Supersymmetry After the Higgs Discovery PDF
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The European Physical Journal C E PJ C I. Antoniadis D. Ghilencea Editors Recognized by European Physical Society Supersymmetry After the Higgs Discovery 123 Supersymmetry After the Higgs Discovery Ignatios Antoniadis • Dumitru Ghilencea Editors Supersymmetry After the Higgs Discovery Editors Ignatios Antoniadis Dumitru Ghilencea Department of Physics Theoretical Physics CERN National Institute of Physics NIPNE Geneva, Switzerland Bucharest-Magurele, Romania Originally published in Eur. Phys. J. C 74, 5 (2014) © Springer-Verlag Berlin Heidelberg 2014 ISBN 978-3-662-44171-8 ISBN 978-3-662-44172-5 (eBook) DOI 10.1007/978-3-662-44172-5 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2014947341 © Springer-Verlag Berlin Heidelberg 2014 This work is subject to copyright. 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Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Eur.Phys.J.C(2014)74:2841 DOI10.1140/epjc/s10052-014-2841-3 Editorial Supersymmetry after the Higgs discovery I.Antoniadis1,a,D.Ghilencea1,2,b 1DepartmentofPhysics,CERN-TheoryDivision,1211Geneva23,Switzerland 2TheoreticalPhysicsDepartment,NationalInstituteofPhysicsandNuclearEngineering(IFIN-HH),077125Bucharest,Romania Publishedonline:27May2014 ©TheAuthor(s)2014.ThisarticleispublishedwithopenaccessatSpringerlink.com These are interesting times for theoretical and experimen- troweaksymmetrybreakingwhichintheStandardModelis talhighenergyphysics.NearlyfivedecadesaftertheHiggs notexplained,beinganad-hocinput.Further,inSUSYmod- particletheoreticalprediction(1964),theATLASandCMS elstheunificationofthefundamentalforcesinNature(weak, experimentsoftheLargeHadronCollider(LHC)atCERN strong,andelectromagnetic)isnaturallyachieved,torealize confirmed (4 July 2012) the existence of the Higgs boson a long-held dream of high energy physics. This unification of the Standard Model (SM) and, implicitly, its associated pictureiscompletedbytheunificationwithgravity,asdone (Brout–Englert–Higgs) mechanism of electroweak (EW) in various string models, like the weakly coupled heterotic symmetry breaking. This confirmation is a great triumph string. SUSY also provides an interesting dark matter can- of theoretical high energy physics and, in particular, of the didate,consistentwiththermalrelicabundancecalculations, principleofsymmetriesthatmodernphysicsisbasedupon, whichmaysoonbedetectedbyaccelerator-orsatellite-based introducedearlylastcenturybyE.Noether. experiments.Allthesefeaturesrelytoalargeextentonthe Supersymmetry (SUSY) is a new symmetry that relates existenceoflow,TeV-scale SUSY,whichisthusaccessible bosons and fermions, which has strong support at both at the ongoing LHC experiments. Exact, non-perturbative the mathematical and the physical level. At the mathemat- resultsarealsopossibleinthepresenceofSUSY.Thecon- ical level, SUSY avoids the restrictions of the Coleman– sistencyofallthesetheoreticalandphenomenologicaladvan- Mandulano-gotheorembytheintroductionofspinorialgen- tagesofSUSYmadeitbecomethemostpopularcandidate erators(supercharges)thatmakesSUSYtheonlypossibility for“newphysics”beyondtheStandardModel. in which space-time beyond Poincaré and internal symme- One initial drawback of this theory is that it more than tries of the S-matrix can be combined consistently (Haag– doubles the SM spectrum, something regarded with seri- Lopuszanski–Sohnius). The existence of a super-Poincaré ousskepticismbysomeexperimentalistsandeventheorists. (gradedLie)algebraanditsrepresentations(superfields)fur- SUSY predicts a plethora of new particles (superpartners) ther supported this new symmetry on strong mathematical thatsofarwerenotdetectedbylargeandsmallscalephysics grounds.Moreover,ifimposedasalocalsymmetry,general experiments. In particular the constraints from the first run relativityisincludedautomatically(supergravity).Itisthen oftheLHC(7and8TeV)restrictedsignificantlytheparam- no surprise that SUSY is also a fundamental ingredient in eterspaceofvariousminimalsupersymmetricmodels,such string theory where it plays such a crucial role, even if no astheconstrainedminimalsupersymmetricstandardmodel. traceofthissymmetryisleftatlowenergies. Anotherproblemisanincreasedfinetuning(instability)of Atthephysicallevel,themotivationisevenstronger,when theEWscaleinsomesimplemodels,whichmayquestionthe appliedtotheStandardModel,toobtaina(minimal)super- successofSUSYinsolvingthehierarchyproblemthatmoti- symmetricextensionofitthatcouldbevalidatenergiesas vateditsintroductioninthefirstplace.Theseproblemspoint lowastheTeVscale.ThemotivationisthatTeV-scaleSUSY tothebreakingmechanism ofSUSY,whosedetailsremain solvesthemasshierarchyproblemoftheSMandstabilizes somewhatmysterious. the EW scale in the presence of quantum corrections, by Theseare,however,earlydaysinthegreatefforttodetect ensuringanimprovedultravioletbehaviorofthetheory.TeV- SUSY experimentally. Until Run 2 of the LHC (13 and 14 scaleSUSYisconsistentwithadynamical(radiative)elec- TeV)isperformedandcompleteditisdifficulttomakedefi- nitestatementsabouttheexistenceofTeV-scaleSUSY,even inminimalmodels.Sofar,theexistenceofaHiggsboson,in ae-mail:[email protected] a(perturbative)regionperfectlywellcompatiblewithSUSY, be-mail:[email protected] 123 v Reprintedfromthejournal 2841 Page2of2 Eur.Phys.J.C(2014)74:2841 givesushopethatthisscalarparticleisonlyoneofmanyother Contentsofthisvolume: scalarsthatwesofarfailedtodiscover.Whyshouldtherebe 1. P. Ramond, “SUSY: the early years (1966–1976)”. onlyasinglescalarparticle,butsomanyfermionsandgauge doi:10.1140/epjc/s10052-013-2698-x bosons? The optimistwould even say that we already have 2. P. Fayet, “The supersymmetric standard model”. doi: a scalar particle and with a mass range, both predicted by 10.1140/epjc/s10052-014-2837-z SUSY,theHiggsboson,sowemustbeontherighttrack. 3. I. Melzer-Pellmann (CMS), P. Pralavorio (ATLAS), Thecurrentvolumeintendstobeareviewoftheseideas, “Lessons for SUSY from the LHC after the first run”. followingthedevelopmentofSUSYfromitsveryearlydays doi:10.1140/epjc/s10052-014-2801-y up to present. The order of the contributions should pro- 4. J. Ellis, “Supersymmetric fits after the Higgs discovery videthereaderwiththehistoricaldevelopmentaswellasthe andimplicationsformodelbuilding”.doi:10.1140/epjc/ latesttheoreticalupdatesandexperimentalconstraintsfrom s10052-014-2732-7 particle accelerators and dark matter searches. It is a great 5. A.Djouadi,“ImplicationsoftheHiggsdiscoveryforthe pleasuretobringtogetherinthisvolumecontributionsfrom MSSM”.doi:10.1140/epjc/s10052-013-2704-3 peoplewhoinitiatedorcontributedsignificantlytothedevel- 6. G. G. Ross, “SUSY: Quo Vadis?”. doi:10.1140/epjc/ opment of this theory over so many years. For a balanced s10052-013-2699-9 pointofview,thevolumealsoincludesa(last)contribution 7. R.Catena,L.Covi,“SUSYdarkmatter(s)”.doi:10.1140/ that attempts to describe the physics beyond the Standard epjc/s10052-013-2703-4 ModelintheabsenceofSUSY. 8. H.P.Nilles,“Thestringsconnection:MSSM-likemodels Belovedbymanytheoristsorshunnedbyasmanyexper- fromstrings”.doi:10.1140/epjc/s10052-013-2712-3 imentalists,theideaofSUSYremainsattractive.Wearefor- 9. B.Bellazzini,C.Csáki,J.Serra,“CompositeHiggses”. tunatethattheLHChasgoodchancestoclarifythequestion doi:10.1140/epjc/s10052-014-2766-x if SUSY really exists near the TeV scale. Its experimental confirmation would certainly dominate particle physics for manydecadestocomewithanimpactthatishardtoimagine at this moment. The alternative is that this scale is pushed OpenAccess ThisarticleisdistributedunderthetermsoftheCreative higher and higher, moving this beautiful idea further away CommonsAttributionLicensewhichpermitsanyuse,distribution,and fromourexperimentalreach.Thiswouldmaketheoristswon- reproductioninanymedium,providedtheoriginalauthor(s)andthe sourcearecredited. derwhethertheypinnedtheirhopesfortoolongonasingle, FundedbySCOAP3/LicenseVersionCCBY4.0. mostbeautifulbutelusiveideaandwhetherthetimeisripe tore-considerourviewonphysicsneartheTeVscale. Geneva,March2014. 123 Reprintedfromthejournal vi Contents SUSY: the early years (1966–1976) ................................................................................... 1 Pierre Ramond The Supersymmetric standard Model ............................................................................... 9 Pierre Fayet Lessons for SUSY from the LHC after the first run ...................................................... 29 I. Melzer-Pellmann and P. Pralavorio Supersymmetric fits after the Higgs discovery and implications for model building ................................................................................................. 59 John Ellis Implications of the Higgs discovery for the MSSM ....................................................... 71 Abdelhak Djouadi SUSY: Quo Vadis? ............................................................................................................ 99 G. G. Ross SUSY dark matter(s) ....................................................................................................... 121 Riccardo Catena and Laura Covi The strings connection: MSSM-like models from strings ........................................... 137 Hans Peter Nilles Composite Higgses ........................................................................................................... 151 Brando Bellazzini, Csaba Csáki, and Javi Serra vii Eur.Phys.J.C(2014)74:2698 DOI10.1140/epjc/s10052-013-2698-x Review SUSY: the early years (1966–1976) PierreRamonda InstituteforFundamentalTheory,PhysicsDepartment,UniversityofFlorida,Gainesville,USA Received:20November2013/Accepted:27November2013/Publishedonline:27May2014 ©TheAuthor(s)2014.ThisarticleispublishedwithopenaccessatSpringerlink.com Abstract Wedescribetheearlyevolutionoftheorieswith wasthenattheUniversityofWisconsinatMadison,arefugee fermion–bosonsymmetry. fromPrinceton,whichhaddeniedhimtenure.Itwasnotan easy paper to read, but its results were very simple: there were five types of representations labeled by the values of 1 Introduction P2 ≡ pμpμ = m2, one of the Poincaré group’s Casimir operator. By the 1940s, physicists had identified two classes of ‘ele- All but two representations describe familiar particles mentary’ particles with widely different group behavior, found in Nature. Massive particles come with momentum bosons and fermions. The prototypic boson is the photon p,spinj,and2j+1statesofpolarization,e.g.electronsand whichgenerateselectromagneticforces;electrons,theessen- nucleonswithspin1/2.Therearealsofourtypesofmassless tialconstituentsofmatter,arefermionswhichsatisfyPauli’s representations with spin replaced by helicity (spin projec- exclusionprinciple.Thisdistinctionwasquicklyextendedto tionalongthemomentum).Thefirsttwodescribemassless Yukawa’s particle (boson), the generator of Strong Interac- particleswithasinglehelicity(photonswithhelicity±1),or tions,andtonucleons(fermions).Acompellingcharacteri- half-oddintegerhelicity,suchas“massless”neutrinoswith zationfollowed:matterisbuiltoutoffermions,whileforces helicity+1/2. aregeneratedbybosons. The last two representations O(Ξ) and O(cid:3)(Ξ) describe Einstein’sprematuredreamofunifyingallconstituentsof states which look like massless ‘objects’, particle-like in the physical world should have provided a clue for that of the sense that they have four-momentum, but with bizarre fermions and bosons; yet it took physicists a long time to helicities: each representation contains an infinite tower relatethembysymmetry.Thisfermion–bosonsymmetryis of helicities, one with integer helicities, the other with called‘supersymmetry’. half-odd integer helicities. These have no analogues in Supersymmetry, a necessary ingredient of string theory, Nature.1 turnsouttohavefurtherremarkableformalpropertieswhen Physicists were slow in recognizing the importance of appliedtolocalquantumfieldtheory,byrestrictingitsultravi- group representations, even though Pauli provided the first oletbehavior,andprovidingunexpectedinsightsintoitsnon- solution of the quantum-mechanical hydrogen atom using perturbative behavior. It may also play a pragmatic role as grouptheory.Wigner’spaperdoesnotseemtohavemoved thegluethatexplainstheweaknessoftheelementaryforces anymountains,andinfinitespinrepresentationsweresimply within the Standard Model of Particle Physics at short dis- ignored,exceptofcoursebyWigner. tances. Yet, O(Ξ)and O(cid:3)(Ξ)containedimportantinformation: theyare‘supersymmetricpartners’ofoneanother! 2 Earlyhint 3 HadronsandMesons In 1937, Wigner [1], with some help from his brother-in- Symmetries were gaining credence among physicists, not law,publishes oneofhismanyfamous papers‘OnUnitary as a simplifying device but as a guide to the organiza- RepresentationsoftheInhomogeneousLorentzGroup’.He 1 ‘Infinitespin’representationsdonotappearinthePoincarédecom- ae-mail:[email protected]fl.edu positionoftheconformalgroup. 123 1 Reprintedfromthejournal 2698 Page2of8 Eur.Phys.J.C(2014)74:2698 tion of Nature. Wigner and Stückelberg’s ‘supermultiplet example generated by the three Pauli matrices σ+,σ−,σ3. model’ unified SU(2) isospin and spin. Once Gell-Mann Physical applications are not discussed, although Berezin’s and Ne’eman generalized isospin to SU(3), it did not advocacy of Grassmann variables in path integrals was no take long for Gürsey and Radicati [2], as well as Sakita doubtamotivation. [3], to propose its unification with spin into SU(6). Pseu- doscalar and vector mesons (bosons) were found in the 35 representation of SU(6), while the hadrons (fermions) 4 Dualresonancemodels surprisingly lived in 56, not in 20 [3], as expected by the statistics of the time. This non-relativistic unification Inthe1960s,physicistshadallbutgivenuponaLagrangian proved very successful, both experimentally and conceptu- description of the Strong Interactions, to be replaced by ally, since it led to the hitherto unsuspected color quantum the S-matrix program: amplitudes were determined from number. general principles and symmetries, locality, causality, and In1966,Miyazawa[4]proposedfurtherunification.His Lorentz invariance. Further requirements on the ampli- aimwastoassemblethefermionic56andthebosonic35into tudes such as Regge behavior and its consequent boot- onemathematicalstructure,suchasSU(9)butatthecostof strap program were still not sufficient to determine the disregardingspin-statistics. amplitudes. Toexplainthebountyofstrangeparticlediscoveredinthe In 1967, Dolen et al. [8] discovered a peculiar relation 1950s,SakatahadproposedtoexplainmesonsasTT bound in π − N scattering. At tree-level, its fermionic s-channel statesofthespinone-halftriplet (π N → π N) is dominated by resonances (Δ++, …), as shown by countless experiments. On the other hand, its T = (p, n, Λ). bosonic t-channel (ππ¯ → N N) is dominated by the ρ- meson. Using the tools of S-matrix theory in the form of Miyazawaaddsapseudoscalartriplet ‘finiteenergysumrules’,theyfoundthattheReggeshadowof t = (K+,K0, η), thebosonict-channel’sρ-mesonaveragedthefermionicres- onancesinthes-channel!Thiswastotallyunexpected,since to the Sakata spinor triplet. The hadron octet would then thesetwocontributions,describedbydifferentFeynmandia- ¯ be described by another bound state, Tt, but he could not grams,shouldhavebeenindependent.Wasthistheadditional describethespinthree-halfbaryonsdecimetinthe56. pieceofinformationneededtofullydeterminetheamplitudes He introduces a toy model with two fundamental con- ofStrongInteractions?Thisearlyexampleoffermion–boson stituents, a spin one-half and a spin zero particle, p = kinship led, through an unlikely tortuous path, to modern (α↑,α↓,γ).Theninecurrents supersymmetry. (cid:2) An intense theoretical search for amplitudes where the p†λ p= Fi, i =0,1,2,3,8; s- and t-channel contributions are automatically related to i Gi, i =4,5,6,7, one another followed. Under the spherical cow principle, spinwassetasideandthesearchforDHS-typeamplitudes satisfy a current algebra with both commutators and anti- focusedonthepurelybosonicprocessω→πππ [9].Soon commutators thereafter, Veneziano [10] proposed a four-point amplitude (cid:3) (cid:4) F, F =if F , withthedesiredcrossingsymmetry, i j ijk k (cid:3) (cid:4) Fi, Gj =ifijkGk, A(s,t)∼ Γ(−α(s))Γ(−α(t)), (cid:5) (cid:6) Γ(−α(s)−α(t) G , G =d F , i j ijk k where α(x) = α + α(cid:3)x is the linear Regge trajectory. It 0 a‘generalizedJordanalgebra’whichhecalls V(3).Thisis displays an infinite number of poles in both s-channel s > the first example, albeit non-relativistic, of a superalgebra, 0,t <0andt-channels <0,t >0. todaycalledSU(2/1)withevenpartSU(2)×U(1). Veneziano’s construction was quickly generalized to n- In 1967, he expanded his construction [5], to general point ‘dual’ amplitudes. The infinite series of poles were superalgebrashecallsV(n,m)withtheideaofincludingthe recognizedasthevibrationsofastring[11–13]. decimet.Alas,thephenomenologywasnotascompellingas The amplitudes were linear combinations of tree chains thatofSU(6);twoofthequarksinsideanucleondonotseem whichfactorizeintothree-pointverticesandpropagators.A tolivetogetherinanantitripletcolorstate. generalizedcoordinateemerged[14]fromthisanalysis In1969,BerezinandG.I.Kac[6,7]showthemathemati- (cid:7)∞ (cid:8) (cid:9) 1 ccaolmcmonustaistoternscaynodfagnrtaidceodmLmiuetaatlogresb;rathweyhigcihvecointstasinimspbloetsht Qμ(τ)= xμ+τ pμ+ √2nα(cid:3) anμeinτ −an†μe−inτ , n=1 123 Reprintedfromthejournal 2
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