outstanding questions: physics beyond the standard...

Phil. Trans. R. Soc. A (2012) 370, 818–830doi:10.1098/rsta.2011.0452

REVIEW

Outstanding questions: physics beyond theStandard Model

BY JOHN ELLIS1,2,*1Theory Division, Department of Physics, CERN, 1211 Geneva 23, Switzerland

2Theoretical Particle Physics and Cosmology Group, Department of Physics,King’s College London, The Strand, London WC2R 2LS, UK

The Standard Model of particle physics agrees very well with experiment, but manyimportant questions remain unanswered, among them are the following. What isthe origin of particle masses and are they due to a Higgs boson? How does one understandthe number of species of matter particles and how do they mix? What is the origin of thedifference between matter and antimatter, and is it related to the origin of the matterin the Universe? What is the nature of the astrophysical dark matter? How does oneunify the fundamental interactions? How does one quantize gravity? In this article, Iintroduce these questions and discuss how they may be addressed by experiments at theLarge Hadron Collider, with particular attention to the search for the Higgs boson andsupersymmetry.

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 aredescribed well by the Standard Model. Within the Standard Model, the stronginteractions reflect invariance under the local SU(3) colour gauge group, andthe electromagnetic and weak interactions are described by a Lagrangian thatis invariant under local weak isospin and hypercharge gauge transformations,described using the SU(2) ⊗ U (1) group, which can be written as

L = −14Fa

mnFamn

+ ij̄/Dj + h.c.

+ jiyijjjf + h.c.

+ |Dmf|2 − V (f). (1.1)

*[email protected]

One contribution of 15 to a Discussion Meeting Issue ‘Physics at the high-energy frontier: the LargeHadron Collider project’.

This journal is © 2012 The Royal Society818

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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 interactionsbetween the matter fields j and the gauge fields. The third line is the Yukawasector and incorporates the interactions between the matter fields and the Higgsfield, f, which are thought to be responsible for giving fermions their masseswhen 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 secondpiece 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 linesof (1.1) have been confirmed in many different experiments, there is no directexperimental evidence for the last two lines. One of the main objectives of theLarge 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 gaugecouplings and a charge-parity (CP)-violating phase in the strong interactions.The task of simplifying this sector is the problem of unification. The Yukawainteractions have a total of 13 parameters: three charged-lepton masses, six quarkmasses, three Cabibbo–Kobayashi–Maskawa angles and another CP-violatingphase. Understanding this sector is the problem of flavour. Finally, the minimalHiggs sector shown in (1.1) has two parameters, namely quadratic and quarticcouplings. Understanding this sector is the problem of mass. Overall, the totalnumber of parameters in the Standard Model is 19, and then there are neutrinomasses and mixing to think about . . .. Surely nobody can believe that theStandard Model is the end of the particle story?

2. The Large Hadron Collider and the open questions beyond theStandard Model

As we have seen above, there is a standard list of open questions beyond theStandard Model of particle physics. What is the origin of particle masses, andare they due to a single elementary Higgs boson, or to something else? Whyare there so many types of matter particles, and why and how do matter andantimatter particles differ (the origin of CP violation)—perhaps the answer tothis question is related to the origin of matter in the Universe? How does oneunify the fundamental forces, and how does one construct a quantum theory ofgravity? To these one might add a question whose answer surely lies beyond theStandard Model, namely, what is the nature of the cold dark matter that makesup some 80 per cent of the matter in the Universe?

The LHC may be able to address all these questions. One of its mainmotivations has been to solve the mass problem, and its experiments should tellus definitively whether or not there exists a Higgs boson resembling that in theStandard Model. There is a large class of models in which cold dark matter iscomposed of particles that were in thermal equilibrium in the early Universe, inwhich case they should weigh approximately 1 TeV, and be produced at the LHC.

Phil. Trans. R. Soc. A (2012)



820 J. Ellis

One example of such a theory is supersymmetry, which would also assist in theunification of the fundamental forces. Measuring the masses of supersymmetricparticles, if they exist, would be a great way of testing predictions based on suchtheories. Finally, supersymmetry and extra dimensions are key aspects of stringtheory, the only promising candidate for a consistent quantum theory of gravity,which could be tested in very novel ways if the LHC produces microscopic blackholes. In the following, I review in more detail the prospects that the LHC mightcast light on these enticing scenarios. However, I would also like to emphasizethat the LHC is not the only game in particle physics: many phenomena such assupersymmetry, extra dimensions, neutrino masses, grand unification and stringtheory may be fully revealed only at very high energies that could be accessibleonly 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 equationE = mc2. Unfortunately, these two honourable gentlemen forgot to explain to uswhere the mass came from in the first place. The mechanism described in thetwo bottom lines of (1.1) was proposed independently by Francois Englert andRobert Brout and by Peter Higgs. The latter also pointed out explicitly thatthis mechanism implied the existence of an unseen particle, now called the Higgsboson, which has become in some sense the Holy Grail of particle physics, andcertainly the first target of the LHC.

As an analogy as to how the Englert–Brout–Higgs mechanism works, let usimagine an infinite, featureless, flat, homogeneous and isotropic field of snow(northern Canada, maybe). If we try to cross this snow field on skis, we skimacross it very fast, hardly interacting with it. This resembles a massless particlethat does not interact with the Higgs field, acquires no mass and always travelsat the speed of light. Now consider somebody with snowshoes: this person willsink somewhat into the snow field (interact with the Higgs field), and be sloweddown (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 deeplyand travel very slowly, just like a particle with a large mass that travels at muchless than the speed of light. According to this theory, masses are proportionalto couplings to the Higgs snow field, which are the Yukawa couplings yij seen inthe third line of (1.1). The Englert–Brout–Higgs mechanism does not explain thepattern of these couplings, which is part of the flavour problem.

This analogy is not perfect (analogies are, by definition, imperfect), but itcan be carried further. For example, snow is made out of snowflakes and, byanalogy, the quantum of the Englert–Brout–Higgs field is the Higgs boson. Justas snowflakes are composite objects, with no pair identical, it could also bethat the Higgs boson is not an elementary particle, but actually is composedof more elementary constituents, and just one of a whole new spectroscopy ofparticles. Then again, snow melts when you heat it and, by analogy, we expectthat the Englert–Brout–Higgs field would have been molten at the very hightemperatures in the very early Universe, at which epoch particles would havehad no masses.





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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 positroncollider (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 is169 GeV, if only the precision electroweak data are used. Recently, the Tevatronexperiments CDF and D0 have excluded a range of heavier masses within the95% CL range [4]:

162 GeV < mh < 166 GeV. (4.2)

A combined fit to all the data, shown in figure 1, yields the asymmetricestimate [3]

mh = 120+12−5 GeV (4.3)

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), andrenormalization effects cause it to blow up at some relatively low scale L, asseen in figure 2, heralding the appearance of new non-perturbative physics. Onthe other hand, if mh is small, negative renormalization by the large t-quark




822 J. Ellis

LEP exclusionat >95% CL

Tevatron exclusion at >95% CL

perturbativity bound

stability bound

finite-T metastability bound

zero-T metastability bound

shown are1s error bands, without theoretical errors

l = 2pl = p

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Figure 2. If the Standard Model Higgs boson weighs more than approximately 180 GeV, the Higgsself-coupling blows up at some scale L below the Planck scale, inducing new non-perturbativephysics. 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 ofmh ∈ (130, 180) GeV is compatible with the survival of the Standard Model at allscales 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! Aswe have seen, the precision electroweak data favour small values of mh and hencel, and the combination with the Tevatron exclusion (4.2) excludes the blow-upscenario at the 99% CL [5]. The unstable-vacuum scenario of the Standard Modelis 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 thetop quark that destabilizes the electroweak potential, the simplest option is tointroduce a scalar particle with similar couplings. This can delay the collapse ofthe potential, but the new coupling must be very finely tuned in order to avoidanother blow-up. The answer is to stabilize it with a new fermion. The new scalaris much like the stop quark, the fermion is just like the Higgsino and the resultingtheory is very much like supersymmetry!

The stakes in the search for the Higgs boson are very high. How is theelectroweak 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? Didmass appear when the Universe was a picosecond old? Does the Higgs boson needhelp, e.g. from supersymmetry? Did the Higgs boson play a role in generating thematter 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 darkenergy, despite the propensity of the Higgs field to contribute many orders ofmagnitude too much? What will we discover beyond the Higgs door?





6. Where does the matter in the Universe come from?

This became an issue over 80 years ago, when Paul Dirac pointed out thatcombining special relativity and quantum mechanics necessitated the existenceof antimatter, which was discovered among the cosmic rays soon after. Diracpredicted that matter and antimatter particles would have equal masses butopposite internal properties such as electric charges. It came as a big shock in1964 when it was discovered that the weak interactions of matter and antimatterwere not quite equal and opposite. This small difference can be accommodated,but not really explained, in the Standard Model via the electroweak phasementioned in §1.

The Russian physicist Andrei Sakharov proposed in 1967 that the smalllaboratory difference between matter and antimatter might explain the fact thatthe Universe today contains a (relatively) small amount of matter and a lot ofradiation, but no significant quantities of antimatter. He laid out three conditionsfor generating this matter asymmetry: interactions capable of changing quarksinto leptons (which are predicted to exist in unified theories, but have never beenobserved), a breakdown of thermal equilibrium during the early expansion of theUniverse (as might have occurred during a cosmological phase transition), and amatter–antimatter difference (C and CP violation) as observed experimentally.

However, the charge conjugation (C) and CP violation observed so far, asdescribed within the Standard Model via phases in the Yukawa couplings yij , isinsufficient to generate the amount of matter seen in the Universe today, whichrequires new physics beyond the Standard Model. There are some extensionsof the Standard Model at the TeV scale, such as supersymmetry, which arein principle capable of generating enough matter, which might show up in theHiggs sector. Alternatively, it might be generated by physics at a higher energyscale, e.g. in the neutrino sector. Either way, there may be direct or indirectindications of this new physics at the LHC, and the LHCb experiment is dedicatedto exploring such possibilities.

7. Dark matter

Another cosmological puzzle that requires new physics beyond the StandardModel for its solution is the nature of dark matter. Astrophysicists andcosmologists assure us that the formation of structures in the Universe andtheir persistence today is possible only with the help of additional gravitationalattraction provided by some form of invisible non-relativistic matter. Variousastrophysical candidates such as black holes seem to be excluded, so attentionis focused on particle candidates for dark matter. In many scenarios, these darkmatter particles were once in thermal equilibrium with the rest of the particles inthe Universe, in which case, general arguments suggest that they probably weighless 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, withthe prototypical example being the lightest supersymmetric particle (LSP) [7].However, there are other possibilities: the basic requirement is some conservedquantum number to guarantee the stability of the dark matter particle, whichwould be provided by a combination of baryon number, lepton number and spin




824 J. Ellis

in the supersymmetric case, called R-parity. A general feature of such scenariosis the production of pairs of invisible particles at the LHC that would carry awayenergy and momentum.

8. Unifying the fundamental interactions

It has been the dream of theoretical physicists ever since Einstein to unify thefundamental interactions in a simplified mathematical framework. Einstein neversucceeded, but some of the ideas he developed find echos in modern theories ofunification. Most prominent among these is string theory, which offers a consistentquantum-theoretical framework capable of unifying gravity with the other particleinteractions. String theory seems to require supersymmetry and also, in somesense, extra dimensions of space, one of Einstein’s pet ideas.

There are many ways in which extra dimensions might show up at theLHC ([8] and references therein), depending on their sizes and whether all thefundamental interactions ‘feel’ them, or only gravity. In some of these scenarios,energy and momentum ‘leak’ away into the extra dimensions; in others, there areresonant Kaluza–Klein excitations of the known particles whose wave functionsare 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 dimensionssufficiently to become strong at the TeV scale, making possible the productionof microscopic black holes at the LHC. Theories predicting such a possibilityalso tell us that these microscopic black holes would be very unstable, and decayspectacularly with the emission of energetic quarks, gluons, leptons, photons andneutrinos. If such objects were to exist and be produced at the LHC, they wouldprovide wonderful laboratories for checking quantum theories of gravity such asstring 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 initiallyenthusiastic about supersymmetry because of its beauty, but its prospectiverelevance to experiments at the LHC stems from its ability to render the hierarchyof mass scales more natural. This issue arose from calculations of the quantumcorrections to the Higgs mass and hence to the mass scale of the weak interactions,which are quadratically divergent:

Dm2H = − y2

f

16p2

[2L2 + 6m2

f log(

L

mf

)+ . . .

]

and Dm2H = + l

16p2

[L2 − 2m2

f log(

L

mS

)+ . . .

],

⎫⎪⎪⎪⎬⎪⎪⎪⎭

(9.1)

where yf is a generic Yukawa fermion–Higgs coupling (cf. line 3 of (1.1)), lSis a generic scalar–Higgs coupling and L is a cut-off in momentum space. Ifthe Standard Model were to remain valid without modification up to some





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Figure 3. The (m1/2, m0) plane of the CMSSM for sample values of the other supersymmetric modelparameters, showing the different theoretical, phenomenological, experimental and cosmologicalconstraints. (a) tan b = 10, m > 0; (b) tan b = 55, m > 0. There is no consistent electroweak vacuumin the dark pink-shaded region at large m0, the LSP would be charged in the brown-shaded regionat small m0, b → sg excludes the green-shaded region, LEP excludes the regions to the left of thedashed black and red lines by unsuccessful chargino and Higgs searches, respectively, and gm − 2favours the paler shaded pink region. The LSP would have the appropriate cosmological densityin the narrow turquoise strip close to the boundaries of the allowed region [11]. ATLAS and CMSconstraints from 2010 LHC data are shown as yellow and purple lines, respectively [12,13]. (Onlineversion 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 physicalvalue. However, we note that these would cancel if lS = 2y2

f , which is preciselythe relation predicted in a supersymmetric theory. Moreover, this relation alsoremoves all the quadratic higher order quantum corrections, as well as some of thelogarithmic corrections. In this way, supersymmetry makes a light Higgs bosontechnically ‘natural’, though it does not provide an explanation for the magnitudeof 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 beingneeded for the consistency of string theory. Moreover, supersymmetry couldexplain the apparent discrepancy between experiment and the Standard Modelcalculation of the anomalous magnetic moment of the muon, gm − 2.

There are important constraints on supersymmetry owing to the absence ofparticles at LEP and the Tevatron, the LEP lower limit on mh and the consistencyof b-quark decays with the Standard Model. Some hint of new physics at the TeVscale may be provided by the measurement [9] of the anomalous magnetic momentof the muon, gm − 2, which could be explained by supersymmetry, although thereare still uncertainties in the Standard Model calculation of gm − 2 [10]. Themeasured density of dark matter, 0.097 < UDMh2 < 0.122, provides a very tightconstraint on some combination of supersymmetric model parameters, if the LSP




826 J. Ellis

jets + MET (CMS)

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Figure 4. The preferred region in the (m0, m1/2) plane of the CMSSM before the start-up of theLHC, compared with the estimated discovery sensitivity of the LHC with different amounts ofluminosity and centre-of-mass energy [14]. The best-fit point is shown as a black circle, and the68% and 95% CL regions are indicated by blue and red hatching, respectively. (Online versionin colour.)

provides the dark matter. The interplay of these constraints is shown in figure 3for one particularly simple supersymmetric model with universal supersymmetry-breaking 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 afrequentist approach to analyse the precision electroweak data, the LEP Higgsmass limit, the cold dark matter density, b-decay data and (optionally) gm − 2. Wecombined the likelihood functions from these different observables to constructa global likelihood function that can be used to infer preferred regions of thesupersymmetric parameter space [14–16].

We see in figure 4 that the preferred region of the (m0, m1/2) plane in theCMSSM corresponds to relatively low masses where the relic LSP density isbrought into the Wilkinson Microwave Aniostropy Probe (WMAP) range bycoannihilations with light sleptons, particularly the lighter stau. The ‘focus-point’region at large m0 is disfavoured, principally but not exclusively by gm − 2. If onedrops 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 the5s discovery reach of the LHC with given amounts of integrated luminosity atcertain centre-of-mass energies. The 5s discovery reach of the LHC with 1 fb−1 of





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Figure 5. The preferred region in the (m0, m1/2) plane of the CMSSM before and after incorporationof 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, inblack, is the region excluded by an initial examination of 165 pb−1 of 2011 ATLAS data. (Onlineversion in colour.)

luminosity at 7 TeV in the centre of mass would probably include all the 68% CLregions in figure 4. It should be noted, however, that this conclusion is dependenton the interpretation of gm − 2 and the theoretical calculation of b → sg decayin 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 havepublished the results of several (unsuccessful) searches for supersymmetricparticles at the LHC using data taken in 2010 [12,13], focusing mainly onthe missing-energy signatures expected if the LSP provides the astrophysicaldark matter. These constraints are shown in figure 3 as yellow and red lines,respectively. In addition, the LHCb experiment at the LHC has joined theCDF and D0 experiments at the Fermilab Tevatron collider in setting upperlimits on the rare decay Bs → m+m−, which is also an important constraint onsupersymmetric models. Another constraint comes from searches by ATLAS andCMS for the heavier neutral Higgs bosons predicted in supersymmetric modelsusing 2010 data.

Based on these constraints and including also the constraint imposed by theXENON100 experiment looking directly for cold dark matter [17], we found innew global supersymmetric fits the results shown in figure 5 [18,19]. The best-fitpoints are represented by green stars, and the 68% and 95% CL regions by solidred and blue contours, respectively (the dotted lines are the current results if the




828 J. Ellis

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Figure 6. CMSSM fit points are projected on the (m0, m1/2) plane. The best-fit points for differentdatasets are indicated by different symbols: stars for pre-LHC fits, diamonds and circles for fitsincluding the first SUSY searches by CMS and ATLAS, triangles including all relevant 2010 LHCdata, and squares for estimates of the impacts of future LHC datasets with 1, 2, 7 fb−1 if SUSYis not discovered. Also shown as crosses are two older benchmark points: SPS1a [20] and a similarbenchmark point B′′ [21,22], which yields the right dark matter density. The various symbolsare also coded with different colours for different fitting groups, as shown in the legend. Theline illustrates the trend of these fits as stronger constraints are incorporated. (Online versionin colour.)

LHC constraints are omitted). Also shown in figure 5 are the preliminary resultsfrom the early 2011 running of the LHC [12], which cut very close to the best-fitpoint in the CMSSM.

Figure 6 shows the possible trajectory of best fits to the CMSSM parametersif supersymmetry is excluded by larger amounts of integrated LHC luminosity. Ifsupersymmetry were not to be discovered with several inverse femtobarns of data,one should undoubtedly consider alternative signatures of supersymmetry, and/orquestion 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 visitedCERN and was introduced to British physicists. When she was told I was atheoretical physicist, she asked me ‘What do you do?’ I explained that my job wasto think of things for the experiments to look for, and hope they find somethingdifferent. ‘Wouldn’t it be better if they found what you predicted?’ asked Mrs T.,





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 theLHC will be remembered in the history of physics for something not described inthis article.

It is a pleasure to thank the organizers for their kind invitation to the Discussion Meeting, andI acknowledge my collaborators, particularly the members of the MasterCode collaboration. Thiswork was supported partly by the London Centre for Terauniverse Studies (LCTS), using fundingfrom the European Research Council via the Advanced Investigator Grant 267352.

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outstanding questions: physics beyond the standard...

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