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Desperately Seeking SUSY Ben Allanacha (University of Cambridge) Please ask questions while I’m talking a BCA, Outlook in Particle Physics, KCL, 2012 Gripaios, 1202.6616; BCA, Sridhar 1205.5170 B.C. Allanach – p Supersymmetric Copies H Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Supersymmetric Copies H ×2 Outlook in Particle Physics, KCL, 2012 H̃ × 2 B.C. Allanach – p Review of R-Parity The superpotential of the MSSM can be seperated into two parts: W Rp = heij Li H1 Ēj + hdij Qi H1 D̄j W 6RP +huij Qi H2 Ūj + µH1 H2 , 1 = λijk Li Lj Ēk + λ′ijk Li Qj D̄k 2 1 ′′ + λijk Ūi D̄j D̄k + κi Li H2 . 2 W Rp is what is usually meant by the MSSM. Q: Why ban W 6RP ? A: “Proton decay” Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Definition of R-Parity Q: How is W 6RP normally banned? A: By defining discrete symmetry Rp Rp = (−1)3B+L+2S . → SM fields have Rp = +1 and superpartners have Rp = −1. There are two important consequences: • Because initial states in colliders are Rp EVEN, we can only pair produce SUSY particles • The lightest superpartner is stable Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Candidate Event: High ET (j) Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Natural SUSY The particles coupling the most strongly to the higgs are the stopsa . Minimising the MSSM Higgs potential, MZ2 ≈ |µ|2 + m2H2 , − 2 2 −3ht 2 ΛU V 2 mt̃ ln δmH2 ≈ 2 4π mt̃ t̃ H2 a H2 H2 t̃ g̃ H2 H2 t̃ H2 M. Papucci, J. T. Ruderman and A. Weiler, arXiv:1110.6926; C. Brust, A. Katz, S. Lawrence and R. Sundrum, arXiv:1110.6670 Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Natural SUSY The particles coupling the most strongly to the higgs are the stopsa . Minimising the MSSM Higgs potential, MZ2 ≈ |µ|2 + m2H2 , − 2 2 −3ht 2 ΛU V 2 mt̃ ln δmH2 ≈ 2 4π mt̃ No cancellation⇒ < < mt̃ ∼ 700 GeV, mg̃ ∼ 1000 GeV. Experimental E 6 T searches⇒ mt̃ > 500 GeV, mg̃ > 900 GeV. a M. Papucci, J. T. Ruderman and A. Weiler, arXiv:1110.6926; C. Brust, A. Katz, S. Lawrence and R. Sundrum, arXiv:1110.6670 Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p g̃ t̃: E 6 T > 50/120 GeV, Nb ≥ 2, #j ≥ 2, HT > 320 GeV Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Direct Stop Seach Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Jets Plus E 6 T Search Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Bottom Up Implications of 2012 Data Naturalness is under pressure. Ways to get around it: • First two generation squarks > 1.8 TeV, mt̃ = 0.5 − 0.7 TeV, mg̃ = 0.9 − 1 TeV, mχ01 < 0.5 TeV. Ruled out soon? • Compressed spectraa : ISR monojets/6E T searches give you mg̃ > 500 GeV only. • RPV decreases/removes the E 6 T b. • Explains why natural SUSY hasn’t been found yet • Like-sign dileptons is a generic signature, as we’ll see a Dreiner, Kramer, Tattersall arxiv:1207.1613 b BCA, Gripaios arXiv:1202.6616 Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p RPV and Dark Matter If one gives up R−parity, χ01 is no longer a good dark matter candidate, since it decays. One then has to have something else, eg: • Gravitino - still decays, but lifetime may be much longer than the age of the universe • Hidden sector matter • Axion/axino The implications of each of these is that (in-)direct dark matter searches shouldn’t find anything. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Upper Bounds on Outlook in Particle Physics, KCL, 2012 ′′ λijk B.C. Allanach – p Bottom up thinking We are not assuming • MSSM: don’t put higgs constraints - there might be higher dimension operators coming from heavier fields. • Some specific (or even generic) string model. • We only put in the particles important for our analysis. Others may be decoupled, or light: it shouldn’t matter. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Gluino/stop LHC7 1e+06 100000 production at gluino stop σprod NLO /pb 10000 1000 100 10 1 0.1 0.01 0.001 100 200 300 400 500 600 700 800 900 1000 mass/GeV Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Gluinos With Rp Violation • • • Outlook in Particle Physics, KCL, 2012 We assume lightish g̃, t̃R . If one has lepton number violating LLE or LH1 operators, the gluinos decay producing various leptons. These cases ought to be easy to find, and are good candidates for searches. Get same-sign leptons. With LQD operators, the stops will again decay into leptons, easy to see. Flavour constraints imply that L3 QD operators are likely to be the largest. Get same-sign leptons in ∼ 79 of g̃g̃ events. With U DD operators, the (right-handed) top decays direcly into jets. B.C. Allanach – p Baryon Number Violating Example t g̃ b dj t̃∗ dj t̃∗ g̃ t Can lead to natural SUSY with light stops and gluinos that hasn’t been excluded yet. A difficult casea : W ⊃ λ′′ijk Ui Dj Dk . a BCA and Ben arXiv:1202.6616 Gripaios, b g̃g̃ production dominates. Here, you can look for like-sign di-leptons since gluinos decay into t and t̄ with equal branching ratios. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Other Light States How robust is the same-sign dilepton signature in the case that other states are also light? Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Can we avoid SS dileptons? • For mH ± > mt + mb , H + → tb̄ dominates, which again will yield same-sign dileptons. • H + → τ + ντ is also OK, since we’ll get like-sign di-taus. Only fly in the ointment comes from Fig. 1c: when H + → cb̄ (but only happens when tan β ≪ mt Vcb/mτ ∼ 3, which seems unlikely). • Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Same-sign E 6 T Limits CMSSll1a : HT > 400 GeV, |6E T | > 120 GeV a CMS-PAS-SUS-010; Outlook in Particle Physics, KCL, 2012 ATLAS-CONF-2012-004 B.C. Allanach – p AF B in the Standard Model 1.96 TeV pp̄ collisions at the Tevatron. AF B N (c > 0) − N (c < 0) , c = cos θ. = N (c > 0) + N (c < 0) SM Prediction: 0.066. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Measurements of AF B S Leone (CDF) talk at Electroweak session of Rencontres de Moriond 2012. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Other Constraints σtLHC7 = 173.4 ± 10.6 pb, t̄ y AC σtSM = 163 ± 10 pb t̄ N (|yt | > |yt̄ |) − N (|yt̄ | > |yt |) = −0.015±0.04, = N (|yt | > |yt̄ |) + N (|yt̄ | > |yt |) where yi = 1/2 ln(Ei − pi z )/(Ei + pi z ) is the rapidity SM = 0.006 ± 0.002. of particle i. AyC Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p ∆AF B Many models of random particles have been proposed, but most don’t fit all the data. However, this one does: λ′′313 tR dR bR W = 2 λ′′ ∗313 dR (p1 ) tR (q1 ) b̃R dR (p2 ) tR (q2 ) λ′′313 Figure 1: SUSY contribution to AF B a a BCA, Outlook in Particle Physics, KCL, 2012 Sridhar arXiv:1205.5170 B.C. Allanach – p New Physics Contribution " (βc − 1) |λ′′313 |4 βŝ d∆σ = dc 384π ŝ(βc − 1) + 2m2t − 2m2b̃ R #2 + 4m2t + ŝ(βc − 1)2 αs |λ′′313 |2 β , 2 2 72ŝ ŝ(βc − 1) + 2mt − 2mb̃ R p where β = 1 − 4m2t /ŝ, ŝ = (p1 + p2 )2 , αs is the strong coupling constant and mt is the top quark mass. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Calculate observables with MadGraph arXiv:1205.5170 Allanach and Sridhar, 2012 ∆AFB 5 0.25 0.2 4.5 Allanach and Sridhar, 2012 ∆AyC 0.06 5 0.04 4.5 0.15 0.1 4 0 λ’’313 4 0.02 0.053.5 3.5 0 3 -0.02 3 -0.04 -0.05 2.5 -0.1 2 -0.15 2.5 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 msbottom/TeV Outlook in Particle Physics, KCL, 2012 -0.06 -0.08 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 msbottom/TeV B.C. Allanach – p Constraints and Predictions 0.037 < ∆AF B < 0.205 −0.65 < ∆σtTt̄ EV /pb < 1.51 −0.38 < ∆AlF B < 0.23 −19.2 < ∆σtLHC7 /pb < 39.2 t̄ y −0.079 < ∆AC < 0.061 4 < ∆σtTt̄ EV (bin)/fb< 156 0.062 < ∆AhF B < 0.33 Table 1: 95% CL constraints 0.037 < ∆AF B < 0.09 0.02 < ∆AyC < 0.06 0 < ∆σtTt̄ EV /pb < 1.8 110 < ∆σtTt̄ EV (bin)/fb< 156 0.062 < ∆AhF B < 0.14 0.005 < ∆AlF B < 0.04 LHC8 8 < ∆σtLHC7 /pb < 25 13 < ∆σ /pb < 33 t̄ tt̄ Table 2: Predicted values in good fit region Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Summary • • • • • Outlook in Particle Physics, KCL, 2012 Rp violation allows natural SUSY with lightish gluinos and squarks that have not yet been ruled out by searches. Same-sign dilepton searches without huge E 6 T cut will be interesting. It covers almost all possible cases of RPV operator. In case of Ui Dj Dk operators, current searches ⇒ mg̃ > 550 GeV. Anomalous AF B measurements can also be explained by Ui Dj Dk type operator - fits all data Other models tend to fail one or more checks B.C. Allanach – p Backup Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Technical Hierarchy Problem A problem with light, fundamental scalars. Their mass receives quantum corrections from heavy particles in the theory: F 2 Z n cλ d k h λ h λ ∼− + ... 2 2 2 16π k − mF F Quantum correction to Higgs mass: phys mh = mtree + O(mF /100). h mF ∼ 1019 GeV/c2 is heaviest mass scale present. Higgs is eaten by W, Z to give O(MW,Z ) ∼ 90 2 tot < GeV/c ⇒ mh ∼ 1 TeV/c2 . Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Symmetry Standard model gauge symmetry is internal, but supersymmetry (SUSY) is a space-time symmetry. We call extra SUSY generators Q, Q̄. Q|fermioni → |bosoni Q|bosoni → |fermioni In the simplest form of SUSY, we have multiplets spin 0 spin 1/2 , , spin 1/2 spin 1 where each spin component in the multiplet should have identical quantum numbers (except spin). Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Supersymmetric Solution Exact supersymmetry adds 2 scalars f˜L,R for every massive fermion with mf˜L,R = mF and they couple to h with the same strength: F f˜L,R + h λ λ h =0 h λ2 h F Q: Where are the selectrons? Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Supersymmetric Solution Exact supersymmetry adds 2 scalars f˜L,R for every massive fermion with mf˜L,R = mF and they couple to h with the same strength: F f˜L,R + h λ λ h =0 h λ2 h F Q: Where are the selectrons? A: SUSY must be softly broken. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Supersymmetric Solution Exact supersymmetry adds 2 scalars f˜L,R for every massive fermion with mf˜L,R = mF and they couple to h with the same strength: F f˜L,R + h λ λ h =0 h λ2 h F When we break SUSY, we must make sure that we don’t reintroduce the naturalness problem: “soft breaking”. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Soft breaking Make scalar partners heavier than fermions: mf2˜ L,R = m2F + δ 2 Then we find a quantum correction to mh of (Drees) 2 2 λ mF 2 2 2 4 4δ + 2δ ln 2 + O(δ ). ∆mh ∼ 2 16π µ < So, if δ ∼ O(1) TeV/c2 , there’s no fine tuning in mh . Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Soft breaking Make scalar partners heavier than fermions: mf2˜ L,R = m2F + δ 2 Then we find a quantum correction to mh of (Drees) 2 2 λ mF 2 2 2 4 4δ + 2δ ln 2 + O(δ ). ∆mh ∼ 2 16π µ < So, if δ ∼ O(1) TeV/c2 , there’s no fine tuning in mh . We should see supersymmetric particles in the Large Hadron Collider. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Broken Symmetry 3 components of the Higgs particles are eaten by W ± , Z 0 , leaving us with 5 physical states: h0 , H 0 (CP+), A0 (CP-), H± SUSY breaking and electroweak breaking imply particles with identical quantum numbers mix: (B̃, W̃3 , H̃10 , H̃20 ) → χ01,2,3,4 (t̃L , t̃R ) → t̃1,2 (b̃L , b̃R ) → b̃1,2 (τ̃L , τ̃R ) → τ̃ 1,2 Outlook in Particle Physics, KCL, 2012 (W̃ ± , H̃ ± ) → χ± 1,2 B.C. Allanach – p Electroweak Breaking Both Higgs get vacuum expectation values: 0 + H1 v1 H2 0 → → − 0 H1 0 H2 v2 and to get MW correct, match with vSM = 246 GeV: vSM β v2 tan β = v2 v1 v1 L = ht t̄L H20 tR + hb b̄L H10 bR + hτ τ̄L H10 τR hb,τ vSM mt mb,τ ht vSM = √ , = √ ⇒ . sin β cos β 2 2 Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Hierarchy problem solved The supersymmetric copies cancel the quantum fluctuations. (This is a very difficult problem to solve). Not only that, the model contains a dark matter candidate the neutralino χ01 : • Weakly interacting • Stable • Massive To predict how much of it is around today, we must make assumptions on our cosmology, and on the particle physics. If we can measure the particle physics, we have a handle on the cosmology. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Sets of Cuts Signal Region mµµ /GeV test /fb σSSµµ A/10−3 95 /fb σSSµµ ATLASµµ1 >15 12 1.3 58 ATLASµµ2 >100 7.5 0.86 16 ATLASµµ3 >200 2.1 0.29 8.4 ATLASµµ4 >300 0.41 0.077 5.3 Table 3: The ATLAS same-sign di-muon analysis search regions. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Sets of Cuts Signal Region |~pmiss T |/GeV mT (l1 )/GeV A/10−3 95 σSSll /fb ATLASll1 > 150 >0 1.0 1.6 ATLASll2 > 150 > 100 0.6 1.5 Table 4: ATLAS same sign-di lepton analysis search regions. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Sets of Cuts Signal Region HT /GeV |~pmiss T |/GeV Nll /fb A × ǫ/10−3 Nll95 CMSll1 >400 >120 2.4 3.5 <3.7 CMSll2 >400 > 50 4.6 6.8 <8.9 CMSll3 >200 >120 2.5 3.7 <7.3 Table 5: Number of events past cuts for the CMS same sign-di lepton analysis Nll predicted by our test point over SM backgrounds, and acceptance A times efficiency ǫ of the signal selection, for the test point. Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Test Point mg̃ = 588 GeV, mt̃ = 581 GeV. 500 500 400 400 300 300 200 200 100 0 100 0 100 200 300 400 500 600 700 0 0 1000 2000 LH panel: E 6 T /GeV , RH panel: HT /GeV Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Test Point mg̃ = 588 GeV, mt̃ = 581 GeV. 400 300 300 200 200 100 100 0 0 500 1000 0 0 100 200 300 LH panel: pT (j1 )/GeV , RH panel: pT (l1 )/GeV Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Test Point mg̃ = 588 GeV, mt̃ = 581 GeV. 6000 5000 2000 4000 3000 1000 2000 1000 0 2.5 5 7.5 10 0 0 1 2 3 LH panel: NJ , RH panel: Nisol e,µ Outlook in Particle Physics, KCL, 2012 B.C. Allanach – p Efficiencies of CMSll6E T mgluino/TeV SUSY events past cuts ǫ= SUSY events You pay for the di-leptonic tt branching ratio. 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.2 Outlook in Particle Physics, KCL, 2012 ε/% 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Allanach and Gripaios, 2012 0.4 0.6 0.8 mstop/TeV 1 B.C. Allanach – p