Status of low energy SUSY models confronted with the 125 GeV Higgs data

Transcription

1 Status of low energy SUSY models confronted with the 5 GeV Higgs data Junjie Cao On behalf of my collaborators J. M. Yang, et al Based on our works arxiv: , , ,.58,.439 junjiec@itp.ac.cn Henan Normal University, Xinxiang, China HFCPV- October 8, / 35

2 Conclusion: The MSSM can explain the LHC data quite well, but it suffers from severe fine tuning problem; The CMSSM is disfavored since it is hard to predict a 5 GeV Higgs boson, and at the same time cannot enhance the di-photon rate; The nearly Minimal Supersymmetric Standard Model (nmssm) is excluded at 3σ level after considering available Higgs data; The most favored model is the Next to Minimal Supersymmetric Standard Model (NMSSM), whose predictions about the Higgs boson can naturally agree with the experimental data at σ level. / 35

3 Catalogue I II III IV Experimental progress in Higgs physics The Next to Minimal Supersymmetric Standard Model (NMSSM) General overview SM-like Higgs boson mass in the NMSSM How to compare SUSY with the LHC Higgs data SUSY vs experimental Higgs data Di-photon signal rate Four lepton signal rate Fine tuning extent χ for Golden samples Information about low χ samples Various signal rates Representative points Dark matter direct detection Summary 3 / 35

4 I. Experimental Progress in Higgs physics Announced discovery on July 4,, by combining 5fb 7-TeV data with 5fb 8-TeV data. 4 3 Atlas 7 CMS 7 8 CDF D CMS 7 Atlas 7 8 CMS 7 8 CDF D Atlas 7 8 CMS 7 8 Atlas 7 8 CMS 7 8 CDF D CMS 7 CMS 8 Atlas 7 CMS 7 8 Rate SM rate bbv bbv bbv WWV WW WW WW ZZ ZZ ΓΓ ΓΓ ΓΓ ΓΓ jj ΓΓ jj ΤΤ ΤΤ 4 / 35

5 I. Experimental Progress in Higgs physics Properties: Mass: most precisely determined. Preferred region 5.5 ±.54GeV. Couplings: large uncertainty, may be greatly improved with the whole data. Largest deviation from γγ rate (Especially γγjj rate). Enhanced by a factor about.5. Suppressed hgg coupling and enhanced hγγ coupling is currently favored. Spin: Can not be determined in near future. May be spin and, can not be spin. CP: CP even state is favored, but there are discussions about CP-odd case. Favored conclusions: The particle is at least partially responsible for EW breaking. The particle is at least partially responsible for mass generation. Agree with the SM predictions about the Higgs boson at σ level. 5 / 35

6 II. NMSSM: General overview NMSSM: singlet extension of the MSSM with Z 3 invariant superpotential. Superpotential: W = W MSSM + λε ij Ĥ i uĥj dŝ + κ 3 Ŝ 3. Soft breaking terms: W MSSM : MSSM Superpotential without µ-term. V MSSM : MSSM soft masses. V soft = V MSSM + m d H d + m u H u + m S S µ parameter is dynamically generated, µ = λ s. +(λa λ ε ij H i uh j d S + κ 3 A κs 3 + h.c.). Ŝ: singlet superfield. i ε ij ĤuĤj dŝ: doublet-singlet Higgs interaction. 3 CP-even Higgs bosons, CP-odd Higgs bosons and 5 neutralinos. Rich Higgs physics and dark matter physics. May change squark decay signal. In the limit λ, κ, the singlet superfield decouples from the rest of... If µ is fixed, phenomenology of NMSSM is same as that of MSSM. Only for large λ case can one expect large difference between the models. 6 / 35

7 II. NMSSM: SM-like Higgs boson mass Define H SM = sin βh u + ε cos βhd, H NEW = cos βh u ε sin βhd, ( ) ( ) G + H + H SM = v + φsm+ig, H NEW = φ new+ip, H S = s + (φ s + ip ). Elements of CP-even Higgs mass matrix in the basis (φ new, φ sm, φ s ): M = M A + (m Z λ v ) sin β, M = (m Z λ v ) sin 4β, M 3 = (MA sin β + κµ λ )λv cos β, µ M = mz cos β + λ v sin β, [ M 3 = λµv ( M A sin β ) κ sin β µ λ M 33 = 4 λ v ( M A sin β ) + κµ µ λ (A κ + 4κµ λ ) λκv sin β. ], 7 / 35

8 II. NMSSM: SM-like Higgs boson mass Large M A Limit: M M M and (M M 33 ) M 3. In this case, φ new decouples from (φ sm, φ s ) system. M = mz cos β + λ v sin β [ ] λµv ( M A sin β µ ) κ λ sin β λµv [ ( M A sin β µ ) κ λ sin β ] M 33 Two new features of the SM-like Higgs boson mass: Additional contribution λ v sin β at tree-level. Doublet-singlet mixing may push up or pull down the mass. 8 / 35

9 II. NMSSM: How to compare SUSY with data Select parameter points favored by low energy experiments and dark matter. Scan randomly over the SUSY parameter space. Calculate observables in low energy physics and dark matter physics. Exclude points with the help of experimental data. Optimize the scan region and repeat the scan. For each favored point, calculate χ by available Higgs data. Investigate the properties of the SM-like Higgs boson for low χ points. Perform similar study in the CMSSM, MSSM and nmssm. Scan region: Assuming: m q, = TeV, m g = TeV, M = M. All soft parameters in the slepton sector have a common value m l..5 < λ.7, < κ.7, 9 GeV M A TeV, A κ TeV, GeV M Q3, M U3, M D3 TeV, A t, A b 5 TeV, tan β 6, GeV µ, m l TeV, 5 GeV M 5 GeV. 9 / 35

10 II. NMSSM: Strategy to compare SUSY with data Constraints: LEP constraints: Electroweak precision observables such as ρl, sin θeff l, M W, R b. Agree with experimental fit values at 95% CL; Lower bound on sparticle masses; Constraints on electroweak -ino sector: Z χ χ, e + e χ i χ j, χ + χ ; B-physics constraints: For B Xsγ, B B mixing, D D mixing, K K mixing and B τν τ, agree with experimental measurements at σ level; 95% CL upper bound: B s,d µ + µ, B X sµ + µ ; Higgs physics constraints: Stability of vacuum state; SM-like Higgs mass satisfies 3GeV mh 7GeV; Constraints from the Tevatron and LHC search for Non-standard Higgs boson; Dark matter physics constraints: Dark matter relic density agrees with WMAP fit value at σ level; 9% CL upper bound on spin independent rate of χ-nucleon scattering; Require SUSY to explain muon g anomaly at σ level. / 35

11 III. SUSY vs data: Di-photon rate Curves: central value (green) and σ region of the di-photon signal obtained by combing the ATLAS and CMS data with the method introduced in arxiv: (by P. P. Giardino). σ best-fit mass: 5.5 ±.54GeV. see arxiv: 7.374, by P. P. Giardino. Predictions of the MSSM and the NMSSM about the di-photon rate can agree with data at σ level. σ(h γγ)/σ(h γγ) SM σ(h γγ)/σ(h γγ) SM h γγ, incl, (ATLAS+CMS, +) CMSSM SM NMSSM SM σ best-fit Higgs mass 4 6 M h (GeV) MSSM nmssm σ best-fit Higgs mass M h (GeV) Fig.: Surviving samples projected on the plane of the di-photon rate versus the SM-like Higgs mass. Only consider samples with 3GeV m h 7GeV. / 35

12 III. SUSY vs data: Di-photon rate In CMSSM, mh 4GeV. Reason: Muon g and B s µ + µ forbid too large M, M / and A. Di-photon rate is reduced. Reason: The h bb coupling is slighted enhanced. σ(h γγ)/σ(h γγ) SM σ(h γγ)/σ(h γγ) SM h γγ, incl, (ATLAS+CMS, +) CMSSM SM NMSSM MSSM nmssm In nmssm, di-photon rate is.5 severely suppressed. SM Reason: Dark matter is light.5 ( 4GeV) and singlinolike, must annihilate via σ best-fit -.5 Higgs mass - resonant CP-odd Higgs 4 6 M in early universe to get h (GeV) correct relic density. Fig.: vertical axis: di-photon rate. As a result, h χ χ, A A will be dominant decay modes. σ best-fit Higgs mass M h (GeV) / 35

13 III. SUSY vs data: 4 lepton rate Curves: central value (green) and σ region of the 4 lepton signal obtained by combing the ATLAS and CMS data with the method introduced in arxiv: (by P. P. Giardino). σ best-fit mass: 5.5 ±.54GeV. see arxiv: 7.374, by P. P. Giardino. Except nmssm, SUSY predictions about the 4 lepton signal can agree well with corresponding experimental data. σ(h ZZ * )/σ(h ZZ * ) SM σ(h ZZ * )/σ(h ZZ * ) SM h ZZ * 4l, incl, (ATLAS+CMS, +).5 CMSSM SM NMSSM SM σ best-fit Higgs mass 4 6 M h (GeV) MSSM nmssm σ best-fit Higgs mass M h (GeV) Fig.: Same as Fig., but for 4 lepton rate. 3 / 35

14 III. SUSY vs data: Fine tuning extent Fine tuning extent : = Max{ ln m Z }. ln pi GUT +: Samples with m h in the range 5.5 ±.54GeV, hereafter called Golden Sample. In CMSSM,. In MSSM,. for samples with enhanced di-photon rate. In NMSSM with large λ, is usually less than. may be as low as 4 for samples with enhanced di-photon rate. Δ Δ 3 CMSSM NMSSM.5.5 σ(h γγ)/σ(h γγ) SM Fine-tuning MSSM nmssm.5.5 σ(h γγ)/σ(h γγ) SM Fig.3 Same as Fig., but show Fine tuning extent for surviving samples as a function of the di-photon rate. 4 / 35

15 III. SUSY vs data: χ for Golden Samples Golden Sample: 4.9GeV m h 6.GeV. χ : Computed with 6 sets of latest experimental data for m h = 5, 5.5, 6GeV. For calculation method, see by P. P. Giardino. SM: χ /d.o.f = 6.5/6. In MSSM: χ /d.o.f may be as low as 9./6. In NMSSM with large λ, χ /d.o.f may be as low as./6. χ > 3 for some samples. In nmssm, χ > 6. Excluded by Higgs data. χ MSSM m h (GeV) NMSSM m h (GeV) nmssm SM m h (GeV) Fig.4 χ for Golden samples in different models. 6 sets of latest experimental data were used. 5 / 35

16 III. SUSY vs data: Di-photon signal information Categorize Golden samples into: χ 6.5, better than SM. 6.5 < χ 6.3, Agree with data at σ. χ > 6.3, excluded at σ. Enhanced di-photon rate is strongly preferred by Higgs data, which is realized by enhanced Br(h γγ). In MSSM, the enhancement of the Br is mainly by the increase of hγγ coupling (through light τ loop). Samples with low χ, >. In NMSSM, the enhancement of the Br is by the suppression of h bb coupling (through the singlet component in h). BR(h γγ)/sm Higgs coupling to γ/sm MSSM σ(gg h γγ)/sm= Higgs coupling to g/sm MSSM Higgs coupling to b/sm NMSSM χ <χ 6.3 χ >6.3 σ(gg h γγ)/sm= Higgs coupling to g/sm NMSSM Higgs coupling to b/sm Fig.5 Detailed information about di-photon rate. Only Golden samples are considered. 6 / 35

17 III. SUSY vs data: Four lepton signal information Unlike the di-photon rate, an enhanced 4 lepton rate is not necessary to get a low χ. Although the hzz coupling in the MSSM is same as that in the SM, the 4 lepton signal is never enhanced due to the reduction of Br(h ZZ ) (through the enhancement of hb b coupling). In the NMSSM, the 4 lepton signal may be enhanced by the increase of Br(h ZZ ) (through the suppression of hb b coupling). BR(h ZZ * )/SM Higgs coupling to Z/SM MSSM σ(gg h ZZ * )/SM= Higgs coupling to g/sm MSSM Higgs coupling to b/sm NMSSM χ <χ 6.3 χ >6.3 σ(gg h ZZ * )/SM= Higgs coupling to g/sm NMSSM Higgs coupling to b/sm Fig.6: Same as Fig.4, but show the details about 4 lepton rate. 7 / 35

18 III. SUSY vs data: Coupling information In the MSSM, Top quark Yukawa coupling is almost same as that in the SM. Bottom quark Yukawa coupling is always enhanced. In the NMSSM with large λ, Top quark Yukawa coupling is usually reduced. Bottom quark Yukawa coupling may be either reduced or enhanced. Higgs coupling to t/sm MSSM χ <χ 6.3 χ > Higgs coupling to b/sm NMSSM Higgs coupling to b/sm Fig.7: Same as Fig.4, but show the information about Top and Bottom quark Yukawa coupling. 8 / 35

19 III. SUSY vs data: Representative points information MSSM P MSSM P NMSSM P3 NMSSM P4 m h (GeV) χ σ(h γγ)/sm σ(h ZZ )/SM (fine-tuning) tan β m t (GeV) m τ (GeV) m χ (GeV) Ω CDM h Br(B s µ + µ )/ δa µ / σ(hv bbv )/SM σ(hjj WW jj)/sm σ(h WW )/SM σ(hjj γγjj)/sm σ(h τ τ)/sm SI 46 9 / 35

20 III. SUSY vs data: Representative points information 4 3 m h =5., χ =9. P, MSSM m h =5.4, χ =9.6 P, MSSM m h =5.5, χ =6.5 SM Higgs m h =5.5, χ =7.3 Free couplings m h =5.9, χ =.9 P3, NMSSM m h =5., χ =. P4, NMSSM m h =5.5, χ =6.5 SM Higgs m h =5.5, χ =7.3 Free couplings Rate/SM rate bbv WWjj WW ZZ γγ γγjj ττ bbv WWjj WW ZZ γγ γγjj ττ Fig.8: Predictions of two representative points for the MSSM and the NMSSM respectively. Free coupling scenario: χ = 7.3. Varying freely all Higgs couplings, including hγγ and hgg coupling. For four benchmark points, their predictions about various signal rates agree with data at σ. / 35

21 III. SUSY vs data: Dark matter detection information MSSM XENON() NMSSM XENON() σ SI ( -44 cm ) χ <χ 6.3 χ > m χ (GeV) m χ (GeV) Fig.9: Spin-independent cross section of χ-nucleon scattering with f Ts =.. In MSSM, samples with χ < 6.5 predicts small cross section. Reason: µ > TeV so that the dark matter is highly bino-like. Have considered constraints from Bs µ + µ. For large tan β, m H very heavy. In NMSSM with large tan β, dark matter mass is limited: 6GeV m χ 4GeV. / 35

22 IV. Conclusion The MSSM can explain the LHC data quite well, but it suffers from severe fine tuning problem; The CMSSM is disfavored since it is hard to predict a 5 GeV Higgs boson, and at the same time cannot enhance the di-photon rate; The nearly Minimal Supersymmetric Standard Model (nmssm) is excluded at 3σ level after considering available Higgs data; The most favored model is the Next to Minimal Supersymmetric Standard Model (NMSSM), whose predictions about the Higgs boson can naturally agree with the experimental data at σ level. / 35

23 What are we doing? (Study Technique) Global Fit of SUSY models using latest experimental data; Simulation of sparticle production at the LHC; Implication of new data on SUSY models; Perform similar study for other new physics models. 3 / 35

24 Addendum: the nmssm.general overview Superpotential: W = W MSSM + λε ij Ĥ i uĥj dŝ + ξ F M nŝ. Soft breaking terms: V soft = V MSSM + m d H d + m u H u + m S S +(λa λ ε ij HuH i j d S + h.c.) + (ξ SMnS 3 + h.c.). W MSSM : MSSM superpotential without µ-term. Ŝ: gauge singlet superfield. V MSSM : gaugino and sfermion soft masse. ξ F M nŝ, ξ SM 3 ns: Tadpole terms. 5 CP-even Higgs bosons, CP-odd Higgs bosons and 5 neutralinos. In N= supergravity model with a Z 5 symmetry, the tadpole terms arise by supergravity effects at the six loop level. M n is naturally at EW scale, not destabilize the gauge hierarchy! The tadpole terms can avoid the domain wall problem. The parameter µ is dynamically generated, µ = λ s. In the limit ξ S, ξ F, a Peccei-Quinn symmetry exists so that m A. nmssm is similar to NMSSM with no cubic self interaction of singlet field. Differences: the tree-level mass matrices and the minimization conditions. 4 / 35

25 Addendum: the nmssm. Higgs sector: λ, v u, v d, µ, m S, A λ and m A = (µa λ + λξ F M n)/ sin β as input parameters. Basis [Re(Hu), Re(Hd ), Re(S)], CP-even Higgs boson mass matrix: ma cos β + mz sin β (λ v mz m A ) sin β cos β λv cos β(µ tan β A λ) ma sin β + mz cos β λv cos β(µ A λ tan β) ms + λ v Basis [Ã = cos β Im(H u) + sin β Im(H d ), Im(S)]: M P = ( m A λa λ v m S + λ v Two solutions to the Little Hierarchy Problem suffered by the MSSM: Consider tan β and A λ µ, m h = (m A + m Z ) cos β + λ v sin β. Choose the Peccei-Quinn symmetry limit. A is light, h A A is the dominant decay. The LEP mass bound on h is not valid! ). 5 / 35

26 Addendum: the nmssm 3. Neutralino sector: Define ṽ, = (v ± v ). Basis: ψ = { iλ, iλ 3, (ψ u ψ d ), (ψ u + ψ d ), ψ s } M g ṽ g ṽ M gṽ gṽ M χ = µ λṽ µ λṽ. χ is singlino-dominated with mass given by m χ λ µv (µ +λ v )(tan β+cot β). Three characters of m χ : The larger λ is, the heavier χ will be. The large tan β is, the lighter χ will be. The large µ is, the lighter χ will be. Since a light, singlino-like neutralino is difficult to annihilate, dark matter relic density can impose constraints on λ, tan β, µ and also m χ. 6 / 35

27 Addendum: the nmssm 5 m A 5 Fig.: Scatter plot of the parameter space allowed by current experiments including constraints from a µ with m µ = GeV, projected in m χ m A (in GeV) plane. 3 4 m χ : Characterized by m A m Z. In this case, χ mainly annihilates through exchanging a Z-boson. : Characterized by m A < m Z and m A m χ. Most samples. In this case, χ mainly annihilates through exchanging a light A. 7 / 35

28 Addendum: the nmssm Br(h χ χ ) SM-like Higgs boson h Mass varies from 7 GeV to 45 GeV. Dominant decay may be any of the following: h χ χ ; h χ χ ; h AA ; h hh. Br(h b b) is always suppressed. For m h 5GeV, Br(h b b) %. Br(h bb ) m A Fig.: Decay rates of the SM-like Higgs boson as a function of the lightest CP-odd Higgs boson mass. 8 / 35

29 Addendum: the CMSSM M / (GeV) CMSSM Satisfy B s μ + μ - Excluded by B s μ + μ - 3GeV<M h < 7GeV tanβ M / (GeV) M (GeV) CMSSM Satisfy R <.3 Excluded by R 3GeV<M h < 7GeV tanβ CMSSM A (GeV) CMSSM μ (GeV) 9 / 35

30 Addendum: the CMSSM 6 M ~ t (GeV) 8 4 σ(gg h γγ) / σ SM CMSSM Satisfy B s μ + μ - Excluded by B s μ + μ - CMSSM Satisfy R <.3 Excluded by R M h (GeV) M h (GeV) 3 / 35

31 Addendum: Stop sector in MSSM and NMSSM m (GeV) t MSSM (R γγ < ) NMSSM (R γγ < ) A t A t m (GeV) t MSSM (R γγ > ) NMSSM (R γγ > ) A t A t 3 / 35

32 Addendum: Stop sector in MSSM and NMSSM Relative light Stop can not be exclude by current LHC data. Consider Semi-leptonic Analysis: pp t t (tχ )( tχ ) (bl+ ν χ )( bjj χ ) or (bjj χ )( bl ν χ ) ~ ~ ~ This channel can not impose 3 t t any constraints after taking ( t production, t 3 ) σ NLO+NLL pp t t + X [pb] into account t tχ decay ATLAS 5 miss -lepton + jets + E T - L dt = 4.7 fb, s=7 TeV branching ratio: Br( t tχ ) 5%. 5 For σ( t t ) at NLO, see W. Beenakker, For ATLAS recent search result, see arxiv: [GeV] 3 S =7TeV m [GeV] t 55 m t ~ [GeV] m m - m < m t ~ t SUSY Observed limit ( ) theory Expected limit ( exp ) All limits at 95% CL s pp t t (bχ+ )( bχ ) (bl+ ν χ )( bjj χ ) or (bjj χ )( bl ν χ ). The decay of χ + is rather complicated: χ+ χ W, τ + ν τ, ν τ τ +. S/ B < 3 when m χ+ = 5GeV for 5 fb luminosity at 8TeV LHC. See our work, arxiv: excluded model cross sections [pb] s Numbers give 95% CL 3 / 35

33 Addendum: Part of LHC data 33 / 35

34 Addendum: Part of LHC data 4 3 Atlas 7 CMS 7 8 CDF D CMS 7 Atlas 7 8 CMS 7 8 CDF D Atlas 7 8 CMS 7 8 Atlas 7 8 CMS 7 8 CDF D CMS 7 CMS 8 Atlas 7 CMS 7 8 Rate SM rate bbv bbv bbv WWV WW WW WW ZZ ZZ ΓΓ ΓΓ ΓΓ ΓΓ jj ΓΓ jj ΤΤ ΤΤ 34 / 35

35 Addendum: Data Treatment (See 3.454) h γγ, incl. (ATLAS+CMS,+) R γγ =σ(pp h γγ)/σ SM R VV =σ(pp h ZZ * 4l)/σ SM σ best-fit Higgs mass M h (GeV) h ZZ * 4l, incl. (ATLAS+CMS,+) σ best-fit Higgs mass SM SM Fiting Combining µ i = R observed R expected σ i = R expected.96 µ = µ aσc + µ c σa σa + σc σ a σ c σ = σ a + σc M h (GeV) 35 / 35