Alessandro Strumia Talk at CERN, Updated to March 28, 2012 Legal Disclaimer

Higgs weights 125 GeV! Now what?

1) Is the Higgs standard? (http://arxiv.org/abs/1203.4254) 2) Higgs and SUSY (http://arxiv.org/abs/1108.6077) 3) WIll the SM vacuum decay? (http://arxiv.org/abs/1112.3022)

Alessandro Strumia Talk at CERN, updated to March 28, 2012 Legal disclaimer

I assume that the hint for a 125 GeV Higgs is a 125 GeV Higgs rather than a statistical ﬂuctuation or a superluminal cable

While this is believed to be a correct information, nobody makes any warranty, express or implied, or assumes any legal liability or responsibility for the accu- racy, completeness, or usefulness of the information. Reference herein to any speciﬁc experiment does not necessarily constitute or imply its endorsement, recommendation, or favoring.

By not abandoning the room you accept the above assumption.

Thank you Is the Higgs standard?

with P.P. Giardino, K. Kannike, M. Raidal Observables mh = 125 GeV is a lucky mass for LHC; several BR BR(h → b¯b) = 58%, BR(h → WW ∗) = 21.6%, BR(h → τ +τ −) = 6.4%, BR(h → ZZ∗) = 2.7%, BR(h → gg) = 8.5%, BR(h → γγ) = 0.22% and production mechanisms σ(pp → h) = (15.3 ± 2.6) pb, σ(pp → jjh) = 1.2 pb, σ(pp → W h) = 0.57 pb, σ(pp → Zh) = 0.32 pb, allow to disentangle Higgs couplings and test Higgs properties.

Naturalness suggests that light stops or other new physics aﬀect the Higgs Higgs data: CMS, ATLAS, CDF, D0

mh = 125 GeV 2.0 4 D0 D0 D0 - - - Atlas Atlas Atlas Atlas Atlas Atlas 1.5 CMS CMS CMS CMS CMS CMS CMS

3 CDF CDF CDF

1.0 2 rate rate

SM 0.5 SM T jj p Rate ΤΤ ΤΤ

1 ΓΓ ΓΓ ΓΓ ZZ ZZ Rate bbV bbV bbV ΓΓ WW WW WW ΓΓ

0.0 WWjj

-0.5 0

-1.0 110 115 120 125 130 135 140 -1 Higgs mass in GeV Fermiophobic searches

CMS looked for pp → jjγγ measuring, at mh ≈ 125 GeV: [0.033σ(pp → h) + σ(pp → jjh)] × BR(h → γγ) = SM × (3.3 ± 1.1)

ATLAS looked for pp → γγ with pT γγ > 40 GeV measuring [0.3σ(pp → h) + σ(pp → W h, Zh, jjh)] × BR(h → γγ) = SM × (3.3 ± 1.1)

For data I would like this format. So far we have to approximately deduce:

R95% µ ≈ R95% − R95% , σ = expected, observed expected 2 and get weights of production channels by asking or doing MC simulations. Non-standard BR for loop processes

mh = 125 GeV 6

68,95% CL 5

4 SM L

ΓΓ 3 ® h

H SM + top

BR partner 2

1 SM

0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 BRHh®ggLSM Best ﬁt χ2 ≈ 5.5 (13 dof) away from SM and at BR(h ↔ gg) BR(h → γγ) ≈ 0.3, ≈ 4, BR(h → gg)SM BR(h → γγ)SM Non standard best ﬁts

Atlas CMSCDF-D0CMS Atlas CMSCDF-D0Atlas CMS Atlas CMSCDF-D0Atlas CMS Atlas CMS

Χ2 = 20. SM 2 6 Χ = 8.8 best fit: free BRΓΓ, BRgg Χ2 = 9.0 best fit: free couplings Χ2 = 13. best fit: free positive couplings 2 4 Χ = 26. top-phobic Χ2 = 29. fermio-phobic rate SM

Rate 2 1 0

bbV bbV bbV WWjj WW WW WW ZZ ZZ ΓΓ ΓΓ ΓΓ ΓΓ ΓΓ jj ΤΤ ΤΤ pT

SM χ2 is good. BSM ﬁt is better. Maybe too good. Fermiophobia not much worse than SM Fits to Higgs couplings: dysfermiophilia

SM Latest fermiophobic analyses prefer enhanced h → γγ obtained for yt ≈ −yt .

mh = 125 GeV mh = 125 GeV 2 2

c 1 SM 1 SM SM t to fermions to 0 FP 0 FP 0t coupling coupling Higgs

Higgs -1 -1

68,95% CL 68,95% CL -2 -2 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 Higgs coupling to vectors a Higgs coupling to b and ΤSM Global ﬁt

2 4

1 SM 3 SM SM t Τ to to

0 2 coupling coupling Higgs Higgs -1 1 SM

68,95% CL -2 0 0.0 0.5 1.0 1.5 2.0 0 1 2 3 4 Higgs coupling to WSM Higgs coupling to bSM E.g. in the MSSM: 2  2 yt mt 1 1 (At − µ/ tan β) ghW ghZ = 1 +  + −  = = cos(α − β) MS 4 m2 m2 m2 m2 SM SM ˜t1 ˜t1 ˜t1 ˜t1 Fit to the Higgs invisible width

BRinv = 0 ± 25%depending on the ﬁt

4Σ all data 15

no ΓΓVBF 2 10 DΧ 3Σ free

BRgg,BRΓΓ 5 2Σ

1Σ 0 0.0 0.2 0.4 0.6 0.8 1.0 Invisible Higgs BR

Data can test and disfavor an invisible width because Γ(gg → h) = Γ(h → gg). Higgs and SUSY

with G. Giudice 125 GeV is in no man’s land

> SM is stable up to the Planck scale for mh∼ 130 GeV but can go down to 115 < MSSM with weak scale SUSY likes mh∼ 120 GeV but can go up to 130

...but quasi-maximal stop mixing is needed (or NMSSM...) ...but best ﬁt CMSSM regions are getting excluded (or LHC-phobic SUSY...) ...but the naturalness motivation for weak scale SUSY is mostly gone (light ˜t?)

CMSSM 10-42 20

4Σ 10-43 15

2 » direct detection cm 10-44 in 2

DM 10

DΧ 3Σ M Z -45 M 10 SI Σ bound 5 2Σ - 10 46 LHC 1Σ present 0 10-47 » 0 10 20 30 40 50 0 500 1000 1500 2000 10 Gluino mass in GeV 10 ∆gΜ

(global CMSSM ﬁt of all latest data but mh: we are no longer ﬁtting anything) Predicting mh(mSUSY, tan β)

Time to consider mSUSY MZ (SUSY... GUT... string) and consider:

• Split-SUSY (SUSY scalars at mSUSY and SUSY fermions around MZ). Gives good uniﬁcation and maybe makes theoretical sense.

• High-Scale-SUSY (all sparticles at mSUSY) aka “Super-Split-SUSY”.

Such a nice joke that its authors forgot to notice that there is one prediction 1 3 λ(m ) = g2(m ) + g2(m ) cos2 2β + loops SUSY 4 2 SUSY 5 1 SUSY λ(mh, mSUSY)

High-Scale Supersymmetry Split Supersymmetry

200 200 3 3 Non-pert Non-pert 10 urbative 10 urbative 180 180 0.5 0.5 2 2 1 1 GeV 160 GeV 160 in in

h 0.3 h 0.3 m m

0.2 mass mass 140 0.1 140 0.2 0.05 SplitSUSY Higgs Higgs High-Scale SUSY 0 Metastable

-0.05 120 Metastable 120

-0.1 Unstable Unstable 100 100 104 106 108 1010 1012 1014 1016 1018 104 106 108 1010 1012 1014 1016 1018 Supersymmetry breaking scale in GeV Supersymmetry breaking scale in GeV

Light green: with maximal stop mixing, which is not possible in Split-SUSY. Full NLO computation

The total result does not depend on the regularization scheme: One loop thresholds at the weak scale

+ One loop thresholds at the SUSY scale

2 loop Split-SUSY RGE between MZ and mSUSY 2 2 2 2 2 2 2 5 25˜g1d 5˜g1u 15˜g2d 15˜g2u 5gτ 7g1 99g2 2 β2(g ) = −12g + g g + + + + + + + 4g + t t t b 8 8 8 8 4 80 16 3 2 2 2 2 2 2 23˜g1d 3˜g1u 9˜g2d 9˜g2u 9g2 19g3 +g + + + − + − 3˜g ˜g1u˜g ˜g2u + 1 16 16 16 16 20 15 1d 2d 15˜g2 15˜g2 165˜g2 165˜g2 5 9 9˜g4 +g2 1d + 1u + 2d + 2u + 9g2 − ˜g2 ˜g2 − ˜g2 ˜g2 − 1d + 2 16 16 16 16 3 4 1d 1u 8 1d 2d 16 9 9˜g4 3 45˜g4 45˜g4 g4 9g4 − ˜g2 ˜g2 − 1u − ˜g2 ˜g2 − 2d − 2u − b − τ + 8 1u 2u 16 4 2d 2u 16 16 4 4 15g2 15g2 1303g4 15g4 284g4 3λ2 + 1 + 2 g2 + 1 − 2 − 3 + + 8 8 τ 600 4 3 2 9˜g2 9˜g2 27˜g2 27˜g2 11g2 9g2 393g2 225g2 +g3 − 1d − 1u − 2d − 2u − b − τ + 1 + 2 + 36g2 − 6λ t 8 8 8 8 4 4 80 16 3 pages and pages and pages of RGE in SplitSusy Uncertain uncertainties at high energy mSUSY MZ allows to get analytic expressions for everything, but one loop thresholds at the SUSY scale depend on unknown heavy sparticle masses: 9 3 3 cos2 2β (4π)2δλ(m ) = − g4 − g2g2 − ( − )g4 + SUSY 100 1 10 1 2 4 6 2 2 2 2 1 2 2 mQ +3gt [gt + (5g2 − g1) cos 2β] ln 2 + ··· + ··· 10 mSUSY In non-minimal SUSY models one can even have tree level corrections, positive 2 or negative. E.g. in the NMSSM λN NHuHd + MN /2 (B − 2A)M + m2 − A2 δλ = λ2 sin2 2β N 2(M2 + m2 + BM) Or neutrino Yukawa couplings in see-saw models.

For example, the theory of everything could be N = 1 SUSY with E6 uniﬁcation broken at the Planck scale by three fundamentals 27i. The Higgs is one slepton that remains light due to anthropic selection. The Yukawa couplings come from:

W = λijk27i27j27k Eﬀect of SM uncertainties

Predicted range for the Higgs mass

160 tanΒ = 50 Split SUSY tanΒ = 4 tanΒ = 2 150 tanΒ = 1 GeV

in 140 h m

High-Scale SUSY mass 130 Experimentally favored Higgs 120

110 104 106 108 1010 1012 1014 1016 1018 Supersymmetry breaking scale in GeV

Thickness is ±1σ on α3 and on Mt. SUSY thresholds give more uncertainties. “Central values” for mSUSY and tan β

High-scale Supersymmetry Split Supersymmetry

50 125 135 140 50 145 150 155 40 130 40 140 30 30 135 130 20 20 115 120125 10 10 110

Β 8 Β 8 tan 6 tan 6 5 5 4 4 3 3

2 2

1 110115 120 1 105 104 106 108 1010 1012 1014 1016 1018 104 106 108 1010 1012 1014 1016 1018 Supersymmetry breaking scale in GeV Supersymmetry breaking scale in GeV

(Assuming degenerate heavy spectrum at mSUSY) (Split-SUSY assumes M1 = mt, M2 = µ, uniﬁed gauginos) Implications for mSUSY and tan β

High-Scale supersymmetry Split supersymmetry

30 30

20 20 mh = 124 GeV mh = 124 GeV 68, 95, 99% CL 68, 95, 99% CL

10 10 8 8

Β 6 Β 6

tan 5 tan 5 4 4 3 3

2 2

1 1 104 106 108 1010 1012 1014 1016 1018 103 104 105 106 107 108 109 1010 Supersymmetry breaking scale in GeV Supersymmetry breaking scale in GeV mSUSY ≈ MZ and maximal stop mixing and large tan β? 2 mSUSY ≈ (4π) MZ and moderate tan β? Maybe M2 ≈ 3 TeV and M3 =? mSUSY ≈ MPl and tan β = 1? Disfavored, unless extra couplings come in Vacuum meta-stability

with J.E. Mir´o,J.R. Espinosa, G. Giudice, G. Isidori, A. Riotto RGE running makes λ < 0

mh = 124 GeV mh = 126 GeV 0.06 0.06

mt = 173.2 GeV mt = 173.2 GeV 0.04 0.04 Α3HMZL = 0.1184 Α3HMZL = 0.1184 L L Μ Μ H H Λ 0.02 Λ 0.02

mt = 171.4 GeV coupling 0.00 mt = 171.4 GeV coupling 0.00 Α3HMZL = 0.1198 Α3HMZL = 0.1198 quartic quartic

-0.02 -0.02 Α3HMZL = 0.117 Α3HMZL = 0.117 Higgs Higgs mt = 175. GeV -0.04 mt = 175. GeV -0.04

-0.06 -0.06 102 104 106 108 1010 1012 1014 1016 1018 1020 102 104 106 108 1010 1012 1014 1016 1018 1020 RGE scale Μ in GeV RGE scale Μ in GeV

CAUTION: ±3 GeV theory uncertainty. Instability, meta-stability and stability

180 6 7 8 9 10 10 10 10 10 10 14 1016 InstabilityInstability Meta-stability 10 GeV

in 175 t m mass

top 170 Stability Pole 1012 165 110 115 120 125 130 135 140

Higgs mass mh in GeV

M − 173.2 GeV α (M ) − 0.1184! m > 130 GeV+1.8 GeV t −0.5 GeV 3 Z ±3 GeV h 0.9 GeV 0.0007

τ ∼ 10100 yr Tree level stabilization

Add a singlet S with a vev (possibly the axion):

† 22 † 22 † 2 † 2 V = λH H H − v + λS S S − w + 2λHS H H − v S S − w Integrating out S at tree level gives a threshold correction that stabilizes V : 2 λHS λlow energy = λH − λS

mh = 125 GeV, Mt = 173.2 GeV 0.06 SM SM plus a singlet

0.04 MS LI

Λ coupling 0.02 quartic

ΛH Higgs 0.00

Instability

for ΛHS > 0

-0.02 104 106 108 1010 1012 1014 1016 1018 RGE scale Μ in GeV (with J. Elias-Miro, J.R. Espinosa, G. Giudice, H.M. Lee) The fate of the Universe

Does mh ≈ 126 GeV correspond to λ(MPl) = 0 within the SM? (This would be the main message bla bla quantum gravity bla bla)

It is so close that so far the answer is BOH NNLO computation needed to reduce the theory uncertainty. The answer is... 4 2 2 6 2 2 yt g3v 2 yt v δm (¯µ = mt)|NNLO = 0 − 2(6 + π ) + O(λ, g1, g2) h (4π)4 (4π)4 which means... NO [with Degrassi, Espinoza, Isidori, Giudice, to appear. Please don’t scoop us] Conclusions

• SM Higgs gives a good fit to data. Reduced gg → h and enhanced h → γγ improves the fit. Too good: is this just over-fitting fluctuations?

• SUSY: at the weak scale, or one loop above, or much above.

• mh ≈ 125 GeV corresponds to λ = 0 at the Planck scale? Almost, but NO. λ gets slightly negative and the SM vacuum is meta-stable.

Implications for European Strategy for Particle Physics: The Higgs could be the last particle. Carpe diem.