Download Outstanding questions: physics beyond the Standard Model

Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
Phil. Trans. R. Soc. A (2012) 370, 818–830
doi:10.1098/rsta.2011.0452
REVIEW
Outstanding questions: physics beyond the
Standard Model
B Y J OHN E LLIS1,2, *
1 Theory
Division, Department of Physics, CERN, 1211 Geneva 23, Switzerland
Particle Physics and Cosmology Group, Department of Physics,
King’s College London, The Strand, London WC2R 2LS, UK
2 Theoretical
The Standard Model of particle physics agrees very well with experiment, but many
important questions remain unanswered, among them are the following. What is
the origin of particle masses and are they due to a Higgs boson? How does one understand
the number of species of matter particles and how do they mix? What is the origin of the
difference between matter and antimatter, and is it related to the origin of the matter
in the Universe? What is the nature of the astrophysical dark matter? How does one
unify the fundamental interactions? How does one quantize gravity? In this article, I
introduce these questions and discuss how they may be addressed by experiments at the
Large Hadron Collider, with particular attention to the search for the Higgs boson and
supersymmetry.
Keywords: particle physics; Higgs boson; supersymmetry; Large Hadron Collider
1. The Standard Model and its open questions
All the visible matter in the Universe and the known forces between matter are
described well by the Standard Model. Within the Standard Model, the strong
interactions reflect invariance under the local SU(3) colour gauge group, and
the electromagnetic and weak interactions are described by a Lagrangian that
is invariant under local weak isospin and hypercharge gauge transformations,
described using the SU(2) ⊗ U (1) group, which can be written as
1
L = − Famn Famn
4
+ ij̄/
Dj + h.c.
+ ji yij jj f + h.c.
+ |Dm f|2 − V (f).
(1.1)
*[email protected]
One contribution of 15 to a Discussion Meeting Issue ‘Physics at the high-energy frontier: the Large
Hadron Collider project’.
818
This journal is © 2012 The Royal Society
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
Review. Outstanding questions
819
The first line in (1.1) contains the kinetic terms for the gauge sector of the theory,
with a running over all the gauge fields. Associated with the three gauge groups,
there are three couplings g1,2,3 . The second line in (1.1) describes the interactions
between the matter fields j and the gauge fields. The third line is the Yukawa
sector and incorporates the interactions between the matter fields and the Higgs
field, f, which are thought to be responsible for giving fermions their masses
when electroweak symmetry breaking occurs. The fourth and final line in (1.1)
describes the Higgs sector itself. The first piece is the kinetic term, and the second
piece of the final line of (1.1) is the Higgs potential V (f), which takes the form
V (f) = −m2 |f|2 + l|f|4
(1.2)
in the Standard Model. It should be noted that, whereas the first two lines
of (1.1) have been confirmed in many different experiments, there is no direct
experimental evidence for the last two lines. One of the main objectives of the
Large Hadron Collider (LHC) is to discover whether it is right, needs modification,
or is simply wrong.
The gauge sector of the Standard Model has four parameters: the three gauge
couplings and a charge-parity (CP)-violating phase in the strong interactions.
The task of simplifying this sector is the problem of unification. The Yukawa
interactions have a total of 13 parameters: three charged-lepton masses, six quark
masses, three Cabibbo–Kobayashi–Maskawa angles and another CP-violating
phase. Understanding this sector is the problem of flavour. Finally, the minimal
Higgs sector shown in (1.1) has two parameters, namely quadratic and quartic
couplings. Understanding this sector is the problem of mass. Overall, the total
number of parameters in the Standard Model is 19, and then there are neutrino
masses and mixing to think about . . .. Surely nobody can believe that the
Standard Model is the end of the particle story?
2. The Large Hadron Collider and the open questions beyond the
Standard Model
As we have seen above, there is a standard list of open questions beyond the
Standard Model of particle physics. What is the origin of particle masses, and
are they due to a single elementary Higgs boson, or to something else? Why
are there so many types of matter particles, and why and how do matter and
antimatter particles differ (the origin of CP violation)—perhaps the answer to
this question is related to the origin of matter in the Universe? How does one
unify the fundamental forces, and how does one construct a quantum theory of
gravity? To these one might add a question whose answer surely lies beyond the
Standard Model, namely, what is the nature of the cold dark matter that makes
up some 80 per cent of the matter in the Universe?
The LHC may be able to address all these questions. One of its main
motivations has been to solve the mass problem, and its experiments should tell
us definitively whether or not there exists a Higgs boson resembling that in the
Standard Model. There is a large class of models in which cold dark matter is
composed of particles that were in thermal equilibrium in the early Universe, in
which case they should weigh approximately 1 TeV, and be produced at the LHC.
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
820
J. Ellis
One example of such a theory is supersymmetry, which would also assist in the
unification of the fundamental forces. Measuring the masses of supersymmetric
particles, if they exist, would be a great way of testing predictions based on such
theories. Finally, supersymmetry and extra dimensions are key aspects of string
theory, the only promising candidate for a consistent quantum theory of gravity,
which could be tested in very novel ways if the LHC produces microscopic black
holes. In the following, I review in more detail the prospects that the LHC might
cast light on these enticing scenarios. However, I would also like to emphasize
that the LHC is not the only game in particle physics: many phenomena such as
supersymmetry, extra dimensions, neutrino masses, grand unification and string
theory may be fully revealed only at very high energies that could be accessible
only via high-energy astrophysics and cosmology.
3. Why do particles weigh?
We all learnt at school that weight is proportional mass, as discovered by Newton,
and Einstein taught us that energy is related to mass via the famous equation
E = mc 2 . Unfortunately, these two honourable gentlemen forgot to explain to us
where the mass came from in the first place. The mechanism described in the
two bottom lines of (1.1) was proposed independently by Francois Englert and
Robert Brout and by Peter Higgs. The latter also pointed out explicitly that
this mechanism implied the existence of an unseen particle, now called the Higgs
boson, which has become in some sense the Holy Grail of particle physics, and
certainly the first target of the LHC.
As an analogy as to how the Englert–Brout–Higgs mechanism works, let us
imagine an infinite, featureless, flat, homogeneous and isotropic field of snow
(northern Canada, maybe). If we try to cross this snow field on skis, we skim
across it very fast, hardly interacting with it. This resembles a massless particle
that does not interact with the Higgs field, acquires no mass and always travels
at the speed of light. Now consider somebody with snowshoes: this person will
sink somewhat into the snow field (interact with the Higgs field), and be slowed
down (rather as a massive particle travels at less than the speed of light). Finally,
if you try to cross the Higgs snow field in just your boots, you will sink in deeply
and travel very slowly, just like a particle with a large mass that travels at much
less than the speed of light. According to this theory, masses are proportional
to couplings to the Higgs snow field, which are the Yukawa couplings yij seen in
the third line of (1.1). The Englert–Brout–Higgs mechanism does not explain the
pattern of these couplings, which is part of the flavour problem.
This analogy is not perfect (analogies are, by definition, imperfect), but it
can be carried further. For example, snow is made out of snowflakes and, by
analogy, the quantum of the Englert–Brout–Higgs field is the Higgs boson. Just
as snowflakes are composite objects, with no pair identical, it could also be
that the Higgs boson is not an elementary particle, but actually is composed
of more elementary constituents, and just one of a whole new spectroscopy of
particles. Then again, snow melts when you heat it and, by analogy, we expect
that the Englert–Brout–Higgs field would have been molten at the very high
temperatures in the very early Universe, at which epoch particles would have
had no masses.
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
821
Review. Outstanding questions
Δχ2
8
6
G fitter
Tevatron exclusion at 95% CL
10
4
2
0
100
150
SM
Mar 09
LEP exclusion at 95% CL
12
3s
2s
1s
200
mh (GeV)
250
300
Figure 1. The c2 function for the Standard Model as a function of the Higgs mass, combining [3]
the precision electroweak data [2] with the LEP [1] and Tevatron [4] exclusions. Green region,
theory uncertainty; solid line, fit including theory errors; dashed line, fit excluding theory errors.
(Online version in colour.)
4. The hunt for the Higgs
Direct searches for the Higgs boson by experiments at the large electron positron
collider (LEP) accelerator established the lower bound mh > 114.4 GeV [1].
Precision electroweak data [2] are sensitive to mh through quantum corrections,
and yield the preferred range [3]
mh = 96+31
−24 GeV.
(4.1)
The 95% confidence level (CL) upper limit on the mass of the Higgs boson is
169 GeV, if only the precision electroweak data are used. Recently, the Tevatron
experiments CDF and D0 have excluded a range of heavier masses within the
95% CL range [4]:
(4.2)
162 GeV < mh < 166 GeV.
A combined fit to all the data, shown in figure 1, yields the asymmetric
estimate [3]
(4.3)
mh = 120+12
−5 GeV
at the 68% CL, and a 95% CL upper limit of 143 GeV.
5. The Higgs boson as the door to new physics
If the Higgs mass is large, so is the Higgs quartic self-coupling l (1.2), and
renormalization effects cause it to blow up at some relatively low scale L, as
seen in figure 2, heralding the appearance of new non-perturbative physics. On
the other hand, if mh is small, negative renormalization by the large t-quark
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
822
J. Ellis
350
300
perturbativity bound
stability bound
finite-T metastability bound
zero-T metastability bound
l = 2p
mh (GeV)
l=p
shown are1s error bands, without theoretical errors
250
200
Tevatron exclusion at >95% CL
150
LEP exclusion
at >95% CL
100
4
6
8
10
12
14
16
18
log10 (L (GeV))
Figure 2. If the Standard Model Higgs boson weighs more than approximately 180 GeV, the Higgs
self-coupling blows up at some scale L below the Planck scale, inducing new non-perturbative
physics. If it weighs less than approximately 130 GeV, our current electroweak vacuum is unstable.
The data summarized in figure 1 disfavour the blow-up scenario at the 99% confidence level [5].
(Online version in colour.)
Yukawa coupling drives l < 0, leading to an instability in the electroweak vacuum,
unless new physics such as supersymmetry intervenes [6]. Only a narrow range of
mh ∈ (130, 180) GeV is compatible with the survival of the Standard Model at all
scales up to the Planck mass. This could be the ‘maximal conceivable disaster’
scenario for the LHC: a single Standard Model Higgs boson and nothing else! As
we have seen, the precision electroweak data favour small values of mh and hence
l, and the combination with the Tevatron exclusion (4.2) excludes the blow-up
scenario at the 99% CL [5]. The unstable-vacuum scenario of the Standard Model
is preferred, but the ‘disaster’ scenario is not even disfavoured at the 1s level.
How could one stabilize a theory with a light Higgs boson? Since it is the
top quark that destabilizes the electroweak potential, the simplest option is to
introduce a scalar particle with similar couplings. This can delay the collapse of
the potential, but the new coupling must be very finely tuned in order to avoid
another blow-up. The answer is to stabilize it with a new fermion. The new scalar
is much like the stop quark, the fermion is just like the Higgsino and the resulting
theory is very much like supersymmetry!
The stakes in the search for the Higgs boson are very high. How is the
electroweak symmetry broken? Is there such a thing as an elementary scalar field?
What is the fate of the Standard Model at high energies and temperatures? Did
mass appear when the Universe was a picosecond old? Does the Higgs boson need
help, e.g. from supersymmetry? Did the Higgs boson play a role in generating the
matter in the Universe? Was a related inflaton (or even the Higgs boson itself)
responsible for making the Universe so big and old? Why is there so little dark
energy, despite the propensity of the Higgs field to contribute many orders of
magnitude too much? What will we discover beyond the Higgs door?
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
Review. Outstanding questions
823
6. Where does the matter in the Universe come from?
This became an issue over 80 years ago, when Paul Dirac pointed out that
combining special relativity and quantum mechanics necessitated the existence
of antimatter, which was discovered among the cosmic rays soon after. Dirac
predicted that matter and antimatter particles would have equal masses but
opposite internal properties such as electric charges. It came as a big shock in
1964 when it was discovered that the weak interactions of matter and antimatter
were not quite equal and opposite. This small difference can be accommodated,
but not really explained, in the Standard Model via the electroweak phase
mentioned in §1.
The Russian physicist Andrei Sakharov proposed in 1967 that the small
laboratory difference between matter and antimatter might explain the fact that
the Universe today contains a (relatively) small amount of matter and a lot of
radiation, but no significant quantities of antimatter. He laid out three conditions
for generating this matter asymmetry: interactions capable of changing quarks
into leptons (which are predicted to exist in unified theories, but have never been
observed), a breakdown of thermal equilibrium during the early expansion of the
Universe (as might have occurred during a cosmological phase transition), and a
matter–antimatter difference (C and CP violation) as observed experimentally.
However, the charge conjugation (C) and CP violation observed so far, as
described within the Standard Model via phases in the Yukawa couplings yij , is
insufficient to generate the amount of matter seen in the Universe today, which
requires new physics beyond the Standard Model. There are some extensions
of the Standard Model at the TeV scale, such as supersymmetry, which are
in principle capable of generating enough matter, which might show up in the
Higgs sector. Alternatively, it might be generated by physics at a higher energy
scale, e.g. in the neutrino sector. Either way, there may be direct or indirect
indications of this new physics at the LHC, and the LHCb experiment is dedicated
to exploring such possibilities.
7. Dark matter
Another cosmological puzzle that requires new physics beyond the Standard
Model for its solution is the nature of dark matter. Astrophysicists and
cosmologists assure us that the formation of structures in the Universe and
their persistence today is possible only with the help of additional gravitational
attraction provided by some form of invisible non-relativistic matter. Various
astrophysical candidates such as black holes seem to be excluded, so attention
is focused on particle candidates for dark matter. In many scenarios, these dark
matter particles were once in thermal equilibrium with the rest of the particles in
the Universe, in which case, general arguments suggest that they probably weigh
less than about 1 TeV. In order to be ‘dark’ and not bind to ordinary matter,
dark matter particles should have neither electric charge nor strong interactions.
Many such dark matter particles have been proposed in the literature, with
the prototypical example being the lightest supersymmetric particle (LSP) [7].
However, there are other possibilities: the basic requirement is some conserved
quantum number to guarantee the stability of the dark matter particle, which
would be provided by a combination of baryon number, lepton number and spin
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
824
J. Ellis
in the supersymmetric case, called R-parity. A general feature of such scenarios
is the production of pairs of invisible particles at the LHC that would carry away
energy and momentum.
8. Unifying the fundamental interactions
It has been the dream of theoretical physicists ever since Einstein to unify the
fundamental interactions in a simplified mathematical framework. Einstein never
succeeded, but some of the ideas he developed find echos in modern theories of
unification. Most prominent among these is string theory, which offers a consistent
quantum-theoretical framework capable of unifying gravity with the other particle
interactions. String theory seems to require supersymmetry and also, in some
sense, extra dimensions of space, one of Einstein’s pet ideas.
There are many ways in which extra dimensions might show up at the
LHC ([8] and references therein), depending on their sizes and whether all the
fundamental interactions ‘feel’ them, or only gravity. In some of these scenarios,
energy and momentum ‘leak’ away into the extra dimensions; in others, there are
resonant Kaluza–Klein excitations of the known particles whose wave functions
are wrapped around the extra dimensions.
However, the possibility that has attracted the most widespread attention
(not all of it positive) has been that gravity might feel the extra dimensions
sufficiently to become strong at the TeV scale, making possible the production
of microscopic black holes at the LHC. Theories predicting such a possibility
also tell us that these microscopic black holes would be very unstable, and decay
spectacularly with the emission of energetic quarks, gluons, leptons, photons and
neutrinos. If such objects were to exist and be produced at the LHC, they would
provide wonderful laboratories for checking quantum theories of gravity such as
string theory.
9. The search for supersymmetry
Supersymmetry has already made several appearances in the above discussion,
unsurprisingly in view of the many motivations for it. Theorists were initially
enthusiastic about supersymmetry because of its beauty, but its prospective
relevance to experiments at the LHC stems from its ability to render the hierarchy
of mass scales more natural. This issue arose from calculations of the quantum
corrections to the Higgs mass and hence to the mass scale of the weak interactions,
which are quadratically divergent:
⎫
y2
L
⎪
+ ... ⎪
DmH2 = − f 2 2L2 + 6mf2 log
⎪
⎬
mf
16p
(9.1)
⎪
⎪
l
L
⎪
2
2
2
and
DmH = +
L − 2mf log
+ . . . ,⎭
16p2
mS
where yf is a generic Yukawa fermion–Higgs coupling (cf. line 3 of (1.1)), lS
is a generic scalar–Higgs coupling and L is a cut-off in momentum space. If
the Standard Model were to remain valid without modification up to some
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
825
Review. Outstanding questions
(a) 800
700
m0 (GeV)
600
500
(b) 1500
mh = 114 GeV
mh = 114 GeV
m χ ± = 104 GeV
ATLAS 0l 95% CL
1000
400
300
CMS MHT 95% CL
200
100
0
100 200 300 400 500 600 700 800 900 1000
m1/2 (GeV)
0
100
1000
2000
3000
m1/2 (GeV)
Figure 3. The (m1/2 , m0 ) plane of the CMSSM for sample values of the other supersymmetric model
parameters, showing the different theoretical, phenomenological, experimental and cosmological
constraints. (a) tan b = 10, m > 0; (b) tan b = 55, m > 0. There is no consistent electroweak vacuum
in the dark pink-shaded region at large m0 , the LSP would be charged in the brown-shaded region
at small m0 , b → sg excludes the green-shaded region, LEP excludes the regions to the left of the
dashed black and red lines by unsuccessful chargino and Higgs searches, respectively, and gm − 2
favours the paler shaded pink region. The LSP would have the appropriate cosmological density
in the narrow turquoise strip close to the boundaries of the allowed region [11]. ATLAS and CMS
constraints from 2010 LHC data are shown as yellow and purple lines, respectively [12,13]. (Online
version in colour.)
large scale L 1 TeV, each of the quadratically divergent expressions in (9.1)
would give contributions to the Higgs mass that greatly exceeds its physical
value. However, we note that these would cancel if lS = 2yf2 , which is precisely
the relation predicted in a supersymmetric theory. Moreover, this relation also
removes all the quadratic higher order quantum corrections, as well as some of the
logarithmic corrections. In this way, supersymmetry makes a light Higgs boson
technically ‘natural’, though it does not provide an explanation for the magnitude
of the electroweak scale.
In addition, supersymmetry predicts that the Higgs boson should be light,
with a mass around 120 GeV, as suggested by the available experimental data.
Furthermore, supersymmetry would facilitate grand unification, as well as being
needed for the consistency of string theory. Moreover, supersymmetry could
explain the apparent discrepancy between experiment and the Standard Model
calculation of the anomalous magnetic moment of the muon, gm − 2.
There are important constraints on supersymmetry owing to the absence of
particles at LEP and the Tevatron, the LEP lower limit on mh and the consistency
of b-quark decays with the Standard Model. Some hint of new physics at the TeV
scale may be provided by the measurement [9] of the anomalous magnetic moment
of the muon, gm − 2, which could be explained by supersymmetry, although there
are still uncertainties in the Standard Model calculation of gm − 2 [10]. The
measured density of dark matter, 0.097 < UDM h 2 < 0.122, provides a very tight
constraint on some combination of supersymmetric model parameters, if the LSP
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
826
J. Ellis
1000
900
t1 LSP
tan b = 10, A0 = 0, m > 0
1 fb–1 at 14 TeV
jets + MET (CMS)
800
100 pb–1 at 14 TeV
700
50 pb–1 at 10 TeV
600
500
400
full CMSSM
parameter space
300
68% CL
200
95% CL
100
0
NO EWSB
200
400
600
800
1000
1200
1400
1600
1800
2000
Figure 4. The preferred region in the (m0 , m1/2 ) plane of the CMSSM before the start-up of the
LHC, compared with the estimated discovery sensitivity of the LHC with different amounts of
luminosity and centre-of-mass energy [14]. The best-fit point is shown as a black circle, and the
68% and 95% CL regions are indicated by blue and red hatching, respectively. (Online version
in colour.)
provides the dark matter. The interplay of these constraints is shown in figure 3
for one particularly simple supersymmetric model with universal supersymmetrybreaking parameters m1/2 and m0 assumed at the grand unified theory (GUT)
scale, the constrained minimal supersymmetric model (CMSSM) [11].
10. Where is supersymmetry?
Before the start-up of the LHC, we made a global supersymmetric fit using a
frequentist approach to analyse the precision electroweak data, the LEP Higgs
mass limit, the cold dark matter density, b-decay data and (optionally) gm − 2. We
combined the likelihood functions from these different observables to construct
a global likelihood function that can be used to infer preferred regions of the
supersymmetric parameter space [14–16].
We see in figure 4 that the preferred region of the (m0 , m1/2 ) plane in the
CMSSM corresponds to relatively low masses where the relic LSP density is
brought into the Wilkinson Microwave Aniostropy Probe (WMAP) range by
coannihilations with light sleptons, particularly the lighter stau. The ‘focus-point’
region at large m0 is disfavoured, principally but not exclusively by gm − 2. If one
drops this constraint, considerably larger ranges of m0 and m1/2 would be allowed,
though small values were also slightly preferred by other pre-LHC data [14–16].
Figure 4 also compares the preferred regions of these (m0 , m1/2 ) planes with the
5s discovery reach of the LHC with given amounts of integrated luminosity at
certain centre-of-mass energies. The 5s discovery reach of the LHC with 1 fb−1 of
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
827
Review. Outstanding questions
1000
900
800
m1/2 (GeV/c2)
700
600
500
400
300
200
100
0
100
200
300
400
500
600
2
m0 (GeV/c )
700
800
900
1000
Figure 5. The preferred region in the (m0 , m1/2 ) plane of the CMSSM before and after incorporation
of the 2010 LHC data; ATLAS, CMS are compared [18,19]. The best-fit points are shown as stars,
and the 68% and 95% CL contours are indicated by red and blue lines, respectively. Also shown, in
black, is the region excluded by an initial examination of 165 pb−1 of 2011 ATLAS data. (Online
version in colour.)
luminosity at 7 TeV in the centre of mass would probably include all the 68% CL
regions in figure 4. It should be noted, however, that this conclusion is dependent
on the interpretation of gm − 2 and the theoretical calculation of b → sg decay
in the Standard Model. If the interpretations of these constraints are questioned,
more time might be required to discover supersymmetry.
Subsequent to these analyses, the CMS and ATLAS experiments have
published the results of several (unsuccessful) searches for supersymmetric
particles at the LHC using data taken in 2010 [12,13], focusing mainly on
the missing-energy signatures expected if the LSP provides the astrophysical
dark matter. These constraints are shown in figure 3 as yellow and red lines,
respectively. In addition, the LHCb experiment at the LHC has joined the
CDF and D0 experiments at the Fermilab Tevatron collider in setting upper
limits on the rare decay Bs → m+ m− , which is also an important constraint on
supersymmetric models. Another constraint comes from searches by ATLAS and
CMS for the heavier neutral Higgs bosons predicted in supersymmetric models
using 2010 data.
Based on these constraints and including also the constraint imposed by the
XENON100 experiment looking directly for cold dark matter [17], we found in
new global supersymmetric fits the results shown in figure 5 [18,19]. The best-fit
points are represented by green stars, and the 68% and 95% CL regions by solid
red and blue contours, respectively (the dotted lines are the current results if the
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
828
J. Ellis
1000
900
800
m1/2 (GeV/c2)
700
600
SPS1A #dagger
benchB2 #dagger
ben0
ben1
ben2
fittino pre
fittino35
fittino1
fittino2
fittino7
MC preLHC
MC + CMSαt
MC + ATLAS 1|
MC + ATLAS 0| + CMS MEt
500
400
300
200
100
0
100
200
300
400
500
m0
600
700
800
900
1000
(GeV/c2)
Figure 6. CMSSM fit points are projected on the (m0 , m1/2 ) plane. The best-fit points for different
datasets are indicated by different symbols: stars for pre-LHC fits, diamonds and circles for fits
including the first SUSY searches by CMS and ATLAS, triangles including all relevant 2010 LHC
data, and squares for estimates of the impacts of future LHC datasets with 1, 2, 7 fb−1 if SUSY
is not discovered. Also shown as crosses are two older benchmark points: SPS1a [20] and a similar
benchmark point B [21,22], which yields the right dark matter density. The various symbols
are also coded with different colours for different fitting groups, as shown in the legend. The
line illustrates the trend of these fits as stronger constraints are incorporated. (Online version
in colour.)
LHC constraints are omitted). Also shown in figure 5 are the preliminary results
from the early 2011 running of the LHC [12], which cut very close to the best-fit
point in the CMSSM.
Figure 6 shows the possible trajectory of best fits to the CMSSM parameters
if supersymmetry is excluded by larger amounts of integrated LHC luminosity. If
supersymmetry were not to be discovered with several inverse femtobarns of data,
one should undoubtedly consider alternative signatures of supersymmetry, and/or
question the interpretations of gm − 2 and b → sg used in the above analyses.
11. A conversation with Mrs Thatcher
Back in 1982, while she was Prime Minister of the UK, Mrs Thatcher visited
CERN and was introduced to British physicists. When she was told I was a
theoretical physicist, she asked me ‘What do you do?’ I explained that my job was
to think of things for the experiments to look for, and hope they find something
different. ‘Wouldn’t it be better if they found what you predicted?’ asked Mrs T.,
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
Review. Outstanding questions
829
who always liked her ideas to be vindicated. My response was that, in that case,
we would not be learning anything really new. Likewise, I sincerely hope that the
LHC will be remembered in the history of physics for something not described in
this article.
It is a pleasure to thank the organizers for their kind invitation to the Discussion Meeting, and
I acknowledge my collaborators, particularly the members of the MasterCode collaboration. This
work was supported partly by the London Centre for Terauniverse Studies (LCTS), using funding
from the European Research Council via the Advanced Investigator Grant 267352.
References
1 Barate, R. et al. [ALEPH, DELPHI, L3 and OPAL Collaborations, LEP Working Group for
Higgs boson searches]. 2003 Search for the standard model Higgs boson at LEP. Phys. Lett. B
565, 61–75. (doi:10.1016/S0370-2693(03)00614-2)
2 ALEPH, CDF, D0, DELPHI, L3, OPAL and SLD Collaborations, LEP Electroweak Working
Group, Tevatron Electroweak Working Group and SLD electroweak and heavy flavour
groups. 2009 Precision electroweak measurements and constraints on the standard model.
(http://arxiv.org/abs/0911.2604)
3 Flacher, H., Goebel, M., Haller, J., Hocker, A., Moenig, K. & Stelzer, J. 2009 Revisiting the
global electroweak fit of the standard model and beyond with Gfitter. Eur. Phys. J. C 60,
543–583. (doi:10.1140/epjc/s10052-009-0966-6)
4 Aaltonen, T. et al. [CDF and D0 Collaborations]. 2010 Combination of Tevatron searches for
the standard model Higgs boson in the W+ W− decay mode. Phys. Rev. Lett. 104, 061802.
(doi:10.1103/PhysRevLett.104.061802)
5 Ellis, J., Espinosa, J. R., Giudice, G. F., Hoecker, A. & Riotto, A. 2009 The probable fate of
the standard model. Phys. Lett. B 679, 369–375. (doi:10.1016/j.physletb.2009.07.054)
6 Ellis, J. & Ross, D. 2001 A light Higgs boson would invite supersymmetry. Phys. Lett. B 506,
331–336. (doi:10.1016/S0370-2693(01)00156-3)
7 Ellis, J., Hagelin, J. S., Nanopoulos, D. V., Olive, K. A. & Srednicki, M. 1984 Supersymmetric
relics from the big bang. Nucl. Phys. B 238, 453–476. (doi:10.1016/0550-3213(84)90461-9)
8 Grojean, C. 2009 New theories for the Fermi scale. (http://arxiv.org/abs/0910.4976)
9 Bennett, G. W. et al. 2006 Final report of the E821 muon anomalous magnetic moment
measurement at BNL. Phys. Rev. D 73, 072003. (doi:10.1103/PhysRevD.73.072003)
10 Davier, M., Hoecker, A., Malaescu, B., Yuan, C. Z. & Zhang, Z. 2010 Reevaluation of the
hadronic contribution to the muon magnetic anomaly using new e + e − → p+ p− cross section
data from BABAR. Eur. Phys. J. C 66, 1–9. (doi:10.1140/epjc/s10052-010-1246-1)
11 Ellis, J. & Olive, K. A. 2010 Supersymmetric dark matter candidates. In Particle dark matter:
observations, models and searches (ed. G. Bertone), ch. 8, pp. 142–163. Cambridge, UK:
Cambridge University Press. (http://arxiv.org/abs/1001.3651)
12 Aad, G. et al. ATLAS Collaboration. https://twiki.cern.ch/twiki/bin/view/AtlasPublic/Super
symmetryPublicResults.
13 Chatrchyan, S. et al. CMS Collaboration. https://twiki.cern.ch/twiki/bin/view/CMSPublic/
PhysicsResultsSUS.
14 Buchmueller, O. et al. 2008 Predictions for supersymmetric particle masses in the CMSSM
using indirect experimental and cosmological constraints. J. High Energy Phys. 2008, 117.
(doi:10.1088/1126-6708/2008/09/117)
15 Buchmueller, O. et al. 2009 Likelihood functions for supersymmetric observables in frequentist
analyses of the CMSSM and NUHM1. Eur. Phys. J. C 64, 391–415. (doi:10.1140/epjc/
s10052-009-1159-z)
16 Buchmueller, O. et al. 2011 Frequentist analysis of the parameter space of minimal supergravity.
Eur. Phys. J. C 71, 1583. (doi:10.1140/epjc/s10052-011-1583-8)
17 Aprile, E. et al. [XENON100 Collaboration]. 2011 Dark matter results from 100 live days of
XENON100 data. Phys. Rev. Lett. 107, 131302. (doi:10.1103/PhysRevLett.107.131302)
Phil. Trans. R. Soc. A (2012)
Downloaded from http://rsta.royalsocietypublishing.org/ on May 2, 2017
830
J. Ellis
18 Buchmueller, O. et al. 2011 Implications of initial LHC searches for supersymmetry. Eur. Phys.
J. C 71, 1634. (doi:10.1140/epjc/s10052-011-1634-1)
19 Buchmueller, O. et al. 2011 Supersymmetry and dark matter in light of LHC 2010 and Xenon100
data. (http://arxiv.org/abs/1106.2529)
20 Allanach, B. C. et al. 2002 The snowmass points and slopes: benchmarks for SUSY searches.
Eur. Phys. J. C 25, 113–123. (doi:10.1007/s10052-002-0949-3)
21 Battaglia, M., De Roeck, A., Ellis, J., Gianotti, F., Matchev, K. T., Olive, K. A., Pape, L. &
Wilson, G. 2001 Proposed post-LEP benchmarks for supersymmetry. Eur. Phys. J. C 22,
535–561. (doi:10.1007/s100520100792)
22 De Roeck, A., Ellis, J. R., Gianotti, F., Moortgat, F., Olive, K. A. & Pape, L. 2007
Supersymmetric benchmarks with non-universal scalar masses or gravitino dark matter. Eur.
Phys. J. C 49, 1041–1066. (doi:10.1140/epjc/s10052-006-0182-6)
Phil. Trans. R. Soc. A (2012)