mh = 125 GeV and SUSY naturalness

Transcription

1 mh = 125 GeV and SUSY naturalness Josh Ruderman (UC Berkeley) March 13, 212 Lawrence Hall, David Pinner, JTR

2 h! ATLAS CMS p Observed p SM H expected p Data 211, s = 7 TeV Ldt = 4.9 fb p-value 1-2 Interpretation Requires LEE CMS preliminary s = 7 TeV L = 4.76 fb 1σ 2σ 95% CL limit on / SM ATLAS Preliminary Observed CL s limit Expected CL limit s H ± 1 ATLAS Preliminary ± 2 Data 211, s = 7 TeV Ldt = 4.9 fb m H [GeV] m H [GeV] γ) /σ(h γ SM 95%CL γ) σ(h γ m H (GeV/c ) Observed CLs Limit Median Expected CLs Limit ± 1σ Expected CLs ± 2σ Expected CLs Median Expected (HIG1-33) Observed Asymptotic Observed Ensemble cat-3 (Non-VBFTag) cat4 (VBFTag) CMS preliminary s = 7 TeV L = 4.76 fb m H (GeV/c ) 1 σ SM usion limit on the cross section of a SM Higgs boson decaying into t 3σ

3 h! ZZ! 4l ATLAS CMS Events/5 GeV DATA Background Signal (m =125 GeV) H Signal (m =15 GeV) H Signal (m =19 GeV) H Syst.Unc. (*) 4l H ZZ Ldt = 4.8 fb s = 7 TeV ATLAS Events/2 GeV CMSs = 7 TeV L = 4.71 fb s = 7 TeV L = 4.7 fb LEP excluded (95% CL) Data [ 4e, 4μ, 2e 2μ ] Z+X DATA Z+X ZZ =14 2 m H =12 GeV/c ZZ mh = 12 GeV mh = 14 GeV Local p [GeV] m 4l ATLAS (*) -4 Observed H ZZ 4l Expected Ldt = 4.8 fb s=7 TeV [GeV] m H 2 3 local p-value m4 [GeV] CMS L = 4.7 fb w/o m4 uncertainties with m4 uncertainties int s = 7 TeV σ 2σ 3σ MH [GeV/c 2 ]

4 Tevatron Tevatron Run II Preliminary, L fb 95% CL Limit/SM Tevatron Exclusion Expected Observed ±1 Expected ±2 Expected Tevatron Exclusion 1 SM=1 February 27, m H (GeV/c 2 )

5 Taking these excesses seriously already allows a precise determination of the Higgs mass! 6 all data % probability per.1 GeV bin m h = ±.8 GeV Jens Erler M H [GeV] anyway, there is nowhere else to look: ATLAS excludes (95%): , , GeV CMS excludes (95%): GeV

6 my view on the Higgs is: guilty until proven innocent for the rest of this talk: m h GeV let s explore the implications!

7 Nima Arkani-Hamed, Madrid 12/16/11

8 SUSY 125 sits in the battleground between natural and not natural m h = 125 GeV unnatural Predicted range for the Higgs mass tanb = 5 tanb = 4 tanb = 2 tanb = 1 Split SUSY topic of this talk Higgs mass m h in GeV High-Scale SUSY Experimentally favored Supersymmetry breaking scale in GeV Giudice, Strumia

9 the plan: consequences of m h = 125 GeV for: 1. MSSM 2. NMSSM 3. SUSY SH u H d..7 >.7

10 MSSM

11 higgs mass in MSSM in general V = m 2 H h 2 + h 4 h 4 m h = h v 2 v = 174 GeV tree-level MSSM in decoupling limit, m A m Z D-terms contribute: h = g2 + g 2 2 cos 2 2 m h = m Z cos 2

12 higgs mass in MSSM 1-loop: t t i t i h h h h h h m 2 h m 2 Z cos m 4 t (4 ) 2 v 2 " log m2 t m 2 t + X2 t m 2 t 1 X 2 t 12m 2 t!# m2 Q 3 + m 2 t + t L m Z m t X t m t X t m 2 U 3 + m 2 t + t R m 2 Z 1 C A X t = A t µ tan maximal mixing: X t = p 6 m t

13 higgs mass in MSSM 2-loop calculations: O ( t s ) Suspect Djouadi, et al. DR scheme FeynHiggs Heinemeyer et al. On-Shell scheme There has also been a recent 3-loop calculation: O t 2 s Harlander, Kant, Mihaila, Steinhauser ,

14 MSSM Higgs Mass m h = GeV X t = Suspect FeynHiggs m t1 é X t 6 m t é

15 fine tuning in the MSSM tree-level: m 2 Z 2 = µ2 + m 2 H u + O 1 tan 2 one-loop: m 2 H u 3y2 t 8 2 m2 Q 3 + m 2 u 3 + A t 2 log m t m 2 H u m 2 Z 2 signals fine tuning

16 model-independent fine tuning write the potential in the direction that gets the VEV, V = m 2 H h 2 + h 4 h 4 extremizing, m 2 h = h v 2 = 2m 2 H m 2 H m 2 h /2 1 signals fine tuning Kitano and Nomura 6296

17 naturalness bounds higgsinos: µ 2. (3 GeV) 2 % 1 stops: m 2 t. (5 GeV)2 1 1+A 2 t /2m 2 t % 1 3 log /m t maximal mixing has the same fine tuning cost as doubling the stop masses A 2 t 6 m 2 t

18 the direct LHC squark limit: squark mass [GeV] Squark-gluino-neutralino model, m( ) = GeV 1 ATLAS Combined Preliminary CL s observed 95% C.L. limit CL s median expected limit Expected limit ±1 ATLAS EPS 211 L dt = 4.71 fb, SUSY s=7 TeV = 1 fb 12 SUSY = fb 8 SUSY = fb gluino mass [GeV] if the squarks are degenerate: m t m q & TeV

19 direct stop limit theorist-level reinterpretation shows weak limits: Left-Handed Stop ê Sbottom Right-Handed Stop m H ATLAS 2-4 j, 1.4 fb CMS a T, 1.14 fb CMS H T ê MET, 1.1 fb D b é b é, 5.2 fb m é bl = m é H m H ATLAS 2-4 j, 1.4 fb CMS a T, 1.14 fb CMS H T ê MET, 1.1 fb D b é b é, 5.2 fb m tr é = m H é m é m é points to SUSY models with flavor violating soft masses for the squarks Michele Papucci, JTR, Andreas Weiler

20 Higgs points to heavy stops and fine tuning: 3 Higgs Mass vs. Fine Tuning 3 Lightest Stop Mass Suspect FeynHiggs 25 2 Suspect FeynHiggs 2 m t m t D mh m t1 é X t êmé t m h m h & = max log m 2 log p i X t êmé t X 2 t m 2 t 1 X 2 t 12m 2 t!

21 BSM higgs higgs rates open a window into BSM and naturalness g γ g h γ R = ( gg!h Br h! ) MSSM ( gg!h Br h! ) SM important modifications: g t i h h H h t i γ g γ

22 g g Æ h Æ g g Suspect.85 m t FeynHiggs R gg gg m é t X t êm t é R = ( gg!h Br h! ) MSSM ( gg!h Br h! ) SM

23 NMSSM

24 NSSM consider the superpotential: W SH u H d + µh u H d + M S S 2 which generates: F S 2 2 H u H d 2 and soft terms: V soft m S S 2 +( A SH u H d +h.c.) the lightest CP even eigenvalue satisfies the bound: m 2 h apple m 2 Z cos v 2 sin 2 2 saturated when m s M S

25 tan and m 2 h apple m 2 Z cos v 2 sin 2 2 want small tan Cos 2 2b Sin 2 2b Tan b perturbativity until the GUT scale requires: d 2 dt 16 2 dy2 t dt = y2 t = y 2 t 3g 2 2 6yt g2 3 3g2 2

26 NMSSM Higgs Mass m h = GeV l =.6,.7 m t é = 12, 5 GeV X t = Tan b

27 m h = 125 GeV 3 Tan b = 2 3 Tan b = m t 15 m t 15 m t 15 5 l =,.3,.5,.6,.7 5 l =,.3,.5,.6,.7 5 m é t1 < GeV X t êmé t m é t1 < GeV X t êmé t

28 fine tuning in the NMSSM 3 Tan b = 2 3 Tan b = m t 15 2 Suspect FeynHiggs m t 15 Suspect FeynHiggs 2 D mh 2 5 D mh m é t1 < GeV X t êmé t m é t1 < GeV X t êmé t m h. 15 possible with low mixing

29 m é X t = 6 m t é Stop Mass X t = 6 4 Suspect FeynHiggs Tan b = l Dmh Fine Tuning X t = 6 m t é X t = Tan b = 2 5 Suspect FeynHiggs l fine tuning highly prefers large (and small mixing)

30 SUSY

31 what about larger? W SH u H d top-down: fat higgs Harnik, Kribs, Larson, Murayama bottom-up: SUSY Barbieri, Hall, Nomura, Rychkov we restrict to. 2 so the theory is perturbative until. few TeV

32 higgs mass [GeV] 9 λ = 2 8 A 7 H H + the original papers focus on a heavy higgs masses A H H + 3 m h 2 3 GeV 2 h h tanβ Barbieri, Hall, Nomura, Rychkov the singlet was decoupled, m s & 1TeV this limit cannot be taken without spoiling naturalness: dm 2 H u,d dt = 2 m2 S

33 singlet-higgs mixing M 2 = 2 v 2 sin MZ 2 cos2 2 v(µ, M S,A ) v(µ, M S,A ) m 2 s 5 lsusy Higgs Mass s 2 5 h m h = GeV m

34 a reference point parameters =2 tan =2 µ =2GeV M S =GeV m S =5GeV m H + =47GeV m Q3 = m u3 =5GeV A t,a = with, m h = 125 GeV m h =5

35 m h 2 < Tan b m h D mh 125 ms HGeVL l m includes the fine-tuning from h the level-splitting Figure : The Higgs mass and fine-tuning contours, m h and tan and on the right we vary and the singlet soft ma

36 non-decoupling of H bb y2 b (y 2 b ) SM h H bb =1+ sin 4 tan mz m H ± 2 bb =1 sin 4 tan v m H ± 2 MSSM l SUSY m h = 125 GeV xi xi.5 x tt x WW x gg Tan b = 2 x bb m H + HGeVL.5 x tt x WW x gg Tan b = 2 x bb m H + HGeVL

37 non-decoupling of H R = ( gg!h Br h! ) SUSY ( gg!h Br h! ) SM m H + = 47 GeV m h R gg Tan b l

38 SUSY predictions: h! enhanced: h! WW,ZZ (including VBF) depleted: h! bb,

39 SUSY predictions: h! enhanced: h! WW,ZZ (including VBF) CMS depleted: h! bb, ATLAS Dijet Tag Class 3 Class 2 Class 1 Class Combined Best Fit σ/σ SM µ 3 Best fit H ± 1 ATLAS Data 211, s = 7 TeV Ldt = 4.9 fb m H [GeV]

40 ombined obs. xp. for SM Higgs omb. ensemble bb (4.7 fb ) ττ (4.6 fb ) γγ (4.8 fb ) WW (4.6 fb ) ZZ (4.7 fb ) 4σ ass (GeV) SUSY Higgs boson mass (GeV) enhanced: alue p (left) and best-fit ˆµ = s/s SM (right) as a function of ange GeV. The local p-values for individual channels ed with the asymptotic formula (lines); the combined local p- ensembles h of background-only! pseudo-datasets (points). The (including VBF) ocal p-values p (m H ), should a Higgs boson with a mass m H orresponds to the ±1s uncertainties on the ˆµ values. h! WW,ZZ predictions: depleted: h! bb, CMS ATLAS S Preliminary s = 7 TeV = fb m H = 125 GeV Combined (68%) Single channel CMS Preliminary s = 7 TeV L = fb (local) 1 ATLAS Preliminary H WW lνlν H bb p -2 2σ H ττ -3 3σ est fit σ/σ SM H γγ H WW H ZZ Best fit σ/σ SM Ldt = 4.7 fb s = 7 TeV Observed Expected m H [GeV] Figure 12: Top left: fitted signal strength parameter (µ) as a function of m H for the whole mass range. 4σ 5σ

41 SUSY predictions: h! enhanced: h! WW,ZZ (including VBF) depleted: h! bb, Tevatron Best Fit σ / σ SM Tevatron RunII Preliminary SM H bb, L int Best Fit ±1 s.d. 9.7 fb Higgs Boson Mass (GeV/c ) Feb

42 super-preliminary scorecard: h! enhanced: h! WW,ZZ (including VBF) depleted: h! bb, m H = 125 GeV Combined (68%) Single channel CMS Preliminary s = 7 TeV L = fb H bb H ττ H γγ H WW H ZZ Best fit σ/σ SM

43 fine-tuning for a 1D potential, V = m 2 H h 2 + h 4 h 4 = m2 H m 2 h /2 including singlet-doublet mixing, m2 H m 2 h /2 where m h is the higgs mass before mixing

44 large protects against fine tuning 25 2 Hm t él max Hm H +L max m max Naturalness Bounds D v = H2L mass HGeVL l

45 A Natural SUSY Spectrum & - TeV strong dynamics 3 15 g t 1,2, b L H, H ± s H h mass (GeV) flavor-degenerate squarks OK!

46 some remaining options for natural SUSY m h = 125 GeV NMSSM NMSSM + RPV SUSY m t <m q 1,2 m t = m q 1,2

47 take away points the MSSM requires maximal stop mixing and is ~1% tuned or worse the NSSM can be ~% tuned at the edge of its parameter space,.7, tan. 3 mh = 125 GeV is natural in SUSY because SUSY R of singlet-doublet mixing in, can be enhanced and flavor degen squarks are naturally accommodated

48 backup

49 what about m 6= m Q3 u3? the higgs mass is mostly determined by: (m t,x t) where: m 2 t m Q m 3 u3 m t m Q3 êm u3 =.5, 1, X t êmé t D ê Ddegen splitting the soft masses makes fine tuning worse m Q3 ê m u3

50 fine tuning in the MSSM to generalize we will adopt the definition: m h = max log m 2 log p i p i = m 2 Q 3, m 2 u 3, A t, µ, Bµ, m 2 H u, m 2 H d all defined at a cutoff to be conservative, we take = TeV

51 combo ATLAS CMS Local P-Value ATLAS Preliminary Observed Expected Ldt = fb s = 7 TeV 211 Data M H [GeV] Local p-value Best fit σ/σ SM CMS Preliminary, s = 7 TeV, Combined, L = fb int Interpretation requires look-elsewhere effect correction 1 ±1σ from fit Higgs boson mass (GeV/c ) 1σ 2σ 3σ 4σ 95% CL Limit on / SM 1 ATLAS Preliminary 211 Data Observed Expected Ldt = fb ±1 ± 2 s = 7 TeV 95% CL limit on σ/σ SM 1 CMS Preliminary, s = 7 TeV Combined, L = fb int Observed Expected ± 1σ Expected ± 2σ CLs Limits M H [GeV] Higgs boson mass (GeV/c 2 )

52 non-decoupling of H the heavy Higgs doublet cannot be taken arbitrarily heavy consistently with naturalness 2 v 2 = 2B µ sin 2 m 2 H ± + m 2 W l SUSY non-decoupling effects are generic in the most natural part of parameter space! m H ±. TeV xi m h = 126 GeV.6 x tt.4 x WW x.2 gg tanhbl= 2 x bb m H + HGeVL

53 precision electroweak m H ± 35 t= tan β 68 % CL.15.1 m H ±=35 GeV m H ±=7 GeV T % CL T st sb m h (SM) t= S tanβ

54 m c < m h ê2 25 m h D mh ms HGeVL m h 2 < M s HGevL