Sven Heinemeyer WIN (Heidelberg),

Sven Heinemeyer WIN (Heidelberg), 09.06.2015 1

New Developments for SUSY Higgses Sven Heinemeyer, IFCA (CSIC, Santander) Heidelberg, 06/2015 1. Why it is not the SM Higgs 2. Higgs bosons in the MSSM 3....at the LHC and Beyond 4. Conclusions Sven Heinemeyer WIN (Heidelberg), 09.06.2015 1

1. Why it is not the SM Higgs Fact I: We have a discovery! 0 Local p 10 10 10 10 10 10 10 10 10 10 1-1 -2-3 -4-5 -6-7 -8-9 -10-11 10 ATLAS 2011-2012 -1 s = 7 TeV: Ldt = 4.6-4.8 fb -1 s = 8 TeV: Ldt = 5.8-5.9 fb Obs. Exp. ±1 σ 110 115 120 125 130 135 140 145 150 m H [GeV] 0σ 1σ 2σ 3σ 4σ 5σ 6σ Sven Heinemeyer WIN (Heidelberg), 09.06.2015 2

Fact II: The SM cannot be the ultimate theory! Some facts: 1. gravity is not included 2. the hierarchy problem 3. Dark Matter is not included 4. neutrino masses are not included 5. anomalous magnetic moment of the muon shows a 4σ discrepancy Sven Heinemeyer WIN (Heidelberg), 09.06.2015 3

Fact I & II: We have a discovery! The SM cannot be the ultimate theory! Conclusion: It cannot be the SM Higgs! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 4

Fact I & II: We have a discovery! The SM cannot be the ultimate theory! Conclusion: It cannot be the SM Higgs! Q: Does the BSM physics have any (relevant) impact on the Higgs? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 4

Fact I & II: We have a discovery! The SM cannot be the ultimate theory! Conclusion: It cannot be the SM Higgs! Q: Does the BSM physics have any (relevant) impact on the Higgs? A: check changed properties A: check for additional Higgs bosons Sven Heinemeyer WIN (Heidelberg), 09.06.2015 4

Which model should we focus on? Some recent measurements: top quark mass Higgs boson mass Higgs boson couplings Dark Matter (properties) Sven Heinemeyer WIN (Heidelberg), 09.06.2015 5

Which model should we focus on? Some recent measurements: top quark mass Higgs boson mass Higgs boson couplings Dark Matter (properties) Simple SUSY models predicted correctly: top quark mass Higgs boson mass Higgs boson couplings Dark Matter (properties) Sven Heinemeyer WIN (Heidelberg), 09.06.2015 5

2. Higgs bosons in the MSSM: Superpartners for Standard Model particles Sven Heinemeyer WIN (Heidelberg), 09.06.2015 6

The simplest case: MSSM with real paremeters Enlarged Higgs sector: Two Higgs doublets H 1 = H 2 = H1 1 H1 2 H1 2 H 2 2 = = v 1 +(φ 1 +iχ 1 )/ 2 φ 1 φ + 2 v 2 +(φ 2 +iχ 2 )/ 2 V = m 2 1 H 1 H 1 +m 2 2 H 2 H 2 m 2 12 (ǫ abh a 1 Hb 2 +h.c.) physical states: h 0,H 0,A 0,H ± Goldstone bosons: G 0,G ± + g 2 +g 2 (H 1 H 1 H 2 H 2 ) 2 + g2 H 1 H 2 2 }{{ 8 }}{{} 2 gauge couplings, in contrast to SM m h M Z Input parameters: (to be determined experimentally) tanβ = v 2 v 1, MA 2 = m2 12 (tanβ +cotβ) Sven Heinemeyer WIN (Heidelberg), 09.06.2015 7

The lightest MSSM Higgs boson MSSM predicts upper bound on M h : tree-level bound: m h < M Z, excluded by LEP Higgs searches! Large radiative corrections: Yukawa couplings: em t 2M W s W, em 2 t M W s W,... Dominant one-loop corrections: M 2 h G µm 4 t log ( m t 1 m t 2 m 2 t The MSSM Higgs sector is connected to all other sector via loop corrections (especially to the scalar top sector) Present status of M h prediction in the MSSM: Complete 1L, almost complete 2L available, LL+NLL resummed,... ) Sven Heinemeyer WIN (Heidelberg), 09.06.2015 8

t sector of the MSSM: Stop mass matrix M 2 t = M 2 t L +m 2 t +DT t 1 m t X t θ t m 2 t 1 0 m t X t M 2 t R +m 2 t +DT t 2 0 m 2 t 2 with X t = A t µ/tanβ mixing important in stop sector! Simplifying abbreviation: M SUSY, M S := M t L = M t R Sven Heinemeyer WIN (Heidelberg), 09.06.2015 9

Upper bound on M h in the MSSM: Unconstrained MSSM : M A, tanβ, 5 parameters in t b sector, µ, m g, M 2 M h < 135 GeV for m t = 173.2±0.9GeV and m t < O(few TeV) (including theoretical uncertainties from unknown higher orders) clear prediction for the LHC Obtained with: FeynHiggs www.feynhiggs.de [T. Hahn, S.H., W. Hollik, H. Rzehak, G. Weiglein 98 15] all Higgs masses, couplings, BRs, XSs (easy to link, easy to use :-) Sven Heinemeyer WIN (Heidelberg), 09.06.2015 10

Upper bound on M h in the MSSM: Unconstrained MSSM : M A, tanβ, 5 parameters in t b sector, µ, m g, M 2 M h < 135 GeV Note : 125 < 135! for m t = 173.2±0.9GeV and m t < O(few TeV) (including theoretical uncertainties from unknown higher orders) clear prediction for the LHC Obtained with: FeynHiggs www.feynhiggs.de [T. Hahn, S.H., W. Hollik, H. Rzehak, G. Weiglein 98 15] all Higgs masses, couplings, BRs, XSs (easy to link, easy to use :-) Sven Heinemeyer WIN (Heidelberg), 09.06.2015 10

The embarrasing situation: The Higgs mass accuracy in the MSSM: Sven Heinemeyer WIN (Heidelberg), 09.06.2015 11

The embarrasing situation: The Higgs mass accuracy in the MSSM: Experiment: ATLAS: CMS: combined: M exp h M exp h M exp h = 125.36±0.37±0.18 GeV = 125.03±0.27±0.15 GeV = 125.09±0.21±0.11 GeV Theory: δm theo h 3 GeV Theory prediction must be improved to match the experimental accuracy! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 11

Sven Heinemeyer WIN (Heidelberg), 09.06.2015 12

Possible (likely?) omplication: The MSSM Higgs sector with CP violation H 1 = H 2 = H1 1 H1 2 H1 2 H 2 2 = = v 1 +(φ 1 +iχ 1 )/ 2 φ 1 φ + 2 v 2 +(φ 2 +iχ 2 )/ 2 e iξ V = m 2 1 H 1 H 1 +m 2 2 H 2 H 2 m 2 12 (ǫ abh a 1 Hb 2 +h.c.) physical states: h 0,H 0,A 0,H ± + g 2 +g 2 (H 1 H 1 H 2 H 2 ) 2 + g2 H 1 H 2 2 }{{ 8 }}{{} 2 gauge couplings, in contrast to SM 2 CP-violating phases: ξ, arg(m 12 ) can be set/rotated to zero Input parameters: (to be determined experimentally) tanβ = v 2 v 1, M 2 H ± Sven Heinemeyer WIN (Heidelberg), 09.06.2015 13

The Higgs sector of the cmssm at the loop-level: Complex parameters enter via loop corrections: µ : Higgsino mass parameter A t,b,τ : trilinear couplings X t,b,τ = A t,b,τ µ {cotβ,tanβ} complex M 1,2 : gaugino mass parameter (one phase can be eliminated) M 3 : gluino mass parameter can induce CP-violating effects Result: with (A,H,h) (h 3,h 2,h 1 ) m h3 > m h2 > m h1 strong changes in Higgs couplings to SM gauge bosons and fermions see Sebastian Paßehr s talk this afternoon! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 14

CPV effects on Higgs boson searches: CPX: benchmark scenario in the cmssm [M. Carena, J. Ellis, A. Pilaftsis, C. Wagner 00] LEP Higgs production cross sections: [LEPHiggsWG 06] σ (10-2 pb) 10 8 6 H 1 H 2 bb bb H 1 H 2 H 1 H 1 H 1 bb bb bb H 1 Z bb Z H 2 Z H 1 H 1 Z bb bb Z s =202 GeV 4 2 0 2 4 6 8 10 12 14 tanβ Sven Heinemeyer WIN (Heidelberg), 09.06.2015 15

Results of LEP searches in CPX scenario: [LEPHiggsWG 06] m t = 169.3 GeV m t = 174.3 GeV tanβ (a) Excluded by LEP tanβ (b) Excluded by LEP 10 10 1 CPX Theoretically Inaccessible 1 CPX Theoretically Inaccessible 0 20 40 60 80 100 120 140 m H1 (GeV/c 2 ) 0 20 40 60 80 100 120 140 m H1 (GeV/c 2 ) The LEP analysis showed unexcluded holes in the m h1 tanβ plane masses below 62 GeV ruled out, but above...? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 16

3....at the LHC and beyond Can we learn something on SUSY from the Higgs mass measurement? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 17

3....at the LHC and beyond Can we learn something on SUSY from the Higgs mass measurement? A simple exercise on stop masses: Dominant one-loop corrections: M 2 h G µm 4 t log ( m t 1 m t 2 m 2 t ) The MSSM Higgs sector is connected to all other sector via loop corrections (especially to the scalar top sector) only certain combinations of stop parameters are compatible with the Higgs discovery. clear prediction for the LHC? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 17

Stop masses: [P. Bechtle, S.H., O. Stål, T. Stefaniak, G. Weiglein, L. Zeune 15 PRELIMINARY] M h = 125±3 GeV : best-fit point red: χ 2 < 2.3 orange: χ 2 < 5.99 blue: all points HiggsBounds allowed gray: all scan points M h 125 GeV requires large X t and/or large M SUSY Sven Heinemeyer WIN (Heidelberg), 09.06.2015 18

Stop masses: [P. Bechtle, S.H., O. Stål, T. Stefaniak, G. Weiglein, L. Zeune 15 PRELIMINARY] M h = 125±3 GeV : best-fit point red: χ 2 < 2.3 orange: χ 2 < 5.99 blue: all points HiggsBounds allowed gray: all scan points light and heavy stops compatible with M h 125 GeV Sven Heinemeyer WIN (Heidelberg), 09.06.2015 19

Stop masses for M h = 125 GeV [A. Arbey et al., 11] M h 125 GeV requires large X t and/or large M SUSY no clear prediction for the LHC! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 20

(MSSM) Higgs limit setting at the LHC and beyond Two complementary methods for searches and limits: 1. obtain model independent limits on cross sections and branching ratios What is interesting to look out for? How to take the Higgs discovery into account? 2. obtain limits in representative benchmark scenarios Which constraints should be taken into account? Which not? And why? some (representative?) examples Sven Heinemeyer WIN (Heidelberg), 09.06.2015 21

The Vanilla solution: the discovery is interpreted as the light CP-even Higgs measure its couplings, any deviation from the SM? search for additional heavier Higgs bosons re-interpretation of SM Higgs searches? special issues for heavy Higgs phenomenology Higgs SUSY decays? Higgs production from SUSY decays? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 22

Coupling measurement: [P. Bechtle, S.H., O. Stål, T. Stefaniak, G. Weiglein 14] BR(H inv.) 2σ 1σ 2σ κ V 1σ 2σ κ u 1σ 2σ κ d 1σ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Very general model: κ V,κ u,κ d,κ l,κ g,κ γ,br(h inv.) using HiggsSignals with 80 channels from ATLAS, CMS, CDF, DØ κ l κ g κ γ 2σ 1σ 2σ 1σ 2σ 1σ 0 0.5 1 1.5 2 2.5 Sven Heinemeyer WIN (Heidelberg), 09.06.2015 23

Beyond LHC: HL-LHC vs. ILC in the most general κ framework: [P. Bechtle, S.H., O. Stål, T. Stefaniak, G. Weiglein 14] assumption: BR(H NP) = BR(H inv.) BR(H inv.) κw κz κu κd κl κg κγ 0.0 0.01 0.02 0.03 0.04 0.05 0.82 1.15 HiggsSignals 0.90 0.925 0.95 0.975 1.00 1.025 1.05 1.075 1.10 HL LHC (S2, opt.) ILC 250 ILC 500 ILC 1000 ILC 1000 (LumiUp) strong improvement with the ILC! deviations from SM? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 24

Re-interpretation of SM Higgs search results: g 2 hvv = sin2 (β α)g 2 HVV,SM, g2 HVV = cos2 (β α)g 2 HVV,SM some coupling strength could remain for the heavy Higgs go ahead for stronger limits! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 25

Search (interpretation) in new benchmark scenarios: [LHCHXSWG M. Carena, S.H., O. Stål, C. Wagner, G. Weiglein, 13] designed to have M h 125±3 GeV and to reproduce rate measurements designed to exhibit certain features of Higgs phenomenology light Higgs phenomenlogy heavy Higgs phenomenology Not taken into account on purpose: Flavor contraints Precision observables Dark Matter... can all be avoided easily by small model modification that do not change the Higgs phenomenology do not overconstrain yourself! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 26

m mod+ h scenario: m t = 173.2 GeV, M SUSY = 1000 GeV, µ = 200 GeV, M 2 = 200 GeV, X OS t = 1.5M SUSY A b = A τ = A t, m g = 1500 GeV, m l 3 = 1000 GeV. M h 125 GeV nearly everywhere Sven Heinemeyer WIN (Heidelberg), 09.06.2015 27

m mod+ h scenario: effect of non-sm Higgs decays: strong impact from H/A χ 0 i χ0 j, χ± k χ l disover heavy Higgses and SUSY at the same time! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 28

Higgs production from SUSY decays: ATLAS and CMS are now also searching for pp χ ± 1 χ0 2 W± χ 0 1 χ0 2 W± χ 0 1 h χ0 1 W± χ 0 1 b b χ 0 1 Sven Heinemeyer WIN (Heidelberg), 09.06.2015 29

Phenomenology at very low tanβ: look at the m max h scenario: m t = 173.2 GeV, M SUSY = 1000 GeV, µ = 200 GeV, M 2 = 200 GeV, X OS t = 2M SUSY A b = A τ = A t, m g = 1500 GeV, m l 3 = 1000 GeV. tanβ > 4 for M SUSY < few TeV But what happens for M SUSY > 10 TeV? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 30

Example scenario: low-tb-high [S.H. (LHCHXSWG??) 14] M SUSY and X t adjusted to give M h 125 GeV everywhere 10 9 8 low-tb-high M h < 120 120 < M h < 122 122 < M h < 124 tanβ 7 6 5 124 < M h < 126 126 < M h < 128 128 < M h < 130 130 < M h 4 3 2 1 200 300 400 500 M A [GeV] lower tan β values possible! Relevant? new relevant decay channels! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 31

Example scenario: low-tb-high : H hh [S.H. (LHCHXSWG??) 15] M SUSY and X t adjusted to give M h 125 GeV everywhere 10 9 8 7 6 low-tb-high 0.8 < BR(H -> hh) < 0.9 0.7 < BR(H -> hh) < 0.8 0.6 < BR(H -> hh) < 0.7 0.5 < BR(H -> hh) < 0.6 0.4 < BR(H -> hh) < 0.5 0.3 < BR(H -> hh) < 0.4 0.2 < BR(H -> hh) < 0.3 0.1 < BR(H -> hh) < 0.2 tanβ 5 4 3 2 important at low tanβ 1 200 300 400 500 M A [GeV] Sven Heinemeyer WIN (Heidelberg), 09.06.2015 32

The exotic solution: the discovery is interpreted as the heavy CP-even Higgs In principle also possilbe: M h < 125 GeV M H 125 GeV Consequences: all Higgs bosons very light easy(?) discovery of additional Higgs bosons at the LHC Constraints: direct searches for the lightest CP-even Higgs direct searches for the heavy neutral Higgses direct searches for the charged Higgses flavor constraints (BR(B s µ + µ ) etc.) Sven Heinemeyer WIN (Heidelberg), 09.06.2015 33

The general possibility: the discovered Higgs is the second-lightest one more contrived in the MSSM with real parameters easier (?) possible in the MSSM with complex parameters easier (!) possible in the NMSSM light Higgs can be singlet like can more easily escape detection Is such a light Higgs detectable at the LHC? h 2 h 1 h 1 possible, but strongly suppressed for M h1 > 63 GeV so far few (and weak ) LHC searches for a Higgs with M h1 < 100 GeV Possible: SUSY SUSY h 1, e.g. χ 0 2 χ0 1 h 1 Sven Heinemeyer WIN (Heidelberg), 09.06.2015 34

LHC Higgs searches below 100 GeV: crucial to cover extended Higgs sectors needed to re-check LEP exclusions ( 2.xσ excess around 98 GeV) S95 1 10-1 (a) LEP s = 91-209 GeV SM branching ratios Observed Expected for background Best/only channel? h 1 γγ?? 10-2 20 40 60 80 100 120 m H1 (GeV/c 2 ) we cannot encourage you enough to perform this search! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 35

4. Conclusinos LHC: we have a HIGGS DISCOVERY!!! M H 125.1±0.2 GeV It is impossible that it is SM Higgs Impact of BSM physics on Higgs sector?? impact on couplings of the discovered Higgs search for additional Higgs bosons Implications in the rmssm, cmssm, NMSSM The discovered Higgs could be the lightest or second-lightest Higgs of each model various, different implications Searches/interpretation via general limits benchmark scenarios always take into account the discovery (mass, properties) rmssm, M H 125 GeV: disfavored by charged Higgs searches but well possible in other models (cmssm, NMSSM,...) search for new states above and below 125 GeV Sven Heinemeyer WIN (Heidelberg), 09.06.2015 36

Sven Heinemeyer WIN (Heidelberg), 09.06.2015 37

Back-up Sven Heinemeyer WIN (Heidelberg), 09.06.2015 38

Beyond LHC: HL-LHC vs. ILC in the most general κ framework: [P. Bechtle, S.H., O. Stål, T. Stefaniak, G. Weiglein 14] assumption: κ V 1 BR(H NP) κw κz κu κd κl κg κγ 0.0 0.01 0.02 0.03 0.04 0.05 0.82 1.15 HiggsSignals 0.90 0.925 0.95 0.975 1.00 1.025 1.05 1.075 1.10 HL LHC (S2, opt.) ILC 250 ILC 500 ILC 1000 ILC 1000 (LumiUp) strong improvement with the ILC! deviations from SM? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 39

Beyond LHC: HL-LHC vs. ILC in the most general κ framework: [P. Bechtle, S.H., O. Stål, T. Stefaniak, G. Weiglein 14] no theory assumptions, full fit BR(H NP) κw κz κu κd κl κg κγ 0.0 0.01 0.02 0.03 0.04 0.05 ILC 250 ILC 500 ILC 1000 0.82 1.16 ILC 1000 (LumiUp) HiggsSignals 0.90 0.925 0.95 0.975 1.00 1.025 1.05 1.075 1.10 high ILC precision, not possible at the LHC deviations from SM? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 40

Beyond LHC: HL-LHC vs. ILC in the most general κ framework: [P. Bechtle, S.H., O. Stål, T. Stefaniak, G. Weiglein 14] no theory assumptions, full fit BR(H NP) κw κz κu κd κl κg κγ 0.0 0.01 0.02 0.03 0.04 0.05 HiggsSignals HL LHC (Γ tot free) HL LHC ILC 250 (σzh total) HL LHC ILC 250 HL LHC ILC 500 HL LHC ILC 1000 0.90 0.925 0.95 0.975 1.00 1.025 1.05 1.075 1.10 HL LHC ILC 1000 (LumiUp) strong improvement with the ILC! deviations from SM? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 41

b effects on b b H/A b b: b = 2α s 3π m gµ tanβ I(m b 1,m b 2,m g )+ α t 4π A tµ tanβ I(m t 1,m t 2,µ) Additional factors wrt. the SM: σ(b bh/a) BR(H/A b b) tanβ2 (1+ b ) 2 60 50 µ = -1000 GeV µ = -200 GeV µ = +200 GeV µ = +1000 GeV m h -mod+ 60 50 µ = -1000 GeV µ = -200 GeV µ = +200 GeV µ = +1000 GeV m h -mod- 40 40 tan β 30 tan β 30 20 20 10 10 0 100 150 200 250 300 350 0 100 150 200 250 300 350 M A [GeV] M A [GeV] phenomenology can depend on new parameters! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 42

Where is the light Higgs in the heavy Higgs case? low M h values, strongly reduced couplings Sven Heinemeyer WIN (Heidelberg), 09.06.2015 43

low-m H scenario: m t = 173.2 GeV, M A = 110 GeV, M SUSY = 1500 GeV, M 2 = 200 GeV, X OS t 2.45M SUSY A b = A τ = A t, m g = 1500 GeV, m l 3 = 1000 GeV. M H 125 GeV can in principle be realized Sven Heinemeyer WIN (Heidelberg), 09.06.2015 44

low-m H scenario: m t = 173.2 GeV, M A = 110 GeV, M SUSY = 1500 GeV, M 2 = 200 GeV, X OS t 2.45M SUSY A b = A τ = A t, m g = 1500 GeV, m l 3 = 1000 GeV. Interesting prospects also for the charged Higgs searches Sven Heinemeyer WIN (Heidelberg), 09.06.2015 45

Latest ATLAS results for charged Higgs searches: [ATLAS 13] + B t bh 10-1 ATLAS Preliminary Data 2012 Observed CLs s = 8 TeV Expected ± 1σ ± 2σ Ldt = 19.5 fb -1-2 10 90 100 110 120 130 140 150 160 [GeV] model independent limits! + m H Sven Heinemeyer WIN (Heidelberg), 09.06.2015 46

Latest ATLAS results for charged Higgs searches: [ATLAS 13] tan β 60 50 40 30 20 Median expected exclusion Observed exclusion 95% CL Observed +1σ theory Observed -1σ theory Expected exclusion 2011 Observed exclusion 2011 ATLAS Preliminary max s=8 TeV m h Ldt = 19.5 fb -1 Data 2012 τ+jets 10 0 90 100 110 120 130 140 150 160 [GeV] + m H exclusion of light M H ± in the m max h scenario!...low-m H? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 47

Application of charged Higgs limits on low-m H scenario: [HiggsBounds 4.1] that (particular incarnation of the) low-m H scenario is excluded? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 48

Application of charged Higgs limits on low-m H scenario: [HiggsBounds 4.1] that (particular incarnation of the) low-m H scenario is excluded? Sven Heinemeyer WIN (Heidelberg), 09.06.2015 49

Analysis of χ 0 2 χ0 1 h 1 in the cmssm: [A. Fowler, G. Weiglein 09] Sven Heinemeyer WIN (Heidelberg), 09.06.2015 50

Recent FeynHiggs update: some numerical results [FeynHiggs 2.10.0] Parameters: M S = m t 1 m t 2 M A = 1000 GeV µ = 1000 GeV M 2 = 1000 GeV m g = 1600 GeV tanβ = 10 Vary M S, X t to analyze effects Sven Heinemeyer WIN (Heidelberg), 09.06.2015 51

M h (X t /M S ): 145 M SUSY = 1 TeV FeynHiggs 2.10.0 [FeynHiggs2.10.0] M SUSY = 2 TeV 140 M SUSY = 5 TeV M SUSY = 10 TeV 135 M SUSY = 15 TeV M SUSY = 20 TeV M h [GeV] 130 125 120 115-2.5-2.0-1.5-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 X t /M S [GeV] increase with M S, maxima at X t /M S = ±2 Sven Heinemeyer WIN (Heidelberg), 09.06.2015 52

M h (M S ) for various approximations: 155 150 FH295 3-loop 4-loop FeynHiggs 2.10.0 [FeynHiggs2.10.0] 145 140 5-loop 6-loop 7-loop LL+NLL X t /M S = 2 M h [GeV] 135 130 125 X t = 0 120 115 5000 10000 15000 20000 M S [GeV] 3-loop good for M S < 2 TeV, 7-loop: 1 GeV for M S = 20 TeV Sven Heinemeyer WIN (Heidelberg), 09.06.2015 53

M h (M S ) compared with H3m: 155 3-loop, O(α t α s 2 ) FeynHiggs 2.10.0 [FeynHiggs2.10.0] 150 145 3-loop full LL+NLL H3m A 0 = 0, tanβ = 10 140 M h [GeV] 135 130 125 120 115 5000 10000 15000 20000 M S [GeV] 3-loop O ( α 2 t α s,α 3 t ) beyond 3-loop important for precise Mh prediction! Sven Heinemeyer WIN (Heidelberg), 09.06.2015 54