Theoretical Implications of the Higgs Discovery G.F. Giudice DaMeSyFla Meeting Padua, 11 April 2013 GFG, A. Strumia, arxiv:1108.6077 J. Elias-Miró, J.R. Espinosa, GFG, G. Isidori, A. Riotto, A. Strumia, arxiv: 1112.3022 J. Elias-Miró, J.R. Espinosa, GFG, H.M. Lee, A. Strumia, arxiv:1203.0237 G. Degrassi, S. Di Vita, J. Elias-Miró, J.R. Espinosa, GFG, G. Isidori, A. Strumia, arxiv:1205.6497 D. Buttazzo, G. Degrassi. P.P. Giardino, GFG, F. Sala, A. Salvio, A. Strumia, in preparation
Higgs quartic coupling lhml 0.10 0.08 0.06 0.04 0.02 0.00 M h = 125.66 GeV 3s bands in M t = 173.36 ± 0.66 GeV a s HM Z L = 0.1184 ± 0.0007 M t = 171.4 GeV a s HM Z L = 0.1205 Extrapolate the SM up to very high energies é Higgs mass ê Top quark mass -0.02 a s HM Z L = 0.1163-0.04 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 Strumia et al. RGE scale m in GeV M t = 175.3 GeV V = λ ( 4 h 2 v 2 ) 2 V Quantum tunneling Thermal tunneling h
High precision required Full NNLO calculation in progress (3-loop RGE, 2-loop matching conditions) NNLO matching condition of λ: about 1 GeV
Tunneling at T=0 Probability of nucleating a true-vacuum bubble V Dominated at late times. Action of the bounce of size Λ B : h At the classical level, λh 4 is scale-invariant. RG breaks scale invariance and fixes Λ B as the scale where λ is minimized:
200 Instability 10 4 5 6 810 14 Top mass Mt in GeV 150 100 50 0 Meta-stability 6 7 8 5 L I =10 4 GeV 9 10 12 Stability 19 16 14 0 50 100 150 200 Higgs mass M h in GeV We seem to live near a critical condition Strumia et al. Non-perturbativity Top pole mass Mt in GeV 180 178 176 174 172 170 10 7 10 8 10 9 Instability 10 18 Meta-stability 1,2,3 s 10 19 10 16 10 10 10 11 10 12 10 13 10 14 168 120 122 124 126 128 130 132 Higgs pole mass M h in GeV Stability
Precise determinations of M h and M t are necessary to establish the fate of our universe Top pole mass Mt in GeV 180 178 176 174 172 170 Strumia et al. 10 7 10 8 10 9 Instability 10 18 Meta-stability 1,2,3 s 10 19 10 16 10 10 10 11 10 12 10 13 10 14 168 120 122 124 126 128 130 132 Stability condition: Higgs pole mass M h in GeV Stability M h =125.8±0.4 GeV
1.0 0.8 y t g s SM couplings 0.6 0.4 g g 1 0.2 m in TeV Strumia et al. 0.0 y b l 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 RGE scale m in GeV λ and β λ nearly vanish at high energies?
Higgs quartic is negative at the Planck mass 0.04 0.02 3s bands in M t Hgray dashedl a s Hred dottedl lhm Pl L 0.00 Strumia et al. -0.02-0.04 115 120 125 130 135 140 Higgs mass M h in GeV
The instability scale 10 18 10 16 1s bands in M t = 173.1 ± 0.7 GeV a s HM Z L = 0.1184 ± 0.0007 M h = 125.5 ± 0.5 GeV 10 18 10 16 Mh = 124.5 GeV Mh = 126.5 GeV Instability scale in GeV 10 14 10 12 Instability scale in GeV 10 14 10 12 10 10 10 10 1s bands in a s HM Z L = 0.1184 ± 0.0007 10 8 115 120 125 130 135 Strumia et al. Higgs mass M h in GeV 10 8 170 171 172 173 174 175 176 If new physics avoids instability, it must enter before 10 10-13 GeV Top mass M t in GeV
See-saw neutrino destabilize potential. Useful bound? m ν = y 2 ν v 2 M R Strumia et al. Right-handed n mass in GeV 10 15 10 14 10 13 m h = 115 HlowerL, 120, 125, 130 GeV HupperL Meta-stable Non-perturbative Unstable 10 12 0.06 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1 Neutrino mass in ev
Why is the universe near-critical?
Strumia et al.
Explanations? 1. Matching conditions.
2. Criticality as an attractor (multiverse but not anthropic arguments) V ( H) = m 2 H H 2 + λ H 4 SM Broken EW Unbroken EW 0 m H 2 Why is nature so close to the critical line? Symmetry? Supersymmetry: m H 2 = 0, λ = g 2 Goldstone boson: m H 2 = λ = 0 Do we live near a critical condition because of dynamics or because of statistics in the multiverse?
3. Living dangerously. (multiverse but not criticality) Statistical pressure + (Meta)stability as an anthropic boundary
In terms of high-energy parameters: 0.8 18 17 Planck-scale dominated MSSM Top Yukawa coupling ythm Pl L 0.6 0.4 0.2 0.0 16 15 14 13 12 11 10 9 8 7 6 5 10 4 14 15 18 16 13 12 11 10 96 78 5 4 Instability Metastability 10 5 4 69 16 13 15 10 13 14 18 12 17 10 78 14 14 15 16 17 8 4 5 7 17 18 16 15 14 10 11 96 5 4 10 11 12 13 10 No EW vacuum 5 4 6 105 4 6 8 7 9 10 11 12 13 14 15 16 7 10 76 5 8 79 9 10 911 11 4 1517 6 78 86 5 4 10 11 9 17 1418 16 13 12 10 18 17 16 15-0.06-0.04-0.02 0.00 0.02 0.04 0.06 Higgs coupling lhm Pl L Stability λ(m P ) is the min y t (M P ) is the min g(m P ) is the max compatible with stability Strumia et al.
4. Statistics (multiverse but neither criticality nor anthropic) Toy model of the multiverse with N fields and p N vacua
1.0 0.8 y t g s SM couplings 0.6 0.4 g g 1 0.2 0.0 y b l m in TeV 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 RGE scale m in GeV
An upper bound on the Higgs bilinear 10 15 Phase diagram of the SM potential Higgs mass term mhm Pl L in GeV 10 10 10 5 0-10 5 h = 0 unstable h ª m unstable h = 0 meta-stable h ª m meta stable h = 0 h ª m -10 10 h ª Strumia et al. -10 15-0.10-0.05 0.00 0.05 0.10 Higgs coupling lhm Pl L
160 150 tan 50 tan 4 tan 2 tan 1 Split SUSY Higgs mass m h in GeV 140 130 120 High Scale SUSY Experimentally favored 110 Strumia et al. 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 Supersymmetry breaking scale in GeV m h 126 GeV rules out grossly split susy, but mildly split susy is OK Anomaly mediation with M g = O(TeV), m 4πM g = O(10 TeV) Susy broken at Planck mass is ruled out
Reheating temperature T RH in GeV Instability at finite temperature 10 16 10 14 10 12 10 10 10 8 10 6 M t = (173.2 + _ 0.9) GeV α S = 0.1184 115 120 125 Strumia et al. Higgs mass m h in GeV
CONCLUSIONS Higgs near-criticality is the most important lesson we have learned from the LHC so far Why is the Higgs mass near-critical? Is this a good question? Matching conditions? Multiverse? Criticality as an attractor? Living dangerously? Statistics?