G.F. Giudice. Theoretical Implications of the Higgs Discovery. DaMeSyFla Meeting Padua, 11 April 2013

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1 Theoretical Implications of the Higgs Discovery G.F. Giudice DaMeSyFla Meeting Padua, 11 April 2013 GFG, A. Strumia, arxiv: J. Elias-Miró, J.R. Espinosa, GFG, G. Isidori, A. Riotto, A. Strumia, arxiv: J. Elias-Miró, J.R. Espinosa, GFG, H.M. Lee, A. Strumia, arxiv: G. Degrassi, S. Di Vita, J. Elias-Miró, J.R. Espinosa, GFG, G. Isidori, A. Strumia, arxiv: D. Buttazzo, G. Degrassi. P.P. Giardino, GFG, F. Sala, A. Salvio, A. Strumia, in preparation

2 Higgs quartic coupling lhml M h = GeV 3s bands in M t = ± 0.66 GeV a s HM Z L = ± M t = GeV a s HM Z L = Extrapolate the SM up to very high energies é Higgs mass ê Top quark mass a s HM Z L = Strumia et al. RGE scale m in GeV M t = GeV V = λ ( 4 h 2 v 2 ) 2 V Quantum tunneling Thermal tunneling h

3 High precision required Full NNLO calculation in progress (3-loop RGE, 2-loop matching conditions) NNLO matching condition of λ: about 1 GeV

4 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:

5 200 Instability Top mass Mt in GeV Meta-stability L I =10 4 GeV Stability 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 Instability Meta-stability 1,2,3 s Higgs pole mass M h in GeV Stability

6 Precise determinations of M h and M t are necessary to establish the fate of our universe Top pole mass Mt in GeV Strumia et al Instability Meta-stability 1,2,3 s Stability condition: Higgs pole mass M h in GeV Stability M h =125.8±0.4 GeV

7 y t g s SM couplings g g m in TeV Strumia et al. 0.0 y b l RGE scale m in GeV λ and β λ nearly vanish at high energies?

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9 Higgs quartic is negative at the Planck mass s bands in M t Hgray dashedl a s Hred dottedl lhm Pl L 0.00 Strumia et al Higgs mass M h in GeV

10 The instability scale s bands in M t = ± 0.7 GeV a s HM Z L = ± M h = ± 0.5 GeV Mh = GeV Mh = GeV Instability scale in GeV Instability scale in GeV s bands in a s HM Z L = ± Strumia et al. Higgs mass M h in GeV If new physics avoids instability, it must enter before GeV Top mass M t in GeV

11 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 m h = 115 HlowerL, 120, 125, 130 GeV HupperL Meta-stable Non-perturbative Unstable Neutrino mass in ev

12 Why is the universe near-critical?

13 Strumia et al.

14 Explanations? 1. Matching conditions.

15 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?

16 3. Living dangerously. (multiverse but not criticality) Statistical pressure + (Meta)stability as an anthropic boundary

17 In terms of high-energy parameters: Planck-scale dominated MSSM Top Yukawa coupling ythm Pl L Instability Metastability No EW vacuum 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.

18 4. Statistics (multiverse but neither criticality nor anthropic) Toy model of the multiverse with N fields and p N vacua

19 y t g s SM couplings g g y b l m in TeV RGE scale m in GeV

20 An upper bound on the Higgs bilinear Phase diagram of the SM potential Higgs mass term mhm Pl L in GeV h = 0 unstable h ª m unstable h = 0 meta-stable h ª m meta stable h = 0 h ª m h ª Strumia et al Higgs coupling lhm Pl L

21 tan 50 tan 4 tan 2 tan 1 Split SUSY Higgs mass m h in GeV High Scale SUSY Experimentally favored 110 Strumia et al 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

22 Reheating temperature T RH in GeV Instability at finite temperature M t = ( _ 0.9) GeV α S = Strumia et al. Higgs mass m h in GeV

23 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?