British Prime minister - Spelling mistakes

Robin Michael   Tue Nov 10, 2009 4:27 am GMT
The British Prime minister wrote a personal letter of condolences to the mother of a soldier killed in Afganistan. The letter was written in black felt tip pen and contained a number of spelling mistakes. The letter was published on the front page of 'The Sun'.
Robin Michael   Tue Nov 10, 2009 4:28 am GMT
Sorry - Prime Minister
Higg   Tue Nov 10, 2009 5:07 am GMT
Interesting. I like spotting spelling mistakes in letters and publications. I feel a sense of grandeur when I find one.
In fact, in the following publication I found a spelling mistake. Can anyone else find it?




HIGGS BOSONS: THEORY AND SEARCHES
Written November 2007 by G. Bernardi (LPNHE, CNRS/IN2P3,
U. of Paris VI & VII), M. Carena (FNAL), and T. Junk (FNAL).
I. Introduction
Understanding the mechanism that breaks electroweak symmetry
and generates the mass of all known elementary particles
is one of the most fundamental problems in particle physics.
The Higgs mechanism [1] provides a general framework to explain
the observed masses of the W± and Z gauge bosons
by means of charged and neutral Goldstone bosons that end
up as the longitudinal components of the gauge bosons. These
Goldstone bosons are generated by the underlying dynamics
of electroweak symmetry breaking (EWSB). However, the fundamental
dynamics of the electroweak symmetry breaking are
unknown, and there are two main classes of theories proposed
in the literature, those with weakly coupled dynamics - such
as in the Standard Model (SM) [2] - and those with strongly
coupled dynamics.
In the SM, the electroweak interactions are described by a
gauge field theory based on the SU(2)L×U(1)Y symmetry group.
The Higgs mechanism posits a self-interacting complex doublet
of scalar fields, and renormalizable interactions are arranged
such that the neutral component of the scalar doublet acquires
a vacuum expectation value v = 246 GeV which sets the scale of
EWSB. Three massless Goldstone bosons are generated, which
are absorbed to give masses to the W± and Z gauge bosons.
The remaining component of the complex doublet becomes the
Higgs boson - a new fundamental scalar particle. The masses
of all fermions are also a consequence of EWSB since the Higgs
doublet is postulated to couple to the fermions through Yukawa
interactions. If the Higgs mass mH is below 180 GeV, all fields
remain weakly interacting up to the Planck scale, MPl.
The validity of the SM as an effective theory describing
physics up to the Planck scale is questionable, however, because
of the following “naturalness” argument. All fermion masses
and dimensionless couplings are logarithmically sensitive to the
scale Λ at which new physics becomes relevant. In contrast,
CITATION: C. Amsler et al. (Particle Data Group), PL B667, 1 (2008) (URL: http://pdg.lbl.gov)
July 16, 2008 11:42
– 2–
scalar squared masses are quadratically sensitive to Λ. Thus,
the observable SM Higgs mass has the following form:
m2
H = (m2
H)0 +
kg2Λ2
16π2 ,
where the first term, (mH)0, is a fundamental parameter of the
theory. The second term is a one-loop correction in which g
is an electroweak coupling and k is a constant, presumably of
O(1), that is calculable within the low-energy effective theory.
The two contributions arise from independent sources and one
would not expect that the observable Higgs mass is significantly
smaller than either of the two terms. Hence, if the scale of new
physics Λ is much larger than the electroweak scale, unnatural
cancellations must occur to remove the quadratic dependence
of the Higgs mass on this large energy scale and to give
a Higgs mass of order of the electroweak scale, as required
from unitarity constraints [3,4], and as preferred by precision
measurements of electroweak observables [5]. Thus, the SM
is expected to be embedded in a more fundamental theory
which will stabilize the hierarchy between the electroweak scale
and the Planck scale in a natural way. A theory of that type
would usually predict the onset of new physics at scales of the
order of, or just above, the electroweak scale. This prediction
is somewhat in tension with the fact that precision electroweak
measurements strongly constrain contributions of new physics
below the TeV scale. Theorists strive to construct models of
new physics that keep the successful features of the SM while
curing its shortcomings, including the absence of a dark matter
candidate or an electroweak scale explanation of the observed
baryon asymmetry of the universe.
In the weakly-coupled approach to electroweak symmetry
breaking, supersymmetric (SUSY) extensions of the SM provide
a possible explanation for the stability of the electroweak energy
scale in the presence of quantum corrections [6]. These theories
predict a spectrum of Higgs scalars [7]. The properties of the
lightest Higgs scalar often resemble those of the SM Higgs
boson, with a mass that is predicted to be less than 135 GeV
in the simplest supersymmetric model. Additional neutral and
charged Higgs bosons with masses of order of the weak scale
July 16, 2008 11:42
– 3–
are also predicted. Moreover, low-energy supersymmetry with a
supersymmetry breaking scale of order 1 TeV allows for grand
unification of the electromagnetic, weak and strong gauge
interactions in a consistent way, strongly supported by the
prediction of the electroweak mixing angle at low energy scales,
with an accuracy at the percent level [8,9].
Alternatively, new strong interactions near the TeV scale
can induce strong breaking of the electroweak symmetry [10].
Recently, the so-called “Little Higgs” models have been proposed
in which the scale of the new strong interactions is pushed
up above 10 TeV [11], and the lightest Higgs scalar resembles
the weakly-coupled SM Higgs boson.
In a more speculative direction, a new approach to electroweak
symmetry breaking has been explored in which extra
space dimensions beyond the usual 3+1 dimensional space-time
are introduced [12] with characteristic sizes of order (1 TeV)−1.
In such scenarios, the mechanisms for electroweak symmetry
breaking are inherently extra-dimensional and the resulting
Higgs phenomenology can depart significantly from the SM
paradigm [13].
Prior to 1989, when the e+e− collider LEP at CERN came
into operation, searches for Higgs bosons were sensitive only
to Higgs bosons with masses below a few GeV [14]. In the
LEP1 phase, the collider operated at center-of-mass energies
close to MZ. During the LEP2 phase, the energy was increased
in steps, reaching 209 GeV in the year 2000 before the final
shutdown. The combined data of the four LEP experiments,
ALEPH, DELPHI, L3, and OPAL, was sensitive to neutral
Higgs bosons with masses up to about 115 GeV and to charged
Higgs bosons with masses up to about 90 GeV [15,16].
The search for the Higgs boson continues at the Tevatron pp
collider, operating at a center-of-mass energy of 1.96 TeV. The
sensitivity of the two experiments, CDF and DØ, is improving,
and with the full Tevatron integrated luminosity, should be
high enough to probe SM Higgs boson masses beyond the
LEP reach [17]. Other neutral and charged Higgs particles
postulated in most theories beyond the SM are also actively
sought at the Tevatron. The searches for Higgs bosons will
July 16, 2008 11:42
– 4–
continue with significantly higher sensitivities in the coming
years at the LHC pp collider, and is expected to cover masses
up to about 1 TeV for the SM Higgs boson [18,19]. Once
evidence for the dynamics of electroweak symmetry breaking
is obtained, a more complete understanding of the mechanism
will require measurements at future e+e− [20] and perhaps
μ+μ− colliders [21].
In order to keep this review up to date, some unpublished
results are quoted. LEP results are marked with (*) in the
reference list and can be accessed conveniently from the public
web page
http://lephiggs.web.cern.ch/LEPHIGGS/pdg2008/.
Preliminary results from the CDF collaboration are marked
with (**) and can be obtained from the public web page
http://www-cdf.fnal.gov/physics/physics.html;
those from DØ are marked with (***) and can be obtained at
http://www-d0.fnal.gov/Run2Physics/WWW/results.htm.
II. The Standard Model Higgs Boson
In the SM, the Higgs  boson mass is given by mH =
λ/2 v, where λ is the Higgs self-coupling parameter and
v is the vacuum expectation value of the Higgs field, v =
(√2GF )−1/2 = 246 GeV, fixed by the Fermi coupling GF .
Since λ is presently unknown, the value of the SM Higgs
boson mass mH cannot be predicted. However, besides the
upper bound on the Higgs mass from unitarity constraints [3,4],
additional theoretical arguments place approximate upper and
lower bounds on mH [22]. There is an upper bound based on
the perturbativity of the theory up to the scale Λ at which
the SM breaks down, and a lower bound derived from the
stability of the Higgs potential. If mH is too large, then the
Higgs self-coupling diverges at some scale Λ below the Planck
scale. If mH is too small, then the Higgs potential develops a
second (global) minimum at a large value of the scalar field of
order Λ. New physics must enter at a scale Λ or below, so that
the global minimum of the theory corresponds to the observed
SU(2)L×U(1)Y broken vacuum with v = 246 GeV. Given a
July 16, 2008 11:42
– 5–
value of Λ, one can compute the minimum and maximum
allowed Higgs boson mass. Conversely, the value of mH itself
can provide an important constraint on the scale up to which
the SM remains sucessful as an effective theory. In particular, a
Higgs boson with mass in the range 130 GeVmH 180 GeV
is consistent with an effective SM description that survives all
the way to the Planck scale, although the hierarchy problem
between the electroweak scale and Λ = MPl still persists. The
lower bound on mH can be reduced to about 115 GeV [23], if
one allows for the electroweak vacuum to be metastable, with a
lifetime greater than the age of the universe.
The SM Higgs couplings to fundamental fermions are proportional
to the fermion masses, and the couplings to bosons are
proportional to the squares of the boson masses. In particular,
the SM Higgs boson is a CP-even scalar, and its couplings to
gauge bosons, Higgs bosons and fermions are given by:
gHf ¯ f =
mf
v
, gHV V =
2m2
V
v
, gHHVV =
2m2
V
v2
gHHH =
3m2
H
v
gHHHH =
3m2
H
v2
where V = W± or Z. In Higgs boson production and decay
processes, the dominant mechanisms involve the coupling of
the H to the W±, Z and/or the third generation quarks and
leptons. The Higgs boson’s coupling to gluons, Hgg, is induced
by a one-loop graph in which the H couples to a virtual tt
pair. Likewise, the Higgs boson’s coupling to photons, Hγγ,
is also generated via loops, although in this case the oneloop
graph with a virtual W+W− pair provides the dominant
contribution [7]. Reviews of the SM Higgs boson’s properties
and its phenomenology, with an emphasis on the impact of loop
corrections to the Higgs decay rates and cross sections, can be
found in Refs. [24,25].
The cross sections for the production of SM Higgs bosons
are summarized in Fig. 1 for pp collisions at the Tevatron,
and in Fig. 2 for pp collisions at the LHC [26]. The cross
section for the gg → H + X process is known at next-to-nextto-
leading order (NNLO) QCD, in the large top-mass limit, and
at NLO in QCD for arbitrary top mass [27]. The NLO QCD
July 16, 2008 11:42
– 6–
corrections approximately double the leading-order prediction,
and the NNLO corrections add approximately 50% to the NLO
prediction. NLO electroweak corrections are also available for
Higgs boson masses below 2MW, and range between 5% and 8%
of the LO term. The electroweak corrections are not included in
the figures. The residual uncertainty for this process is ∼ 10%.
The cross sections for the associated production processes qq →
W±H+X and qq → ZH+X are known at NNLO for the QCD
corrections and at NLO for the electroweak corrections [28,29].
The residual uncertainty is rather small, less than 5%. For the
vector boson fusion processes qq → qqH + X, corrections to
the production cross section are known at NLO in QCD and
the remaining theoretical uncertainties are less than 10% [30].
The cross section for the associated production process ttH has
been calculated at NLO in QCD [31], while the bottom fusion
Higgs boson production cross section is known at NNLO in the
case of five quark flavors [28,32,33].
The branching ratios for the most relevant decay modes of
the SM Higgs boson are shown in Fig. 3 as functions of mH,
and the total decay width is shown in Fig. 4, also as function of
mH [34]. For masses below 135 GeV, decays to fermion pairs
dominate, of which the decay H → bb has the largest branching
ratio. Decays to τ+τ−, cc and gluon pairs together contribute
less than 15%. For such low masses, the total decay width is
less than 10 MeV. For Higgs boson masses above 135 GeV, the
W+W− decay dominates (below the W+W− threshold, one of
the W bosons is virtual) with an important contribution from
H → ZZ, and the decay width rises rapidly, reaching about
1 GeV at mH = 200 GeV and 100 GeV at mH = 500 GeV.
Above the tt threshold, the branching ratio into top-quark
pairs increases rapidly as a function of the Higgs boson mass,
reaching a maximum of about 20% at mH ∼ 450 GeV.
July 16, 2008 11:42
– 7–
1
10
10 2
10 3
100 120 140 160 180 200
qq → WH
qq → ZH
gg → H
bb → H
gg,qq → ttH
qq → qqH
mH [GeV]
σ [fb]
SM Higgs production
TeV II
TeV4LHC Higgs working group
Figure 1: SM Higgs production cross sections
for pp collisions at 1.96 TeV [26].
10 2
10 3
10 4
10 5
100 200 300 400 500
qq → WH
qq → ZH
gg → H
bb → H
qb → qtH
gg,qq → ttH
qq → qqH
mH [GeV]
σ [fb]
SM Higgs production
LHC
TeV4LHC Higgs working group
Figure 2: SM Higgs production cross sections
for pp collisions at 14 TeV [26].
July 16, 2008 11:42
– 8–
mH [GeV]
Figure 3: Branching ratios for the main decays
of the SM Higgs boson [34].
mH [GeV]
Figure 4: The total decay width of the SM
Higgs boson, shown as a function of mH [34].
Also shown are the decay widths for the CP-even
neutral Higgs bosons, h and H, for two choices
of tan β, in the MSSM benchmark scenario mhmax,
described in Section III.
July 16, 2008 11:42
– 9–
Searches for the SM Higgs Boson at LEP
The principal mechanism for producing the SM Higgs boson
in e+e− collisions at LEP energies is Higgs-strahlung in the schannel,
e+e− → HZ [35]. The Z boson in the final state is
either virtual (LEP1), or on mass shell (LEP2). The SM Higgs
boson can also be produced by W+W− and ZZ fusion in the
t-channel [36], but at LEP these processes have small cross
sections. The sensitivity of the LEP searches to the Higgs boson
is primarily a function of the center-of-mass energy, ECM. For
mH < ECM − MZ, the cross section is quite large, of order
1 pb or more, while for mH > ECM −MZ, the cross section is
smaller by an order of magnitude or more.
During the LEP1 phase, the ALEPH, DELPHI, L3 and
OPAL collaborations analyzed over 17 million Z decays and
set lower bounds of approximately 65 GeV on the mass of the
SM Higgs boson [37]. At LEP2, substantial data samples were
collected at center-of-mass energies up to 209 GeV.
Each production and decay mode was analyzed separately.
Data recorded at each center-of-mass energy were studied independently
and the results from the four LEP experiments were
then combined. Distributions of neural network discriminants
which are functions of reconstructed event quantities such as
invariant masses and b-tagging discriminants were assembled
for the data, and also for the signal and background predictions.
The CLs method [38] was used to compute the observed
and expected limits on the Higgs boson production cross section
as functions of the Higgs boson mass sought, and from
that, a lower bound on mH was derived. The p-value for the
background-only hypothesis, which is the probability for the
background model to produce a fluctuation as signal-like as
that seen in the data or more, was also computed.
Higgs bosons were sought in four final state topologies: The
four-jet topology in which H → bb and Z → qq; the final states
with tau leptons produced in the processes H → τ+τ− where
Z → qq, together with the mode H → bb with Z → τ+τ−; the
missing energy topology produced mainly in the process H → bb
with Z → ν¯ν, and finally the leptonic states H → bb with
Z → e+e−, μ+μ−. At LEP1, only the modes with Z → +−
July 16, 2008 11:42
– 10–
and Z → ν¯ν were used because the backgrounds in the other
channels were prohibitive. For the data collected at LEP2, all
decay modes were used.
For very light Higgs bosons, with mH < 2mτ , the decay
modes exploited above are not kinematically allowed, and
decays to jets, muons, pion pairs and lighter particles dominate,
depending sensitively on mH. For very low masses, OPAL’s
decay-mode independent search [39] for the Bjorken process
e+e− → S0Z, where S0 denotes a generic neutral, scalar
particle, provides sensitivity. This search is based on studies
of the recoil mass spectrum in events with Z → e+e− and
Z → μ+μ− decays, and on the final states Z → νν and
S0 → e+e− or photons. Upper bounds on the cross section are
produced for scalar masses between 1 KeV and 100 GeV.
The LEP searches did not show any conclusive evidence
for the production of a SM Higgs boson. However, in the
LEP2 data, ALEPH reported an excess of about three standard
deviations, suggesting the production of a SM Higgs boson with
mass ∼ 115 GeV [40]. Analyses of the data from DELPHI [41],
L3 [42], and OPAL [43] did not show evidence for such an
excess, but could not, however, exclude a 115 GeV Higgs
boson at the 95% C.L. When the data of the four experiments
are combined, the overall significance of a possible signal at
mH = 115 GeV is low, as given by the background-only p-value
of 0.09 [15]. The same combination of the LEP data yields
a 95% C.L. lower bound of 114.4 GeV for the mass of the
SM Higgs boson. The median limit one would expect to obtain
in a large ensemble of identical experiments with no signal
present is 115.3 GeV. Fig. 5 shows the observed production
cross section limits, relative to the SM Higgs boson production
rate (including vector-boson fusion), assuming SM Higgs boson
branching ratios.
Indirect Constraints on the SM Higgs Boson
Indirect experimental bounds for the SM Higgs boson mass
are obtained from fits to precision measurements of electroweak
observables. The Higgs boson contributes to the W± and Z vacuum
polarization through loop effects, leading to a logarithmic
sensitivity of the ratio of the W± and Z gauge boson masses
July 16, 2008 11:42
– 11–
10
-2
10
-1
1
20 40 60 80 100 120
mH(GeV/c2)
95% CL limit on ξ2
LEP
√s = 91-210 GeV
Observed
Expected for background
Figure 5: The 95% confidence level upper
bound on the ratio ξ2 = (gHZZ/gSM
HZZ)2 [15].
The solid line indicates the observed limit, and
the dashed line indicates the median limit expected
in the absence of a Higgs boson signal.
The dark and light shaded bands around the expected
limit line correspond to the 68% and 95%
probability bands, indicating the range of statistical
fluctuations of the expected outcomes.
The horizontal line corresponds to the Standard
Model coupling. Standard Model Higgs boson
decay branching fractions are assumed.
on the Higgs boson mass. A global fit to precision electroweak
data, accumulated in the last decade at LEP, SLC, Tevatron
and elsewhere [5], gives mH = 76+33
−24 GeV, or mH < 144 GeV
at 95% C.L. [5]. The top quark contributes to the W± boson
vacuum polarization through loop effects that depend quadratically
on the top mass, which plays an important role in the
global fit. A top quark mass of 170.9 ± 1.8 GeV [44] and a W±
boson mass of 80.398 ± 0.025 GeV [45] were used. If the direct
July 16, 2008 11:42
– 12–
LEP search limit of mH > 114.4 GeV is taken into account, an
upper limit of mH < 182 GeV at 95% C.L. is obtained.
Searches for the SM Higgs Boson at the Tevatron
At the Tevatron, the most important SM Higgs boson
production processes are gluon fusion (gg → H) and Higgs
boson production in association with a vector boson (W±H
or ZH) [46]. For masses less than about 135 GeV, the most
promising discovery channels are W±H and ZH with H → bb.
The contribution of H → W∗W is dominant at higher masses,
mH > 135 GeV. Using this decay mode, both the direct
(gg → H) and the associated production (pp → W±H or
ZH) channels are explored, and the results of both Tevatron
experiments are combined to maximize the sensitivity to the
Higgs boson.
The signal-to-background ratio is much smaller in the Tevatron
searches than in the LEP analyses, and the systematic
uncertainties on the estimated background rates are typically
larger than the signal rates. In order to estimate the background
rates in the selected samples more accurately, auxiliary
measurements are made in data samples which are expected
to be depleted in Higgs boson signal. These auxiliary samples
are chosen to maximize the sensitivity to each specific background
in turn. Then, Monte Carlo simulations are used to
extrapolate these measurements into the Higgs signal regions.
The dominant physics backgrounds such as top-pair, diboson,
W±bb and single-top production are estimated by Monte Carlo
simulations in this way, i.e. after having been tuned or verified
by corresponding measurements in dedicated analyses, thereby
reducing the uncertainty on the total background estimate. The
uncertainties on the background rates diminish with increasing
integrated luminosity because increasingly larger data samples
are used to constrain them, and thus these uncertainties are not
expected to be limiting factors in the sensitivity of the searches.
At masses below about 135 GeV, the searches for associated
production, pp → W±H,ZH are performed in different
channels:
July 16, 2008 11:42
– 13–
a) pp → W±H, where the W± decays leptonically and H → bb;
such searches have been published by the CDF and DØ collaborations
on ∼ 0.3 fb−1 of data [47,48] and are regularly
updated with larger data samples [49,50]. The latest updates
(August 2007) are based on 1.7 fb−1 of data [51,52]; the Higgs
boson production cross section limits obtained by both collaborations
are about ten times higher than the SM expectation in
this channel. These updates use advanced analysis techniques
such as neural networks to separate a potential signal from the
background processes, and also to separate correctly identified
b-jets from jets originating from gluons or from u, d, s or c
quarks, mistakenly identified as b-jets.
b) pp → ZH, where the Z decays into ν¯ν, is also a sensitive
channel, but, since the final state is characterized by missing
transverse energy and two b-jets, multijet backgrounds without
Z bosons require special care. The sensitivity of this search is
enhanced by W±H events in which the charged lepton from
the W± decay escapes detection; these events have the same
experimental signature as the ZH → ν¯ν signal. The DØ Collaboration
has published a result in this channel with 0.3 fb−1
of data [53]. Updates with 0.9 fb−1 (DØ [54]) and 1.7 fb−1
(CDF [55]) have been released in 2007 using multivariate techniques
and enhanced event reconstruction and selection, which
increase the signal acceptance. The sensitivity is comparable to
that obtained in the W±H channel.
c) pp → ZH, where the Z decays into charged leptons (e or
μ), suffers from a smaller Z branching fraction, but has lower
background, so its sensitivity is not much lower than that of the
previous two channels. The DØ Collaboration has published
a result based on 0.45 fb−1 of data [56], and updates with
∼ 1 fb−1 of data are available from both CDF and DØ [57,58].
When combining the three low-mass channels of the two
collaborations, the expected (observed) limit is 4.3 (6.2) times
higher than the expected SM production cross section for mH =
115 GeV, as can be seen in Fig. 6 [59]. With the projected
improvements in analysis sensitivity, and the accumulation of
July 16, 2008 11:42
– 14–
more integrated luminosity (up to 7 to 8 fb−1), the low-mass
Higgs boson is expected to be probed at the Tevatron.
1
10
10 2
110 120 130 140 150 160 170 180 190 200
mH(GeV/c2)
95% CL Limit/SM
Tevatron Run II Preliminary, L=0.9-1.9 fb-1
D∅ Expected
CDF Expected
Tevatron Expected
Tevatron Observed
LEP Limit
SM
Figure 6: Upper bound on the SM Higgs boson
cross section obtained by combining CDF
and DØ search results, as a function of the mass
of the Higgs boson sought. The limits are shown
as a multiple of the SM cross section. The ratios
of different production and decay modes
are assumed to be as predicted by the SM. The
solid curve shows the observed upper bound, the
dashed black curve shows the median expected
upper bound assuming no signal is present, and
the colored bands show the 68% and 95% probability
bands around the expected upper bound.
The CDF and DØ combined expected limits are
also shown separately. See Ref. 59 for details
and status of these results.
Around mH = 135 GeV, where all branching fractions are
below 50%, no channel is dominant and the overall sensitivity is
July 16, 2008 11:42
– 15–
weaker. At these masses, the WH → WWW∗ channel 1 brings
further sensitivity [60–62] beyond the bb channel alone.
To probe masses above 135 GeV, the dominant H → WW∗
decay mode is best exploited in direct gg → H production,
using the leptonic decays of the W± which provide a clean,
distinct final state. The WW pair issued from a Higgs boson
decay has a spin correlation which is different from that of
the dominant background, electroweak WW production. These
spin correlations are transmitted to the distributions of observed
leptons, providing a handle to separate the signal from
the background. The invariant mass of the Higgs boson decay
products cannot be reconstructed due to the undetected neutrinos,
but the sensitivity is nevertheless significant. Results
were published with 0.4 fb−1 [63,64]. The current updates
with ∼ 2 fb−1 of data [65,66] allow to set a combined expected
(observed) upper limit on the gg → H cross section 1.9 (1.4)
times higher than the SM prediction at mH = 160 GeV [59].
Overall, the combined CDF and DØ analyses are expected
to test, at the 95% C.L. or better, the SM Higgs boson predictions
for masses between the LEP limit and about 185 GeV
before the end of Run II (see Fig. 6). The channels used at
the Tevatron for Higgs masses below 130 GeV are different
from those dominantly used at the LHC, hence with the full
Run II luminosity, they are expected to provide complementary
information if a low mass Higgs boson exists.
Studies to assess the sensitivity to diffractive Higgs production
at the Tevatron and the LHC are being actively pursued
[67]. Three different diffractive production mechanisms
can be considered: exclusive production, p¯p, pp → p +H + ¯p, p;
inclusive production, p¯p, pp → X +H +Y ; and central inelastic
production, p¯p, pp → p+(HX)+¯p, p, where a plus sign indicates
the presence of a rapidity gap. Tests of the different production
mechanisms using appropriate final states in the Tevatron data
are important for improving predictions for diffractive Higgs
production at the LHC.
1 The star indicates that below the H → W+W− threshold, one of the
W± bosons is virtual.
July 16, 2008 11:42
– 16–
Prospects for SM Higgs Boson Searches at the LHC
At the LHC, the main production processes will be gluon
fusion (gg → H), Higgs boson production in association with a
vector boson (W±H or ZH) or with a top-quark pair (ttH),
and the vector boson fusion process (qqH or qqH) [46]. This
array of production and decay modes, together with a large
integrated luminosity, allows for a variety of search channels.
Search strategies have been explored in many analyses over
the last years [18,19]. The searches in the inclusive channels
H → γγ (for low mass) and H → ZZ∗ → 4 (for high
mass) will be complemented with more exclusive searches in
order to strengthen the discovery potential, particularly at low
mass. Vector boson fusion processes, making use of forward
jet tagging and the decay modes H → τ+τ−, H → γγ as
well as H → W+W− [68] will provide additional sensitivity.
Other analyses, expected to be relevant at higher integrated
luminosities, select Higgs boson decays to bb or γγ in association
with a lepton from the decay of an associated W± boson, Z
boson, or top quark.
The projections of the ATLAS and CMS collaborations
show that, with an integrated luminosity of 10 - 30 fb−1, the
SM Higgs boson is expected to be discovered if it exists and
has a mass below 1 TeV. With a lower integrated luminosity,
the discovery of a Higgs boson with a mass below 130 GeV is
challenging. If the Higgs boson’s mass is in this range, a few
years of running may be needed to discover it. However, the
combination of the results in all channels of the two experiments
could allow for a 5σ discovery with about 5 fb−1 of data, once
the detectors and the composition of the selected event samples
are understood [69].
If a SM Higgs boson is discovered, its properties could
be studied at the LHC. Its mass could be measured by each
experiment with a precision of ∼0.1% in the 100–400 GeV mass
range [19,70]. This projection is based on the invariant mass
reconstruction from electromagnetic calorimeter objects, using
the decays H → γγ or H → ZZ∗ → 4. The precision would
be degraded at higher masses because of the larger decay width,
but even at mH ∼ 700 GeV a precision of 1% on mH is expected
July 16, 2008 11:42
– 17–
to be achievable. The width of the SM Higgs boson would be too
narrow to be measured directly for mH < 200 GeV; nonetheless,
it could be constrained indirectly using partial width measurements
[71,72]. For 300 < mH < 700 GeV, a direct measurement
of the decay width could be performed with a precision
of about 6%. The possibilities for measuring other properties
of the Higgs boson, such as its spin, its CP-eigenvalue, its
couplings to bosons and fermions, and its self-coupling, have
been investigated in numerous studies [70,73]. Given a sufficiently
high integrated luminosity (300 fb−1), most of these
properties are expected to be accessible to analysis for some
specific mass ranges. The measurement of Higgs self-couplings,
however, appears to be impossible at the LHC, although a
luminosity upgrade, the so-called Super-LHC, could allow for
such a measurement. The results of these measurements could
either firmly establish the Higgs mechanism, or point the way
to new physics.
III. Higgs Bosons in the MSSM
Electroweak symmetry breaking driven by a weakly-coupled
elementary scalar sector requires a mechanism to explain the
smallness of the electroweak symmetry breaking scale compared
with the Planck scale [74]. Within supersymmetric extensions
of the SM, supersymmetry-breaking effects, whose origins may
lie at energy scales much larger than 1 TeV, can induce a radiative
breaking of the electroweak symmetry due to the effects of
the large Higgs-top quark Yukawa coupling [75]. In this way,
the electroweak symmetry breaking scale is intimately tied to
the mechanism of supersymmetry breaking. Thus, supersymmetry
provides an explanation for the stability of the hierarchy
of scales, provided that supersymmetry-breaking masses are of
O(1 TeV) or less [74].
A fundamental theory of supersymmetry breaking is unknown
at this time. Nevertheless, one can parameterize the
low-energy theory in terms of the most general set of soft
supersymmetry-breaking renormalizable operators [76]. The
Minimal Supersymmetric extension of the Standard Model
(MSSM) [77] associates a supersymmetric partner to each
July 16, 2008 11:42
– 18–
gauge boson and chiral fermion of the SM, and provides a
realistic model of physics at the weak scale. However, even
in this minimal model with the most general set of soft
supersymmetry-breaking terms, more than 100 new parameters
are introduced [78]. Fortunately, only a small number of
these parameters impact the Higgs phenomenology through tree
level and quantum effects.
The MSSM contains the particle spectrum of a two-Higgsdoublet
model (2HDM) extension of the SM and the corresponding
supersymmetric partners. Two Higgs doublets, Hu
and Hd, are required to ensure an anomaly-free SUSY extension
of the SM and to generate mass for both “up”-type and
“down”-type quarks and charged leptons [7]. After the spontaneous
breaking of the electroweak symmetry, five physical Higgs
particles are left in the spectrum: one charged Higgs pair, H±,
one CP-odd scalar, A, and two CP-even states, H and h.
The supersymmetric structure of the theory imposes constraints
on the Higgs sector of the model. In particular, the
parameters of the Higgs self-interaction are not independent
of the gauge coupling constants. As a result, all Higgs sector
parameters at tree level are determined by only two free
parameters: the ratio of the Hu and Hd vacuum expectation
values,
tan β = vu/vd,
with v2u
+v2
d = (246 GeV)2; and one Higgs mass, conventionally
chosen to be mA. The other tree-level Higgs masses are then
given in terms of these parameters
m2
H± = m2
A +M2W
m2
H,h =
1
2

m2
A +M2Z
±

(m2
A +M2Z
)2 − 4(MZmA cos 2β)2

and α is the angle that diagonalizes the CP-even Higgs squaredmass
matrix.
An important consequence of these mass formulae is that
the mass of the lightest CP-even Higgs boson is bounded from
above:
mh ≤ MZ| cos 2β|.
July 16, 2008 11:42
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This contrasts sharply with the SM, in which this Higgs mass is
only constrained by perturbativity and unitarity bounds. In the
large mA limit, also called the decoupling limit [79], one finds
m2
h  (MZ cos 2β)2 and mA  mH  mH±, up to corrections
of O(MZ
2/mA). Below the scale mA, the effective Higgs sector
consists only of h, which behaves very similarly to the SM Higgs
boson.
The phenomenology of the Higgs sector depends on the
couplings of the Higgs bosons to gauge bosons and fermions.
The couplings of the two CP-even Higgs bosons to W± and Z
bosons are given in terms of the angles α and β by
ghV V = gVmV sin(β − α) gHV V = gVmV cos(β − α) ,
where gV ≡ 2mV /v. There are no tree-level couplings of A or
H± to V V . The couplings of the Z boson to two neutral Higgs
bosons, which must have opposite CP-quantum numbers, are
given by
ghAZ = gZ cos(β − α)/2
gHAZ = −gZ sin(β − α)/2 .
Charged Higgs-W boson couplings to neutral Higgs bosons and
four-point couplings of vector bosons and Higgs bosons can be
found in Ref. 7.
The tree-level Higgs couplings to fermions obey the following
property: the neutral components of one Higgs doublet
couples exclusively to down-type fermion pairs while the neutral
components of the other couples exclusively to up-type fermion
pairs [7,80]. This pattern of Higgs-fermion couplings defines
the Type-II (2HDM)2. Fermion masses are generated when the
neutral Higgs components acquire vacuum expectation values.
The relations between Yukawa couplings and fermion masses
are (in third-generation notation)
hb = √2mb/vd = √2mb/(v cos β)
ht = √2mt/vu = √2mt/(v sin β) .
2 In the Type-I 2HDM, one field couples to all fermions while the other
field is decoupled from them.
July 16, 2008 11:42
– 20–
Similarly, one can define the Yukawa coupling of the Higgs
boson to τ -leptons (the latter is a down-type fermion).
The couplings of the neutral Higgs bosons to f ¯ f relative to
the SM value, gmf/2MW, are given by
hb¯b : −sin α/ cos β = sin(β − α) − tan β cos(β − α) ,
ht¯t: cosα/ sin β = sin(β − α) + cot β cos(β − α) ,
Hb¯b : cosα/ cos β = cos(β − α) + tanβ sin(β − α) ,
Ht¯t: sinα/ sin β = cos(β − α) − cot β sin(β − α) ,
Ab¯b : γ5 tan β , At¯t : γ5 cot β ,
where the γ5 indicates a pseudoscalar coupling. In each relation
above, the factor listed for bb also pertains to τ+τ−. The
charged Higgs boson couplings to fermion pairs are given by
gH−t¯b =
g
√2MW
[mt cotβ PR + mb tanβ PL] ,
gH−τ+ν =
g
√2MW
[mτ tanβ PL] ,
with PL,R = (1 ∓ γ5)/2.
The Higgs couplings to down-type fermions can be significantly
enhanced at large tan β in the following two cases: (i) If
mA  MZ, then | cos(β − α)| 1, mH  mA, and the bbH
and bbA couplings have equal strength and are significantly
enhanced by a factor of tan β relative to the SM bbH coupling,
whereas the V VH coupling is negligibly small. The values of
the V V h and bbh couplings are equal to the corresponding couplings
of the SM Higgs boson. (ii) If mA <MZ and tan β  1,
then | cos(β − α)| ≈ 1 and mh  mA. In this case, the bbh
and bbA couplings have equal strength and are significantly
enhanced by a factor of tan β relative to the SM bbH coupling,
while the V V h coupling is negligibly small. In addition, the
V VH coupling is equal in strength to the SM VVH coupling
and one can refer to H as a SM-like Higgs boson, although the
value of the bbH coupling can differ from the corresponding SM
bbH coupling. Note that in both cases (i) and (ii) above, only
two of the three neutral Higgs bosons have enhanced couplings
to bb.
July 16, 2008 11:42
– 21–
Radiative Corrections to MSSM Higgs Masses and
Couplings
Radiative corrections can have a significant impact on the
values of Higgs masses and couplings in the MSSM. Important
contributions come from loops of SM particles as well as their
supersymmetric partners. The dominant effects arise from the
incomplete cancellation between top and scalar-top (stop) loops.
For large tan β, effects from the bottom-sbottom sector are also
relevant. The stop and sbottom masses and mixing angles depend
on the supersymmetric Higgsino mass parameter μ and on
the soft-supersymmetry-breaking parameters [77]: MQ, MU,
MD, At and Ab, where the first three are the left-chiral and the
two right-chiral top and bottom scalar quark mass parameters,
respectively, and the last two are the trilinear parameters that
enter the off-diagonal squark mixing elements: Xt ≡ At−μ cot β
and Xb ≡ Ab − μ tan β. The corrections affecting the Higgs boson
masses, production, and decay properties depend on all
of these parameters. For simplicity, we shall initially assume
that At, Ab and μ are real parameters. The impact of complex
phases on MSSM parameters, which will induce CP-violation
in the Higgs sector, is addressed below.
The radiative corrections to the Higgs masses have been
computed using a number of techniques, with a variety of
approximations [81–91]. They depend strongly on the top
quark mass (∼ m4t
) and the stop mixing parameter Xt, and
there is also a logarithmic dependence on the stop masses. One
of the most striking effects is the increase of the upper bound
of the light CP-even Higgs mass, as first noted in [81,82].
The value of mh is maximized for large mA  MZ, when all
other MSSM parameters are fixed. Moreover, tan β  1 also
maximizes mh, when all other parameters are held fixed. Taking
mA large (the decoupling limit) and tan β  1, the value of mh
can be further maximized at one-loop level for Xt  √6MSUSY,
where MSUSY  MQ  MU  MD is an assumed common value
of the soft SUSY-breaking squark mass parameters. This choice
of Xt is called the “maximal-mixing scenario” which will be
indicated by mh-max. Instead, for Xt = 0, which is called the
“no-mixing scenario,” the value of mh has its lowest possible
July 16, 2008 11:42
– 22–
value, for fixed mA and all other MSSM parameters. The value
of mh also depends on the specific value of MSUSY and μ
and more weakly on the electroweak gaugino mass as well as
the gluino mass at two-loop level. For example, raising MSUSY
from 1 TeV to 2 TeV can increase mh by 2-5 GeV. Variation
of the value of mt by 1 GeV changes the value of mh by about
the same amount. For any given scenario defined by a full set
of MSSM parameters, we will denote the maximum value of
mh by mmax
h (tan β), for each value of tan β. Allowing for the
experimental uncertainty on mt and for the uncertainty inherent
in the theoretical analysis, one finds for MSUSY 2 TeV, large
mA and tan β  1, mmax
h = 135 GeV in the mh-max scenario,
and mmax
h = 122 GeV in the no-mixing scenario. In practice,
parameter values leading to maximal mixing are not obtained
in most models of supersymmetry breaking, so typical upper
limits on mh will lie between these two extremes. The relatively
small mass of the lightest neutral scalar boson is a prediction
for both the CP-conserving (CPC) and CP-violating (CPV )
scenarios [92,93], which emphasizes the importance of the
searches at currently available and future accelerators.
Radiative corrections also modify significantly the values of
the Higgs boson couplings to fermion pairs and to vector boson
pairs. The tree-level Higgs couplings depend strongly on the
value of cos(β−α). In a first approximation, when radiative corrections
of the Higgs squared-mass matrix are computed, the diagonalizing
angle α is shifted from its tree-level value, and hence
one may compute a “radiatively-corrected” value for cos(β−α).
This shift provides one important source of the radiative corrections
to the Higgs couplings. In particular, depending on the
sign of μXt and the magnitude of Xt/MSUSY, modifications of α
can lead to important variations of the SM-like Higgs boson
coupling to bottom quarks and tau leptons [90]. Additional
contributions from the one-loop vertex corrections to tree-level
Higgs couplings must also be considered [86,94–100]. These
contributions alter significantly the Higgs-fermion Yukawa couplings
at large tan β, both in the neutral and charged Higgs
sector. Moreover, these radiative corrections can modify the
July 16, 2008 11:42
– 23–
basic relationship gh,H,Ab¯b /gh,H,Aτ+τ− ∝ mb/mτ , and change
the main features of MSSM Higgs phenomenology.
Decay Properties of MSSM Higgs Bosons
In the MSSM, neglecting CP-violating effects, one must
consider the decay properties of three neutral Higgs bosons
and one charged Higgs pair. In the region of parameter space
where mA  mZ and the masses of supersymmetric particles
are large, the decoupling limit applies, and the decay rates of
h into SM particles are nearly indistinguishable from those of
the SM Higgs boson. Hence, the h boson will decay mainly
to fermion pairs, since the mass, less than about 135 GeV, is
far below the W+W− threshold. The SM-like branching ratios
of h are modified if decays into supersymmetric particles are
kinematically allowed [101]. In addition, if light superpartners
exist that can couple to photons and/or gluons, then the decay
rates to gg and γγ could deviate from the corresponding SM
rates. In the decoupling limit, the heavier Higgs states, H,
A and H±, are roughly mass degenerate, and their decay
branching ratios strongly depend on tan β as shown below.
For values of mA ∼ O(MZ), all Higgs boson states lie below
200 GeV in mass. In this parameter regime, there is a significant
area of the parameter space in which none of the neutral Higgs
boson decay properties approximates that of the SM Higgs
boson. For tan β  1, the resulting Higgs phenomenology shows
marked differences from that of the SM Higgs boson [102] and
significant modifications to the bb and/or the τ+τ− decay rates
may occur via radiative effects.
After incorporating the leading radiative corrections to
Higgs couplings from both QCD and supersymmetry, the following
decay features are relevant in the MSSM. The decay
modes h,H,A → bb, τ+τ− dominate the neutral Higgs boson
decay modes when tan β is large for all values of the Higgs
masses. For small tan β, these modes are significant for neutral
Higgs boson masses below 2mt (although there are other
competing modes in this mass range), whereas the tt decay
mode dominates above its kinematic threshold. In contrast to
the SM Higgs boson, the vector boson decay modes of H are
strongly suppressed at large mH due to the suppressed HV V
July 16, 2008 11:42
– 24–
couplings in the decoupling limit. For the charged Higgs boson,
H+ → τ+ντ dominates below t¯b threshold, while H+ → t¯b
dominates for large values of mH±. For low values of tan β
(1) and low values of the charged Higgs mass ( 120 GeV),
the decay mode H+ → c¯s becomes relevant.
In addition to the decay modes of the neutral Higgs bosons
into fermion and gauge boson final states, additional decay
channels may be allowed which involve scalars of the extended
Higgs sector, e.g., h → AA. Supersymmetric final states
from Higgs boson decays into charginos, neutralinos and thirdgeneration
squarks and sleptons can be important if they are
kinematically allowed [103]. One interesting possibility is a significant
branching ratio for the decay of a neutral Higgs boson
to the invisible mode ˜χ01
˜χ01
(where the lightest neutralino ˜χ01
is the lightest supersymmetric particle) [104], which poses a
significant challenge at hadron colliders.
Searches for Neutral Higgs Bosons (CPC Scenario)
Most of the experimental investigations carried out at LEP
and the Tevatron assume CP-conservation (CPC) in the MSSM
Higgs sector. In many cases the search results are interpreted in
a number of specific benchmark models where a representative
set of the relevant SUSY breaking parameters are specified [92].
Some of these parameter choices illustrate scenarios in which
the detection of Higgs bosons at LEP or in hadron collisions is
experimentally challenging due to the limited phase space or the
suppression of the main discovery channels. For instance, the
mh-max scenario defined above maximizes the allowed values
of mh, for a given tanβ, MSUSY, and mt, leading to relatively
conservative exclusion limits.
Searches for Neutral MSSM Higgs Bosons at LEP
In e+e− collisions at LEP energies, the main production
mechanisms of the neutral MSSM Higgs bosons are the Higgsstrahlung
processes e+e− → hZ, HZ and the pair production
processes e+e− → hA, HA, while the fusion processes play a
marginal role. The cross sections can be expressed in terms of
the SM cross section and the parameters α and β introduced
July 16, 2008 11:42
– 25–
above. For the light CP-even Higgs boson h the following
expressions hold, in good approximation,
σhZ = sin2(β − α)σSM
hZ, σhA = cos2(β − α)λ σSM
hZ
where σSM
hZ stands for a SM cross section with a SM Higgs boson
of mass equal to mh. The phase space functions are
λ = λ3/2
Ah /

λ1/2
Zh (12M2Z
/s + λZh)

and λij = [1 − (mi +mj)2/s][1 − (mi −mj )2/s], where s is the
square of the e+e− collision energy. These Higgs-strahlung and
pair production cross sections are complementary since sin2(β−
α)+cos2(β−α) = 1. The cross sections for the heavy scalar boson
H are obtained by interchanging sin2(β−α) and cos2(β−α)
and replacing the index h by H in the above expressions, and
by defining σSM
HZ similarly to σSM
hZ . The Higgs-strahlung process
e+e− → hZ is relevant for large mA > mmax
h (tan β) or
low mA < mmax
h (tan β) and low tanβ; while the pair-production
process e+e− → hA is relevant for low mA < mmax
h (tan β).
The heavy CP-even H boson contributes when kinematically
allowed via the Higgs-strahlung process for low mA <
mmax
h (tan β), or for large mA > mmax
h (tan β) via the pair
production process e+e− → HA.
The searches at LEP exploit the complementarity between
the Higgs-strahlung process e+e− → hZ, and the pairproduction
process e+e− → hA. In addition, when mA <
mmax
h (tan β), the H boson has SM-like couplings to the Z boson,
so if kinematically allowed, e+e− → HZ is also considered.
For Higgs-strahlung, the searches for the SM Higgs boson are
re-interpreted, taking into account the MSSM reduction factor
sin2(β −α) for h (cos2(β −α) for H). For pair production, dedicated
searches are performed for the (bb)(bb) and (τ+τ−)(qq)
final states.
July 16, 2008 11:42
– 26–
1
10
0 20 40 60 80 100 120 140
mh (GeV/c2)
tanβ
Excluded
by LEP
Theoretically
Inaccessible
mh-max
Figure 7: The MSSM exclusion contours, at
95% C.L. (light-green) and 99.7% CL (darkgreen),
obtained by LEP for the CPC mh-max
benchmark scenario, with mt = 174.3 GeV. The
figure shows the excluded and theoretically inaccessible
regions in the (mh, tan β) projection.
The upper edge of the theoretically allowed region
is sensitive to the top quark mass; it is
indicated, from left to right, for mt = 169.3,
174.3, 179.3 and 183.0 GeV. The dashed lines
indicate the boundaries of the regions which are
expected to be excluded on the basis of Monte
Carlo simulations with no signal (from Ref. 16).
The limits from the four LEP experiments are described in
Refs. [40,41,105,106]. The combined LEP data did not reveal
any excess of events which would indicate the production of
Higgs bosons, and combined limits were derived [16]. These
limits are shown in Fig. 7 for the mh-max scenario, in the (mh,
tan β) parameter plane (see Ref. 16 for other projections and
July 16, 2008 11:42
– 27–
other benchmark models). For values of tan β below ∼ 5, the
limit on mh is nearly that of the SM searches, as sin2(β−α) ≈ 1.
For higher values of tan β, the e+e− → hA searches become the
most important, and they do not set as stringent a limit on mh.
In this scenario, the 95% C.L. mass bounds are mh > 92.8 GeV
and mA > 93.4 GeV, and values of tan β from 0.7 to 2.0 are
excluded taking mt = 174.3 GeV. This excluded tan β range
depends on MSUSY and mt; larger values of either of these
masses increase the Higgs mass, and reduce the excluded range
of tan β. Furthermore, the uncertainty on the SM-like Higgs
mass from higher-order corrections, which were not included in
the current analysis, is about 3 GeV [107].
The neutral Higgs bosons may also be produced by Yukawa
processes e+e− → ffφ, where the Higgs particle φ ≡ h, H, A,
is radiated off a massive fermion (f ≡ b or τ±). These processes
can be dominant at low masses, and whenever the e+e− → hZ
and hA processes are suppressed. The corresponding ratios of
the ffh and ffA couplings to the SM coupling are sin α/ cos β
and tan β, respectively. The LEP data have been used to search
for bb bb, bbτ+τ−, and τ+τ− τ+τ− final states [108,109]. Regions
of low mass and high enhancement factors are excluded
by these searches.
Searches for Neutral MSSM Higgs Bosons at Hadron
Colliders
The production mechanisms for the SM Higgs boson at
hadron colliders can also be relevant for the production of
the MSSM neutral Higgs bosons. However, one must take into
account the possibility of enhanced or suppressed couplings
with respect to those of the Standard Model, since these can
significantly modify the production cross-sections of neutral
Higgs bosons. The supersymmetric-QCD corrections due to the
exchange of virtual squarks and gluinos may modify the cross
sections depending on the values of these supersymmetric particle
masses. The MSSM neutral Higgs production cross sections
at hadron colliders have been computed in Refs. [90,100,110].
Over a large fraction of the MSSM parameter space, one
of the CP-even neutral Higgs bosons (h or H) couples to the
July 16, 2008 11:42
– 28–
vector bosons with SM-like strength and has a mass below
135 GeV. As shown in the SM Higgs section above (Fig. 6), the
current searches for SM-like Higgs bosons at the Tevatron are
not yet able to cover that mass range. However, if the expected
improvements in sensitivity are achieved, the regions of MSSM
parameter space in which one of these two scalars behaves like
the SM Higgs will also be probed [111].
Scenarios with enhanced Higgs boson production cross sections
are studied at the Tevatron. The best sensitivity is in
the regime with low to moderate mA and with large tan β
which enhances the couplings of the Higgs bosons to down-type
fermions. The corresponding limits on the Higgs production
cross section times the branching ratio of the Higgs boson into
down-type fermions can be interpreted in MSSM benchmark
scenarios [112]. If φ = A,H for mA > mmax
h , and φ = A, h for
mA < mmax
h , the most promising channels at the Tevatron are
bbφ, φ → bb or φ → τ+τ−, with three tagged b-jets or bτ τ in
the final state, respectively, and the inclusive pp → φ → τ+τ−
process, with contributions from both gg → φ and bbφ production.
Although Higgs boson production via gluon fusion has a
higher cross section than via associated production, it cannot
be used to study the φ → bb decay mode since the signal is
overwhelmed by QCD background.
The CDF and DØ collaborations have searched for neutral
Higgs bosons produced in association with bottom quarks
and which decay into bb [113,114], or into τ+τ− [115]. The
most recent searches in the bbφ channel with φ → bb analyze
approximately 1 fb−1 of data. Dedicated triggers are used to
collect the data samples, but the multijet QCD background remains
very large. These triggers require the presence of at least
three jets, and also require tracks reconstructed with large impact
parameters which point near calorimeter energy deposits.
The data are analyzed by requiring three well-separated jets
with reconstructed secondary vertices indicating the presence
of B hadrons. The invariant mass of the two leading jets would
be more sharply peaked for the Higgs boson signal than for
the background. The QCD background rates and shapes are
July 16, 2008 11:42
– 29–
1
10
10 2
100 120 140 160 180 200 220 240
mφ (GeV/c2)
95% C.L. Limit on σ×BR (pb)
Tevatron Run II Preliminary
CDF bbb Observed Limit 1 fb-1
CDF bbb Expected Limit
D∅ bbb Observed Limit 0.3 fb-1
D∅ bbb Expected Limit
D∅ ττ Observed Limit 1 fb-1
D∅ ττ Expected Limit
CDF ττ Observed Limit 1.8 fb-1
CDF ττ Expected Limit
Figure 8: The 95% C.L. limits on the production
cross section times the relevant decay
branching ratios for the Tevatron searches for
φ → b¯b and φ → τ+τ−. The observed limits
are indicated with solid lines, and the expected
limits are indicated with dashed lines. The limits
are to be compared with the sum of signal
predictions for Higgs boson with similar masses.
The decay widths of the Higgs bosons are assumed
to be much smaller than the experimental
resolution.
inferred from data control samples, in particular, the sample
with two b tagged jets and a third, untagged jet. Monte Carlo
models are used to estimate the biases on the shapes of the
background predictions due to the requirement of a third b tag.
Separate signal hypotheses are tested and limits are placed on
σ(pp → bbφ)×BR(φ → b¯b). Fig. 8 shows the upper limits from
CDF and DØ assuming that the decay widths of the Higgs
bosons are small compared with the experimental resolution.
CDF and DØ have also performed searches for inclusive
production of Higgs bosons with subsequent decays to τ+τ−
July 16, 2008 11:42
– 30–
using dedicated triggers designed for these searches [116–119].
Tau leptons are more difficult to identify than jets containing
B-hadrons, as only some of the possible τ lepton decays are
sufficiently distinct from the jet backgrounds. Both CDF and
DØ search for pairs of isolated tau leptons; one of the tau leptons
is required to decay leptonically (either to an electron and
two neutrinos, or a muon and two neutrinos), while the other
tau may decay either leptonically or hadronically. Requirements
placed on the energies and angles of the visible tau decay products
help to reduce the background from W+jets processes,
where a jet is falsely reconstructed as a tau lepton. The dominant
remaining background process is Z → τ+τ−, which can
be separated from a Higgs boson signal by using the invariant
mass of the observed decay products of the tau leptons. Fig. 8
shows the limits on σ(pp → φ + X) × BR(φ → τ+τ−) for the
CDF and DØ searches, which use 1.0 and 1.8 fb−1 of data,
respectively. The decay widths of the Higgs bosons are assumed
to be small compared with the experimental resolution, which
is much broader in the tau channels than in the bbb(b) search,
due to the presence of energetic neutrinos in the tau decay
products.
In order to interpret the experimental data in terms of
MSSM benchmark scenarios, it is necessary to consider carefully
the effect of radiative corrections on the production and
decay processes. The bounds from the bbφ, φ → bb channel
depend strongly on the radiative corrections affecting the relation
between the bottom quark mass and the bottom Yukawa
coupling. In the channels with τ+τ− final states, however, compensations
occur between large corrections in the Higgs boson
production and decay. The total production rate of bottom
quarks and τ pairs mediated by the production of a CP-odd
Higgs boson in the large tan β regime is approximately given by
σ(bbA) × BR(A → bb) 
σ(bbA)SM
tan2 β
(1 + Δb)2
9
(1 + Δb)2 + 9
,
July 16, 2008 11:42
– 31–
and
σ(gg → A, bbA) × BR(A → τ+τ−) 
σ(gg → A, bbA)SM
tan2 β
(1 + Δb)2 + 9
,
where σ(bbA)SM and σ(gg → A, bbA)SM denote the values of
the corresponding SM Higgs boson cross sections for a SM
Higgs boson mass equal to mA. The function Δb includes
the dominant effects of SUSY radiative corrections for large
tan β [98,99]. The main radiative contributions in Δb depend
strongly on tan β and on the SUSY mass parameters [90]. The
bbA channel is more sensitive to the value of Δb through the
factor 1/(1 + Δb)2 than the inclusive τ+τ− channel, for which
this leading dependence on Δb cancels out. As a consequence,
the limits derived from the inclusive τ+τ− channel depend less
on the precise MSSM scenario chosen than those of the bbA
channel.
The production and decay rates of the CP-even Higgs
bosons with tan β-enhanced couplings to down-type fermions –
H (or h) for mA larger (or smaller) than mmax
h , respectively –
are governed by formulae similar to the ones presented above.
At high tan β, one of the CP-even and the CP-odd Higgs
bosons are nearly degenerate in mass enhancing the signal cross
section by roughly a factor of two, without complicating the
experimental signature except in a small mass region in which
the three neutral MSSM Higgs boson masses are close together
and each boson contributes to the total production rate. A
detailed discussion of the impact of radiative corrections in
these search modes is presented in Ref. 112.
The excluded domains for the inclusive φ → τ+τ− channels
are shown in Fig. 9, in the (mA, tan β) projection, considering
the contribution of both the CP-odd and CP-even neutral
Higgs bosons with enhanced couplings to bottom quarks. Also
shown in the figure are the LEP limits, for the no-mixing
and the mh-max scenarios. The limits from the Tevatron are
shown only for the no-mixing scenario, but, as discussed above,
due to the tiny dependence of this channel under variations
of the SUSY parameter space, the Tevatron limits are nearly
July 16, 2008 11:42
– 32–
0 100 120 140 160 180 200 220 240
20
40
60
80
100
LEP 2
mA (GeV/c2)
no mixing
no mixing
mh- max
tanβ
CDF

μ<0
Tevatron Preliminary
MSSM Higgs →ττ
95% CL Exclusion
DØ (1.0 fb-1)
CDF (1.8 fb-1)
Figure 9: The 95% C.L. MSSM exclusion contours
obtained by CDF and DØ in the H → τ+τ− searches in the no-mixing benchmark scenario
with μ = −200 GeV, projected onto the
(mA, tan β) plane [118,119]. The Tevatron limits
for the mh-max scenario are nearly the same
as in the no-mixing scenario. Also shown are the
regions excluded by LEP searches [16], separately
for the mh-max scenario (darker shading)
and the no-mixing scenario, (lighter shading).
The LEP limits are shown for a top quark
mass of 174.3 GeV (the Tevatron results are not
sensitive to the precise value of the top mass).
identical in the mh-max scenario. Even though BR(φ → b¯b)
exceeds BR(φ → τ+τ−) by an order of magnitude for the
models considered, the bbb(b) channel limits are weaker due to
the much larger background, and the τ+τ− channels exclude
the domain tested by the bbb(b) channels. The interpretation
of the bbb(b) data includes treatment of the Higgs boson decay
widths [114], further reducing the sensitivity of this channel.
The sensitivity of the Tevatron searches will improve with
the continuously growing data samples and with the combination
of all channels of both experiments. The small backgrounds
in the τ+τ− channels, and the fact that better exclusions in the
July 16, 2008 11:42
– 33–
bbb(b) channel imply narrower Higgs decay widths, which feeds
back to improve the sensitivity of the searches, mean that the
limits on the cross sections are expected to improve faster than
1/√L, where L is the integrated luminosity. Eventually, tan β
down to about 20 should be tested for values of mA up to a few
hundred GeV. The projected sensitivity by the end of Run II
for the associated production of a SM Higgs boson in W±H
and ZH should have a strong impact on the excluded domains
in Fig. 9. In the no-mixing benchmark scenario, the LEP limits
have been obtained assuming mt = 174.3 GeV. For a lower top
mass, as presently measured, the excluded LEP region becomes
larger towards higher tan β, and for MSUSY  1 TeV, this
scenario would be strongly constrained. The combination of the
LEP and Tevatron searches is expected to probe vast regions of
the tan β-mA plane.
Searches for charged Higgs bosons at the Tevatron are
presented in Section IV, in the more general framework of the
2HDM.
Prospects for discovering the MSSM Higgs bosons at the
LHC have been explored in detail, see Refs. [70,73] for reviews
of these studies. They predict that the reach of the LHC
experiments would be sufficient to discover MSSM Higgs bosons
in many different channels. The main channels for the SM-like
Higgs boson are expected to be qqφ → qqτ+τ− and inclusive
φ → γγ,
Robin Michael   Tue Nov 10, 2009 7:31 am GMT
I use a spell checker.