Natural Electroweak Symmetry Breaking in NMSSM and Higgs at 100 GeV

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1 Natural Electroweak Symmetry Breaking in NMSSM and Higgs at 100 GeV Radovan Dermíšek Institute for Advanced Study, Princeton R.D. and J. F. Gunion, hep-ph/ R.D. and J. F. Gunion, hep-ph/ Natural EWSB in NMSSM p.1/23

2 EWSB in MSSM Minimum of the Higgs potential: 1 2 m2 Z = µ 2 + m2 H d tan 2 β m 2 H u tan 2 β 1, tan β = v u v d tan β = 10: m 2 Z 2.0 µ 2 (0) M3 2 (0) m 2 t L (0) m 2 t R (0) 1.2 m 2 H u (0) 0.7 M 3 (0)A t (0) +... Without specific relations between SSB parameters and/or µ: m Z M 3 (0), m t L (0), m t R (0) m g, m t natural EWSB light gluino and stop! Natural EWSB in NMSSM p.2/23

3 Higgs Mass in MSSM m 2 h m 2 Z cos 2 2β + 3 ( 4π 2 v2 yt 4 sin 4 β log m t 1 m t 2 m 2 t ) +... m 2 h (91GeV) 2 + (38GeV) 2 log ( m t 1 m t 2 m 2 t ) LEP limit: m h 115 GeV m t 1 m t 2 ( 900 GeV ) 2 LEP heavy stop! Natural EWSB in NMSSM p.3/23

4 Little Hierarchy Problem in MSSM + m h < 115 GeV x m h > 115 GeV M 1 (m Z ) = 100 GeV M 2 (m Z ) = 200 GeV M 3 (m Z ) = 300 GeV tan β = 10 other SSB parameters randomly generated Fine tuning measure: F = max p F p = max p p dm Z m Z dp m 2 Z = 1 2 (g2 2 + g 2 )(vu 2 + vd 2) v u = v u (a), v d = v d (a). p {M i (0), i = 1, 2, 3; m 2 s(0), s = Q, u, d, L, e, H u, H d ; A t (0), µ(0), B µ (0)} Natural EWSB in NMSSM p.4/23

5 Little Hierarchy Problem in MSSM Large A t : L SSB λ t A t Q ūh u Natural EWSB in NMSSM p.5/23

6 NMSSM - brief review MSSM + one additional singlet superfield (results in one CP-even and one CP-odd neutral Higgs bosons, and one additional neutralino): W = W MSSM + λ ŜĤuĤd + κ 3 Ŝ3 L SSB = L SSB MSSM + λa λ SH u H d + κ 3 A κs 3 + m 2 SSS tan β = v u v d, µ eff = λs m 2 H u, m 2 H d, m 2 S m 2 Z = 1 2 (g2 2 + g 2 )(v 2 u + v 2 d ) determined by 3 minimization eqs. of the scalar potential Higgs mass at tree level: m 2 h m 2 Z cos 2 2β + m 2 Z 2λ 2 g g 2 sin2 2β Natural EWSB in NMSSM p.6/23

7 Natural Higgs mass in NMSSM tan β = 10, M 3 (M Z ) = 300 GeV no constraints Natural EWSB in NMSSM p.7/23

8 Natural Higgs mass in NMSSM tan β = 10, M 3 (M Z ) = 300 GeV no constraints SUSY constraints Natural EWSB in NMSSM p.7/23

9 Natural Higgs mass in NMSSM tan β = 10, M 3 (M Z ) = 300 GeV no constraints SUSY constraints m h > 114 GeV or h aa Natural EWSB in NMSSM p.7/23

10 Natural Higgs mass in NMSSM tan β = 10, M 3 (M Z ) = 300 GeV no constraints SUSY constraints m h > 114 GeV or h aa h aa, m a < 2m b Natural EWSB in NMSSM p.7/23

11 Natural Higgs mass in NMSSM tan β = 10, M 3 (M Z ) = 300 GeV no constraints SUSY constraints m h > 114 GeV or h aa h aa, m a < 2m b Maybe Higgs is at 100 GeV Natural EWSB in NMSSM p.7/23

12 Precision electroweak data Theory uncertainty α had = α (5) ± ± incl. low Q 2 data χ Excluded m H [GeV] Natural EWSB in NMSSM p.8/23

13 Precision electroweak data Theory uncertainty α had = α (5) ± ± incl. low Q 2 data Maybe Higgs is at 100 GeV 3 χ Excluded m H [GeV] Natural EWSB in NMSSM p.8/23

14 Search for the SM Higgs at LEP LHWG CL b 1 LEP σ 10-2 Observed Expected for signal plus background Expected for background 3σ m H (GeV/c 2 ) Natural EWSB in NMSSM p.9/23

15 Search for the SM Higgs at LEP LHWG CL b 1 LEP 10-1 Maybe Higgs is at 100 GeV 2σ 10-2 Observed Expected for signal plus background Expected for background 3σ m H (GeV/c 2 ) Natural EWSB in NMSSM p.9/23

16 Explaining m h 100 GeV excess m h1 /m a1 Branching Ratios n obs /n exp s95 NSD LHC (GeV) h 1 b b h 1 a 1 a 1 a 1 τ + τ units of 1σ 98.0/ / / / / / / / / / / / / / / / n obs = (1 CL b ) observed n exp = (1 CL b ) expected thanks to P. Bechtle, LHWG C 2b eff = [g2 ZZh /g2 ZZh SM ]B(h b b) Natural EWSB in NMSSM p.10/23

17 Is light CP-odd Higgs natural? V NMSSM has U(1) R symmetry in the limit A λ, A κ 0 B. A. Dobrescu and K. T. Matchev, hep-ph/ Superpotential is U(1) R invariant for R S = 1/2 R Hu H d : W = W MSSM + λ ŜĤuĤd + κ 3 Ŝ3 U(1) R spontaneously broken by v u, v d, s NG boson! A λ, A κ explicitely break U(1) R : L SSB = L SSB MSSM + λa λ SH u H d + κ 3 A κs 3 + m 2 SSS m a1 A κ, A λ U(1) R also broken by gaugino masses (effect at 1-loop level) Natural EWSB in NMSSM p.11/23

18 Is light CP-odd Higgs natural? V NMSSM has U(1) R symmetry in the limit A λ, A κ 0 B. A. Dobrescu and K. T. Matchev, hep-ph/ m 2 a 1 3s ( κa κ sin 2 θ A + 3λA λ cos 2 ) θ A 2 sin 2β a 1 cos θ A a MSSM + sin θ A a S cos θ A 2v s tan β Natural EWSB in NMSSM p.11/23

19 Is light CP-odd Higgs natural? V NMSSM has U(1) R symmetry in the limit A λ, A κ 0 B. A. Dobrescu and K. T. Matchev, hep-ph/ m 2 a 1 3s ( κa κ sin 2 θ A + 3λA λ cos 2 ) θ A 2 sin 2β a 1 cos θ A a MSSM + sin θ A a S cos θ A 2v s tan β RG running: A κ, A λ 0 at M GUT da λ /dt = ` 6A t λ 2 t + 8λ2 A λ 4κ 2 A κ 6g 2 2 M 2 (6/5)g 2 1 M 1 /(16π 2 ) A κ A λ O(M 2 ) at M Z da κ /dt = 12 ` λ 2 A λ + κ 2 A κ /(16π 2 ) Natural EWSB in NMSSM p.11/23

20 Is light CP-odd Higgs natural? V NMSSM has U(1) R symmetry in the limit A λ, A κ 0 B. A. Dobrescu and K. T. Matchev, hep-ph/ m 2 a 1 3s ( κa κ sin 2 θ A + 3λA λ cos 2 ) θ A 2 sin 2β a 1 cos θ A a MSSM + sin θ A a S cos θ A 2v s tan β A κ and A λ terms comparable for: cos θ A 1, equivalent to a 1 a s m a1 < m h1 /2, mostly singlet, is natural! Natural EWSB in NMSSM p.11/23

21 Is light CP-odd Higgs natural? LEP allowed LEP excluded { A λ F MAX = max m 2 a dm 2 a da λ, A κ m 2 a dm 2 a da κ } 5-10 % tuning of A κ to A λ is required for m a < 2m b! Natural EWSB in NMSSM p.12/23

22 Br(h aa) vs. A κ and A λ LEP allowed LEP excluded haa coupling: c λ A λ + c κ A κ for A κ few GeV, h aa always dominates no additional constraints from Br(h aa) Natural EWSB in NMSSM p.13/23

23 Conclusions Higgs 100 GeV wanted by SUSY/natural EWSB preferred by precision EW data indicated by LEP data possible and natural in NMSSM! h aa τ + τ τ + τ, B(h aa) 0.9 h b b, B(h b b) 0.1 can fully explain 2σ excess Natural EWSB in NMSSM p.14/23

24 Conclusions Higgs 100 GeV wanted by SUSY/natural EWSB preferred by precision EW data indicated by LEP data possible and natural in NMSSM! h aa τ + τ τ + τ, B(h aa) 0.9 h b b, B(h b b) 0.1 can fully explain 2σ excess important to study Higgs to Higgs decays at LEP, Tevatron and LHC similar results to be expected in many SUSY models with more complicated Higgs sector than that of CP conserving MSSM Natural EWSB in NMSSM p.14/23

25 F vs. m 2 s, m 2 H u, m 2 H d (M GUT ) Natural EWSB in NMSSM p.15/23

26 F vs. A t, A κ, A λ Natural EWSB in NMSSM p.16/23

27 F vs. m 2 s, m 2 H u, m 2 H d All constraints satisfied! Natural EWSB in NMSSM p.17/23

28 Is light CP-odd Higgs natural? Natural EWSB in NMSSM p.18/23

29 Fine Tuning in NMSSM, tan β = 10 + escapes LEP because h aa Fine tuning measure: x escapes LEP because m h > 115 GeV F = max F p = max p dm Z p p m Z dp. p {M i (0), i = 1, 2, 3; m 2 s(0), s = Q, u, d, L, e, H u, H d, S; A t (0), A λ (0), A κ (0)} Natural EWSB in NMSSM p.19/23

30 Fine Tuning in NMSSM, tan β = 10 + (m h1 < 115 GeV) h 1 a 1 a 1 dominates Fine tuning measure: x (m h1 > 115 GeV) h 1 b b dominates F = max F p = max p dm Z p p m Z dp. p {M i (0), i = 1, 2, 3; m 2 s(0), s = Q, u, d, L, e, H u, H d, S; A t (0), A λ (0), A κ (0)} Natural EWSB in NMSSM p.19/23

31 Comparing MSSM and NMSSM Natural EWSB in NMSSM p.20/23

32 h aa b bb b (m a > 2m b ) Natural EWSB in NMSSM p.21/23

33 LHC Discovery Potential for an integrated luminosity: L = 300fb 1 Standard decay modes: gg h/a γγ associated W h/a or t th/a prod. with γγl ± in the final state t th/a prod. with h/a b b b bh/a prod. with h/a τ + τ gg h ZZ ( ) 4 leptons gg h W W ( ) l + l ν ν W W h τ + τ W W h W W ( ) W W h invisible Natural EWSB in NMSSM p.22/23

34 Search for the SM Higgs at LEP LHWG CL b 1 ALEPH (a) 1-CL b 1 DELPHI (b) 1-CL b 1 LEP four-jet (e) σ 2σ 2σ σ m H (GeV/c 2 ) 3σ m H (GeV/c 2 ) 3σ m H (GeV/c 2 ) 1-CL b 1 L3 (c) 1-CL b 1 OPAL (d) 1-CL b 1 LEP all except four-jet (f) σ 2σ 2σ σ m H (GeV/c 2 ) 3σ m H (GeV/c 2 ) 3σ m H (GeV/c 2 ) Natural EWSB in NMSSM p.23/23