mh = 125 GeV and SUSY naturalness Josh Ruderman (UC Berkeley) March 13, 212 Lawrence Hall, David Pinner, JTR 1112.273
h! ATLAS CMS p Observed p 1-2 1 2 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 -3-4 8 7 6 5 4 3 2 3 ATLAS Preliminary 1 115 12 125 13 135 14 145 15 1 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] 1 115 12 125 13 135 14 145 15 m H [GeV] γ) /σ(h γ SM 95%CL γ) σ(h γ -3-4 1 115 12 125 13 135 14 145 15 2 m H (GeV/c ) 4 3.5 3 2.5 2 1.5 1.5 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 1 115 12 125 13 135 14 145 15 2 m H (GeV/c ) 1 σ SM usion limit on the cross section of a SM Higgs boson decaying into t 3σ
h! ZZ! 4l ATLAS CMS Events/5 GeV 8 6 4 2 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 5 4 3 2 1 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 15 2 25 [GeV] 1-2 -3 m 4l ATLAS (*) -4 Observed H ZZ 4l Expected Ldt = 4.8 fb s=7 TeV -5 1 12 13 14 15 16 17 18 19 2 [GeV] m H 2 3 local p-value 1-2 -3 1 12 13 14 15 16 m4 [GeV] CMS L = 4.7 fb w/o m4 uncertainties with m4 uncertainties int s = 7 TeV -4 1 115 12 125 13 135 14 145 15 155 16 1σ 2σ 3σ MH [GeV/c 2 ]
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, 212 1 12 13 14 15 16 17 18 19 2 m H (GeV/c 2 )
Taking these excesses seriously already allows a precise determination of the Higgs mass! 6 all data % probability per.1 GeV bin 5 4 3 2 1 m h = 124.5 ±.8 GeV Jens Erler 121.695 1 115 12 125 13 135 M H [GeV] anyway, there is nowhere else to look: ATLAS excludes (95%): 1 117.5, 118.5 122.5, 129 539 GeV CMS excludes (95%): 127.5 6 GeV
my view on the Higgs is: guilty until proven innocent for the rest of this talk: m h 124 126 GeV let s explore the implications!
Nima Arkani-Hamed, Madrid 12/16/11
SUSY 125 sits in the battleground between natural and not natural m h = 125 GeV unnatural Predicted range for the Higgs mass 16 15 tanb = 5 tanb = 4 tanb = 2 tanb = 1 Split SUSY topic of this talk Higgs mass m h in GeV 14 13 High-Scale SUSY Experimentally favored 12 1 4 6 8 12 14 16 18 Supersymmetry breaking scale in GeV Giudice, Strumia 18.677
the plan: consequences of m h = 125 GeV for: 1. MSSM 2. NMSSM 3. SUSY SH u H d..7 >.7
MSSM
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
higgs mass in MSSM 1-loop: t t i t i h h h h h h m 2 h m 2 Z cos 2 2 + 3 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!# B @ 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
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 83.672, 1111.7213
MSSM Higgs Mass mh @GeVD 14 13 12 1 m h = 12426 GeV X t = Suspect FeynHiggs 9 2 3 5 7 15 2 3 m t1 é X t = @GeVD 6 m t é
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
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
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
the direct LHC squark limit: squark mass [GeV] 2 18 16 14 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 6 6 8 12 14 16 18 2 gluino mass [GeV] if the squarks are degenerate: m t m q & TeV
direct stop limit theorist-level reinterpretation shows weak limits: Left-Handed Stop ê Sbottom Right-Handed Stop m H é @GeVD 24 22 2 18 16 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 é @GeVD 24 22 2 18 16 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 14 14 12 12 18 2 22 24 26 28 3 m é tl @GeVD 16 18 2 22 24 m é tr @GeVD points to SUSY models with flavor violating soft masses for the squarks Michele Papucci, JTR, Andreas Weiler 11.6926
Higgs points to heavy stops and fine tuning: 3 Higgs Mass vs. Fine Tuning 3 Lightest Stop Mass 25 25 2 Suspect FeynHiggs 25 2 Suspect FeynHiggs 2 m t é @GeVD 15 75 5 m t é @GeVD 15 15 5 5 2 5 5 75 25 D mh 2 5 3 m t1 é -4-2 2 4 X t êmé t m h m h & = max i @ log m 2 h @ log p i -4-2 2 4 X t êmé t X 2 t m 2 t 1 X 2 t 12m 2 t!
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
g g Æ h Æ g g 12 12 Suspect.85 m t é @GeVD 8.95 8 FeynHiggs.8.75 6 6 R gg gg m é t1 4.9.7 2 1. 1.5 2. 2.5 3. 3.5 X t êm t é R = ( gg!h Br h! ) MSSM ( gg!h Br h! ) SM
NMSSM
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 2 2 + 2 v 2 sin 2 2 saturated when m s M S
tan and m 2 h apple m 2 Z cos 2 2 + 2 v 2 sin 2 2 want small tan 1..8.6.4.2. Cos 2 2b Sin 2 2b 2 4 6 8 Tan b perturbativity until the GUT scale requires:..7 16 2 d 2 dt 16 2 dy2 t dt = y2 t = 2 4 2 +3y 2 t 3g 2 2 6yt 2 + 2 16 3 g2 3 3g2 2
NMSSM Higgs Mass mh @GeVD 14 13 12 1 m h = 12426 GeV l =.6,.7 m t é = 12, 5 GeV X t = 9 2 4 6 8 Tan b
m h = 125 GeV 3 Tan b = 2 3 Tan b = 5 3 25 25 25 2 2 2 m t é @GeVD 15 m t é @GeVD 15 m t é @GeVD 15 5 l =,.3,.5,.6,.7 5 l =,.3,.5,.6,.7 5 m é t1 < GeV -4-2 2 4 X t êmé t m é t1 < GeV -4-2 2 4 X t êmé t
fine tuning in the NMSSM 3 Tan b = 2 3 Tan b = 5 25 25 5 2 5 2 5 5 m t é @GeVD 15 2 Suspect FeynHiggs m t é @GeVD 15 Suspect FeynHiggs 2 D mh 2 5 D mh 5 25 5 15 m é t1 < GeV -4-2 2 4 X t êmé t 5 2 25 m é t1 < GeV -4-2 2 4 X t êmé t m h. 15 possible with low mixing
m é t @GeVD 1 16 14 12 8 X t = 6 m t é Stop Mass X t = 6 4 Suspect FeynHiggs Tan b = 2 2.4.45.5.55.6.65.7 l Dmh 25 2 15 Fine Tuning X t = 6 m t é X t = Tan b = 2 5 Suspect FeynHiggs.4.45.5.55.6.65.7 l fine tuning highly prefers large (and small mixing)
SUSY
what about larger? W SH u H d top-down: fat higgs Harnik, Kribs, Larson, Murayama 311349 bottom-up: SUSY Barbieri, Hall, Nomura, Rychkov 67332 we restrict to. 2 so the theory is perturbative until. few TeV
higgs mass [GeV] 9 λ = 2 8 A 7 H H + the original papers focus on a heavy higgs masses 6 5 4 A H H + 3 m h 2 3 GeV 2 h h 1 1.5 2 2.5 3 3.5 4 tanβ Barbieri, Hall, Nomura, Rychkov 67332 the singlet was decoupled, m s & 1TeV this limit cannot be taken without spoiling naturalness: dm 2 H u,d dt = 2 m2 S 8 2 +...
singlet-higgs mixing M 2 = 2 v 2 sin 2 2 + MZ 2 cos2 2 v(µ, M S,A ) v(µ, M S,A ) m 2 s 5 lsusy Higgs Mass s Mass @GeVD 2 5 h m h = 12426 GeV 2 3 5 7 m S @GeVD
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
3. 3 2 m h 2 < 2.5 25 5 15 2 Tan b 2. 1.5 6 15 m h D mh 125 ms HGeVL 5 1. 5 16 2.8 1. 1.2 1.4 1.6 1.8 2. 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
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 1.5 1.5 m h = 125 GeV 1. 1. xi xi.5 x tt x WW x gg Tan b = 2 x bb. 3 5 75 15 m H + HGeVL.5 x tt x WW x gg Tan b = 2 x bb. 3 5 75 15 m H + HGeVL
non-decoupling of H R = ( gg!h Br h! ) SUSY ( gg!h Br h! ) SM 2. 1.25 m H + = 47 GeV 1.75 1.8 m h R gg 1.1 1.5 Tan b 1.6 1.4 125 1.2 1.9 16 2 1. 1. 1.2 1.4 1.6 1.8 2. l
SUSY predictions: h! enhanced: h! WW,ZZ (including VBF) depleted: h! bb,
SUSY predictions: h! enhanced: h! WW,ZZ (including VBF) CMS depleted: h! bb, ATLAS Dijet Tag Class 3 Class 2 Class 1 Class Combined -2 2 4 6 Best Fit σ/σ SM µ 3 Best fit H ± 1 ATLAS 2 1-2 -3 Data 211, s = 7 TeV 1 115 12 125 13 135 14 145 15 Ldt = 4.9 fb m H [GeV]
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 35 14 145 ass (GeV).5. -.5 SUSY. 1 115 12 125 13 135 14 145 Higgs boson mass (GeV) enhanced: alue p (left) and best-fit ˆµ = s/s SM (right) as a function of ange 1 145 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 = 4.6-4.8 fb m H = 125 GeV Combined (68%) Single channel CMS Preliminary s = 7 TeV L = 4.6-4.8 fb (local) 1 ATLAS Preliminary H WW lνlν H bb p -2 2σ H ττ -3 3σ 2 3 4 est fit σ/σ SM H γγ H WW H ZZ -.5.5 1 1.5 2 2.5 3 3.5 4 Best fit σ/σ SM -4-5 -6-7 Ldt = 4.7 fb s = 7 TeV Observed Expected 1 115 12 125 13 135 14 145 15 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
SUSY predictions: h! enhanced: h! WW,ZZ (including VBF) depleted: h! bb, Tevatron Best Fit σ / σ SM 5 4 3 Tevatron RunII Preliminary SM H bb, L int Best Fit ±1 s.d. 9.7 fb 2 1 5 1 115 12 125 13 135 14 145 15 2 Higgs Boson Mass (GeV/c ) Feb 24 212
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 = 4.6-4.8 fb H bb H ττ H γγ H WW H ZZ -.5.5 1 1.5 2 2.5 3 3.5 4 Best fit σ/σ SM
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
large protects against fine tuning 25 2 Hm t él max Hm H +L max m max Naturalness Bounds D v = H2L mass HGeVL 15 5 1.2 1.4 1.6 1.8 2. l
A Natural SUSY Spectrum & - TeV strong dynamics 3 15 g t 1,2, b L 5 125 H, H ± s H h mass (GeV) flavor-degenerate squarks OK!
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
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
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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 é @GeVD 3 25 2 15 5 m Q3 êm u3 =.5, 1, 2 5-4 -2 2 4 X t êmé t D ê Ddegen 4 3 2 splitting the soft masses makes fine tuning worse 1.1.2.5 1. 2. 5.. m Q3 ê m u3
fine tuning in the MSSM to generalize we will adopt the definition: m h = max i @ log m 2 h @ 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
combo ATLAS CMS Local P-Value 1-2 -3-4 -5-6 -7 ATLAS Preliminary Observed Expected Ldt = 1.-4.9 fb s = 7 TeV 211 Data 1 115 12 125 13 135 14 145 15 M H [GeV] 2 3 4 5 Local p-value Best fit σ/σ SM 1-2 -3-4 CMS Preliminary, s = 7 TeV, Combined, L = 4.6-4.7 fb int Interpretation requires look-elsewhere effect correction 1 ±1σ from fit 1 115 12 125 13 135 14 145 15 155 16 2 Higgs boson mass (GeV/c ) 1σ 2σ 3σ 4σ 95% CL Limit on / SM 1 ATLAS Preliminary 211 Data Observed Expected Ldt = 1.-4.9 fb ±1 ± 2 s = 7 TeV 95% CL limit on σ/σ SM 1 CMS Preliminary, s = 7 TeV Combined, L = 4.6-4.7 fb int Observed Expected ± 1σ Expected ± 2σ CLs Limits 1 115 12 125 13 135 14 145 15 M H [GeV] 1 115 12 125 13 135 14 145 15 155 16 Higgs boson mass (GeV/c 2 )
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 1.4 1.2 1..8 m h = 126 GeV.6 x tt.4 x WW x.2 gg tanhbl= 2 x bb. 3 5 75 15 m H + HGeVL
precision electroweak.3.25.2.15 m H ± 35 t=5 4 3 2.5 tan β 68 % CL.15.1 m H ±=35 GeV m H ±=7 GeV T.1.5 7 2 95 % CL T st sb 1.5.5.1 m h (SM) t=1 35.1.5.5.1.15.2 S.5 1 1.5 2 2.5 3 3.5 4 4.5 5 tanβ
2 2 15 15 16 m c < m h ê2 25 m h D mh 126 5 ms HGeVL 15 2 5 m h 2 < - -8-6 -4-2 2 4 M s HGevL