The Standard Model: How far can it go and how can we tell?

0.25 MB·

by  Jon Butterworth

The Standard Model: How far
can it go and how can we tell?
rsta.royalsocietypublishing.org J. M. Butterworth1
1
DepartmentofPhysics&Astronomy,University
Research CollegeLondon
TheStandardModelofparticlephysicsencapsulates
Articlesubmittedtojournal our current best understanding of physics at the
smallestdistancesandhighestenergies.Itincorporates
Quantum Electrodynamics (the quantised version
6 SubjectAreas: of Maxwell’s electromagnetism) and the weak and
1 Maxwell,ParticlePhysics strong interactions, and has survived unmodified
0 for decades, save for the inclusion of non-zero
2 neutrino masses after the observation of neutrino
Keywords:

n oscillations in the late 1990s. It describes a vast
QCD,QED,electroweak
a array of data over a wide range of energy scales.
J
I review a selection of these successes, including

1 Authorforcorrespondence: the remarkably successful prediction of a new scalar
2
boson,aqualitativelynewkindofobjectobservedin
JonButterworth
2012attheLargeHadronCollider.Newcalculational
] e-mail:[email protected]
x techniques and experimental advances challenge
e
the Standard Model across an ever-wider range of
-
p phenomena, now extending significantly above the
e electroweak symmetry breaking scale. I will outline
h
some of the consequences of these new challenges,
[
andbrieflydiscusswhatisstilltobefound.

2
v
9
5 1. Introduction
7
2
Consider a naive question. If take any object and cut it
0
into half, then cut it in half again, and again, and keep
.
1
doing that, what to I get in the end? What structure is
0
revealed?Indeed,doIreachanend,orcanIcarryonfor
6
ever?
1
: Answeringthisquestionisoneofthegoalsofphysics.
v
Itisreductionistapproachwhichisnotthewholestory,
i
X ofcourse-whatevertinyconstituentsarerevealed,their
r interactionsleadtorichemergentphenomenarevealing
a
newphysics,nottomentionchemistry,biologyandthe
rest. However, knowledge of the structure of matter at
thesmallestaccessiblescalesisimportant,andissurely
oneofthemostexcitingfrontiersofscience.
(cid:13)c TheAuthors. PublishedbytheRoyalSocietyunderthetermsofthe
CreativeCommonsAttributionLicensehttp://creativecommons.org/licenses/
by/4.0/, whichpermitsunrestricteduse, providedtheoriginalauthorand
sourcearecredited.
Theresolutionrequiredtoseetheever-smallerpiecesrequireshigherandhigherenergy,and
2
thusthefrontieroftheverysmallbecomesthehigh-energyfrontier.Similarly,theenergiesand
distancesinvolvedmapthesamefrontierontothephysicsoftheveryearlyuniverse;thehot,
densemomentsafterthebigbang.Butintheend,thequestionisthesame-whatistheuniverse ...rsta
madeof? ....ro
.y
ThecurrentanswerisencapsulatedintheStandardModel.Quarksinsixflavours-up,down, ...als
charm,strange,topandbottom.Leptons-alsosixkinds,theelectron,muonandtau,plusthree ...oc
nofeugtaruingoesb.oTshoenrse-artheealpshooctoornrecsaprorynidnigngelaencttriopmaratigcnleest.isTmhe,stheeinWteraancdtwZitbhoesaocnhsocathrreyribnygethxcehwaneagke .....ietyp
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forcLei,kaenadngylumoonsstcaanrsrwyienrgstihnessctireonncge,ftohricse.isAanpdrionvtihsieobnaaclksgtartoeumnednlti,edsethteermHiingegdsbboysoonu.rcurrent .....blish
abilitytohalvethings,or,lessdestructively,toresolveever-tinierobjects.Butithasjustachieveda ...ing
...o
majorpredictivesuccesswiththediscoveryoftheHiggsboson,anditisremarkablethatwehave .r
.g
.
aself-consistenttheoryinwhichtheseobjectsarepointlike,andwhichcandescribephenomena ..P
.h
osovmereasneleenctoerdmhoiugshlriagnhgtseoofftheneemrgoydealn,danddisltoaonkceatswcahleesr.eIfnurtthheerfopllroowgriensgssmecatyiobneseIxpweicllterdec.ount ....il.T
..ra
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...s.
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2. Atomic scales ...
.S
..o
IwillstartthetouroftheStandardModelattypicalatomicscalesofaround102eV.(Thegluonand ..c.
..A
thephotonmasses,atzero,areoffthelowendofalogarithmicscale,andneutrinomassesIwill ..0
.0
returntolater.)Precisionatomicphysicsmeasurementsplayedacriticalroleinthedevelopment ...00
oftheQEDsectoroftheStandardModel,andthecurrentposter-childforhighprecisionquantum- .0
.0
fieldtheoryistheanomalousmagneticmomentumoftheelectron,wheretheoryandexperiment ..0
.
are in agreement at the level of one part in 1013 [1,2]. Obtaining this precision in the theory
requires the incorporation of electroweak and strong corrections, due to contributions to the
interactionbetweentheelectronandthephotoncomingfromloopsinvolvingvirtualparticles.
Sincenon-StandardModelparticlesmayalsocontributeinsuchloops,thismeasurement,coupled
withprecisemeasurementsofthefinestructureconstant,cansetalimitsonsometypesofnew
physicsmodelsatenergyscalesmuchhigherthanatomicphysicsscales[3].Thesameistrueof
theanomalousmagneticmomentofthemuon,andsincemanynewphysicscontributionsscale
withthesquareoftheleptonmass,thesensitivityofthesemeasurementstosuchcontributionsis
higher.Themuonanomalousmagneticmomentislesspreciselyknownthanthatoftheelectron
(thoughstilltoanimpressiveaccuracyofaboutonepartin1010),andcurrentlyexhibitsa3.6σ
discrepancybetweentheoryandmeasurement.Takenatfacevalue,thisisevidenceforphysics
beyondtheStandardModel,potentiallyatscalesclosetotheelectroweakscale(1011 eV).New
measurementsandimprovedcalculationswillhopefullysoonclarifythesitutation[4].
3. QCD and hadron masses
Movingupwardinenergyscalefromatomicbindingenergies,pasttheelectronmass(0.5×106
eV) and nuclear binding energies (≈107 eV), we reach an energy scale of great importance,
ΛQCD≈2×108 eV. For a specified renormalisation scheme, this scale is equivalent to the
dimensionlessstrongcouplingatsomereferencescale,andisafundamentalparameterofQCD.It
determinesthescaleatwhichquarksandgluonsareconfinedinsidehadrons.Inasenseitisonly
abovethisscalethatquarksandgluonsbecometherelevantdegreesoffreedomintheStandard
Model.Belowthisscale,theycannotberesolvedinsidehadrons,whichare(atleastmostly)qq¯or
qqqboundstates.
Inthisregionthestrongcouplingisstilltoolargetoallowtheconvergenceofaperturbative
expansionintermsofFeynmandiagrams.However,latticetechniquescanbeusedtocalculate
important emergent physical properties such as the confinement potential and hadron masses
(see for example [5,6]). Recent experimental progress in exploring the hadronic mass spectrum
3
andconfinementincludesthediscoveryoftetraquark(qqq¯q¯)andpentaquark(qqqqq¯)states[7–10].
4. ‘Hard’ QCD ...rsta
...r
.o
.y
AstheenergyscaleincreaseswellaboveΛQCDandtypicalhadronmasses,thecouplingconstant, ...als
αs, decreases, and the strong force exhibits the property of asymptotic freedom [11,12]. This ...oc
mdeegarnesesthoaftfraetedscoamle,saonfdacraolucunldat1io0n10sceaVnabnedpearbfoovrme,eqduuasrkinsgapnedrtgulruboantisveareexpinadneseiodntshienrαesle.vant ......ietypu
gluTohnestcwanombeoestxpimloproedrtainnttahnisdednierergctywreagyisminewarheicihntthheeepxriostdeunccteioanndofbhehadavroionuicro’jfetqsu’,aarnksdatnhde .....blish
study of the internal structure hadrons. And as well shall see, both types of measurement are ...ing
...o
interconnected. .r
.g
.
Jets result from a short-distance, high-energy scatters between a pair of partons (a general ..P
.h
tJeertsmasreusseedentoforerfeerxatmoqpulearinksthanedpgroluceosnss)e,+oer−fr→omhtahderodnesc,ayfoorfcaenmtraes-soifv-mepasasrteicnleerigniteospoafrmtoonrse. ....il.T
thanafew109eV,wheretheunderlyingprocessatleadingorderintheperturbativeexpansionis ...ran
takentobetheelectroweakannihilationoftheelectronandpositrontoavirtualphoton(γ)orZ ...s.
.R
boson,whichthendecaystoqq¯.Whileweaklycoupledatshortdistances,thosepartonswill,as ...
.S
theyflyapart,experiencethelinearlyincreasingconfinementpotentialmentionedintheprevious ..o
.c
..
section.Theincreasingpotentialenergywithdistanceimpliesthatitisenergeticallyfavourable ..A
tocreatemorepartons,shorteningthedistancesoverwhichthepotentialacts;aprocessending ..0
.0
atlowerenergiesintheproductionofcolor-neutralhadrons.Thesehadronsformcollimatedjets ...00
.0
whichpreserve,toagreatextent,thekinematicsoftheinitiatingpartons.Theproductionofthree- .0
..0
jetevents[13]atthePetracolliderinDESY[14]wasgenerallyseenasthefirstdirectevidencefor .
theexistenceofgluons,asthekinematicsandcrosssectionswereaspredictedbycalculationsof
theprocesse+e−→qq¯g.Jetshavebeenmeasuredpreciselyine+e−,ep,pp¯andppcollisionsand
provideastringenttestofQCDandasensitiveprobeofshort-distancephysics.
Thefirstevidenceforpointlikeobjectsinsidehadrons-lateridentifiedwiththequarksalready
introducedbyGell-MannandZweigtoexplainhadronproperties-camefromthedeeplyinelastic
scatteringofelectronsoffprotons.Thesquaredfour-momentumtransfer,Q2,insuchcollisions
dictatestheresolution,anditwasseenthatatsomepoint,correspondingtoenergieswellabove
ΛQCD, the cross section approximately ’scaled’. That is, once the propagator dependence was
accounted for, the dependence on Q2 was very weak, as expected if a pointlike particle has
been resolved. The residual dependence on Q2 - scaling violation - is due to the radiation of
gluonsfromthequarks,and,sinceittakesplaceatshortdistances,iscalculableinQCDusing
perturbative techniques [15–19]: the excellent agreement between data - principally from the
HERA ep collider [20] - and fits incorporating these scaling violations to next-to-next-leading
orderinperturbativeQCDisanothervindicationofthetheory.
Thepartondensitiesextractedinthiswayareneededtomakepredictionsforjet(andother)
crosssectionsinhadroncolliders.Andprecisemeasurementsofjetsareusedtoconstrainthose
partondensitiesfurther.
5. The Electroweak scale
Thetransitiontothenextimportantenergyscaleinphysicsisnicelyillustratedbystayingwith
deepinelasticscattering.Electron-protoncollisionscannotonlybemediatedbyphotonexchange,
butalsobytheexchangeofweakbosons,theW andtheZ.SincetheW carrieselectriccharge,
those events will have distinct final states, in which the emerging scattered lepton has turned
intoaneutrino.Asmightbeexpected,theratesofthese’charged-current’eventsaremuchlower
thanthoseoftheelectromagneticscatters,reflectingtherelativestrengthoftheelectromagentic
andweakforces.However,astheenergyscaleincreases,theratesconverge,untilataround1011
eV, they become roughly equal. This effect, measured at HERA [20], reflects the fact that most
oftheapparentdifferenceinstrengthofthetwoforcesatlowerenergiesisduetothedifferent
4
propagatormasses(zeroforthephoton, 1011eVfortheW andZ).Oncetheenergyissuchthat
thesemassesarenolongerimportant,asymmetryisrestored,andtheforcesbecomecomparable
instrength.Thisenergyscaleisknownastheelectroweaksymmetrybreakingscale. ...rsta
...r
.o
.y
(a) The Z and the neutrinos ...als
...oc
SthtuedpireescoisfethinefoZrmbaotsioonn,ornesomnaannytlyfeaptruordeuscoefdeilnecetr+oew−eackollpishiyosniscsa.tOLnEePmaanjdorStLriCum[2p1h],wpraosvtidhee ......ietypu
.b
ppZrreeinccciissleeuldmyinceaagls,cucurrlueamcteiaedlnliytn,oetfhletehctienrodvweisceiabaylkewtdhieedcotahryyo,cafhntahdneinsZesl;estnhZsai→ttiivsen,etthouetarslilhntaohpse.epToohfsestshiebelmeredesaeoscnuaarynecmcheea.nnTtnhseiislnscdoaifnctahbteee .........lishing.o
that there are three, and only three, flavours of neutrinos - and thus only three generations of ..rg
.
matter,assumingeachgenerationcontainsalight,weakly-interactingneutrino. ..P
.h
....il.T
(b) Loops and fits ..ra
.n
...s.
To realise the full potential of the precise data from LEP and LEP2, higher order corrections ...R.
involving virtual-particle loops have to be implemented in the electroweak theory. This means ...So
thatthedatahaveindirectsensitivitytotheexistenceandpropertiesofundiscoveredparticles,too ..c.
heavytobeproduceddirectlyinthecollisions.Atthetimeoftheexperiments,suchundiscovered ....A0
preagritoicnlecsoninscislutednetdwtihthetthoepStqaunadrakr.dTMheoddeislcfiotvs,esrywiotcfhtehdeattotpenqtiuoanrktoatthethlaesTterevmataroinnin[g22u,2n3k]n,oinwna .....0000
.0
particleintheStandardModel,theHiggsboson. ..0
.
The Higgs boson is scalar particle predicted by the mechanism for electroweak symmetry
breaking based on work in the early 1960s [24–29] which was later incorporated into the SM
[30–33].ThismechanismallowstheW,Zandthefermionstoacquiremassbycouplingtoascalar
fieldwithanon-zerovacuumexpectationvalue;introducingmassinthiswaypreservesthegauge
symmetriesofthetheory,andthusthepropertyofrenormalizabilityrequiredtomakethetheory
predictiveathigherordersandhigherenergies.
TheprecisemeasurementsofthetopandW massesattheTevatron[34,35]increasedthepower
oftheSMfits,and-againvialoopcorrections-ledtoconstraintsonthemassoftheSMHiggs
boson, should it in fact exist. Meanwhile, direct searches at LEP2, the Tevatron and early LHC
dataexcludedsignficantrangesofpossiblemassvalues.
(c) Discovery and vindication
ThediscoveryoftheHiggsboson[36,37],withamass(1.25×1011)eV[38]oncemoreconsistent
with the constraints from electroweak precision data, was a remarkable triumph not only for
the accelerator and the experiments, but for the theoretical ideas behind the SM. So far, all the
propertiesoftheboson-charge,spin,parity,andtheproductioncrosssection×branchingratio
forthosedecaymodeswhichhavebeenmeasured-areinagreementwithexpectationsoftheSM.
TheSMnowhasno“missingparticles”.Withouttheexperimentaldiscoveryofthisqualitatively
unique object, the SM could have been just an effective theory valid only up to 1012 eV or so.
WiththeknowledgethattheHiggsbosonexists,thetheoryiscapableofmakingpredictionsat
energiesfarabovetheelectroweakscale.
6. To the TeV scale and beyond
Armed with this new discovery and increased energy at the LHC, particle physics is now
exploringmulti-TeVscalephysics-1012eVandbeyond.MakingpredictionswiththeSMinthis
qualitativelynewregimebringsnewchallengesforthetheory.
(a) New features, new demands
5
As the energy of a collision increases, so does the phase space accessible for the production of
high-energy objects such as high-momentum jets, leptons and photons. Increasing the energy ...rsta
far above the electroweak scale means that objects with masses around the electroweak scale ...r
.o
cqtthhauuenasrtakhplsesrooaorndbyduetctopehdreboeWdreuaq,cbZueliedraetnwsodiirtnHehnpiohgrovgigdashtubivcoeeensoewcnraghslic.aeutDsliaesastnicaodrcni/tbauoilnarltgleiyncwhmhintiheigqahausnuenysrue.ddmIenbgberyperasetr.htoiIecfnuepltxrahperec,eirStsihiMmoenreetnththii.sseTafimhninesaaelnmesdsteaatftonoepssr ............yalsocietyp
thatcalculationsof’inclusive’quantities,whichintegrateoverlargeregionsofphasespace,are ..ub
not sufficient, since the experiments must place selection requirements on the final state. For ....lish
example, the detectors have a limited angular (rapidity) acceptance, and also cannot measure ...ing
jetsorparticlesatarbitrarilylowtransversemomenta.Ifthetheorycanonlycalculatetotalcross ...o
.r
sections, or totally inclusive quantities, then exptrapolations have to be applied to the data in ..g
order to make comparisons. These extrapolations must make some theoretical assumptions - ...Ph
typicallytheywilluseaMonteCarloeventgenerators,whichsimulatethefullyexclusivefinal ....il.T
state [39]. The accuracy of the comparison is likely then not limited by the inclusive theory ..ra
.n
calculation, or by the intrinsic experimental uncertainty, but by the accuracy of the generator, ...s.
as well as by the assumption that no unexpected physics occurs in the regions which are not ...R.
coveredbythedetector. ...So
Forthesereasons,muchactivityinthetheorycommunityisnowfocussedonpreciseexclusive ..c.
..A
calculations,whichinmanycasesareimplementedwithinMonteCarlogenerators.Thisisnot ..0
.0
done so much to improve the accuracy of the extrapolations, but to remove the need for them ...00
altogether,bymakingprecisepredictionsofrealisticmeasurementswithinthefiducialacceptance .0
.0
regionsofthedetectors. ..0
.
AkeyissuehereisthematchingoftwoperturbativeapproachestoQCD.Thematrixelement
calculations at the heart of event generators can be increased in multiplicity, thus filling phase
spacemoreaccurately,andcanalsoincorporatethefullcomplementofhigher-orderterms,which
meansalsoincludingdiagramsinvolvingloops(similartothoseimplicatedinthemuonmagnetic
moment, discussed above). In the latter case the precision of the calculation is systematically
improved. There are, however, regions of phase space which contain kinematic enhancements
whichmeansuchanapproachconvergesveryslowly,ifatall.Suchenhancementstypicallyoccur
whenpartonsaresoftoralmostcolinear-forexampleintheearlystagesofjetformation.They
usuallyoccurinsuchawaythattheemissionofanewpartonintroducesalargelogarithmofthe
ratioofsomekinematicfactors,whichcannegatethesuppressionarisingfromtheintroductionof
anadditionalαsfactor,andimplythattheserieswillnotconverge.Fortunuately,techniqueshave
beendevelopedtocastsuchtermsintheformofsummableseries;theyhavealsobeimplemented
algorithmicallyinMonteCarlogeneratorsintheformof’partonshowers’,whichareessentialto
obtainaccuratedescriptionsofthefinalstate.
The development of methods of matching these parton shower terms to higher multiplicity
[40] and higher order [41,42] matrix elements are breakthroughs without which much of the
LHCprogrammewouldbeseriouslyhampered.Advancescontinue,andtheimportanceofthese
developmentsislikelyonlytoincreaseascollidersextendtheenergyreachoverwhichtheSM
canbeconfrontedwithdata.
(b) Precision Higgs Physics
Given the theoretical advances outlined above, the experiments can increasingly concentrate
on making precise and detailed exclusive and differential measurements. For example, ATLAS
and CMS have already moved into the era of precision Higgs physics, not only measuring
inclusiveproperties,butalsodifferentialfiducialcrosssections.Themultiplicityanddistribution
ofjetsaccompanyingtheHiggsareusedtoobtainseparatesensitivitytothevariousproduction
mechanisms(e.g.betweengluonfusionandvectorbosonfusion)andisintrinsictotheselection
of some types of event. Measuring the transverse momentum distribution of the Higgs boson
6
productionoffersamorerigourousprobeoftheSMthanmeasuringtheintegratedtotal.Several
ofthesemeasurementshavealreadybeenmade(seeforexample[43,44]),andthenumber,reach
andprecisionwillincreaseaslongastheLHCcontinuestoprovidedata. ...rsta
...r
.o
.y
(c) Boost and jet substructure ...als
...oc
iSninjceetsporfotdQuCctDiontakmeasyovexetresnodmuepwhtoerseevareorualn1d0t1h2ee1V0,9meVucrhegoifotnh,eanevdotlhuetieonnerogfythsecasluesbsintrvuocltvuerde .....ietyp
.u
oapfpthroeacjehtetsadkeesscrpiblaecdesabwoivteh.inJetthsuebpsterrutuctrubraetihvaesrinegcrimeaes,edanrdeleavgaanincecwanhebnethperejedtiscctaedleluiessinagbothvee .....blish
theelectroweakscale,sinceparticleswithmassesaroundtheelectroweakscale(W,Z andHiggs ...ing
bosonsandthetopquark)maynowbeproducedwithhighLorentzboosts,andthustheirdecay ....or
.g
products will be highly collimated and, in the case of hadronic decays, may be reconstructed ...P
absacakgsrionugnledsjetca[n45b–e48s]u.pSpurcehssceodn,fibguutrtahteioynrseqhuaivree tthheesatduvdaynotafgtehethsautbcsotrmucbtiunraetoorfiajeltasnidn oortdheerr .....hil.T
..ra
toidentifyandreconstructthedecayingmassiveparticle(see[49]forareview).Techniquesbased .n
ontheseideashavebeenwidelyemployedinmeasurementsattheLHC(forexampleofthetop ...s.
.R
quarktransversemomentum[50]),andinsearchesbothfortheSMHiggsdecayingtob-quarks ...
.S
andprobesoftheSM(andpotentiallybeyond)closetothekinematiclimit. ..o
.c
..
..A
..0
7. Flavour physics .0
...00
.0
Omittedfromthediscussionsofar,becauseitdoesnotfitneatlyintotheprogressofincreasing ...00
energy scale I have been following, is flavour physics. The masses of the different flavours of .
fundamentalfermionsintheSMspanahugerange,fromtheneutrinosataround10−1eVtothe
topat1.7×1011 eV.ThereasonsforthisarenotcontainedwithintheSMitself.Inaddition,the
mass eigenstates of the particles are not identical to their (flavour) eigenstates under the weak
interaction, meaning that a unitary matrix with four free parameters is introduced in both the
quarkandleptonsectors.Thisleadstothephenomenonof’mixing’-theflavourofquarksand
leptons,whichisdefinedastheweakeigenstate,canchangeasthepropagate,mediatedbythe
mass eigenstates. This matrix also encodes the possibility of the simultaneous violation of the
ChargeandParitysymmetries,CPviolation.
(a) Quarks
Quark mixing and CP violation in the SM are described by the Cabbibo-Kobayashi-Masakwa
(CKM) matrix. Measurements in e+e− collisions at the at the B-factories, Babar and Belle
[51], showed that the CP violation observed in the quark sector is, at least to a very good
approximation,consistentwiththemechanismallowedintheSM.Investigationsofquarkflavour
mixingatLHCbcontinuetoprobetheSMandincreasetheprecisionontheelementsoftheCKM
matrix.
(b) Neutrinos
Neutrinos were massless in the original SM, and the observation of neutrino mixing, which
implies that they have non-zero mass, is the only fundamental change that has been imposed
by data on the SM since its inception. Neutrino oscillations were first pointed to by the
observeddeficitofelectron-neutrinoscomingfromtheSun[52,53],andweredirectlyobserved
in atmospheric and Solar neutrino measurement by Super-Kamiokande [54] and SNO [55]
respectively.ThematrixwhichisintroducedtodescribethemixingisknownasthePontecorvo-
Maki-Nakagawa-Sakata (PMNS) matrix, and its elements are now being measured with
increasingprecisionbyacceleratorandreactor-basedneutrinoexperiments[56–59].Itisknown
that, unlike the CKM matrix, the off-diagonal elements are relatively large. That is, unlike the
7
quark case where the flavour and mass eigenstates are almost aligned, the neutrino flavour
eigenstatesareanalmostmaximalmixtureofthemasseigenstates.Itisnotyetknownwhether
CPviolationoccursintheneutrinosector-therelevantparameterofthePMNSmatrixhasnot ...rsta
yetbeenmeasured. ....ro
.y
...als
...oc
8. Conclusion .....ietyp
.u
Withasmallnumberoffundamentalobjectsandprinciples,theStandardModeldescribesand .b
predictsanenormousvarietyofphysicalphenomena,overenergyscalesrangingfromzeroup ....lish
to several 1012 eV and potentially far beyond. Some of the principles behind the theory trace ...ing
their origins back to Maxwell’s equations for electromagnetism, and those equations remain ...o
.r
.g
the classical form of the quantised electromagnetic force within the theory - QED. QED itself, .
..P
as a gauge theory, is the template for the weak and strong forces, themselves based on larger, .h
non-Abeliangaugesymmetries.Thepredictionthatascalarbosonwouldappearatsomescale ....il.T
below 1012 eV, as a consequence of reconciling gauge symmetries and massive bosons, has ..ra
.n
been spectacularly vindicated, and extends the region of applicability of the Standard Model ...s.
.R
potentiallyuptoenergiesbeyondthereachofparticlecolliders. ...
.S
BeforegettingtoopleasedwithourselvesatthepowerandsubtletyoftheSM,(ordespairing ..o
.c
ofourabilitytoextendit)itisworthrememberingthatisfailsentirelytoincorporpateoneofthe ..
..A
fundamentalforces.Gravityisdescribedbythegeneraltheoryofrelativity,andinthatcontextis ..0
.0
aconsequenceofthecurvatureofspace-timeratherthanaforcelikethoseintheSM,mediated ...00
bygaugebosons.Thisisaverysignificantfailureintheambitiontodescribenaturalphenomena ..00
inasingleframework.Worse,eveninpartnershipwithgeneralrelativity,therotationcurvesof ...0
galaxies,weaklensingoflight,andthelargescalestructureoftheuniversecannotbedescribed
without introducing ’Dark Matter’, for which the SM does not contain a compelling candidate
(thoughthepossibilityofstrongly-boundcompositeSMstatesisstilldiscussed,seeforexample
[60]).ThelowlevelofCPviolationpossiblefromSMmechanismshasnotbeenreconciledwiththe
grossviolationinherentinthefactthattheobservableuniverseseemstoconsistoverwhelmingly
ofmatterratherthanantimatter.Andfinally,itisprobablyapparentfromtheprecedingsections
thattheSMcontainsquitealotofparameterswithseeminglyarbitrary,butsuggestive,values.
Theseincludesome,suchastheHiggsmass,thatlookunnaturally’finetuned’,totheextentthat
itisverytemptingtothinkthattheyarefixedbysomeso-farunknownsymmetryorprinciple
inherentinalargertheory,ofwhichtheSMisjustapart.
Sothestory,ofwhichMaxwell’sworkwassuchaimportantcomponent,isnotover.Thereis
moretobefoundbycontinuingtolookmoreandmorecloselyatnature.Wedon’tknowwhether
any of the hints or inconclusive anomalies currently exercising particle physicists’ minds (g-2,
variousbumpsandraredecaysattheLHC,forexample)willfade,orgrowandleadtoanswers
tosomeoftheopenquestionsabove.Butwedoknowthatthereareunknownterritoriestobe
explored,andimportantanswerstobefound.
Acknowledgements. I’dliketothankAnatolyZayats,JohnEllis,RoyPike,andthestaffoftheRoyalSociety
fororganisinganexcellentmeeting,andespeciallyforthechancetoseeMaxwell’soriginalmanuscript[61].
Fundingstatement. FundedbyUCLandSTFC.
Conflictofinterests. Ihavenocompetinginterests.
References
1. B.C.Odom,D.Hanneke,B.D’UrsoandG.Gabrielse,NewMeasurementoftheElectronMagnetic
MomentUsingaOne-ElectronQuantumCyclotron.Phys.Rev.Lett.97(2006)030801[Phys.Rev.
Lett.99(2007)039902].
2. K.A.Oliveetal.[ParticleDataGroupCollaboration],ReviewofParticlePhysics.Chin.Phys.C
8
38(2014)090001.
3. G. F. Giudice, P. Paradisi and M. Passera, Testing new physics with the electron g-2 JHEP 1211
(2012)113[arXiv:1208.6583[hep-ph]]. ...rsta
4. J.Grangeetal.[Muong-2Collaboration],Muon(g-2)TechnicalDesignReport.arXiv:1501.06858 ...r
.o
[physics.ins-det]. .y
5. G.S.Bali,QCDforcesandheavyquarkboundstates.Phys.Rept.343(2001)1[hep-ph/0001312]. ...als
6. S.Aokietal.,Reviewoflatticeresultsconcerninglow-energyparticlephysics.Eur.Phys.J.C74(2014) ...oc
7. S28.9K0.[CarhXoiive:t13a1l.0[.8B5e5ll5e[Cheopll-albato]r]a.tion],Observationofaresonance-likestructureintheπ±ψ(cid:48) mass .....ietyp
.u
d[hisetpri-beuxt]i]o.ninexclusiveB→Kπ±ψ(cid:48)decays.Phys.Rev.Lett.100(2008)142001[arXiv:0708.1790 .....blish
8. K. Chilikin et al. [Belle Collaboration], Experimental constraints on the spin and parity of the ...ing
Z(4430)+.Phys.Rev.D88(2013)7,074026[arXiv:1306.4894[hep-ex]]. ...o
.r
9. R. Aaij et al. [LHCb Collaboration], Observation of the resonant character of the Z(4430)− state ..g
Phys.Rev.Lett.112(2014)22,222002[arXiv:1404.1903[hep-ex]]. ...Ph
10.SRta.teAsainijΛet0baJl./[ψLKH−CpbDCeoclalaybs.oPrahtyios.nR],eOv.bLseertvt.a1ti1o5n(o2f0J1/5ψ)0p7R20es0o1n[aanrcXesivC:1o5n0s7is.0te3n4t1w4i[thhePpe-nexta]q].uark ......il.Tra
11.(1D9.7J3.)G13ro4s3s.andF.Wilczek,UltravioletBehaviorofNonabelianGaugeTheoriesPhys.Rev.Lett.30 .....ns.R
12. H. D. Politzer, Reliable Perturbative Results for Strong Interactions? Phys. Rev. Lett. 30 (1973) ...
.S
1346. ..o
.c
13. J.R.Ellis,M.K.GaillardandG.G.Ross,SearchforGluonsine+e-Annihilation.Nucl.Phys.B ....A
111(1976)253[Nucl.Phys.B130(1977)516]. ..0
14.HRig.hB-ErannedrgeileiskPehtyasl..L[TeAtt.SBSO86C(o19ll7a9b)o2r4a3ti.on], Evidence for Planar Events in e+ e- Annihilation at .....0000
.0
15. V.N.GribovandL.N.Lipatov,Sov.J.Nucl.Phys.15(1972)438[Yad.Fiz.15(1972)781]. ..0
.
16. V.N.GribovandL.N.Lipatov,Sov.J.Nucl.Phys.15(1972)675[Yad.Fiz.15(1972)1218].
17. L.N.Lipatov,Sov.J.Nucl.Phys.20(1975)94[Yad.Fiz.20(1974)181].
18. Y.L.Dokshitzer,Sov.Phys.JETP46(1977)641[Zh.Eksp.Teor.Fiz.73(1977)1216].
19. G.AltarelliandG.Parisi,Nucl.Phys.B126(1977)298.doi:10.1016/0550-3213(77)90384-4
20. H.Abramowiczetal.[H1andZEUSCollaborations],Combinationofmeasurementsofinclusive
deepinelastice±pscatteringcrosssectionsandQCDanalysisofHERAdata.Eur.Phys.J.C75(2015)
12,580[arXiv:1506.06042[hep-ex]].
21. S. Schael et al. [ALEPH and DELPHI and L3 and OPAL and SLD and LEP Electroweak
WorkingGroupandSLDElectroweakGroupandSLDHeavyFlavourGroupCollaborations],
Precision electroweak measurements on the Z resonance. Phys. Rept. 427 (2006) 257 [hep-
ex/0509008].
22. F.Abeetal.[CDFCollaboration],Observationoftopquarkproductioninp¯pcollisionsPhys.Rev.
Lett.74(1995)2626[hep-ex/9503002].
23. S.Abachietal.[D0Collaboration],Phys.Rev.Lett.74(1995)2632[hep-ex/9503003].
24. F.EnglertandR.Brout,BrokenSymmetryandtheMassofGaugeVectorMesons.Phys.Rev.Lett.
13(1964)321.
25. P.W.Higgs,Brokensymmetries,masslessparticlesandgaugefields.Phys.Lett.12(1964)132.
26. P.W.Higgs,BrokenSymmetriesandtheMassesofGaugeBosons.Phys.Rev.Lett.13(1964)508.
27. G.S.Guralnik,C.R.HagenandT.W.B.Kibble,GlobalConservationLawsandMasslessParticles.
Phys.Rev.Lett.13(1964)585.
28. P. W. Higgs, Spontaneous Symmetry Breakdown without Massless Bosons Phys. Rev. 145 (1966)
1156.
29. T.W.B.Kibble,SymmetrybreakinginnonAbeliangaugetheoriesPhys.Rev.155(1967)1554.
30. S.L.Glashow,PartialSymmetriesofWeakInteractionsNucl.Phys.22(1961)579.
31. S.Weinberg,AModelofLeptonsPhys.Rev.Lett.19(1967)1264.
32. A. Salam, Weak and electromagnetic interactions. in Elementary particle physics: relativistic
groups and analyticity, N. Svartholm, ed., p. 367. Almqvist & Wiskell, 1968, Proceedings of
theeighthNobelsymposium.
33. G.’tHooftandM.J.G.Veltman,RegularizationandRenormalizationofGaugeFieldsNucl.Phys.
B44(1972)189.
34. T.Aaltonenetal.[CDFandD0Collaborations],Combinationofthetop-quarkmassmeasurements
fromtheTevatroncollider.Phys.Rev.D86(2012)092003[arXiv:1207.1069[hep-ex]].
35. T.A.Aaltonenetal.[CDFandD0Collaborations],CombinationofCDFandD0W-BosonMass
9
Measurements.Phys.Rev.D88(2013)5,052018[arXiv:1307.7627[hep-ex]].
36. G.Aadetal.[ATLASCollaboration],ObservationofanewparticleinthesearchfortheStandard
ModelHiggsbosonwiththeATLASdetectorattheLHC.Phys.Lett.B716(2012)1[arXiv:1207.7214 ...rsta
[hep-ex]]. ...r
.o
37.thSe.CCMhaStrecxhpyearinmeetnatla.t[CthMeLSHCCo.lPlahbyosr.aLtieotnt.],BO7b1s6er(v2a0t1i2on)3o0f[aanrXewivb:1o2s0on7.7a2t3a5m[hasespo-efx1]2]5. GeVwith ....yals
38.i(n2G0p.1pA5)Ca1do9lel1it8sia0ol3n.[s[AaarTtXL√iAvs:S1=5a0n73d.a0nC7d5M889ST[CehVoelplwa-eibtxoh]r]ta.hteioAnTs]L,ACSomanbidneCdMMSeaEsxupreermimenenttosf.tPhehHysi.ggRseBv.oLsoenttM.1a1s4s .........ocietypu
.b
39.[aArX. Bivu:1c1k0le1y.2e5t99al[.,hGepen-perha]l]-.purpose event generators for LHC physics. Phys. Rept. 504 (2011) 145 ....lish
40. S.Catani,F.Krauss,R.KuhnandB.R.Webber,QCDmatrixelements+partonshowersJHEP ...ing
0111(2001)063[hep-ph/0109231]. ....or
.g
41. S.FrixioneandB.R.Webber,MatchingNLOQCDcomputationsandpartonshowersimulations .
..P
JHEP0206(2002)029[hep-ph/0204244]. .h
42. K.Hamilton,P.Nason,E.ReandG.Zanderighi,NNLOPSsimulationofHiggsbosonproduction ....il.T
JHEP1310(2013)222[arXiv:1309.0017[hep-ph]]. ..ra
.n
43. G. Aad et al. [ATLAS Collaboration], Measurements√of fiducial and differential cross sections for ...s.
Higgsbosonproductioninthediphotondecaychannelat s=8TeVwithATLASJHEP1409(2014) .R
112[arXiv:1407.4222[hep-ex]]. ....S
44. V.Khachatryanetal.[CMSCollaboration],Measurementofdifferentialandintegratedfiducialcross ...oc
..
sectionsforHiggsbosonproductioninthefour-leptondecaychannelinppcollisionsatsqrt(s)=7and ..A
8TeV.arXiv:1512.08377[hep-ex]. ..0
.0
45. M. H. Seymour, Searches for new particles using cone and cluster jet algorithms: A Comparative ...00
study.Z.Phys.C62(1994)127. ..00
46. J.M.Butterworth,B.E.CoxandJ.R.Forshaw,WW scatteringattheCERNLHC.Phys.Rev.D ...0
65(2002)096014[hep-ph/0201098].
47. J. M. Butterworth, A. R. Davison, M. Rubin and G. P. Salam, Jet substructure as a new Higgs
searchchannelattheLHC.Phys.Rev.Lett.100(2008)242001[arXiv:0802.2470[hep-ph]].
48. D. E. Kaplan, K. Rehermann, M. D. Schwartz and B. Tweedie, Top Tagging: A Method
for Identifying Boosted Hadronically Decaying Top Quarks. Phys. Rev. Lett. 101 (2008) 142001
[arXiv:0806.0848[hep-ph]].
49. A.Altheimeretal.,BoostedobjectsandjetsubstructureattheLHC.ReportofBOOST2012,heldat
IFICValencia,23rd-27thofJuly2012Eur.Phys.J.C74(2014)3,2792[arXiv:1311.2708[hep-ex]].
50. G.Aadetal.[ATLASCollaboration],Measurementofthedifferentialcross-sectionofhighlyboosted
√
topquarksasafunctionoftheirtransversemomentumin s=8TeVproton-protoncollisionsusing
theATLASdetector.arXiv:1510.03818[hep-ex].
51. A. J. Bevan et al. [BaBar and Belle Collaborations], Eur. Phys. J. C 74 (2014) 3026
doi:10.1140/epjc/s10052-014-3026-9[arXiv:1406.6311[hep-ex]].
52. B. T. Cleveland, T. Daily, R. Davis, Jr., J. R. Distel, K. Lande, C. K. Lee, P. S. Wildenhain
andJ.Ullman,MeasurementofthesolarelectronneutrinofluxwiththeHomestakechlorinedetector.
Astrophys.J.496(1998)505.
53. J.N.Bahcall,M.H.PinsonneaultandS.Basu,Solarmodels:Currentepochandtimedependences,
neutrinos,andhelioseismologicalpropertiesAstrophys.J.555(2001)990[astro-ph/0010346].
54. Y. Fukuda et al. [Super-Kamiokande Collaboration], Evidence for oscillation of atmospheric
neutrinos.Phys.Rev.Lett.81(1998)1562[hep-ex/9807003].
55. Q.R.Ahmadetal.[SNOCollaboration],Directevidenceforneutrinoflavortransformationfrom
neutralcurrentinteractionsintheSudburyNeutrinoObservatoryPhys.Rev.Lett.89(2002)011301
[nucl-ex/0204008].
56. S. Abe et al. [KamLAND Collaboration], Precision Measurement of Neutrino
Oscillation Parameters with KamLAND Phys. Rev. Lett. 100 (2008) 221803
doi:10.1103/PhysRevLett.100.221803[arXiv:0801.4589[hep-ex]].
57. P. Adamson et al. [MINOS Collaboration], Measurement of the neutrino mass splitting and
flavormixingbyMINOSPhys.Rev.Lett.106(2011)181801doi:10.1103/PhysRevLett.106.181801
[arXiv:1103.0340[hep-ex]].
58. F.P.Anetal.[DayaBayCollaboration],Observationofelectron-antineutrinodisappearanceatDaya
BayPhys.Rev.Lett.108(2012)171803[arXiv:1203.1669[hep-ex]].
59. K. Abe et al. [T2K Collaboration], Precise Measurement of the Neutrino Mixing Parameter θ23 10
from Muon Neutrino Disappearance in an Off-Axis Beam. Phys. Rev. Lett. 112 (2014) 18, 181801
[arXiv:1403.1532[hep-ex]].
60. D.M.Jacobs,G.D.StarkmanandB.W.Lynn,MacroDarkMatterMon.Not.Roy.Astron.Soc. ...rsta
450(2015)4,3418[arXiv:1410.2236[astro-ph.CO]]. ...r
.o
61.(1J.86C5.)M45a9x.well, A dynamical theory of the electromagnetic field Phil. Trans. Roy. Soc. Lond. 155 ....yals
...oc
.....ietyp
.u
.b
....lish
...ing
...o
.r
.g
.
..P
.h
....il.T
..ra
.n
...s.
.R
...
.S
..o
.c
..
..A
..0
.0
...00
.0
.0
..0
.