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EWSB beyond the Standard Model: Supersymmetry?

EWSB beyond the Standard Model: Supersymmetry?. Third Lecture Outline: 1. Why we do believe in S.M.? 2. Why we do not believe in S.M.? 3. Why we believe in Supersymmetry? 4. Phenomenology Particle content, models, parameters, Higgs sector, … 5. Some searches at LEP

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EWSB beyond the Standard Model: Supersymmetry?

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  1. EWSB beyond the Standard Model: Supersymmetry? Third Lecture Outline: 1. Why we do believe in S.M.? 2. Why we do not believe in S.M.? 3. Why we believe in Supersymmetry? 4. Phenomenology Particle content, models, parameters, Higgs sector, … 5. Some searches at LEP Higgs bosons, charginos, neutralinos, sleptons… 6. LSP mass limit, mSUGRA constraints Probes of Electroweak Symmetry Breaking at LEP and SLC

  2. EWSB beyond the SM Supersymmetry? In the Standard Model: 222 114.1 Given the successes of the standard model predictions, why would we need to go beyond and invent a new symmetry between Bosons and Fermions ? Probes of Electroweak Symmetry Breaking at LEP and SLC

  3. Why we do believe in the Standard Model • Standard Model Internal Consistency tested at the 0.1% level • No compelling evidence for any deviation beyond the expected statistical scatter • EWSB Predictions of the Standard Model in agreement with direct measurements. The presence of a (rather light) Higgs boson seems to be required. Probes of Electroweak Symmetry Breaking at LEP and SLC

  4. Why we do not believe in the Standard Model A few conceptual problems related to EWSB, i.e., to the Higgs sector:  Needs gravity quantization (i.e., a coupling of Quantum Field Theory and General Relativity), apparently only possible in Supersymmetry… Probes of Electroweak Symmetry Breaking at LEP and SLC

  5. Why we do believe in Supersymmetry:Experimental Hints (I) • A light Higgs boson is favoured by precision measurements. • A 115 GeV/c2 Higgs boson is hinted at by direct searches. • Just in the range predicted by SUSY • Too light for the SM without New Physics below 106 GeV… LEP 206 LEP 220 MSSM SUGRA GMSB ASB Standard Model (Vacuum Stability Bound) 90 100 110 120 130 mh (GeV/c2) 115 Probes of Electroweak Symmetry Breaking at LEP and SLC

  6. Why we do believe in Supersymmetry:Experimental Hints (II) • New Physics at a scale below 106 GeV would modify the predictions for the EW precision measurements, with radiative corrections parameterized according to e1, e2, e3(or S,T,U) • In the Standard Model, for instance • Supersymmetry does not change much these predictions (better agreement with measured values ?) • Model building with any other New Physics has not yet allowed such an agreement. 39% CL e3 103 e1 103 Probes of Electroweak Symmetry Breaking at LEP and SLC

  7. Why we do believe in Supersymmetry:Experimental Hints (III) • Grand-Unified Theories (GUT), favoured, e.g., by non zero n masses, predict the 3 coupling constants (QED, Weak, QCD) to unify at GUT scale. • This unification does not happen in the Standard Model (+GUT), but does in Supersymmetry with a 1 TeV scale. • Starting from the measured values of aQED(mZ) and sin2W, one finds: • To be compared to the experimental value (mostly constrained by LEP): 1/a1 1/a2 1/a3 Standard Model + GUT aS(mZ) = 0.073  0.002 (Standard GUT) aS(mZ) = 0.129  0.010 (SUSY GUT) aS(mZ) = 0.118  0.003 1/a1 1/a2 1/a3 SUSY at 1 TeV + GUT Probes of Electroweak Symmetry Breaking at LEP and SLC

  8. Why we do believe in Supersymmetry:Experimental Hints (IV) • Large scale structures in the Universe require the presence of cold dark matter (LSP, the Lightest Supersymmetric Particle ?) • Half of the particles have already been discovered… … BUT • Supersymmetry can’t be exact (e.g., me me), thus needs to be broken. • Supersymmetry is therefore a economy of principles. It is neither an economy of particles nor an economy of parameters. Not the end of the story !  Extremely rich phenomenology Probes of Electroweak Symmetry Breaking at LEP and SLC

  9. Phenomenology: Minimal Particle Content • Gauge / Gaugino Sector • Particle / Sparticle Sector  [Two Higgs doublets] [All fermions] And also …  [All scalars] Probes of Electroweak Symmetry Breaking at LEP and SLC

  10. Phenomenology: R-Parity conservation Baryonic Number +1 for Standard Particles Spin Leptonic number -1 for Supersymmetric Partners TODAY Probes of Electroweak Symmetry Breaking at LEP and SLC

  11. Phenomenology: Supersymmetry Breaking • Gravity-Mediated • Heavy gravitino; • LSP: Neutralino, • or Sneutrino. SUSY TODAY Breaking • Gauge-Mediated: • Massless Gravitino; • 10  G:final states • with photons. • Anomaly-Mediated: • Small + and 0 • mass difference; • Chargino invisible.  Probes of Electroweak Symmetry Breaking at LEP and SLC

  12. Phenomenology:Models, Parameters (I) • The Minimal Supersymmetric extension of the Standard Model (MSSM): • mA: pseudoscalar Higgs boson mass • tanb: ratio of vacuum expectation values of the two Higgs doublets • m: Higgs mixing parameter • M1, M2, M3: Gaugino SUSY mass terms(give masses to0,, g) • : “Sfermion” SUSY mass terms • At, Ab, At, …: stop/sbottom/stau/… mixing parameters TODAY  •  100 parameters • Not too predictive Probes of Electroweak Symmetry Breaking at LEP and SLC

  13. Phenomenology:Models, Parameters (II) • The constrained MSSM (C-MSSM): • Constrain the gauginos and sfermions mass parameters • with GUT universality relations: • Unify M1, M2, M3 to a universal gaugino mass m1/2 at the GUT scale • Unify all sfermion mass parameters to a universal scalar mass m0 TODAY  0 g (at the EW scale) • Scalar and gaugino masses related • Third family sfermion masses may have large mixing corrections ( m2top, m2b, m2) Probes of Electroweak Symmetry Breaking at LEP and SLC

  14. Phenomenology:Models, Parameters (III) • Minimal SuperGravity (mSUGRA): • Unify Higgs and scalar sector at the GUT scale • Unify all trilinear couplings at the GUT scale • Break radiatively the ElectroWeak Symmetry • Only FIVE parameters left TODAY • Very predictive • Realized in Nature? Probes of Electroweak Symmetry Breaking at LEP and SLC

  15. Phenomenology: The Higgs Sector (I) • In the Standard Model • One Higgs doublet • v.e.v. v • One physical state • H • One parameter • mH • Radiative corrections to mh • quadratically divergent • In the M.S.S.M • Two Higgs doublets • v.e.v.’s v1 and v2 • Five physical states • h, H, A, H+, H- • Two parameters (at tree-level) • mh, tanb = v2/v1 • Radiative corrections to mh, mH • stabilized and finite CP-even (a) CP-odd Charged  Depend on Probes of Electroweak Symmetry Breaking at LEP and SLC

  16. Phenomenology: The Higgs Sector (II) In exact Supersymmetry In broken Supersymmetry mA  mh Theoretically disallowed mA =  mA = 0 Probes of Electroweak Symmetry Breaking at LEP and SLC

  17. Phenomenology: The Higgs Sector (III) • H too heavy to be produced at LEP; • Therefore, look for h and A • In the MSSM: • Charged Higgs bosons too heavy for LEP2, too. e+e- hZ hA  0.1 pb Complementary e+e- hA hZ *  0.1 pb  Look for both processes ! Probes of Electroweak Symmetry Breaking at LEP and SLC

  18. Searches at LEP: e+e- hZ(I) - Usual topologies: • Standard Model-like decays (mostly bb and t+t-) Four Jets - b b  Limit in the [mh, sin2(b-a)] plane: - q q 115 GeV excess Acoplanar Jets n b - - n b - b b e+e- hA takes over here l+ • SUSY-specific decays? l- Energetic Leptons Probes of Electroweak Symmetry Breaking at LEP and SLC

  19. Searches at LEP: e+e- hZ(II) • Invisible decays: h  10 10 • Decays into Higgses: h  AA with, e.g., A  bb : - - 10 l+ - Z  l+l- Z  qq 10 q Z nn - b n - Efficiency at least as large as for the Standard-Model-decay h  bb b - - 10 l- 10 q b - n Acoplanar Jets (Hnn) Acoplanar Leptons (W+W-) b - - • Flavour-Blind Search: h  bb, cc, gg Similar limits as in the visible case Similar limits as for h  bb - Probes of Electroweak Symmetry Breaking at LEP and SLC

  20. Searches at LEP: e+e- hA - Topologies:h, A bb, +- - bbbb bbtt - • Fit jet energies with the energy and momentum constraint, as for the W+W- events; • Determine the h and A masses as for the W+W- events. b b b b - t+ t- b b mh+mA, s = 200-210 GeV mh+mA, s = 189 GeV Not much of a mass peak Not much of a mass peak Probes of Electroweak Symmetry Breaking at LEP and SLC

  21. Searches at LEP: Limits from e+e- hZ, hA Combining hZ and hA results cos2(b-a) + sin2(b-a) = 1 (!)  Limit in the [mh, cos2(b-a)] plane:  Limit in the [mh, tanb] plane: From e+e- hA with mh  mA mh, mA> 91-92 GeV/c2 at 95% C.L., any tanb. hA 0.5 < tanb < 2.4 excluded at 95% C.L. hZ Note: LEP 220 would have covered the whole MSSM parameter space… i.e., found/excluded Supersymmetry Probes of Electroweak Symmetry Breaking at LEP and SLC

  22. Searches at LEP: e+e- H+H- LIMITS … Topologies: (like W+W- events) BR(H ) - s t- - s c - nt c c t+ - t+ nt nt s Mass Distributions: No excess over exp. background. mH (GeV/c2) Not too useful in the MSSM: Probes of Electroweak Symmetry Breaking at LEP and SLC

  23. Searches at LEP: Charginos, Neutralinos (I) Production Processes Decays Final States 10 pb Four fermions (quark or leptons) with missing E Visible energy proportional to DM _ DM Destructive interference. Cross section may vanish for small sneutrino masses (m0) Two fermions (quark or leptons) with missing E Visible energy proportional to DM 0 0 + DM 0 0 1 1 (invisible) may become dominant for small m0 1 pb Probes of Electroweak Symmetry Breaking at LEP and SLC

  24. Searches at LEP: Charginos, Neutralinos (II) Final State Topologies: WW  qqqq WW  lnqq WW  ln ln Z  qq Z  l+l- l+ 10 10 n 10 10 l+ 10 - n l+ n 10 10 10 10 l- l- 10 Hadrons + E miss Mixed + E miss Acoplanar leptons Acoplanar jets Acoplanar leptons Candidate events selected: Candidate events expected: 100 80 60 40 20 0 100 80 60 40 20 0 DM 50 60 70 80 90 100 50 60 70 80 90 100 Probes of Electroweak Symmetry Breaking at LEP and SLC

  25. Searches at LEP: Charginos, Neutralinos (III) Four-Fermion Background Processes: Large DM 20 pb 2 pb 5 pb 1 pb 10 fb Lepton, Jets Acoplanar Leptons Small DM and missing energy Acoplanar Jets 10 nb Topologies: Probes of Electroweak Symmetry Breaking at LEP and SLC

  26. Searches at LEP: Charginos, Neutralinos (IV) Presentation of the result • Model Independent: 95% C.L. upper limit on the +- and 2010 cross sections in the and planes. Small Dm 10 LSP 10 LSP Kinematic Limit LEP1 … And SO WHAT ? Probes of Electroweak Symmetry Breaking at LEP and SLC

  27. Searches at LEP: Charginos, Neutralinos (V) Small Dm • In the MSSM: The chargino and neutralino production cross section can be computed as a function of the + and 0masses, under the assumption that masses of sfermions are large ( negligible interference in the cross section). (1998, s = 189 GeV)) Anticipation: Not allowed in the Constrained MSSM Small m0 95% C.L. excluded regions in the and the planes Still not extremely exciting … Probes of Electroweak Symmetry Breaking at LEP and SLC

  28. Searches at LEP: Charginos, Neutralinos (VI) • In the C-MSSM: The chargino and neutralino masses unify via m1/2 (M2) and can be expressed as a function of M2, m and tanb. The chargino and neutralino searches results can therefore be combined, and the result reported in the (M2, m) plane for different tanb values. Limit on the LSP mass (m1/2) M2 (GeV) M2 (GeV) (1999) (1999) 300 250 200 150 100 50 0 Limit on M2 (increases with tanb) For smaller m0, the excluded domains shrink, leaving no limit on M2… but … Sleptons become light… -300 -200 -100 0 100 200 300 -300 -200 -100 0 100 200 300 m (GeV) Probes of Electroweak Symmetry Breaking at LEP and SLC

  29. Searches at LEP: Sleptons (I) Results for smuons (2000) Production: 100 80 60 40 20 0 + DM This graph depends only on the slepton mass 50 60 70 80 90 100 Decay: Topology: 100 80 60 40 20 0 10 DM 10 Acoplanar Leptons 50 60 70 80 90 100 Probes of Electroweak Symmetry Breaking at LEP and SLC

  30. Searches at LEP: Sleptons (II) Result expressed in terms of 95% C.L. excluded domains in the plane Small DM Limits for M > 10 GeV/c2 : Again, not terribly exciting … But it allows a LSP mass limit to be set in the C-MSSM at 95% C.L. Probes of Electroweak Symmetry Breaking at LEP and SLC

  31. Interpretation: LSP Mass Lower Limit (I) 40 • Large m0 ( 100 GeV/c2)  Large chargino and neutralino cross section;  Limit on M2 for each tanb value 30 20 10 1 2 3 4 5 6 7 8 9 10 20 30 40 50 • Constrain m1/2 as a function of tanb • Constrain m(10) for each tanb (Large m0) Probes of Electroweak Symmetry Breaking at LEP and SLC

  32. Interpretation: LSP Mass Lower Limit (II) • Small m0 ( 60 GeV/c2) 100 80 60 40 20 0 • A limit on the slepton mass can • constrain m1/2; • … and therefore m(10) (small m0) • But the limit starts to vanish for m0 in excess of 60 GeV/c2. m0 = 60 GeV/c2 m0 = 40 GeV/c2 m0 = 20 GeV/c2 m0 = 0 GeV/c2 m0 = 80 GeV/c2 50 60 70 80 90 100 Probes of Electroweak Symmetry Breaking at LEP and SLC

  33. Interpretation: LSP Mass Lower Limit (III) • Moderate m0 (60-80 GeV/c2) (1997) •  Chargino cross section may • vanish (neg’ve interference) • in a (M2, m) corridor • Neutralinos may become invisible: • The limit from sleptons slowly vanishes due to limited centre-of mass energy; • Weaker constraint from each of the searches on the LSP mass COMBINE THEM ALL ! LEP 1 Probes of Electroweak Symmetry Breaking at LEP and SLC

  34. Interpretation: LSP Mass Lower Limit (IV) With all searches combined Large m0 Any m0 m0 = 75 GeV/c2 tanb = 2 Limit slightly reduced to: Get an m0-independent limit on m1/2, i.e., on the LSP mass, for each value of tanb. obtained for small tanb values Probes of Electroweak Symmetry Breaking at LEP and SLC

  35. Interpretation: LSP Mass Lower Limit (VI) • Impact of the Higgs searches. • The small tanb values (up to 2.4) are covered by the hZ searches for all m0 values up to 1 TeV/c2; • For large tanb values, there is no absolute limit from Higgs searches. The LSP mass limit is set by slepton searches in the “corridor” (small m0) • While tanb decreases, Higgs searches start playing a role again in the corridor (small m0  smaller rad. corr. to mh, thus excluded by searches) • Stronger overall limit on the LSP mass (in the C-MSSM). Probes of Electroweak Symmetry Breaking at LEP and SLC

  36. Interpretation: Constraints in mSUGRA (I) In mSUGRA, the Higgs boson mass itself (not only the radiative corrections to the Higgs boson mass) is fixed by m0 and m1/2. tanb = 50 m > 0 A0 = 0 For moderate m0, m1/2, the Higgs Boson mass remains accessible to LEP searches even at large values of tanb. Scan of the plane: Higgs Regions excluded by: 1. Theory 2. Z width () 3. Charginos, Neutralinos 4. Sleptons 5. Higgs 6. Stable heavy charged LEP 1 Probes of Electroweak Symmetry Breaking at LEP and SLC

  37. Interpretation: Constraints in mSUGRA (II) Even tighter limit on the LSP mass when the mSUGRA constraints are enforced. Probes of Electroweak Symmetry Breaking at LEP and SLC

  38. Conclusions of the 3rd Lecture • Twelve years of searches at LEP put severe constraints on Supersymmetry • In mSUGRA: (with a lot of theoretical assumptions) • In the C-MSSM (SUSY + GUT mass relations): • In the MSSM: for heavy sfermions and with gaugino mass unification • But much weaker LSP limit in the MSSM with light sfermions • No LSP limit without gaugino mass unification • No LSP limit with other SUSY breaking mechanism (e.g., AMSB) Probes of Electroweak Symmetry Breaking at LEP and SLC

  39. Overall Conclusion: The LEP/SLD Legacy • LEP and SLD led to unprecedented precisions tests of the electroweak symmetry breaking mechanism, favouring a rather light Higgs boson (between 114 and 222 GeV/c2 at 95% CL in the Standard Model). • In this respect, the Standard Model has been very successful and was shown to be internally very consistent, up to a precision of 0.1%. • Notwithstanding these successes, the Standard Model suffers from conceptual diseases, which can be cured in practice (with today’s theoretical knowledge) by Supersymmetry only. • Amazingly enough, several experimental hints of Supersymmetry were observed by LEP and SLD. (Mostly indirect, with maybe a light Higgs boson with mass 115.61.0 GeV/c2, just in the range predicted by SUSY) • However, Supersymmetry is already very constrained by LEP1 and LEP2 searches: mh > 91 GeV/c2, tanb > 2.4. If GUT mass relations are assumed in the MSSM, the LSP mass exceeds 46 GeV/c2 at 95% CL. • Direct evidence for SUSY is expected to show up soon (Tevatron, LHC, NLC) Probes of Electroweak Symmetry Breaking at LEP and SLC

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