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! Introduction! What is supersymmetry?! What have we learned?! Summary & Conclusions

The most significant result from the LHC is clearly the discovery of the neutral scalar Higgs boson. m H = 125.09 ± 0.21 ± 0.11 GeV CMS & ATLAS, Phys. Rev. Lett. 114, 191803 (2015)

But, also of potentially monumental significance is the absence (so far) of credible evidence for new physics, in particular, for supersymmetry. If, by the end, of the LHC era it is shown that supersymmetry is irrelevant at the TeV scale, this would be a profound discovery. It might signal that an understanding of physics the TeV scale requires an understanding of physics at a scale many orders of magnitude greater. Takemichi Okui

But, we are not yet able to dismiss the supersymmetry hypothesis and many particle physicists remain gung-ho about it!

! Introduction! What is supersymmetry?! What have we learned?! Summary & Conclusions

! A supersymmetry operation Q transforms a bosonic state into a fermionic one and vice versa: Q boson> = fermion> Q fermion> = boson>! By adding appropriate structures to the Standard Model, it is possible to create versions of it that are invariant under this operation. The simplest such model is called the minimal supersymmetric extension of the SM (MSSM). But, why do this? The SM is, after all, spectacularly successful.

Here are the principal reasons: 1. In the SM, the quantum correction to the Higgs boson mass is given by m 2 2 H = m bare + y 2 m bare t 16π 2 Λ2 +! y t Λ cut-off Since, in principle, Λ ~ 10 18 GeV, one has to fine-tune the bare mass parameter with enormous precision in order to get the measured value of the Higgs boson mass. Langrangian parameter top Yukawa coupling However, fine-tuning is unnecessary in a theory invariant under supersymmetry because such terms cancel exactly.

2. In a supersymmetric theory, it is possible to arrange for the coupling constants of the three forces to unify at a scale ~ O(10 16 ) GeV. Stephen P. Martin, https://arxiv.org/pdf/hep-ph/9709356.pdf

The quantum number (R-parity) R = (-1) 3(B-L) + S B Baryon number L Lepton number S Spin is +1 for every SM particle and -1 for every supersymmetric particle (or super-particle, or sparticle) In the usual definition of the MSSM, R-parity is conserved. Consequently, super-particles are predicted to be created in pairs and the lightest is absolutely stable. If the lightest super-particle (LSP) is neutral and weakly interacting, it is a dark matter candidate.

Supersymmetric Particle Content: neutralinos!χ 0 1,!χ 0 2,!χ 0 0 3,!χ 4 1 / 2 charginos!χ ± ± 1,!χ 2 1 / 2 gluinos!g 1 / 2 Higgs bosons h 0, H 0, A 0, H ± 0 sleptons!e L,R,!µ L,R,!τ 1,2 0!ν e,!ν µ,!ν τ 0 Fermions Bosons squarks!u L,R,!c L,R,!t 1,2 0!d L,R,!s L,R,! b 1,2 0

Hadron collider reactions: Electroweak q! q "χ i+ "χ j, "χ i0 "χ j 0, " li +" l j, "ν l "ν l * ud "χ i+ "χ 0 j, ll+ " "ν l du "χ i "χ 0 j, ll " * "ν l Strong * antiparticles gg!g!g,!q i!q j * q q " *!g!g,!q i!q j gq!g!q i qq!q i!q j

No supersymmetric particles with the same mass as the corresponding SM particle have been found, therefore, the ground state of the Universe is clearly not supersymmetric. In order to accommodate this fact, extra structure has been added to the MSSM (and its variants), consistent with the symmetry of the SM, that breaks (or hides) the supersymmetry. Alas, this causes the number of parameters to explode from the 19 of the SM to the 19 + 105 = 124 of the MSSM!

Model # Pars. msugra 3 CMSSM 4 NUHM1 5 NUHM2 6 SU(5) 7 pmssm 19 MSSM 124 John Ellis

! Introduction! What is supersymmetry?! What have we learned?! Summary & Conclusions

Supersymmetry search results at the LHC are often interpreted in terms of simplified models (SMS) or models that posit specific SUSY-breaking schemes, e.g., the constrained MSSM (CMSSM). simplified models

! p T miss + H T = S T =! p T,i + jets jets jets! p T,i! p T,i! p T,i + leptons + E T miss! p T,i = 0, E miss T = p! miss T photons m T = 2 p T,l E T miss [1 cos Δφ(! p T,i,! p T miss )] M R = (p j1 + p j 2 ) 2 (p j1,z + p j 2,z ) 2 R 2 = ( E miss T (p j1,t + p j 2,T ) p! miss T ( p! j1 + p! j 2 )) / ( 2 2M ) R Chris Rogan, Kinematical variables towards new dynamics at the LHC arxiv:1006.2727v2

Search using boosted W bosons and razor variables m!g = 1 TeV, m! t 1 = 0.325 TeV, m! χ 1 0 = 0.300 TeV CMS collaboration, Search for supersymmetry in pp collisions at s= 8 TeV in final states with boosted W bosons and b jets using razor variables, Phys. Rev. D 93 (2016) 092009

Signal Region S Control Regions W W boson Q QCD T top Control regions used to model background in signal region CMS collaboration, Search for supersymmetry in pp collisions at s= 8 TeV in final states with boosted W bosons and b jets using razor variables, Phys. Rev. D 93 (2016) 092009

RPV slepton EWK gauginos sbottom stop squark gluino production 0 ~ g qq χ 0 ~ g bb χ 0 ~ g tt χ 0 ~ ~ g t( t t χ ) ± 0 ~ g qq( χ Wχ ) ± 0 ~ ~ g b( b t( χ Wχ )) 0 ~ q q χ 0 ~ t t χ + 0 ~ t b( χ Wχ ) 0 0 ~ t t b χ ( χ H G) ~ ~ 0 t ( t t χ ) Z 2 1 ~ ~ 01 t ( t t χ ) H 2 1 1 0 ~ b b χ 0 ~ b tw χ 0 ~ b bz χ 0 ± 0 0 χ χ lll ν χ χ + 2 0 - + - 0 χ χ l l ν ν χ χ 0 0 0 0 χ χ Z Z χ χ 2 02 ± 0 0 χ χ W Z χ χ 2 0 0 0 0 χ χ H Z χ χ 2 2 ± 0 0 0 χ χ H W χ χ 0 2 ± 0 0 χ χ llτ ν χ χ 2 0 ± 0 0 χ χ τττ ν χ χ 2 0 ~ l l χ ~ g qllν λ 122 ~ g qllν λ ~ g qllν λ 123 233 ~ g qbtµ λ ' 231 ~ g qbtµ λ ' ~ g qqb λ '' 233 113/223 ~ g qqq λ '' ~ g tbs λ '' 112 323 ~ g qqqq λ '' ~ q qllν λ 112 122 ~ q qllν λ 123 ~ q qllν λ ~ 233 q qbtµ λ ' 231 ~ q qbtµ λ ' 233 ~ q qqqq λ '' R 112 ~ t µ e ν t λ R 122 ~ t µ τν t λ R 123 ~ t µ τν t λ R 233 ~ t tbtµ λ ' R 233 Summary of CMS SUSY Results* in SMS framework m(mother)-m(lsp)=200 GeV SUS 13-019 L=19.5 /fb SUS-14-011 SUS-13-019 L=19.3 19.5 /fb SUS-13-007 SUS-13-013 L=19.4 19.5 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-13-013 L=19.5 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-13-019 L=19.5 /fb SUS-14-011 L=19.5 /fb SUS-13-011 L=19.5 /fb SUS-13-014 L=19.5 /fb SUS-13-024 SUS-13-004 L=19.5 /fb SUS-13-024 SUS-13-004 L=19.5 /fb SUS-13-018 L=19.4 /fb SUS-13-008 SUS-13-013 L=19.5 /fb SUS-13-008 L=19.5 /fb SUS-13-006 L=19.5 /fb SUS-13-006 L=19.5 /fb SUS-14-002 L=19.5 /fb SUS-13-006 L=19.5 /fb SUS-14-002 L=19.5 /fb SUS-14-002 L=19.5 /fb SUS-13-006 L=19.5 /fb SUS-13-006 L=19.5 /fb SUS-13-006 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb EXO-12-049 L=19.5 /fb EXO-12-049 L=19.5 /fb SUS-13-013 L=19.5 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-12-027 L=9.2 /fb SUS-13-003 L=19.5 9.2 /fb SUS-12-027 L=9.2 /fb SUS-13-003 L=19.5 9.2 /fb SUS-13-003 L=19.5 /fb x = 0.25 x = 0.50 x = 0.75 x = 0.95 x = 0.05 x = 0.50 x = 0.95 x = 0.05 x = 0.50 x = 0.20 x = 0.50 ICHEP 2014 m(lsp)=0 GeV CMS Preliminary For decays with intermediate mass, = x m +(1-x) m m intermediate 0 200 400 600 800 1000 1200 1400 1600 1800 Mass scales [GeV] *Observed limits, theory uncertainties not included Only a selection of available mass limits Probe *up to* the quoted mass limit mother lsp

Model # Pars. msugra 3 CMSSM 4 NUHM1 5 NUHM2 6 SU(5) 7 pmssm 19 MSSM 124 John Ellis

There have been many studies of the CMSSM assessing its status after the 7 and 8 TeV runs of the LHC, including: 1. The CMSSM and NUHM1 after LHC Run 1, O. Buchmueller et al., Eur. Phys. J. C74 (2014), 2922 2. Experimental status of supersymmetry after the LHC Run-1, C. Autermann, Prog. Part. Nucl. Phys. 90 (2016) 125 3. Killing the cmssm softly, P. Bechtle et al., Eur. Phys. J. C76 (2016), 96

(GeV) M 1/2 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 2D 95% CL 1D 68% CL best fit 0 2000 4000 6000 8000 10000 M 0 (GeV) (a) 1s and 2s contour plot in in the (M 0,M 1/2 ) plane for the Small Observable Set. (GeV) M 1/2 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 2D 95% CL 1D 68% CL best fit 0 2000 4000 6000 8000 10000 M 0 (GeV) (b) 1s and 2s contour plot in in the (M 0,M 1/2 ) plane for the Medium Observable Set. (GeV) M 1/2 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 2D 95% CL 1D 68% CL best fit 0 2000 4000 6000 8000 10000 M 0 (GeV) (c) 1s and 2s contour plot in the (M 0,M 1/2 ) plane for the Large Observable Set. tanβ 90 2D 95% CL 80 70 60 50 40 30 20 10 1D 68% CL best fit 0-10000 -5000 0 5000 10000 A 0 (GeV) (d) 1s and 2s contour plot in the (A 0, tanb) plane for the Medium Observable Set. Fig. 2 1s and 2s contour plots for different projections and different observable sets. It can be seen that the preferred parameter region does not Killing depend on the the specificmssm observable set. softly, P. Bechtle et al., Eur. Phys. J. C76 (2016), 96 4.1 Profile likelihood based results In this section we describe the preferred parameter space region of the cmssm and its physical properties. Since a truly complete frequentist determination of a confidence region ally only exact when the observed distribution of c 2 values in a set of toy fits is truly c 2 -distributed, which as discussed in Section 4.3 is not the case. Nevertheless, since the exact method is not computationally feasible, this standard method, as used in the literature in all previous frequentist results, gives a reasonable estimation of the allowed pa-

12 68 % CL 95 % CL best fit 68 value % CL data 95 % CL LLL best fit value FITTINO SUSY SUSY SUSY LLL FITTINO SUSY SUSY SUSY 68 % CL 95 % CL best fit value data LLL FITTINO SUSY SUSY SUSY ATL, h ZZ 4l ATL, h γ γ ggh qqh ATL, h WW lνlν ATL, h ZZ 4l ATL, h γγ CMS, h ZZ 4l Wh ATL, h τ τ ATL, Vh Vbb CMS, h γ γ Zh CMS, h WW lνlν CMS, h ZZ 4l 118 120 122 124 126 128 130 (GeV) m h Fig. 6 Our predicted mass of the light Higgs boson, together with the tth 1s and 2s ranges. The LHC measurements used in the fit are shown as well. Note that the correlated theory uncertainty of Dm htheo = 3 GeV is not shown in the the plot. The relative smallness of the 68% CL region of the fitted mass of Dm h fit = 0.9 1.1 GeV is0.95 caused by constraints 1 from 1.05 other observables. SM σ/σ @ 14 TeV bbh 0 1 2 µ CMS, h γγ CMS, h τ τ CMS, Vh Vbb icle mass spectrum as preiggs observables. dicts a slightly smallerfig. cross 7 Predicted section production in all channels cross sections exceptat 14 TeV of the light Higgs the bbh channel. The predicted boson relative signal to the strengths SM value µ for in athe Higgs dif-bosoferent final states for p-p collisions at a centre-of-mass en- with the same mass ergy of 8 TeV is also slightly pectation smaller values than (vevs). the SM There prediction, could be additional minima as shown in Fig. 8. The of current the scalar precision potential of these which measurements does, however, not would break SU(3) c and/or U(1) allow for a discrimination between EM and thus colour and/or charge [7,138 140]. If these the SM and the cmssm minima based are solely energetically on measurements higher than of the conventional electroweak breaking minimum, then the latter is considered Higgs boson properties. stable. If any of these minima are lower than the conven- Fig. 8 Our predicted µ values of the light Higgs boson relative to the SM value for a Higgs boson with the same mass. The measurements used in the fit are shown as well. Killing the cmssm softly, P. Bechtle et al., Eur. Phys. J. C76 (2016), 96 gion, which typically suffers from the SM-like vacuum being only metastable, decaying to a charge- and/or colourbreaking (CCB) minimum of the potential [145, 146]. For the purpose of a fit, in principle a likelihood value for the compatibility of the lifetime of the SM-like vacuum

Although the standard CMSSM is still viable, there remain only restricted regions of the parameter space of the CMSSM in which a successful prediction for m h can be reconciled with the measured cold dark matter density * Indeed, Bechtle et al. exclude the CMSSM at 90% CL. * Beyond the CMSSM without an Accelerator: Proton Decay and Direct Dark Matter Detection, J. Ellis et al., Eur. Phys. J. C76 (2016), 8

Model # Pars. msugra 3 CMSSM 4 NUHM1 5 NUHM2 6 SU(5) 7 pmssm 19 MSSM 124 John Ellis

3 gaugino mass parameters M 1, M 2, M 3 1 ratio of Higgs vacuum expectation values tan β = v 2 / v 1 1 higgsino mass parameter µ 1 pseudoscalar Higgs boson mass m A 10 sfermion mass parameters m! F 3 trilinear couplings A t, A b, A τ ATLAS collaboration, Summary of the ATLAS experiment s sensitivity to supersymmetry after LHC Run 1 interpreted in the phenomenological MSSM, JHEP 1510 (2015) 134 CMS collaboration, Phenomenological MSSM interpretation of CMS searches in pp collisions at sqrt(s) = 7 and 8 TeV, JHEP 1610 (2016) 129

CMS and ATLAS reach similar conclusions regarding the gluino and lightest neutralino.

Here is an illustration, from ATLAS, of why some caution is needed in drawing conclusions from simplified models.

! Gluino masses < 500 GeV excluded.! Neutralino and chargino masses < 300 GeV strongly disfavored.! A relatively light supersymmetric top is still viable.! About half of the potentially accessible pmssm parameter space excluded.! Of the surviving points, about half have cross sections exceeding ~ 10fb and tend to yield events with missing E T lower than typical missing E T analysis cuts.

! Introduction! What is supersymmetry?! What have we learned! Summary & Conclusions

! The CMSSM has been excluded at 90% CL.! In the pmmsm (a good MSSM proxy), about half of the parameter space, potentially accessible at the LHC, remains.! Of the remaining model points, about half have cross sections exceeding 10fb.! The gluino mass > 500 GeV, a light stop is still possible, but squarks and neutralinos with mass < 300 GeV are strongly disfavored.! Conclusion: weak-scale supersymmetry remains viable!