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DYNAMICAL ELECTROWEAK SYMMETRY BREAKING AT TEVATRON
RUN II AND LHC

By

Alexander S. Blum

A THESIS

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Physics and Astronomy

2005

ABSTRACT

DYNAMICAL ELECTROWEAK SYMMETRY BREAKING AT TEVATRON
RUN II AND LHC

By

Alexander Simon Blum

The Standard Model (SM) of particle physics uniﬁes the electromagnetic and the weak
force under an SU(2) x U(1) gauge group. The fact that these forces are observed
to be so different in strength and range is explained by spontaneous breaking of
this symmetry, induced by the nonzero vacuum expectation value of a scalar Higgs
ﬁeld. There is however no experimental evidence for the Higgs ﬁeld and there are also
theoretical difficulties. In one class of extensions of the SM designed to deal with these
problems, the electroweak symmetry is broken dynamically. This thesis provides a
framework in which SM Higgs searches at Tevatron Run II and at the Large Hadron
Collider (LHC) can be extended to new scalar or pseudoscalar states predicted in
dynamical models of electroweak symmetry breaking. These states can have enhanced
visibility in standard Higgs search channels, making them potentially discoverable at
Tevatron Run II and deﬁnitely visible at the LHC. I discuss the likely sizes of the
enhancements in the various search channels for each model and identify the model
features having the largest inﬂuence on the degree of enhancement. I suggest the mass
reaches of Higgs searches at Tevatron and LHC for these non-standard scalar states. I
compare signals for the non-standard scalars across models and also with expectations
in the SM and the Minimal Supersymmetric Model, another theory beyond the SM,

to show how one could start to identify which state has actually been found.

ACKNOWLEDGEMENTS

I would like to thank my advisor Professor Elizabeth Simmons, as well as Dr.
Alexander Belyaev and Professor Sekhar Chivukula for their constant input and sup—
port. I also would like to acknowledge a scholarship of the German National Academic

Foundation (Studienstiftung des deutschen Volkes).

iii

TABLE OF CONTENTS

LIST OF TABLES .................................................. v
LIST OF FIGURES ................................................ vi
1 Introduction ..................................................... 1
2 Higgs Searches and Enhancement Factors ........................ 3
3 Dynamical Electroweak Symmetry Breaking ..................... 5
' 3.1 General Remarks ............................. 5
3.2 Technicolor ................................ 5

4 Results For Each Model ......................................... 9
4.1 Technicolor ................................ 9
4.1.1 PNGB Production via Gluon Fusion .............. 9

4.1.2 Production via Bottom Quark Annihilation .......... 10

4.1.3 Decays ............................... 13

4.2 Top-Pious ................................. 14

5 Comparison and Interpretation .................................. 17
5.1 Technicolor vs SM ............................ 17
5.2 MSSM vs Technicolor ........................... 19
5.3 Top-Pion vs Heavy SM Higgs ...................... 22

6 Conclusions .............................. V ....................... 24
References .......................................................... 25

iv

LIST OF TABLES

Anomaly Factors for the models under study [23, 25, 30, 2, 3]

Calculated enhancement factors for production at the Tevatron and
LHC of a 130 GeV technipion via 99 alone, via b5 alone, and combined.
Note that the small enhancement in the b5 process slightly reduces the
total enhancement relative to that of gg alone ..............

Branching ratios of a technipion/Higgs of mass 130 GeV .......
Branching ratio of top-pion/Higgs of mass 220 GeV ..........

Enhancement Factors for 130 GeV technipions produced at the Teva-
tron, compared to production and decay of a SM Higgs Boson of the
same mass. The slight suppression of 5;“ due to the b-quark anni-
hilation channel has been included.The rightmost column shows the
cross-section (pb) for pp —> P —) am: at Tevatron Run II. .......

Enhancement Factors for 130 GeV technipions produced at the LHC,
compared to production and decay of a SM Higgs Boson of the same
mass. The slight suppression of ref,“ due to the b-quark annihila-
tion channel has been included.The rightmost column shows the cross-
section (pb) for pp —-> P —+ am: at the LHC ................

Enhancement Factors for 220 GeV top-pions produced at the Teva-
tron and the LHC, compared to production and decay of a SM Higgs
Boson of the same mass. The slight suppression of aged due to the
b—quark annihilation channel is negligible.The rightmost column shows
the cross-section (pb) for pp —> P —-> xx at Tevatron Run II. .....

10

13

17

19

23

LIST OF FIGURES

Total enhancement factor for each technicolor model plotted as a func-
tion of technipion mass and assuming the ﬁnal state is a tau (photon)
pair. The lowest curve is the enhancement factor required to make a
Higgs-like particle visible (50 discovery) in tau(photon)-pairs at Teva-
tron Run II with a total luminosity of 10 fb'1 [9], [38]. ........ 20

Total cross-section times branching ratio for each technicolor model
plotted as a function of technipion mass and assuming the ﬁnal state is
a tau (above) or 7 (below) pair at LHC. The lowest curve is the cross-
section times branching ratio required to make a Higgs-like particle
visible (5 a discovery, total luminosity given in brackets) in tau- or
7-pairs, respectively [10], [11]. ...................... 21

vi

1 Introduction

Even though the electromagnetic and weak forces have been uniﬁed under a single
SU(2) x U(1) gauge group, the origin of the breaking of this electroweak symmetry
(manifest in the massless photon as gauge particle of the electromagnetic force com-
pared to the massive W and Z Bosons of the weak force) remains unknown. While the
Standard Model (SM) of particle physics, which accomplishes the symmetry breaking
by predicting a scalar Higgs ﬁeld with nonzero vacuum expectation value, is consis-
tent with existing data, theoretical considerations show that this theory is only a
low-energy effective theory and must be supplanted by a more complete description
of the underlying physics at energies above those reached so far by experiment.

The CDF and D0 experiments at the Fermilab Tevatron are currently searching
for the Higgs boson of the Standard Model. The production cross-section and decay
branching fractions for this state have been predicted in great detail for the mass
range accessible to Tevatron Run 11. Search strategies have been carefully planned
and optimized.

However, if the Tevatron does ﬁnd evidence for a newuscalar state, it may not
necessarily be the SM Higgs. Many alternative models of electroweak symmetry
breaking have spectra that include new scalar or pseudoscalar states whose masses
could easily lie in the range to which Run II is sensitive. The new scalars tend to
have cross-sections and branching fractions that differ from those of the SM Higgs.
The potential exists for one of these scalars to be more visible in a standard search
than the SM Higgs would be.

In this paper we provide a framework in which one can extract the maximum
possible information about the origin of electroweak symmetry breaking from SM
Higgs searches at Tevatron Run II and CERN LHC.

The idea of using standard Higgs searches to place limits on new scalar states

associated with electroweak symmetry breaking beyond the standard model has been

applied to LEP results (see e.g. Refs. [1, 2, 3, 4, 5, 6, 7, 8]). The Tevatron and
the LHC can potentially access signiﬁcantly heavier scalars than those to which LEP
was sensitive, particularly in models of dynamical symmetry breaking. Reference [9]
has studied the potential of Tevatron Run II to search for the SM Higgs boson in
gg —) hSM ——> 77' and determined what enhancement of the rate would be needed
to make a non-standard Higgs boson, e.g. from the Minimal Supersymmetric Model
(MSSM), a popular extension of the SM, visible in this channel. Similar studies
have been done for LHC for 99 —+ hMSSM —> 7'7 [10] and for 99 —+ hSM -—> 77 [11]
processes.

My work builds on these results, considering an additional production mecha-
nism (b-quark annihilation), more decay channels (b5, WW, Z Z, and 77), and, most
importantly, shifting the focus from theories of Supersyrnmetry to models of Dynam-
ical Electroweak Symmetry Breaking (DEWSB), an extension of the Standard Model
mentioned brieﬂy in [9] and not at all in [10] and [11]. I discuss the likely sizes of
the enhancements in the various search channels for several different models and pin-
point the model features having the largest inﬂuence on the degree of enhancement. I
suggest the mass reach of the standard Higgs searches for each kind of non-standard
scalar state. I also compare the key signals for the non-standard scalars across models
and also with expectations in the SM and the MSSM, to show how one could start
to identify which state has actually been found.

In Section 2, I discuss Higgs searches and the enhancement factors needed to make
scalars of various masses visible. In Section 3, I talk about DEWSB in general and
show how to calculate elements of the enhancement factors in the various models. In
Section 4, I present my results for each model. In Section 5, I compare the different
models to one another and to the SM and MSSM. Section 6 holds my conclusions.

Part of this thesis will appear in a paper submitted for publication in June 2005
by Alexander Belyaev, R Sekhar Chivukula, Elizabeth H. Simmons and me [12].

2 Higgs Searches and Enhancement Factors

As mentioned in the Introduction, [9] studied the potential of Tevatron Run II to
augment its search for the SM Higgs boson by considering the process 99 ——) hSM ~+
7+7‘. While this channel would not sufﬁce as a sole discovery mode,1 the authors
found that it could usefully be combined with other channels such as hSM —-) WW or
associated Higgs production to enhance the overall visibility of the Higgs. At the same
time, the authors determined what additional enhancement of scalar production and
branching rate, such as might be provided in a non-standard model like the MSSM,
would enable a scalar to become visible in the 77' channel alone at Tevatron Run 11.

As these results are easily reinterpreted for DEWSB models, I take this as my
starting point, and examine how various Tevatron Run II searches for the SM Higgs
may provide information about the possible existence and properties of various Higgs-
like states that arise in DEWSB models. I look not only at the production and decay
channels which dominate in the SM, but also consider those which may be more
relevant in non-standard theories. I then go on (using [10] and [11]) to make some
predictions about visibility at the LHC.

Much of my discussion will focus on the degree to which certain standard Higgs
search channels are enhanced in non-standard models due to changes in the production
rate or branching fractions of the non-standard scalar (’H) relative to the values for
the standard Higgs boson (hSM). I deﬁne the enhancement factor for the process
yy —> ’H -—> 2:2: as the ratio of the products of the width of the (exclusive) production

mechanism and the branching ratio of the decay:

% _ F(’H—>yy)xBR(’H—>:rx) _ .H

_ _ 'H
K’yy/za: F(hSM —) yy) X BR(h3M —) 22113) NW prod X K.” dec (1)

 

 

1The authors established that discovery of hSM in this channel alone (assuming a mass in the
range 120 - 140 GeV) would require an integrated luminosity of 14—32 fb"1, which is unlikely to be

achieved.

I will consider both gluon fusion and b5 annihilation as possible production mecha-
nisms, and will study a variety of decay channels. Analytic formulas for the decay
widths of the SM Higgs boson are taken from [13], [14] and numerical values are
calculated using the HDECAY program [15] 2.

 

2With input parameters a,(M§) = 0.118, Mb = 4.60 GeV and Mt = 178 GeV.

3 Dynamical Electroweak Symmetry Breaking

3.1 General Remarks

The Standard Higgs Model of particle physics, based on the gauge group SU(3)c x
SU(2)W x U(1)y, accommodates electroweak symmetry breaking by including a fun—
damental weak doublet of scalar (“Higgs”) bosons ¢ = (:3) with potential function
V(¢) = /\ (qSIqS — %v2)2. However the SM does not explain the dynamics responsible
for the generation of mass. Furthermore, the scalar sector suffers from two serious
problems. The scalar mass is unnaturally sensitive to the presence of physics at any
higher scale (e.g. the Planck scale), through contributions of loops of SM particles
to the Higgs self-energy. This is known as the gauge hierarchy problem [16]. In ad-
dition, if the scalar must provide a good description of physics up to arbitrarily high
scale (i.e., be fundamental), the scalar’s self-coupling (A) is driven to zero at ﬁnite
energy scales. That is, the scalar ﬁeld theory is free (or “trivial”) ( [17], [18]). Then
the scalar cannot ﬁll its intended role: if /\ = 0, the electroweak symmetry is not
spontaneously broken. The scalars involved in electroweak symmetry breaking must
therefore be a party to new physics at some ﬁnite energy scale — e.g., they may be
composite, as in the DEWSB models discussed here. The SM is merely a low-energy
effective ﬁeld theory, and the dynamics responsible for generating mass must lie in
physics outside the SM.

In this section, I brieﬂy introduce those aspects of dynamical electroweak symme-

try breaking which are most germane to my analysis. For a more complete introduc-

tion to dynamical electroweak symmetry breaking, see [19].

3.2 Technicolor

An intriguing class of models, generally referred to as dynamical electroweak symme-

try breaking models, supposes that the scalar states involved in electroweak symmetry

breaking could be manifestly composite at scales not much above the electroweak scale
22 ~ 250 GeV. In these theories, a new asymptotically free strong gauge interaction
(technicolor) breaks the chiral symmetries of approximately massless technifermions
f, which differ from the regular quarks and leptons of the SM in that they also carry a
technicolor charge, at a scale A ~ 1 TeV ( [20], [21]). If the fermions carry appropriate
electroweak quantum numbers (e.g. left-handed weak doublets and right-handed weak
singlets), the resulting condensate ( f1, f3) 96 0 breaks the electroweak symmetry as
desired. Three of the Nambu-Goldstone Bosons (technipions) of the chiral symmetry
breaking become the longitudinal modes of the W and Z. The logarithmic running of
the strong gauge coupling renders the low value of the technicolor scale (and thereby
the electroweak scale) natural. The absence of fundamental scalars obviates concerns
about triviality.

Many models of DEWSB have additional light neutral pseudo N ambu-Goldstone
bosons (PNGBs) which could potentially be accessible to a standard Higgs search;
these are called “technipions” in technicolor models. There is‘not one particular
DEWSB model that has been singled out as a benchmark, in the manner of the
MSSM among supersymmetric theories. Rather, several different classes of models
have been proposed to address various challenges within the DEWSB paradigm of the
origins of mass. In this thesis, I look at several representative technicolor models. I
both evaluate the potential of standard Higgs searches to discover the lightest PNGBs
of each of these models, and also draw some inferences about the characteristics of
technicolor models that have the greatest impact on this search potential.

My analysis will assume, for simplicity, that the lightest PNGB state is signif-
icantly lighter than other neutral (pseudo)sca1ar technipions, so as to heighten the
comparison to the SM Higgs boson. The precise spectrum of any technicolor model
generally depends on a number of parameters, particularly those related to whatever

“extended technicolor” ( [26, 31]) interaction transmits electroweak symmetry break-

ing to the ordinary quarks and leptons. Models in which several light neutral PNGBs
were nearly degenerate would produce even larger signals than those discussed here.

The speciﬁc models we examine are: 1) the traditional one-family model [22] with
a full family of techniquarks and technileptons, 2) a variant on the one-family model
[23] in which the lightest technipion contains only down-type technifermions and is
signiﬁcantly lighter than the other pseudo Nambu-Goldstone bosons, 3) a multiscale
walking technicolor model [24] designed to reduce ﬂavor-changing neutral currents,
and 4) a low-scale technciolor model (the Technicolor Straw Man model) [25] in
which the lightest technipion is composed of technileptons. It must be noted, that
in model 4) we do not consider the lightest technipion for exactly that reason: Since
it is only composed of technileptons it will have no anomalous coupling to gluons,
the main production mechanism for technipions in technicolor models. We therefore
consider a slightly heavier (or possibly degenerate) technipion which is composed of
techniquarks. For simplicity however, the lightest neutral technipion of each model
which couples to gluons will be generically denoted by P; where a speciﬁc model is
meant, a superscript will be used.

One of the key differences among these models is the value of the technipion decay
constant E», which is related to the number N D of weak doublets of technifermions
that contribute to electroweak symmetry breaking. In a model like 2), in which only
a single technifermion condensate breaks the electroweak symmetry, the value of Fp
is simply the weak scale: F15?) = v = 246 GeV. In models where more than one
technifermion condensate breaks the EW symmetry, one ﬁnds 222 = f}; + f: + f: +
For example, in the one-family model 1), all four technidoublets corresponding to
a technifermion “generation” condense, so that the decay constant is ﬁxed to be
F19) = g. In the lowscale model 4), the number of condensing technidoublets is much
higher, of order 10; setting N D = 10 yields F“) = 7%. And in the multiscale model

3), the scales at which various technicondensates form are assumed to be signiﬁcantly

different, so that the lowest scale is simply bounded from above. In keeping with [24]
and to ensure that the technipion mass will be in the range to which the standard
Tevatron Higgs searches are sensitive, I set F19) = f.

In section 4, I study the enhancement factors for several production and decay
modes of the lightest eligible PNGBs of each technicolor model. Then in section 5, I
compare the signatures of these PNGBs to those of a SM Higgs and the Higgs bosons
of the MSSM in order to determine how the standard search modes (or additional
channels) can help tell these states apart.

In section 4.2, I brieﬂy discuss topcolor models, in which new strong interactions
among top quarks form top-pion bound states with masses of order 27m. The signa-
ture of this PN GB will then again be compared to the Higgs boson of the Standard

Model. I will always compare standard and non-standard scalars of the same mass,

so I will be comparing the top-pion with a rather heavy SM Higgs boson.

Table 1: Anomaly Factors for the models under study [23, 25, 30, 2, 3]

 

 

 

 

[[ 1) one-family I] 2) variant one-family I] 3) multiscale I] 4) low-scale
A... u 7 u i: u :3 u 7-
AM [I ’m H 5.7; [I a I] r

 

 

4 Results For Each Model

In this section, I examine the single production of technicolor PNGBs via the two
dominant methods at the Tevatron: gluon fusion and b5 annihilation. I determine
the degree to which these production channels are enhanced relative to production of
a SM Higgs, and ﬁnd which channel dominates for each scalar state. I likewise study
the major decay modes: b5, 77', 77, and WW in order to determine the branching

fractions relative to those of an SM Higgs.

4.1 Technicolor
4.1.1 PNGB Production via Gluon Fusion

Single production of a technipion can occur through the axial-vector anomaly which
couples the technipion to pairs of gauge bosons. For an SU(NTC) technicolor group
with technipion decay constant Fp, the anomalous coupling between the technipion
and a pair of gauge bosons is given, in direct analogy with the coupling of a QCD

pion to gluons, by [27, 28, 29]
NTCAV1V2'87gr%%5puAaki‘kgei\€g (2)

where Amy, is the anomaly factor (determined by the symmetry structure of the
model), 9,- are the gauge boson couplings, and the k,- and e,- are the four-momenta
and polarizations of the gauge bosons. The values of the anomaly factors for the

lightest PNGB coupling to gluons is given in Table 1 for each model.

Table 2: Calculated enhancement factors for production at the Tevatron and LHC of a 130
GeV technipion via gg alone, via bb alone, and combined. Note that the small enhancement
in the b5 process slightly reduces the total enhancement relative to that of 99 alone.

 

 

 

 

 

 

 

 

 

 

1) one family 2) variant one—family 3) multiscale 4) low scale
ref, M, 48 6 1100 120
n5, W, 4 0.67 16 10
53:91 prod 47 5.9 | 1100 n 120 ]

 

 

 

 

The rate of single technipion production in this channel is proportional to the

decay width to gluons. In the technicolor models, we have

NP U 99) _ 2 32am? ( 21er ' (3)

while in the SM, the expression looks like [13]

1 8 a
”h ‘* 99) = 5327'" "‘3 (3%.) (4)

Comparing a PN GB to a SM Higgs boson of the same mass, we ﬁnd the enhancement

in the gluon fusion production rate is

P(P -> 99) v2
”99 prod: W: 4 NTcAig— F2 (5)

The main factors inﬂuencing Egg pm, for a ﬁxed value of NTC are the anomalous
coupling to gluons and the technipion decay constant. The value of It” pm, for each

model (taking NTC = 4) is given in Table 2.

4.1.2 Production via Bottom Quark Annihilation

The PNGBs couple to b-quarks courtesy of the extended technicolor interactions re-
sponsible for producing masses for the ordinary quarks and leptons. The extended

technicolor (ETC) group (of which S U (NTC) is an unbroken subgroup) includes gauge

10

bosons that couple to both ordinary and technicolored fermions so that the ordinary
fermions can interact with the technicondensates that break the electroweak symme-
try.

The rate of technipion production via b5 annihilation is proportional to F(P ——> b5).

In general, the expression for the decay of a technipion to fermions is

 

S
_ N A2 2 4 2
I‘(P—>ff)= C Wm] 1__m,

87r F}; mg. (6)

where NC is 3 for quarks and 1 for leptons. The phase space exponent S is 3 for
scalars and 1 for pseudoscalars; the lightest PNGB in models 1) and 4) is a scalar,
while in models 2) and 3) it is assumed to be a pseudoscalar. For the technipion
masses considered here, the value of the phase space factor in (6) is so close to one
that the value of 3 makes no practical difference. The factor A f is a non-standard
Yukawa coupling distinguishing leptons from quarks. Model 2) has Am”, 2 ﬂ and
Azeptm = J6; model 3) also includes a similar factor, but with average value 1. Finally,
it should be noted that Model 2) assumes that the lightest technipion is composed
only of down-type fermions and cannot decay to c5; since this decay would usually
have a small branching ratio and c5 is not a preferred ﬁnal state for Higgs searches,
this has little impact.
For comparison, decay width of the SM higgs into b-quarks is:

 

3
— 3m2 m 4m2
I‘(h —> bb) = 87:2,," ( 1 — 7”) (7)

The production enhancement for b5 annihilation is (again assuming Higgs and Tech-

nipion have the same mass):

 

The value of mu, mod (shown in Table 4) is controlled by the size of the technipion
decay constant.
We see from Table 2 that nu, pm, is at least one order of magnitude smaller than

n99 pm. in each model. Taking the ratio of equations (5) and (8)

ifs-f: = gives»? (9)
we see that the larger size of it” pm, is due to the factor of N720 coming from the
fact that gluons couple to a technipion via a techniquark loop. The ETC interactions
coupling b—quarks to a technipion have no such enhancement.

In addition, the production cross-section for a SM Higgs boson via b5 annihilation
is 2 to 3 orders of magnitude smaller than that for gluon fusion at the Tevatron [32]
and the LHC [33]. With a smaller SM cross-section and a smaller enhancement factor,
it is clear that technipion production via bf) annihilation is negligible at Tevatron and
LHC. However, since including the bf) production channel reduces the enhancement
in general, I will include it in my calculations to get a more conservative estimate. I

therefore deﬁne a combined total enhancement factor:

n _ U(QQ-+ﬂ—>zx)+a(bb—>’H—>x$)
total/u _ 0(99 —) hSM —+ $2) + U(bb —> hSM —* 333)
leg/n + U(bb —+ ’H —> x2:)/0(99 —* hSM ‘* arr)
1+ U(bb —+ hSM —> x$)/0(99 —> hSM -> $93)
”ii/xx + xii/xxdbb —> hsu -> $$)/0(99 —’ hSM ‘* m)
1 + U(bb —‘> hSM —+ z$)/0(99 —* hSM —’ xx)

[Egg/:1: + K’ﬁ/szbbigg]/[1 + Rbb:gg]- (10)

 

 

 

Here Rum, is the ratio of 05 and gg initiated Higgs boson production, at Tevatron
and LHC respectively, in the Standard Model. The total production enhancement is

also given in Table 2. Note that the small differences in Rwy], between Tevatron and

12

Table 3: Branching ratios of a technipion/Higgs of mass 130 GeV

 

 

 

 

Decay 1) one family 2) variant 3) multiscale 4) low scale SM Higgs
Channel one family
66 0.60 0.53 0.23 0.60 0.53
ca 0.05 0 0.03 0.05 0.02
r+r- 0.03 0.25 0.01 0.03 0.05
99 0.32 0.21 0.73 0.32 0.07
77 2.7 x 10-4 2.9 x 10-3 6.1 x 10-4 6.4 x 10-3 2.2 x 10-3
W+W- 0 0 0 0 0.29

 

 

 

 

 

 

 

 

 

 

 

LHC are negligible, so we get the same total production enhancement for both.

4. 1.3 Decays

The decay width of a light technipion into gluons or fermion / anti-fermion pairs has
been discussed above. Since, in the interesting mass range, the technipions do not
decay to W bosons and decays to Z Bosons (through the axial vector anomaly) are
negligible, the remaining possibility is a decay to photons. Again, this proceeds
through the axial vector anomaly (cf. Equation (2)) and the anomaly factors An are
shown in Table 3.

I now calculate the technipion branching ratios from the above information, taking
NTC = 4. The values are essentially independent of the size of mp within the range
120 GeV - 160 GeV; the branching fractions for mp = 130 GeV are shown in Table 5.
The branching ratios for the SM Higgs at NLO are given for comparison; they were
calculated using HDECAY [15]. Note that, in contrast to the technipions, a SM Higgs
in this mass range already has a noticeable decay rate to off-shell vector bosons.

Comparing the technicolor and SM branching ratios in Table 5, we see immediately
that decay enhancements will be generally of order one, and therefore much smaller
than the production enhancements. Decays to 05 are slightly enhanced, if at all.
Decays to cc are enhanced in our tree-level calculations — but note that it‘is higher-.

order corrections that suppress this mode for the SM higgs; in any case, this is

13

not a primary discovery channel. Decays to 7' leptons have a small enhancement
in general; again, the comparison of tree-level technicolor and loop-level SM Higgs
calculations may be a factor here. Model 2) is an exception; its unusual Yukawa
couplings yield a decay enhancement in the 77 channel of order the technipion’s
(low) production enhancement. In the 77 channel, the decay enhancement strongly
depends on the group-theoretical structure of the model, through the anomaly factor.
Table 6 includes the decay enhancements nfec for the most experimentally promising

search channels.

4.2 Top-Pions

For additional comparison, I discuss a different DEWSBmodel, a topcolor-assisted
Technicolor (TC2) model ([34], [35], [36]), which I will be referring to as model 5).
TC2 models address the difﬁculty of simultaneously generating the large mass of the
top quark (which places an upper bound on the symmetry breaking scale AETC of the
ETC gauge group) and suppressing the experimentally-not-observed ﬂavor-changing
neutral currents (FCN C), which can show up as a relic of ETC symmetry breaking
at low energies (thereby placing a lower bound on Ame). In these models, the
top quark mass is partially generated by another new strong interaction (topcolor)
between top quarks. The Higgs-like scalar here is a heavy top-pion, which I will be
referring to as T, since it is very different from the PNGBs of the other examples. T
is a linear combination of technipions and the composite scalars created by top quark
condensation.

In the TC2 model 5), there are two scales, one for technifermion condensation and
the other for top condensation. FT, the scale of top—pion condensation, is thereby,
as in model 3), only bounded from above. As I am taking the phenomenological

expressions from [37], I will also adhere to their choice of parameters, setting FT =

70 GeV.

14

Model 5) requires a top-pion heavier than the t0p quark, so we can not calculate
the anomalous coupling to gauge bosons in the limit my < m. Instead we must

insert the mass-dependent function ([37])

A5,? = 45—; 1 — %(1— e) arcsin2 (277%) (11)

Further parameters need explaining here: 6 denotes the fraction of the top mass
generated by ETC-interactions (as opposed to being generated by topcolor interac-
tions). We will set it to be e = 0.01 (It must be on the order of the ratio of bottom
to top quark mass). mt is the top quark mass. Note that there is no equivalent to
the NTC- parameter of technicolor models. Also it is important to mention, that the
square-root is neither a real anomaly nor a phase-space factor: it reﬂects the mixing
of techni- and top-pions and will show up several times Using equation 5 we then ﬁnd,

setting mp = 22OGeV (a value at the lower end of, but well within, the theoretically

predicted top-pion mass range)

4 2
K.“ pm, — 36—-4—(— — 1)(1 — e) arcsrn (T) ~ 34. (12)

mp F72"
The top-pion of 5) couples most strongly to the third generation of quarks. It is
expected to be heavier than the technipions of the other models, but since it is not

heavier than 2mt, its main fermionic decay mode is:

N c 1 1 4mg

‘=_ ___ _ﬂ“; 2 __
I‘(T—>bb) 87FW(F72~ v2)(mb mcemt) 1 m} (13)

where the slight correction to 1m arises because there are two distinct sources of the
mass of the bottom quark(ETC and topcolor). - The charm and strange masses are

denoted me and ms reSpectively.

We then get for the production enhancement by bottom quark annihilation (again

setting m = 220 GeV):

15

4m2 _ m
52; W = (1— it?) 1(___(m, — —m—: 6 m»)? z 9.6 (14)

Comparing this with the production enhancement for gluon fusion (Equation 14),
we see that the production enhancements are of the same order of magnitude. Even
though we expect a somewhat larger impact of bottom quark annihilation as a pro-
duction mechansim (since the factor of N%C does not appear in this model), it turns
out that it is in fact negligible at the Tevatron and at the LHC for model 5).

Model 5) has a second fermionic decay mode for the top-pion - T is heavier then
a top quark and due to ﬂavor-non-universality has the following FCNC decay mode:

1 1 2

1‘(T 4 ic) = Kthggtﬁ—qg — 505(1- arms 1— g;— (15)

The factor Kt, is included in the coupling, and must be kept small due to exper-
imental constraints. Following [37], I set it to be Kt, = 0.05. Again, the PNGBs of
model 5) do not decay to W bosons and anomalous decay to Z bosons is negligible,
so we are left with decay to photons, where, for the same reasons as for gluons, we
have to insert the following mass-dependant function instead of the anomaly factor:

16 4m2 FT2 7717‘
5 _ i _ ‘
(7) _3___2 1- .v_2(1 e) arcsm2 (2 ) (16)

The ”pure” anomaly factor, derived from the group theoretical structure of the
coupling is the 339 at the beginning of the equation (note that this was 1 in the case
of gluons). The branching ratios for the top-pion (Table 4) are again calculated using

a mass of 220 GeV.

16

Table 4: Branching ratio of top-pion/Higgs of mass 220 GeV

 

 

 

Decay 5) Topoolor-assisted TC Heavy SM Higgs
b5 0.26 1.7 x 1073
2c 0.63 0
99 0.11 0.69 x 10—3
77 1.4 x 10-3 3.7 x 10-5
W+W" 0 0.71
22 0 0.29

 

 

 

 

5 Comparison and Interpretation

5.1 Technicolor vs SM

My results for the Tevatron Run II (LHC) production enhancements (including both
99 fusion and b5 annihiliation), decay enhancements, and overall enhancements of each
technicolor model relative to the SM are shown in Table 5 (6) for a technipion or Higgs
mass of 130 GeV. Multiplying 765, )m by the cross-section for SM Higgs production
via gluon fusion [33] yields an approximate technipion production cross—section, as
shown in the right-most column of Table 5 (6).

In each technicolor model, the main enhancement of the possible technipion signal
relative to that of an SM Higgs arises at production, making the size of the technip-
ion decay constant the most critical factor in determing the degree of enhancement.
An equally important role is played by the number of technicolors, which is not as
apparent here, since I have assumed it to be the same for all the models I considered.
Still, along with the absence of decays to vector bosons for the technipions, the factor
of N723. is responsible for the fact, that we actually observe a net enhancement for all
models and in all decay channels.

Each decay enhancement is in general of order 1, making it signiﬁcantly smaller
than the typical production enhancement. In model 3) the decay “enhancement” is

actually a suppression, but a tiny one compared to the production enhancement. We

17

 

Table 5: Enhancement Factors for 130 GeV technipions produced at the Tevatron, compared
to production and decay of a SM Higgs Boson of the same mass. The slight suppression
of 5;.“ due to the b—quark annihilation channel has been included.The rightmost column
shows the cross-section (pb) for pp —) P -—) :32: at Tevatron Run II.

 

 

 

 

 

 

 

 

 

 

Model Decay mode “fwd ref“ Kim/m Cross Section

bb 47 1.1 52 14 pb

1) one family 7+7“ 47 0.6 28 0.77 pb
77 47 0.12 5.6 6.4 x 10-3 pb

bb 5.9 1 5.9 1.8 pb

2) variant 7+7' 5.9 5 30 0.84 pb
one family 77 5.9 1.3 7.7 8.7 x 10"3 pb

b5 1100 0.43 470 130 pb

3) multiscale 7+7“ 1100 0.2 220 6.1 pb

77 1100 0.27 300 0.34 pb

bb 120 1.1 130 36 pb

4) low scale 7*?“ 120 0.6 72 2 pb
77 120 2.9 350 0.4 pb

 

 

 

 

 

 

 

 

 

ﬁnd that P -—> bb is very similar to I13}! —+ bf). In contrast, P —-> c5 generally has
signiﬁcant decay enhancement. However, this may be an artifact of our comparing
a tree-level technicolor result to an NLO result for hSM; radiative corrections to
hSM -) c5 tend to suppress the branching fraction. The decay P —+ 77' generally has
a suppressed rate relative to SM expectations; again, this may relate to comparing
leading technicolor and N LO SM results. An exception is model 2), where the special
structure of the Yukawa coupling leads to a 7'7 decay enhancement of the same order
as the production enhancement. The P —) 77 decay enhancement factor depends
strongly on the group-theoretic structure of the model through the anomaly factor,
ranging from a distinct enhancement in model 4) to a factor-of-lO suppression in
model 1).

The net result for the models considered is a distinct enhancement of the P signal
in each of the 77', bf) and 77 search channels. Given the large QCD background for

the bb ﬁnal state, the 77' and 77 channels are likely to be the most promising ways

18

Table 6: Enhancement Factors for 130 GeV technipions produced at the LHC, compared
to production and decay of a SM Higgs Boson of the same mass. The slight suppression
of [€er due to the b-quark annihilation channel has been included.The rightmost column
shows the cross-section (pb) for pp ——> P —-> 2:1: at the LHC.

 

 

 

 

 

 

 

 

 

 

 

Model Decay _mode 5;“, Kim nit/n Cross Section
bb 47 1.1 52 890 pb
1) one family 7+7“ 47 0.6 28 48 pb
77 47 0.12 5.6 0.4 pb
()5 5.9 1 5.9 100 pb
2) variant 7+7" 5.9 5 30 52 pb
one family 77 5.9 1.3 7.7 0.55 pb
55 1100 0.43 473 8000 pb
3) multiscale 7+7” 1100 0.2 220 380 pb
77 1100 0.27 300 21 pb
66 120 1.1 130 2200 pb
4) low scale 7+7’ 120 0.6 72 120 pb
77 120 2.9 350 25 pb

 

 

 

 

 

 

 

 

to discover a technipion.

As illustrated in Figure 1, the available enhancement is

 

well above what is required to render the P of any of these models visible in the 77
channel at the Tevatron. In models 3 and 4, the visibility in the 77 ﬁnal state can be
even more striking, making this a possible discovery channel even at the Tevatron.
Of course since we have net enhancements in all cases, all these models should have
visible technipions at the LHC, where even an SM Higgs would be detectable in the

mass range I have considered (of. Figure 2).

5.2 MSSM vs Technicolor

A brief comparison between the models I have been considering and the MSSM is in
order here. The MSSM is an alternate expansion of the Standard Model, addressing
similar problems as DEWSB models but taking a different approach, proposing a

symmetry of nature relating fermions and bosons. The MSSM introduces two Higgs

19

 

10’
if

 

M3

7 Model 4

[I

Made, 1 Model 2

 

 

 

 

 

 

10?
5oCL(10fb")
1 11114.1“Inuittrtltrrrltt.tlltttluullrrlllrrr
100 105 110 115 120 125 130 135 140 145 150
M,(GeV)
“z; 103
'Modem
10‘—

’ -1
. 5oCL(10fb )//

’0 3 Model 2

1 11111]Ill[Jill]llllllllLLLllleLLlIllAlllllllllll
100 105 110 115 120 125 130 135 140 145 150

MP(GeV)

 

 

 

Figure 1: Total enhancement factor for each technicolor model plotted as a function
of technipion mass and assuming the ﬁnal state is a tau (photon) pair. The lowest
curve is the enhancement factor required to make a Higgs-like particle visible (50
discovery) in tau(photon)-pairs at Tevatron Run II with a total luminosity of 10 f b-1

[9], [38].

 

10’

3
>2— _ Models
ii? 5
3., ‘ Model4
I
m

- Model 1

C Model 2

10 ,— 50 CL (100 to")

 

 

 

1 liLLLlellllllllllllilillllllllllllllllllJlllllll

100 105 110 115 120 125 130 135 140 145 150

MP(GeV)

 

 

Model 3
' Model 4 N
t
E

 

 

 

oxBFi(P——>w)(pb)

1
r-
r-

; Model 2
Mt

 

.1 _
10 g- 5061 (30 m ’)
E
10 lLlllilJiJLLlll1111111111441114411111111111111111

1w 105 110 115 120 125 130 135 140 145 150

MP(GeV)

 

 

 

Figure 2: Total cross-section times branching ratio for each technicolor model plotted
as a function of technipion mass and assuming the ﬁnal state is a tau (above) or
7 (below) pair at LHC. The lowest curVe is the cross-section times branching ratio
required to make a Higgs-like particle visible (5 a discovery, total luminosity given in
brackets) in tau- or 7-pairs, respectively [10], [11].

21

doublets which break the electroweak symmetry and give mass to the fermions of the
SM. Calculations similar to the ones I have done for DEWSB models in this thesis
are performed for supersymmetric models in the paper ”The Meaning of Higgs: 7+7“
and 77 at the Tevatron and the LHC” [12] mentioned earlier. I describe some of the
major differences between DEWSB models and the MSSM here.

One notable difference concerns the production mechanism: While bottom quark
annihilation is, as we have seen, negligible for technipions, this channel can become
very important and even dominant in large sections of the MSSM parameter space.

The more important (since more observable) difference is however the difference
in branching rates for some important decay modes. While 77 decays are enhanced
in both models compared to the SM, decays to photons are heavily suppressed in
the MSSM as opposed to the moderate to large enhancements I have calculated for
technicolor models. While this will probably play no role in analyzing data from
Tevatron Run II, this signiﬁcant difference could be the perfect way to distinguish

between these two non-standard models at the LHC.

5.3 Top-Pion vs Heavy SM Higgs

Model 5) has a special role for several reasons: Mainly of course, its main decay mode
is ﬂavor changing and not even open to the SM higgs. But also, it necessitates a top—
pion with a mass beyond the WW-decay threshold, which can nonetheless not decay to
massive vector bosons. This absence of a signature is almost as striking as the FCNC,
since the SM Higgs boson has a branching ratio of almost 100 percent to massive vector
bosons at a mass of 220 GeV. So this model has very large decay enhancements (on the
order of the production enhancement) in it’s a110wed decay channels, making it easily
detectable if the Higgs Search in this mass range is not limited to only vector-boson-
decays (whose mere absence would of course not necessarily indicate the existence of

the top-pionl). Note however the absence of leptonic decays, since leptons get their

22

Table 7: Enhancement Factors for 220 GeV tOp-pions produced at the Tevatron and the
LHC, compared to production and decay of a SM Higgs Boson of the same mass. The slight
suppression of £51.04 due to the b-quark annihilation channel is negligible.The rightmost
column shows the cross-section (pb) for pp -) P -> :61: at Tevatron Run II.

 

 

Decay mode ref,“ Rice 167;, In Cross Section (Tev) Cross Section (LHC)
bb 34 150 5100 0.77 pb 110 pb
7+7‘ 34 0 0 0 pb 0 pb
77 34 38 1290 4.2 x 10-3 pb 0.6 pb

 

 

 

 

 

 

 

 

 

 

 

mass entirely from ETC.

The enhancement factors for 5) (Table 7) seem excessive at ﬁrst glance, but that
is only because the branching ratios for non-vector-boson decays get extremely small
for the light SM higgs. The ratio of total width to mass for the top-pion is still of the
order of 0.1 percent, which is narrower than the SM Higgs of the same mass. Looking
at the estimated cross-sections brings things back into proportion. For example at
the Tevatron, the cross-section for pp —) P —-> bf) in model 5) is only about ten times
larger than that of pp —) h —> W+W’ in the SM, so we have a much less drastic effect
than just looking at the enhancement factors would indicate and it is unlikely that
top-pions could be detected at the Tevatron. Since the SM background for bb decays
is probably still too large and the 77 mode is not allowed, the only feasible detection
channel at the LHC is the decay to photons. To my knowledge, no calculations have
been made for visibilty in the 77 channel at this mass range, since such a heavy
SM Higgs would be perfectly visible through its decays to vector bosons. It seems

probable however, that a top-pion would be detectable through decay to photons at

the LHC.

23

6 Conclusions

I have shown that searches for a Standard Model Higgs boson at Tevatron Run II and
LHC can provide signiﬁcant results even if the electroweak symmetry is dynamically
broken. The new scalar and pseudoscalar states of DEWSB models can have en-
hanced visibility in standard 7+7‘ and 77 search channels, making them potentially
discoverable at Tevatron Run II and CERN LHC. This enhancement mainly comes
from an increased production rate, rather than from differences in the branching frac-
tions. The model parameters exerting the largest inﬂuence on the enhancements are
NTC and the technipion decay constant.

I also considered a topcolor-assisted technicolor model and compared the top-pion
of this model with a heavy SM Higgs boson. I found that the experimental signatures
of top-pions are so different from the SM Higgs that it is less easy to simply transfer
predictions for the SM. The main conclusion to be drawn is that even for Higgs-like
particles with masses beyond the WW-threshold, the search should not be limited to
decays to vector bosons, which are so dominant in the SM.

For the technicolor models, where a direct comparison to the SM is easier, I
investigated the likely mass reach of the Higgs searches at Tevatron and LHC in
pp ——> P —> 7+7” and pp —> P —+ 77 for each model and found that in all cases there
exist DEWSB models with visible scalar or pseudoscalar states, warranting a close
look even when predictions for the SM Higgs are far from promising, such as for decay
to photons at Tevatron Run II. The enhancement (or suppression) of pp —+ P -—) 77 is
also the best way of distinguishing DEWSB models from supersymmetric extensions

of the standard model at the LHC.

24

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26

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1‘” AA‘ — ...

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