Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery On the fate of the Standard Model in view of the Higgs discovery Gino Isidori [ INFN, Frascati & CERN ] Introduction The Higgs potential at high energies Stability and metastability bounds Vacuum stability at NNLO Speculations on Planck-scale dynamics Conclusions
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery Introduction All known phenomena in particle physics ( leaving aside a few cosmological observations ) can be described with good accuracy by a remarkably simple ( effective ) theory: ℒ SM(+ν) = ℒ gauge ( A a , ψ i ) + ℒ Symm. Break. (ϕ, A a , ψ i ) ℒ SM = 1 a ) 2 + Σ ψ Σ i ψ i i D ψ i Σ a - ( F μν ℒ gauge = Natural 2 4 g a Experimentally tested with high accuracy Stable with respect to quantum corrections (UV insensitive) SU(3) c ×SU(2) L ×U(1) Y local symmetry Highly symmetric Global flavor symmetry
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery Introduction All known phenomena in particle physics ( leaving aside a few cosmological observations ) can be described with good accuracy by a remarkably simple ( effective ) theory: ℒ SM(+ν) = ℒ gauge ( A a , ψ i ) + ℒ Symm. Break. (ϕ, A a , ψ i ) ℒ SM = Ad hoc Natural Necessary to describe data Experimentally tested with [ the electroweak symmetry forbid masses for high accuracy all the elementary particles observed so far... ] Stable with respect to Not stable with respect to quantum corrections quantum corrections (UV sensitive) (UV insensitive) Origin of the flavor structure of the model Highly symmetric [ and of all the problems of the model... ] [ gauge + favor symmetries ]
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery Introduction All known phenomena in particle physics ( leaving aside a few cosmological observations ) can be described with good accuracy by a remarkably simple ( effective ) theory: ℒ SM(+ν) = ℒ gauge ( A a , ψ i ) + ℒ Symm. Break. (ϕ, A a , ψ i ) ℒ SM = Ad hoc Natural Necessary to describe data Experimentally tested with [ we couldn't live in a fully symmetric world... ] high accuracy Not stable with respect to quantum corrections Stable with respect to (UV sensitive) quantum corrections Ugly & unstable, but is what Elegant & stable, (UV insensitive) makes nature interesting...! but also a bit boring... Origin of the flavour structure of the model [ and of all the problems of the model... ] Highly symmetric
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery Introduction LHC experiments have confirmed once more that we understand very well gauge interactions...
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery Introduction LHC experiments have confirmed once more that we understand very well gauge interactions, but the “ breaking-news ” announced July 4 th 2012 is about the symmetry breaking sector of the theory: Clear evidence of a new particle compatible with the properties of the Higgs boson
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery Introduction The more we a look at it, the more this particle looks like the “standard” Higgs boson:
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector The Higgs mechanism, namely the introduction of an elementary SU(2) L scalar doublet, with ϕ 4 potential, is the most economical & simple choice to achieve the spontaneous symmetry breaking of both gauge [ SU(2) L × U(1) Y → U(1) Q ] and flavor symmetries that we observe in nature. potential potential field value field value
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector The Higgs mechanism, namely the introduction of an elementary SU(2) L scalar doublet, with ϕ 4 potential, is the most economical & simple choice to achieve the spontaneous symmetry breaking of both gauge [ SU(2) L × U(1) Y → U(1) Q ] and flavor symmetries that we observe in nature. ℒ higgs (ϕ, A a , ψ i ) = Dϕ + Dϕ - V(ϕ) j ϕ V(ϕ) = - μ 2 ϕ + ϕ + λ(ϕ + ϕ) 2 + Y ij ψ L i ψ R Till very recently only the ground state determined by this potential ( and the corresponding Goldstone boson structure ) was tested with good accuracy: v = 〈 ϕ + ϕ 〉 1/2 ~ 246 GeV [ m W = ½ g v ]
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector The Higgs mechanism, namely the introduction of an elementary SU(2) L scalar doublet, with ϕ 4 potential, is the most economical & simple choice to achieve the spontaneous symmetry breaking of both gauge [ SU(2) L × U(1) Y → U(1) Q ] and flavor symmetries that we observe in nature. ℒ higgs (ϕ, A a , ψ i ) = Dϕ + Dϕ - V(ϕ) j ϕ V(ϕ) = - μ 2 ϕ + ϕ + λ(ϕ + ϕ) 2 + Y ij ψ L i ψ R Till very recently only the ground state determined by this potential ( and the corresponding Goldstone boson structure ) was tested with good accuracy: v = 〈 ϕ + ϕ 〉 1/2 ~ 246 GeV [ m W = ½ g v ] The situation has substantially changed a few weeks ago, with the observation of the 4 th degree of freedom of the Higgs field (or its massive excitation ): 2 / v 2 ~ 0.13 λ (tree) = ½ m h
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector Actually some information about the Higgs mass was already present in the e.w. precision tests ( assuming the validity of the SM up to high scales ):
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector Actually some information about the Higgs mass was already present in the e.w. precision tests ( assuming the validity of the SM up to high scales ):
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector Actually some information about the Higgs mass was already present in the e.w. precision tests ( assuming the validity of the SM up to high scales ): Message n.1: The observation of the physical Higgs boson with m h well consistent with the (indirect) prediction of the e.w. precision tests is a great success of the SM !
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector Actually some information about the Higgs mass was already present in the e.w. precision tests ( assuming the validity of the SM up to high scales ): More generally, we have a strong indication that the symmetry breaking sector of the theory has a minimal and weakly coupled structure (at least around the TeV scale)
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector Still, the SM Higgs potential is “ugly” and hides the most serious theoretical problems of this highly successful theory: j ϕ + ψ L i ψ L Tj ϕ ϕ T V(ϕ) = Λ 4 - μ 2 ϕ + ϕ + λ (ϕ + ϕ) 2 + Y ij ψ L i ψ R V(ϕ) = vacuum instability possible internal inconsistency of the model (λ < 0) at large energies [ key dependence on m h ] Quadratic sensitivity to the cut-off SM flavor problem Δμ 2 ~ Δm h 2 ~ Λ 2 (unexplained span over several orders of magnitude and strongly (indication of new physics hierarchical structure close to the electroweak scale ?) of the Yukawa coupl.)
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector Still, the SM Higgs potential is “ugly” and hides the most serious theoretical problems of this highly successful theory: g ij j ϕ + ψ L i ψ L Tj ϕ ϕ T V(ϕ) = Λ 4 - μ 2 ϕ + ϕ + λ (ϕ + ϕ) 2 + Y ij ψ L i ψ R Λ effective neutrino mass term vacuum instability Cosmological constant prob. possible internal inconsistency of the model (λ < 0) at large energies [ key dependence on m h ] Quadratic sensitivity to the cut-off SM flavor problem Δμ 2 ~ Δm h 2 ~ Λ 2 (unexplained span over several orders of magnitude and strongly (indication of new physics hierarchical structure close to the electroweak scale ?) of the Yukawa coupl.)
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery The SM Higgs sector Still, the SM Higgs potential is “ugly” and hides the most serious theoretical problems of this highly successful theory: g ij j ϕ + ψ L i ψ L Tj ϕ ϕ T V(ϕ) = Λ 4 - μ 2 ϕ + ϕ + λ (ϕ + ϕ) 2 + Y ij ψ L i ψ R Λ effective neutrino mass term vacuum instability Cosmological constant prob. possible internal inconsistency of the model (λ < 0) at large energies [ key dependence on m h ] Quadratic sensitivity to the cut-off SM flavour problem Δμ 2 ~ Δm h 2 ~ Λ 2 (unexplained span over several orders of magnitude and strongly (indication of new physics hierarchical structure close to the electroweak scale ?) of the Yukawa coupl.)
Warsaw, March 2013 G. Isidori – On the fate of the Standard Model in view of the Higgs discovery Stability and metastability bounds
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