Higgs mass implications on the stability of the electroweak vacuum

Transcription

1 Higgs mass implications on the stability of the electroweak vacuum J. Elias-Miró Universitat Autònoma de Barcelona (UAB) Institut de Física d Altes Energies (IFAE) IV Jornadas CPAN, November 2012

2 Work based on collaboration with: J.R. Espinosa, G.F. Giudice, G. Isidori, A. Strumia + A. Riotto + H.M. Lee + G.Degrassi, S. Di Vita [hep-ph/ ], [hep-ph ], [hep-ph/ ] For recent related work see: - M. Holthausen, K.S. Lim, M. Lindner [hep-ph/ ] - F. Bezrukov, M.Y. Kalmykov, B.A. Kniehl, M. Shaposhnikov [hep-ph/ ] -...

3 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.

4 The Higgs sector of the SM Severe fine tuning m 2 Λ 2 L int = m 2 Φ Φ + λ(φ Φ) 2 + Y ij Ψ i LΨ j R Φ Instability for λ < 0 or loss of perturbativity forλ > 4π Puzzling hierarchical structure + huge splitting m t /m e =

5 The Higgs sector of the SM Severe fine tuning m 2 Λ 2 L int = m 2 Φ Φ + λ(φ Φ) 2 + Y ij Ψ i LΨ j R Φ Instability for λ < 0 or loss of perturbativity forλ > 4π Puzzling hierarchical structure + huge splitting m t /m e =

6 The Higgs sector of the SM Severe fine tuning m 2 Λ 2 L int = m 2 Φ Φ + λ(φ Φ) 2 + Y ij Ψ i LΨ j R Φ Instability for λ < 0 or loss of perturbativity forλ > 4π Puzzling hierarchical structure + huge splitting m t /m e =

7 for M h 125 GeV, λ = M 2 h 2v

8 SM effective potential Stability of the EW vacuum Results Assume the SM up to very high energies, is it a consistent model?

9 SM effective potential Stability of the EW vacuum Results For large field values, V eff 1 4 λ eff (φ)φ 4. If λ eff λ < 0 at some high energy scale Λ I, the Electroweak (EW) minimum at φ = v 246 GeV of the Higgs potential is unstable. 0.5 Effective potential V eff

10 SM effective potential Stability of the EW vacuum Results But, can λ become negative? Yes, two main competing effects: µ dλ(µ) d log(µ) = ( # λ # h 4 t +...) +..., makes λ grow, makes λ decrease. h t (v) = 2M t /v and λ(v) = M 2 h /(2v2 ).

11 SM effective potential Stability of the EW vacuum Results But, can λ become negative? Yes, two main competing effects: µ dλ(µ) d log(µ) = ( # λ # h 4 t +...) +..., makes λ grow, makes λ decrease. h t (v) = 2M t /v and λ(v) = M 2 h /(2v2 ).

12 SM effective potential Stability of the EW vacuum Results But, can λ become negative? Yes, two main competing effects: µ dλ(µ) d log(µ) = ( # λ # h 4 t +...) +..., makes λ grow, makes λ decrease. h t (v) = 2M t /v and λ(v) = M 2 h /(2v2 ).

13 For large field values V eff λ(φ) 4 φ4. λ(µ) for M t = 173.1GeV : SM effective potential Stability of the EW vacuum Results Quartic coupling Λ M h 115 GeV M h 120 GeV M h 125 GeV M h 130 GeV

14 SM effective potential Stability of the EW vacuum Results Can the SM be ruled out (and claim that new physics must come in before the instability scale Λ I ) if there is a minimum deeper than the EW minimum at some field value φ I ( Λ I )? - No, the SM can still be consistent if the lifetime of the unstable EW vacuum is much longer than the age of the universe.

15 SM effective potential Stability of the EW vacuum Results We need to compute Decay Probability=Γ/( x 3 t) V u, (1) where V u e 409 [246 GeV] 4 is the past light cone and Γ = Decay Rate. For V λ eff (φ) φ 4, 4 ) Γ/V max (φ 4 exp[ 8π2 3 λ eff (φ) ], (2) where λ eff (φ) < 0. When p << 1, the lifetime of the EW vacuum is much longer than the age of the universe. S. Coleman Phys. Rev. D (1977)

16 SM effective potential Stability of the EW vacuum Results Recall that λ efff = λ + O(1-loop)

17 SM effective potential Stability of the EW vacuum Results State-of-the-art of the NNLO calculation: - 2-loop V eff : Ford, Jack, Jones [hep-ph/ ] - 3-loop RGEs: Chetyrkin, Zoller [hep-ph/ ] loop matching in λ(mh 2 ), h t(m t ): Shaposhnikov et. al [hep-ph/ ] Degrassi et. al [hep-ph/ ]

18 SM effective potential Stability of the EW vacuum Results

19 SM effective potential Stability of the EW vacuum Results A Higgs mass of 125 GeV is a very special value Top mass Mt in GeV Instability Meta stability Stability Non perturbativity Pole top mass Mt in GeV Instability 1,2,3 Σ Meta stability Stability h h G.Degrassi, S. Di Vita, J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Strumia. [hep-ph/ ]

20 SM effective potential Stability of the EW vacuum Results In the absence of BSM physics, some people like λ MP lanck = 0, or doing inflation in the following plateau (λ β λ 0) Higgs vev in GeV M t GeV M t GeV M t GeV but...

21 SM effective potential Stability of the EW vacuum Results

22 - From metastabilty considerations, a SM Higgs with M h 125 GeV does not imply an strict upper bound on the scale of new physics. The SM is such a good model that admits a theoretical extrapolation up to M P lanck without any consistency problem. - The Higgs quartic coupling becomes very small. Very unlikely becomes zero at the Planck scale. However λ(m P lanck ) 0 - Intriguing situation: our vacuum sits just in between absolute stability and metastability.

23 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!

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25 Instability sclae in GeV Σ band in: M t 173.1±0.7 GeV Α s M z ±

26 G.Degrassi, S. Di Vita, J.EM, J. Espinosa, G.F. Giudice, G. Isidori, A. Strumia. [hep-ph/ ]

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