. Tucker-Smith, Little Higgs review, _Ann. Rev. Nucl. Part. Sci._ 55, 229 (2005) [arXiv:hep-ph/0502182], and references therein.
  * (51) T. Han, H. E. Logan, B. McElrath and L. T. Wang, Phenomenology of the little Higgs model, _Phys. Rev. D_ 67, 095004 (2003) [arXiv:hep-ph/0301040]; M. Perelstein, M. E. Peskin and A. Pierce, Top quarks and electroweak symmetry breaking in little Higgs models, _Phys. Rev. D_ 69, 075002 (2004) [arXiv:hep-ph/0310039].
  * (52) G. Azuelos et al., Exploring little Higgs models with ATLAS at the LHC, _Eur. Phys. J. C_ 39S2, 13 (2005) [arXiv:hep-ph/0402037].
  * (53) H.-C. Cheng and I. Low, TeV symmetry and the little hierarchy problem, _JHEP_ 0309, 051 (2003) [arXiv:hep-ph/0308199].
  * (54) For a review, see e.g., R. Barbier et al., R-parity violating supersymmetry, _Phys. Rept._ 420, 1 (2005) [arXiv:hep-ph/0406039], and references therein.
  * (55) C.T. Hill and R.J. Hill, Topological Physics of Little Higgs Bosons, _Phys. Rev. D_ 75, 115009 (2007) [arXiv:hep-ph/0701044]; C.T. Hill and R.J. Hill, $T^{-}$ parity violation by anomalies, _Phys. Rev. D_ 76, 115014 (2007) [arXiv:0705.0697 [hep-ph]].
  * (56) V. Barger, W.-Y. Keung and Y. Gao, T-Anomaly Induced LHC Signals, _Phys. Lett. B_ 655, 228 (2007) [arXiv:0707.3648 [hep-ph]].
  * (57) T. Han, R. Mahbubani, D. Walker and L.-T. Wang, Top Quark Pair plus Large Missing Energy at the LHC, arXiv:0803.3820 [hep-ph].
  * (58) P. Meade and M. Reece, Top partners at the LHC: Spin and mass measurement, _Phys. Rev. D_ 74, 015010 (2006) [arXiv:hep-ph/0601124].
  * (59) H. C. Cheng, I. Low and L. T. Wang, Top partners in little Higgs theories with T-parity, _Phys. Rev. D_ 74, 055001 (2006) [arXiv:hep-ph/0510225].
  * (60) S. Matsumoto, M. M. Nojiri and D. Nomura, Hunting for the top partner in the littlest Higgs model with T-parity at the LHC, _Phys. Rev. D_ 75, 055006 (2007) [arXiv:hep-ph/0612249].
  * (61) T. Han, G. Valencia and Y. Wang, Hadron collider signatures for new interactions of top and bottom quarks, _Phys. Rev. D_ 70, 034002 (2004) [arXiv:hep-ph/0405055].
  * (62) C. Dennis, M. Karagoz Unel, G. Servant and J. Tseng, Multi-W events at LHC from a warped extra dimension with custodial symmetry, arXiv:hep-ph/0701158; M. Carena, A. D. Medina, B. Panes, N. R. Shah and C. E. M. Wagner, Collider Phenomenology of Gauge-Higgs Unification Scenarios in Warped Extra Dimensions, arXiv:0712.0095 [hep-ph]; R. Contino and G. Servant, Discovering the top partners at the LHC using same-sign dilepton final states, arXiv:0801.1679 [hep-ph].
  * (63) B. A. Dobrescu, K. Kong and R. Mahbubani, Massive color-octet bosons and pairs of resonances at hadron colliders, arXiv:0709.2378 [hep-ph]; M. Gerbush, T. J. Khoo, D. J. Phalen, A. Pierce and D. Tucker-Smith, Color-octet scalars at the LHC, arXiv:0710.3133 [hep-ph].
  * (64) B. Lillie, J. Shu and T. M. P. Tait, Top Compositeness at the Tevatron and LHC, arXiv:0712.3057 [hep-ph].
  * (65) F. Larios and F. Penunuri, FCNC production of same sign top quark pairs at the LHC, _J. Phys. G_ 30, 895 (2004) [arXiv:hep-ph/0311056]; J. J. Cao, G. L. Liu and J. M. Yang, Probing topcolor-assisted technicolor from like-sign top pair production at LHC, _Phys. Rev. D_ 70, 114035 (2004) [arXiv:hep-ph/0409334]; S. Kraml and A. R. Raklev, Same-sign top quarks as signature of light stops at the LHC, _Phys. Rev. D_ 73, 075002 (2006) [arXiv:hep-ph/0512284].