Higgs mass implications on the stability of the
Transcript
Higgs mass implications on the stability of the
Introduction SM vacuum stability Conclusions Higgs mass implications on the stability of the electroweak vacuum J. Elias-Miró joint work with J.R. Espinosa, G.Degrassi, S. Di Vita, G.F. Giudice, G. Isidori, A. Riotto, A. Strumia . Universitat Autònoma de Barcelona (UAB) Institut de Fı́sica d’Altes Energies (IFAE) Cargese, August 2012 J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions The Higgs sector of the SM It is the part of the theory from which we have less experimental information. Interestingly, most of the theoretical problems of the SM arise from the Higgs sector. J. Elias-Miró Stability of the EW vacuum 95% CL limit on σ/σSM Introduction SM vacuum stability Conclusions 10 CMS, s = 7 TeV L = 4.6-4.8 fb-1 Observed Expected (68%) Expected (95%) 1 10-1 110 115 120 125 130 135 140 145 Higgs boson mass (GeV) for Mh ≈ 125 GeV, λ = J. Elias-Miró Mh2 2v 2 ≈ 0.129 Stability of the EW vacuum Introduction SM vacuum stability Conclusions SM effective potential Assume the SM up to very high energies, is it a consistent model? J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions SM effective potential For large field values, Vef f ≈ 41 λef f (φ)φ4 . If λef f ≈ λ < 0 at some high energy scale ΛI , the Electroweak (EW) minimum at φ = v ≈ 246 GeV of the Higgs potential is unstable. 0.6 Effective potential Veff 0.5 0.4 0.3 0.2 0.1 0.0 0.0 0.2 0.4 J. Elias-Miró 0.6 0.8 Classical field Φc 1.0 1.2 Stability of the EW vacuum Introduction SM vacuum stability Conclusions SM effective potential But, can λ become negative? Yes, two main competing effects: µ dλ(µ) = ( # λ2 d log(µ) + ... −# h4t + ...) + ... , makes λ grow , makes λ decrease. ht (v) = √ 2Mt /v and λ(v) = Mh2 /(2v 2 ). J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions SM effective potential But, can λ become negative? Yes, two main competing effects: µ dλ(µ) = ( # λ2 d log(µ) + ... −# h4t + ...) + ... , makes λ grow , makes λ decrease. ht (v) = √ 2Mt /v and λ(v) = Mh2 /(2v 2 ). J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions SM effective potential But, can λ become negative? Yes, two main competing effects: µ dλ(µ) = ( # λ2 d log(µ) + ... −# h4t + ...) + ... , makes λ grow , makes λ decrease. ht (v) = √ 2Mt /v and λ(v) = Mh2 /(2v 2 ). J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions SM effective potential J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Riotto, A. Strumia. [hep/1112.3022] J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions SM effective potential A Higgs mass of ∼ 125 GeV is a very special value 180 ili stab taMe 150 100 ty Stability 50 0 0 50 100 150 200 Pole top mass Mt in GeV Instability Non-perturbativity Top mass Mt in GeV 200 107 1010 Instability Instability Meta-stability 175 1,2,3 Σ 170 109 1012 165 115 Stability 120 125 130 135 Higgs mass Mh in GeV Higgs mass Mh in GeV G.Degrassi, S. Di Vita, J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Strumia. [hep-ph/1205.6497] J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions SM effective potential G.Degrassi, S. Di Vita, J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Strumia. [hep-ph/1205.6497] J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions Conclusions - From metastabilty considerations, a SM Higgs with Mh ∼ 125 GeV does not imply an strict upper bound on the scale of new physics. - The Higgs quartic coupling becomes very small. Very unlikely becomes zero at the Planck scale. However λ(MP lanck ) ≈ 0 J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions The SM is such a good model that admits a theoretical extrapolation up to MP lanck without any consistency problem. I hope this analysis will be soon invalidated by nature, due to new physics coming in close to the EW scale... Thank you for your attention! J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions dλH 2 = 12yt2 − 3g 0 − 9g 2 λH − 6yt4 d ln µ i 3h 4 2 + 2g + (g 0 + g 2 )2 + 24λ2H + 4λ2HS , 8 1 dλ 2 HS = λHS [ 12yt2 − 3g 0 − 9g 2 (4π)2 d ln µ 2 + 4 (3λH + 2λS ) + 8λHS ] , dλS (4π)2 = 8λ2HS + 20λ2S . d ln µ (4π)2 J. Elias-Miró Stability of the EW vacuum (1) Introduction SM vacuum stability Conclusions 1018 1 Σ band in: 16 Instability sclae in GeV 10 Mt =173.1±0.7 GeV Αs HMz L=0.1184±0.0007 1014 1012 1010 108 118 120 122 124 126 Higgs mass in GeV J. Elias-Miró 128 Stability of the EW vacuum 130 Introduction SM vacuum stability Conclusions G.Degrassi, S. Di Vita, J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Strumia. [hep-ph/1205.6497] J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions J. Elias-Miró Stability of the EW vacuum Introduction SM vacuum stability Conclusions 126 Higgs mass in GeV 125 124 123 122 1.0 1.2 1.4 1.6 1.8 ΜMt J. Elias-Miró Stability of the EW vacuum 2.0