Standard Model vacuum stability with a 125 GeV Higgs boson

Transcription

1 Standard Model vacuum stability with a 5 GeV Higgs boson Stefano Di Vita DESY Hamburg) Institut für Kern- und Teilchenphysik, TU Dresden February 4, 06

2 For this talk I assume that the diphoton excess recently reported by the ATLAS and CMS collaboration is just a statistical fluctuation.

3 In this talk I will explain where this plot comes from and what it tells us Pole top mass Mt in GeV Instability Meta stability 75,,3 Σ 70 0 Stability [Degrassi, Elias-Mirò, Espinosa, Giudice, Isidori, Strumia, DV ] [Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia 3] h

4 Outline Status of the Standard Model after the Higgs boson discovery Standard Model couplings: matching to observables and running 3 Standard Model vacuum stability at NNLO

5 Outline Status of the Standard Model after the Higgs boson discovery Standard Model couplings: matching to observables and running 3 Standard Model vacuum stability at NNLO

6 Observation of the Higgs boson at the LHC Run I Events / GeV Events - Bkg ATLAS - s=7 TeV, Ldt=4.8fb - s=8 TeV, Ldt=5.9fb Data Sig+Bkg Fit m =6.5 GeV) H Bkg 4th order polynomial) H γγ m γγ [GeV] S/S+B) weighted events / GeV CMS H γγ +0.6 µ = m H = 4.70 ± 0.34 GeV fb 8 TeV) + 5. fb S/S+B) weighted sum Data B component subtracted 7 TeV) S+B fits weighted sum) B component m γγ GeV) ±σ ±σ Most recent ATLAS+CMS combination δm H /M H 0 3 [PRL 05] M H = 5.09 ±0.stat.) ± 0.syst.) GeV ±0.4 S. Di Vita DESY) SM vacuum stability with a 5 GeV H / 33

7 So far, the observed H looks pretty much SM-like ATLAS and CMS combined, s = 7 and 8 TeV [ATLAS-CONF , Sep 5] σgg H ZZ) σ VBF /σ ggf σ WH /σ ggf ATLAS and CMS Preliminary LHC Run ATLAS CMS ATLAS+CMS ± σ ± σ Th. uncert. κ gz λ Zg ATLAS and CMS Preliminary LHC Run ATLAS CMS ATLAS+CMS ± σ ± σ σ ZH /σ ggf λ tg σ tth /σ ggf λ WZ WW ZZ BR /BR λ γ Z γγ ZZ BR /BR ττ ZZ BR /BR bb ZZ BR /BR Parameter value norm. to SM prediction H production and decay norm. to SM λ τz λ bz Parameter value Fit of Higgs couplings modifiers in the κ-framework [see LHCXSWG 3] S. Di Vita DESY) SM vacuum stability with a 5 GeV H / 33

8 Many BSM searches yeld only lower limits... anyone said γγ excess? ATLAS Exotics Searches* - 95% CL Exclusion Status: July 05 ATLAS Preliminary L dt = ) fb s = 7, 8 TeV Model l, γ Jets E miss L dt[fb ] T Limit Reference LQ DM CI Gauge bosons Extra dimensions ADD GKK + g/q j Yes 0.3 MD 5.5 TeV n = ADD non-resonant ll e, µ 0.3 MS 4.7 TeV n = 3 HLZ ADD QBH lq e, µ j 0.3 Mth 5. TeV n = ADD QBH j 0.3 Mth 5.8 TeV n = ADD BH high Ntrk µ SS) 0.3 Mth 4.7 TeV n = 6, MD = 3 TeV, non-rot BH ADD BH high pt e, µ j 0.3 Mth 5.8 TeV n = 6, MD = 3 TeV, non-rot BH ADD BH high multijet j 0.3 Mth 5.8 TeV n = 6, MD = 3 TeV, non-rot BH RS GKK ll e, µ 0.3 GKK mass.68 TeV k/mpl = RS GKK γγ γ 0.3 GKK mass.66 TeV k/mpl = Bulk RS GKK ZZ qqll e, µ j / J 0.3 GKK mass 740 GeV k/mpl = Bulk RS GKK WW qqlν e, µ j / J Yes 0.3 W mass 760 GeV k/mpl = Bulk RS GKK HH b bb b 4 b 9.5 GKK mass GeV k/mpl = Bulk RS gkk tt e, µ b, J/j Yes 0.3 gkk mass. TeV BR = UED / RPP e, µ SS) b, j Yes 0.3 KK mass 960 GeV SSM Z ll e, µ 0.3 Z mass.9 TeV SSM Z ττ τ 9.5 Z mass.0 TeV SSM W lν e, µ Yes 0.3 W mass 3.4 TeV EGM W WZ lν l l 3 e, µ Yes 0.3 W mass.5 TeV EGM W WZ qqll e, µ j / J 0.3 W mass.59 TeV EGM W WZ qqqq J 0.3 W mass.3-.5 TeV HVT W WH lνbb e, µ b Yes 0.3 W mass.47 TeV gv = LRSM W tb e, µ b, 0- j R Yes 0.3 W mass.9 TeV LRSM W tb 0 e, µ b, J R 0.3 W mass.76 TeV CI qqqq j 7.3 Λ.0 TeV ηll = CI qqll e, µ 0.3 Λ.6 TeV ηll = CI uutt e, µ SS) b, j Yes 0.3 Λ 4.3 TeV CLL = EFT D5 operator Dirac) 0 e,µ j Yes 0.3 M 974 GeV at 90% CL for mχ) < 00 GeV EFT D9 operator Dirac) 0 e,µ J, j Yes 0.3 M.4 TeV at 90% CL for mχ) < 00 GeV Scalar LQ st gen e j 0.3 LQ mass.05 TeV β = Preliminary Scalar LQ nd gen µ j 0.3 LQ mass.0 TeV β = Preliminary Scalar LQ 3 rd gen e, µ b, 3 j Yes 0.3 LQ mass 640 GeV β = 0 Preliminary Heavy quarks VLQ TT Ht + X e, µ b, 3 j Yes 0.3 T mass 855 GeV T in T,B) doublet VLQ YY Wb + X e, µ b, 3 j Yes 0.3 Y mass 770 GeV Y in B,Y) doublet VLQ BB Hb + X e, µ b, 3 j Yes 0.3 B mass 735 GeV isospin singlet VLQ BB Zb + X / 3 e, µ / b 0.3 B mass 755 GeV B in B,Y) doublet T5/3 Wt e, µ b, 5 j Yes 0.3 T5/3 mass 840 GeV Excited fermions Other Excited quark q qγ γ j 0.3 q mass 3.5 TeV only u and d, Λ = mq ) Excited quark q qg j 0.3 q mass 4.09 TeV only u and d, Λ = mq ) Excited quark b Wt or e, µ b, j or j Yes 4.7 b mass 870 GeV left-handed coupling Excited lepton l lγ e, µ, γ 3.0 l mass. TeV Λ =. TeV Excited lepton ν lw, νz 3 e, µ, τ 0.3 ν mass.6 TeV Λ =.6 TeV 4.9 LSTC at W γ e, µ, γ Yes 0.3 at mass 960 GeV LRSM Majorana ν e,µ j 0.3 N 0 mass.0 TeV mwr ) =.4 TeV, no mixing Higgs triplet H ±± ll e, µ SS) 0.3 H ±± mass 55 GeV DY production, BRH ±± L ll)= Higgs triplet H ±± lτ 3 e, µ, τ 0.3 H ±± mass 400 GeV DY production, BRH ±± lτ)= L 4.9 Monotop non-res prod) e, µ b Yes 0.3 spin- invisible particle mass 657 GeV anon res = Multi-charged particles 0.3 multi-charged particle mass 785 GeV DY production, q = 5e Magnetic monopoles 7.0 monopole mass.34 TeV DY production, g = gd, spin / Preliminary s = 7 TeV s = 8 TeV 0 0 *Only a selection of the available mass limits on new states or phenomena is shown. Mass scale [TeV] S. Di Vita DESY) SM vacuum stability with a 5 GeV H 3 / 33

9 SM provides with an excellent fit to precision data Full EW -loop Z-partial widths at -loop M W Γ W M Z Γ Z 0 σ had 0 Rlep 0,l A FB A l LEP) A l SLD) lept sin Θ eff Q ) FB A c A b 0,c A FB 0,b A FB 0 Rc 0 Rb m t α s M ) Z 5) α had M ) Z MH ) O fit - O meas ) / σ meas [Gfitter 4] ) 0. 0.) 0. 0.) ) ) ) ) 0. 0.) ) ) ) ) ).5.5) ) ) ).7 0.9) ) [GeV] M W % and 95% CL contours M W M W M H fit w/o M W fit w/o M W, m t direct M W world comb. ± σ = ± 0.05 GeV = 50 GeV M H and m t measurements and M H measurements and m t measurements = 5.4 GeV M H = 300 GeV world comb. ± σ m t = GeV σ = 0.76 GeV σ = theo M H = 600 GeV [Gfitter 4] m t GeV m t [GeV] T all M W asymmetries ΓZ U= S [Ciuchini et al.4] input: αm Z ), α 5) had, M t,c,b), M H, M Z check consistency of fit with M t,w S,T,U parametrize universal contrib s of heavy NP in EFT S. Di Vita DESY) SM vacuum stability with a 5 GeV H 4 / 33

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11 Pre-Higgs era: EW fit and direct searches at LEP χ July 0 m Limit = 6 GeV Theory uncertainty α 5) had = ± ± incl. low Q data - lnq) LEP Excluded m H [GeV] Observed Expected for background Expected for signal plus background m H GeV/c ) LEP/TEV EW WG Summer 0 LEP combined 003 Q = L s+b L b S. Di Vita DESY) SM vacuum stability with a 5 GeV H 5 / 33

12 Pre-Higgs era: include direct searches at Tevatron 09 M H =5 GeV not a real surprise! pdf mh dir&ind EWfit LEP 68 Prob.Upper Lim. 95 Prob.Upper Lim. pdf mh dir&ind EWfit LEP Tevatron 68 Prob.Upper Lim. 95 Prob.Upper Lim m H GeV EW fit + LEP m H GeV EW fit + LEP + Tevatron pdf M H dir. & indir.) QM H )e χ M H )/ M H flat prior in logm H )) S. Di Vita DESY) SM vacuum stability with a 5 GeV H 6 / 33

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14 Standard Model: quite a few shortcomings [Planck 5] [Dell Oro et al.6] Describes 4.9% of universe Not enough CP for baryogenesis Neutrino oscillations m ν Gravity? Inflation? S. Di Vita DESY) SM vacuum stability with a 5 GeV H 7 / 33

15 Fermi theory: when a theory cries for a UV completion A phenomenologically successful theory, but it cried for New Physics! ν µ ν µ µ e = µ ν e W e ν e non-renormalizable L G µ ψψ ψψ Fermi theory = effective field theory EFT) / EFT cutoff Λ G µ predicts e.g. σν µ e ν e µ) = Gµs π optical thm: σ σ tot = s Im A fw π s S-wave) loss of perturbative unitarity for s Gµ S. Di Vita DESY) SM vacuum stability with a 5 GeV H 8 / 33

16 SM: when a theory doesn t cry for a UV completion experimental success QED, QCD, LEP, Tevatron LHC, EW fit... no hints for New Physics at LHC ignore naturalness... no indication of EFT cutoff from precision measurements EWPO, flavor tuned extensions could account for m ν, DM, DE and inflation CC, axion DM, NMSM [Davoudiasl, Kitano, Li, Murayama 05] νmsm [Asaka, Shaposhnikov 05], non-susy SO0) GUT [Altarelli, Meloni 3], Higgs inflation w/ non-min. grav. couplings [Bezrukov, Shaposhnikov 08], [Germani, Kehagias 05]... could L true = L SM + d i >4 c i M 4 d i P More precisely O i? M P = G / N. 0 9 GeV) Is there any theoretical-consistency breakdown of L SM, implying the presence of new physics at Λ M P to save the day? can we reliably compute at large scales? perturbativity is it a consistent QFT? anomaly free, perturbatively unitary, non-trivial, stable vacuum S. Di Vita DESY) SM vacuum stability with a 5 GeV H 9 / 33

17 SM: when a theory doesn t cry for a UV completion experimental success QED, QCD, LEP, Tevatron LHC, EW fit... no hints for New Physics at LHC ignore naturalness... no indication of EFT cutoff from precision measurements EWPO, flavor tuned extensions could account for m ν, DM, DE and inflation CC, axion DM, NMSM [Davoudiasl, Kitano, Li, Murayama 05] νmsm [Asaka, Shaposhnikov 05], non-susy SO0) GUT [Altarelli, Meloni 3], Higgs inflation w/ non-min. grav. couplings [Bezrukov, Shaposhnikov 08], [Germani, Kehagias 05]... could L true = L SM + d i >4 c i M 4 d i P An important point O i? M P = G / N theoretical-inconsistency Λ < M P theoretical- inconsistency Λ M P can we reliably compute at large scales? perturbativity. 0 9 GeV) is it a consistent QFT? anomaly free, perturbatively unitary, non-trivial, stable vacuum S. Di Vita DESY) SM vacuum stability with a 5 GeV H 9 / 33

18 Outline Status of the Standard Model after the Higgs boson discovery Standard Model couplings: matching to observables and running 3 Standard Model vacuum stability at NNLO

19 Renormalization group running of the SM couplings ) couplings acquire dep. on the scale at which they are probed in a mass-independent renormalization scheme like MS, they get a dependence on the t Hooft mass g µ ɛ g) the beta-functions, governing their behaviour, are computed order by order in perturbation theory e.g. QCD beta-function β 0 = C A 4n f T R π µ α [ ] S µ = α S β 0 + α S β + αs β + αs 3 β = 33 n f π βα S ) asy. free n f < 6.5 non-perturbative Λ µe b0α S µ) [Gross,Wilczek 73; Politzer 73] S. Di Vita DESY) SM vacuum stability with a 5 GeV H 0 / 33

20 Renormalization group running of the SM couplings ) loop QCD [Gross, Wilczek 73; Politzer 73] -loop SM [Fischler, Hill 8; Jones 8; Fischler, Oliensis 8; Machacek, Vaughn 83, 84, 85; Jack, Osborn 84, 85; Ford, Jack, Jones 9; Luo, Xiao 03] 3-loop Gauge [Mihaila, Salomon, Steinhauser ; Bednyakov, Pikelner, Velizhanin ] Yukawa [Chetyrkin, Zoller ; Bednyakov, Pikelner, Velizhanin 3] Higgs-quartic [Chetyrkin, Zoller, 3; Bednyakov, Pikelner, Velizhanin 3] 4-loop QCD [van Ritbergen, Vermaseren, Larin 97; Czakon 05; + y t λ Zoller 5] Higgs-quartic [leading-qcd Martin 5] 7g g g + 9g4 6 3y b 4 3y t 4 y τ 4 +λ m 9g 0 9g y t yb y τ 4g 4 g 0 4 9g4 g g ) g g 3 5 y b 7y t 0 3y τ 9g ) g 6 +g 3 3y b 3y t y τ 7g3 4 g3 4 g 0 + 9g 6g3 y b y t 9g 0 9g +6yb +6y t +y τ +λ 4 +3y b +3y t +y τ +6λ ) g 4 9g 4 8g3 + 9y b + 3y t +y τ 7g 0 9g 4 8g3 + 3y b + 9y t +y τ 9g 4 9g 4 +3yb +3y t + 5y τ 9g 0 + 9g 4 3yb 3y t y τ ) ) ) ) ) m 67g g g 45g4 3 +y b 34g g g g4 g + 305g6 54g λ 5 +54g 7y b 7y t 4y τ 56λ y b g g g + 8 +y b yt 87g g g + 8 +y t yτ 37g g g 3g4 4 +6λ +yb 5g 93g g g + 7g4 3 6λ +yb ) +yt 7g g 8 +0g 3 y b 7y t 37g g 6 +36g 3 y b 9y τ 4 λ 393g g 6 +36g 3 y b 4 y t 9y τ 4 λ g 8 +0g 3 7 7y τ 4 4 ) 5g 8 45g 8 0g 3 + 7y b ) ) ) ) +λyτ 5g 4 + 5g 4 y τ )+y τ 4 ) 5yτ 6g 5 36g +λ 5 +36g 36y b 36y t y τ )+y 30λ τ +yt 9g g 6 +4g 3 y b 4 y t 4 + 5y τ +yt 7g g 8 +0g 3 + 3y b 7y t 4 7y τ ) +yt ) 4 )) )) +yb 7g g 6 +4g 3 y b 4 + 5y τ 4 7g 8 45g 8 0g 3 3y b + 7y t 5g ) )) +yτ 537g g 6 3y τ λ ) )) yτ 5g 8 + 5g 8 9y τ 4 )) 8 + 5g 8 9y τ 4 ) g g g g g 3 g + 789g g g g 3 +λ 7g g 0 9λ +y 5 t ) g g g g 5 g 3 g g4 +8g g g 3 +λ 3g 0 + 3g 3λ +yt g3 4 53g g g g 3 g + 09g4 + 65g g g 3 +y t )) 87g g 3 9g y t )) 593g 60 79g 3 7g y t )) 0g 40 93g 8 40g 3 +5y t.508g 8.543g g6 +6.5g4 g λ g g +873y t λ)+λ y t g g g y t ) 0 y t g3 0 m 8.378g g 4.9g 3)g λy t g 38.59g g y t )) ) )) 9 +λ 9g +45g 36λ)+λ 089g g g 7g4 +yt 4 437g 593g 57g y t +98λ g 6+.93g g4 +4.9g 3 g y t g4 +.07λg4 +.8g4 g g4 g g4 y t 78.48g4 3 y t + 35 λ yt 7.57g g 3 y t ) 0 coupled first order ODE system for g S, g, g, λ, y t, y b,... need initial condition for each coupling at a given scale µ 0 S. Di Vita DESY) SM vacuum stability with a 5 GeV H / 33

21 m t µ) matching condition at -loop in QCD warmup i = p m t,0 + =iσ l p) UV divergent i +... = p m t,0 + Σ p) p M pole t i Z p Mpole t + less singular MS renormalization scheme: m t,0 = m t µ) + Re Σ l p) div OS renormalization scheme: m t,0 = M pole t + Re Σ l p = Mpole t ) M pole t -loop m t µ) = Σ l p = Mpole t ) fin µ-dependent S. Di Vita DESY) SM vacuum stability with a 5 GeV H / 33

22 Matching at the EW scale in the SM: state-of-the-art goal: G µ, M H, M t, M W, M Z,... λµ), y t µ), gµ), g µ)... tree-level relations like λ = Gµ M H are modified by quantum effects effects as important if not more!) as running effects! Matching running parameters requires multi-loop computations a physical OS ) renormalization scheme finite parts are the goal! many technicalities Two-loop matching conditions at the weak scale reduction of th. err, especially λ) -loop -loop 3-loop g, full? y t full Oαα s ) Oαs) 3 λ full Oαα s, α ) Oαα s) [Bezrukov, Kalmykov, Kniehl, Shaposhnikov ; Degrassi, Elias-Mirò, Espinosa, Giudice, Isidori, Strumia, DV ] Oαα s, α ) [Degrassi, Elias-Mirò, Espinosa, Giudice, Isidori, Strumia, DV ] S. Di Vita DESY) SM vacuum stability with a 5 GeV H 3 / 33

23 Matching at the EW scale in the SM: state-of-the-art goal: G µ, M H, M t, M W, M Z,... λµ), y t µ), gµ), g µ)... tree-level relations like λ = Gµ M H are modified by quantum effects effects as important if not more!) as running effects! Matching running parameters requires multi-loop computations a physical OS ) renormalization scheme finite parts are the goal! many technicalities Two-loop matching conditions at the weak scale reduction of th. err, especially λ) -loop -loop 3-loop g, full full y t full full Oα 3 s) λ full full [Buttazzo, Degrassi, Giardino, Giudice, Sala, Salvio, Strumia 3] [Kniehl, Pikelner, Veretin 5] S. Di Vita DESY) SM vacuum stability with a 5 GeV H 3 / 33

24 Matching at the EW scale in the SM: state-of-the-art goal: G µ, M H, M t, M W, M Z,... λµ), y t µ), gµ), g µ)... tree-level relations like λ = Gµ M H are modified by quantum effects effects as important if not more!) as running effects! Matching running parameters requires multi-loop computations a physical OS ) renormalization scheme finite parts are the goal! many technicalities Two-loop matching conditions at the weak scale reduction of th. err, especially λ) -loop -loop 3-loop g, full full y t full full Oαs) 3 λ full full Oααs, αα s α t ) M H =0 [Martin 4] S. Di Vita DESY) SM vacuum stability with a 5 GeV H 3 / 33

25 λµ) matching condition at two-loops δλ ) = G µ M H r ) 0 r ) r ) 0 + M H 0 + M H Re l H H p = M h Re l H H p = M h + v OS + 3 v OS l H l H fin To Master Integrals Reduze [Studerus 0; + von Manteuffel ] or Tarcer [Mertig, Scharf 98] MIs for -loop self-energy gauge-less limit g, g 0) [Degrassi et al.] analytic combination of asymptotic expansions and exact results) full SM [Buttazzo et al.3] numerical w/ TSIL [Martin, Robertson 04] S. Di Vita DESY) SM vacuum stability with a 5 GeV H 4 / 33

26 λµ) matching condition at two-loops δλ ) = G µ M H r ) 0 r ) 0 + ) r 0 MH M H Re l H H p = M h Re l H H p = M h + v OS + 3 v OS l l H H fin G µ v OS ) = v 0 [ + V W A WW M W 0 + v 0 B W + E + r 0 AWW M W ) A WW V W M W ] S. Di Vita DESY) SM vacuum stability with a 5 GeV H 4 / 33

27 λµ) matching condition at two-loops δλ ) = G µ M H r ) 0 r ) 0 + ) r 0 MH M H Re l H H p = M h Re l H H p = M h + v OS + 3 v OS l l H H fin [Buttazzo et al. 3] λµ = M t ) = M H GeV 5.5) M t GeV 73.34) ± th S. Di Vita DESY) SM vacuum stability with a 5 GeV H 4 / 33

28 Renormalization group running of the SM couplings 3) yt g 3 SM couplings y b g g m in TeV Λ [Buttazzo et al.3] 3-loop running + 4-loop α s -loop matching full SM SM stays perturbative λ runs fast, then slows down S. Di Vita DESY) SM vacuum stability with a 5 GeV H 5 / 33

29 Outline Status of the Standard Model after the Higgs boson discovery Standard Model couplings: matching to observables and running 3 Standard Model vacuum stability at NNLO

30 SM symmetry-breaking sector Higgs potential V Φ) Λ 4 µ Φ Φ + λ Φ Φ) + Y ij ψ i L ψj Φ + gij Λ ψi L ψjt L ΦΦT Cosmological constant problem worst fine tuning problem ever!) Quadratic sensitivity to heavy dof s when matching onto UV theory do heavy dof s exist?) Vacuum instability at large field values if λ < 0 M H M stability H Loss of perturbativity if λ > 4π M H M triviality H SM flavor problem + M ν : large unexplained hierarchy Mt /M e U3) 5 F Y ij U) B U) 3) L S. Di Vita DESY) SM vacuum stability with a 5 GeV H 6 / 33

31 Higgs mass bounds at NLO in 009 M t = 73. ±.3 GeV α sm Z ) = 0.93 ± [GeV] M H λ = π λ = π Perturbativity bound Stability bound Finite-T metastability bound Zero-T metastability bound Shown are σ error bands, w/o theoretical errors Tevatron exclusion at >95% CL 50 LEP exclusion at >95% CL 5 GeV log Λ / GeV) one-loop V eff + two-loop running + one-loop matching [Ellis et al.09]... not precise enough if M H 5 GeV! S. Di Vita DESY) SM vacuum stability with a 5 GeV H 7 / 33 0

32 Vacuum stability... made easy [shamelessly stolen from A. Strumia] Illustrative If your mexican hat turns out to be a dog bowl you have a problem... S. Di Vita DESY) SM vacuum stability with a 5 GeV H 8 / 33

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34 The effective potential: single real scalar ) Classical level S[φ] = d 4 xlφ) = ] d x[ 4 µφ µ φ m φ + λ 4 φ4) V φ) minimization of V φ) gives v φ tree at the classical level consider quantum fluctuations about v, φ v + φ V φ ) gives the classical) vertices and mass Feynman rules What about quantum corrections? [Coleman and E.Weinberg] V eff φ c ): the order-zero term in the derivative expansion of the effective action Γ[φ c ] gen. of full PI functions) For constant φ c, min of V eff φ c ) gives φ c φ i.e. the true quantum minimum constant we don t want to break Poincaré) S. Di Vita DESY) SM vacuum stability with a 5 GeV H 9 / 33

35 The effective potential: single real scalar ) -loop MS µ 0 is the t Hooft mass) [Coleman and E.Weinberg, Jackiw] V eff φ c ) = m φ c+ λ 4 φ4 c+ m + 3λφ c) 4 6π ln m + 3λφ c µ 0 3 ) Consider for simplicity the massless case m = 0: V φ) = λ 4 φ4 φ = 0 min) { φc = 0 max V eff φ c ) = λ 4 φ4 c+ 9λ ln φ 6π c +...) µ 0 λ ln φc µ π + Oλ) min can we trust the new minimum? higher orders contribute λ ln φc µ 0 ) n! A weapon: dv eff dµ 0 = 0 resum logs with RGE S. Di Vita DESY) SM vacuum stability with a 5 GeV H 0 / 33

36 The effective potential: single real scalar ) -loop MS µ 0 is the t Hooft mass) [Coleman and E.Weinberg, Jackiw] V eff φ c ) = m φ c+ λ 4 φ4 c+ m + 3λφ c) 4 6π ln m + 3λφ c µ 0 3 ) Consider for simplicity the massless case m = 0: V φ) = λ 4 φ4 φ = 0 min) { φc = 0 max V eff φ c ) = λ 4 φ4 c+ 9λ ln φ 6π c +...) µ 0 λ ln φc µ π + Oλ) min can we trust the new minimum? higher orders contribute λ ln φc µ 0 ) n! Solution: V eff λ, m, φ, µ 0 ) = V eff λµ), mµ), φµ), µ) need running couplings, with initial conditions at µ 0 S. Di Vita DESY) SM vacuum stability with a 5 GeV H 0 / 33

37 Renormalization Group Improved SM V eff a first approximation) Veff RGI λµ) φ) φ v 4 φµ)4 + 64π STr Mµ) log Mµ) µ +... STr over particles with field-dependent masses M kφ µ free parameter: µ φ helps minimize logs over wide φ range Shape of V RGI eff at large φ running of λ dλ d ln µ = 6π scalar loop ext. leg corrections gauge bosons loop fermion loop +4N cλ + λ4n cy t 9g 3g ) N cyt g g g g +... B B<0 at EW scale) If B = const, V eff unbounded from below at large φ. Wait: B runs too!! S. Di Vita DESY) SM vacuum stability with a 5 GeV H / 33

38 Ignoring M H = 5 GeV, there a few different scenarios B 0 M H large: λ hits Landau pole triviality problem: λφ 4, but many arguments suggest that one needs λ R = 0 to define continuum limit B never runs negative enough: V eff is bounded from below SM vacuum stable) B stays negative: V eff is unbounded from below SM vacuum unstable, need NP) B flips sign at large φ: V eff develops another min degenerate or lower; SM vacuum metastable) V eff ϕ c ) [GeV] M H λ = π LEP exclusion at >95% CL λ = π Perturbativity bound Stability bound Finite-T metastability bound Zero-T metastability bound Shown are σ error bands, w/o theoretical errors Tevatron exclusion at >95% CL log Λ / 0 ϕ c GeV) 5 S. Di Vita DESY) SM vacuum stability with a 5 GeV H / 33

39 Stability and RGE evolution [Degrassi et al.] At large φ one can approximate V eff λφ)φ 4, but this means ignoring the non-logarithmic loop contrib still, it tells us that instability occurs around 0 0 GeV M Pl better: one can always write choosing µ φ), V eff = λ eff φ)φ Higgs quartic coupling Λ Μ Λ in MS M h 6.5 GeV dashed M h 4.5 GeV dotted Mt 73. GeV Αs M Z 0.84 Λ eff 4V h 4 Higgs quartic coupling Λ Μ Λ in MS M h 6.5 GeV dashed M h 4.5 GeV dotted Mt 7.0 GeV Αs M Z 0.84 Λ eff 4V h 4 Β Λ Β Λ NNLO with prev. world average m t NNLO with m t : λm Pl ) = β λ M Pl ) S. Di Vita DESY) SM vacuum stability with a 5 GeV H 3 / 33

40 Stability and RGE evolution [Degrassi et al.] λm Pl ) 0 crucially depends on M t no stability for central value. what about error bands? λ runs fast and then slows down, never too negative around M Pl both λ and β λ are 0. any meaning? but no RGE fixed point Higgs quartic coupling Λ Μ Λ in MS M h 6.5 GeV dashed M h 4.5 GeV dotted Mt 73. GeV Αs M Z 0.84 Λ eff 4V h 4 Higgs quartic coupling Λ Μ Λ in MS M h 6.5 GeV dashed M h 4.5 GeV dotted Mt 7.0 GeV Αs M Z 0.84 Λ eff 4V h 4 Β Λ Β Λ NNLO with prev. world average m t NNLO with m t : λm Pl ) = β λ M Pl ) S. Di Vita DESY) SM vacuum stability with a 5 GeV H 3 / 33

41 Stability condition and error budget [Degrassi et al.] 0.0 Higgs quartic coupling Λ Σ bands in Mt 73. ± 0.6 GeV gray Α 3 M Z 0.84 ± red M h 5.7 ± 0.3 GeV blue RGE scale in GeV Mt 7.3 GeV Αs M Z 0.05 Αs M Z 0.63 Mt 74.9 GeV Err. Type Err. estimate Impact on M H M t expt. uncert. M t ±.4 GeV α s expt. uncert. α s ±0.5 GeV Expt. Tot. combined in quadr. ±.5 GeV λ scale var. in λ ±0.7 GeV y t OΛ QCD ) correction to M t ±0.6 GeV y t QCD threshold at 4 loops ±0.3 GeV RGE EW 3 loops + QCD 4 loops ±0. GeV Theory Tot. combined in quadr. ±.0 GeV SM absolute stability condition at NNLO gauge-less) ) M H [GeV] > Mt [GeV] αsm Z ) ) ±.0 th S. Di Vita DESY) SM vacuum stability with a 5 GeV H 4 / 33

42 Stability condition and error budget [Degrassi et al.] 0.0 Higgs quartic coupling Λ Σ bands in Mt 73. ± 0.6 GeV gray Α 3 M Z 0.84 ± red M h 5.7 ± 0.3 GeV blue RGE scale in GeV Mt 7.3 GeV Αs M Z 0.05 Αs M Z 0.63 Mt 74.9 GeV Err. Type Err. estimate Impact on M H M t expt. uncert. M t ±.4 GeV α s expt. uncert. α s ±0.5 GeV Expt. Tot. combined in quadr. ±.5 GeV λ scale var. in λ ±0.7 GeV y t OΛ QCD ) correction to M t ±0.6 GeV y t QCD threshold at 4 loops ±0.3 GeV RGE EW 3 loops + QCD 4 loops ±0. GeV Theory Tot. combined in quadr. ±.0 GeV SM absolute stability condition at NNLO full) [Buttazzo et al.3] M H [GeV] > M t / GeV 73.34) 0.5 αsm Z ) ) ±0.3 th S. Di Vita DESY) SM vacuum stability with a 5 GeV H 4 / 33

43 Stability condition and error budget [Degrassi et al.] 0.0 Higgs quartic coupling Λ Σ bands in Mt 73. ± 0.6 GeV gray Α 3 M Z 0.84 ± red M h 5.7 ± 0.3 GeV blue RGE scale in GeV Mt 7.3 GeV Αs M Z 0.05 Αs M Z 0.63 Mt 74.9 GeV Err. Type Err. estimate Impact on M H M t expt. uncert. M t ±.4 GeV α s expt. uncert. α s ±0.5 GeV Expt. Tot. combined in quadr. ±.5 GeV λ scale var. in λ ±0.7 GeV y t OΛ QCD ) correction to M t ±0.6 GeV y t QCD threshold at 4 loops ±0.3 GeV RGE EW 3 loops + QCD 4 loops ±0. GeV Theory Tot. combined in quadr. ±.0 GeV full NNLO stability bound on m t [Buttazzo et al.3] M t [ GeV] < 7.53 ± 0.5 ± 0.3 αs ± 0.5 MH = 7.53 ± 0.4 S. Di Vita DESY) SM vacuum stability with a 5 GeV H 4 / 33

44 Metastability ) at T=0, most conservative, indep of thermal history of universe) QM finite barrier WKB: Γ Ae B. B classical motion of particle in Ux) = V x) with τ = it euclidean, with peculiar boundary conditions Generalizes to ) many dof s [Banks, Bender, Wu 73; Coleman 77; Callan, Coleman 77] φ EW can be a false vacuum: still acceptable if τ EW τ U φ B = O4) bounce solution of classical euclidean EoM V φ) = λ φ4 4 φ Br) = R λ r +R S B S E [φ B ] = 8π 3 λ S B R-indep! semiclassical: p decay τ 4 U R 4 e S B tunneling suppressed even w/o potential barrier, kinematic barrier due to BC S. Di Vita DESY) SM vacuum stability with a 5 GeV H 5 / 33

45 Metastability ) at T=0, most conservative, indep of thermal history of universe) path integral methods allow to go beyond semiclassical approx. [ τ 4 ] quantum: p = max U R R 4 e S Bµ) SµR), S B µ) = 8π 3 λµ) quantum corr. break degeneracy and fix R! S 0 for µ = R [Isidori, Ridolfi, Strumia 0] p dominated by R that maximizes λr ) β λ R ) = 0 R Λ I In the SM one finds at NLO p e 40 RM Pl ) 4 e 600 λr ) /0.0 easily wins ifλr )< 0.5 given M H = 5 GeV and RGE) message: it s ok if λ goes negative, if stays small in magnitude. no NP needed higher dim. operators with Λ R e.g. Λ = M P ) [Di Luzio, Isidori, Ridolfi 5] either are completely irrelevant for vacuum decay if coeff s> 0) or introduce a new ground state around Λ new decay channels ), decreasing τ EW [Branchina, Messina 3] but it s not the SM anymore! S. Di Vita DESY) SM vacuum stability with a 5 GeV H 6 / 33

46 Metastability 3) at T=0, most conservative, indep of thermal history of universe) [Buttazzo et al.3] Beta function of the Higgs quartic Β Λ Σ bands in M t 73.3 ± 0.8 GeV gray Α 3 M Z 0.84 ± red M h 5. ± 0. GeV blue Probability of vacuum decay Σ bands in M h 5.±0. GeV red dotted Α ± gray dashed Life time in yr β λ µ) 73.3± t EW vacuum decay probability S. Di Vita DESY) SM vacuum stability with a 5 GeV H 7 / 33

47 SM Phase diagram 80 Top mass Mt in GeV Instability Meta stability Stability Non perturbativity Top pole mass Mt in GeV Instability Meta stability ,,3 Σ h [Degrassi et al.] [Buttazzo et al.3] h Stability S. Di Vita DESY) SM vacuum stability with a 5 GeV H 8 / 33

48 SM Phase diagram [Bednyakov Kniehl Pikelner Veretin 5] 80 Instability Metastability Mt, GeV M pl 0 7 Absolute stability M H, GeV S. Di Vita DESY) SM vacuum stability with a 5 GeV H 9 / 33

49 SM Phase diagram: LO vs NLO vs NNLO instability Veff < 0 before MPl, τew < τu metastability Veff < 0 before MPl, τew > τu stability Veff > 0 up to MPl, i.e. stable Espinosa MH Mt plane S. Di Vita DESY) SM vacuum stability with a 5 GeV H 30 / 33

50 SM Phase diagram at M P [Buttazzo et al. 3] Λ I > M P Top Yukawa coupling yt M Pl Planck scale dominated Instability No EW vacuum Meta stability Higgs coupling Stability M Pl SM Top Yukawa coupling yt M Pl Meta Stability 0 8 stability No EW vacuum Instability Planck scale dominated Pl λλ EW ) < 0 S. Di Vita DESY) SM vacuum stability with a 5 GeV H 3 / 33

51 The m t issue position in the SM phase diag. m t top mass used is the Tevatron+LHC average mt MC = ± 0.76 GeV extracted with template methods Pythia mass) from decay products. Event modeling is delicate! if one extracts y t µ) from m pole mt MC OΛ QCD ) uncert. + is m pole t t : = m MC t? m pole t EW vacuum instable meta stable stable 95%CL ILC LHC Tevatron 4 6 MH [GeV] [Alekhin, Djouadi, Moch ] stay on the safe side: use m t m t ) = 6.3 ±.3 GeV from t t inclusive σ. But can t say much on the SM vacuum until ILC... exploit high precision in m MC t e.g. m MC t m pole t = GeV [Moch 4] determination with new methods 8 30 S. Di Vita DESY) SM vacuum stability with a 5 GeV H 3 / 33

52 Conclusions A SM-like Higgs with M H 5 GeV does not allow us to infer, in a model independent way, the scale of NP. The SM vacuum is probably metastable, but the tunneling is slow enough that the vacuum has a lifetime longer than the age of the universe. λ gets small at high energies. E.g. around O0 GeV) with the current m t, around the Planck scale if m t 7 GeV If SM is an EFT, we have to match it onto an UV model where the Higgs either is weakly interacting if Λ NP Λ EW has vanishing?) λ if ΛNP Λ Pl Such reasonings strongly depend on m t, M H and α s ). If it s just SM... What about the naturalness problem? Is criticality telling us something about nature? S. Di Vita DESY) SM vacuum stability with a 5 GeV H 33 / 33

53 Thanks for your attention! S. Di Vita DESY) SM vacuum stability with a 5 GeV H 33 / 33