UV completion of the Standard Model

Transcription

1 UV completion of the Standard Model Manuel Reichert In collaboration with: Jan M. Pawlowski, Tilman Plehn, Holger Gies, Michael Scherer,... Heidelberg University December 15, 2015

2 Outline 1 Introduction Limits of the Standard Model Stability of the Higgs-potential Idea of Asymptotic Safety 2 Asymptotic Safety in Quantum Gravity Non-perturbative method: The Functional Renormalisation Group Results Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

3 The Standard Model of particle physics 2012 at LHC: Discovery of Higgs-Boson M H 125 GeV Last missing piece of the SM So far: no signs for physics beyond the Standard Model at the LHC CMS Collaboration (2012) Do we need new degrees of freedom? (Where?) Image: Wikipedia Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

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5 Best before: Λ = M Planck? Λ = Λ New Physics?

6 Holger Gies Best before: Λ = M Planck? Λ = Λ New Physics?

7 RG running of the Standard Model The Standard Model parameters are measured at low energies The interaction strength depends on the scale Running of the coupling is described with β-function Physical picture: Wilsonian block spinning / integrating out of momentum modes Bethke (2006) Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

8 Scale dependence of the Standard Model λ = φ 4 -Higgs-coupling g 1 = gauge-coupling of U(1) g 2 = gauge-coupling of SU(2) g 3 = gauge-coupling of SU(3) Yukawa-couplings are missing in the plot 1 g 2 g 3 SM coupling 0.5 g 1 λ RG scale in GeV Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

9 Scale dependence of the Standard Model Higgs-potentials at different scales: V k (H) = µ(k)2 2 H 2 + λ(k) 4 H4 Vacuum instability at GeV? SM coupling g 2 g 3 g 1 λ RG scale in GeV Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

10 Vacuum instability at GeV? Possible solutions: New degrees of freedom dark matter, SUSY? Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

11 Vacuum instability at GeV? Possible solutions: New degrees of freedom dark matter, SUSY? Metastability V h GeV V k (H k) = λ(k=h) 4 H log 10 hgev Gabrielli et al. (2014) Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

12 Vacuum instability at GeV? Possible solutions: New degrees of freedom dark matter, SUSY? Metastability V h GeV V k (H k) = λ(k=h) 4 H log 10 hgev Gabrielli et al. (2014) Non-perturbative effects of higher dimensional operators V eff (k; H) = µ(k)2 2 H 2 + λ 4(k) H 4 + λ 6(k) 4 8k 2 H Branchina, Messina (2013); Eichhorn, Gies, Jaeckel, Plehn, Scherer, Sondenheimer (2015) Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

13 Scale dependence of the Standard Model Beyond M Planck GeV: Gravity effects are not taken into account Occurrence of Landau poles SM coupling g 2 g 3 g 1 λ RG scale in GeV Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

14 Scale dependence of the Standard Model For RG-scale so far realised in the Standard Model: Coupling 0 (asymptotic freedom) Coupling (Landau pole) Generalisation: Coupling const. (asymptotic safety) SM coupling g 2 g 3 g 1 λ RG scale in GeV Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

15 Summary: Limits of the Standard Model Limits: Issues of vacuum stability of the Higgs potential at GeV Landau pole of g 1 and λ at scales M Pl Missing items: Gravity at M Pl GeV Dark matter (unknown scale)... SM coupling g 2 g 3 g 1 λ RG scale in GeV Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

16 Summary: Limits of the Standard Model Limits: Issues of vacuum stability of the Higgs potential at GeV Landau pole of g 1 and λ at scales M Pl Missing items: Gravity at M Pl GeV Dark matter (unknown scale)... SM coupling g 2 g 3 g 1 λ RG scale in GeV Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

17 Outline 1 Introduction Limits of the Standard Model Stability of the Higgs-potential Idea of Asymptotic Safety 2 Asymptotic Safety in Quantum Gravity Non-perturbative method: The Functional Renormalisation Group Results Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

18 What is the Asymptotic Safety Scenario? Weinberg s proposal (1976) Non-trivial UV fixed point of the renormalisation group flow g S EH = 1 16πG N g(2λ R) x ġ β g λ β λ k 0 k λ Reuter, Saueressig (2001) Codello, Percacci, Rahmede (2008); Benedetti, Machado, Saueressig (2009); Eichhorn, Gies (2010); Benedetti, Caravelli (2012); Donkin, Pawlowski (2012); Falls, Litim, Nikolakopoulos (2013); Dietz, Morris (2013); Codello, D Odorico, Pagani (2013);... Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

19 The Functional Renormalisation Group General problem: Gravity is perturbatively non-renormalisable [G N ] = 2 Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

20 The Functional Renormalisation Group General problem: Gravity is perturbatively non-renormalisable [G N ] = 2 Non-perturbative method: Wetterich equation t Γ k = 1 [ ] 2 STr (Γ (2) k + R k ) 1 t R k R k = regulator Γ k = effective average action Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

21 The Functional Renormalisation Group General problem: Gravity is perturbatively non-renormalisable [G N ] = 2 Non-perturbative method: Wetterich equation t Γ k = 1 [ ] 2 STr (Γ (2) k + R k ) 1 t R k R k = regulator Γ k = effective average action Γ k=λ = S bare Exact one-loop equation β functions in non-perturbative regime Γ k=0 Γ Image: Holger Gies Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

22 The Functional Renormalisation Group General problem: Gravity is perturbatively non-renormalisable [G N ] = 2 Non-perturbative method: Wetterich equation t Γ k = 1 [ ] 2 STr (Γ (2) k + R k ) 1 t R k R k = regulator Γ k = effective average action Exact one-loop equation β functions in non-perturbative regime The resulting theory is fundamental IR fixed point UV fixed point Image: Holger Gies Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

23 Our computation Einstein-Hilbert ansatz 1 S EH = d 4 x g(2λ R) + S gf + S gh 16πG N Linear metric split g µν = ḡ µν + h µν Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

24 Our computation Einstein-Hilbert ansatz 1 S EH = d 4 x g(2λ R) + S gf + S gh 16πG N Linear metric split g µν = ḡ µν + h µν Vertex expansion to compute dynamical n-point correlation functions, e.g. Graviton two-point function: (Flow of µ and Z h (p 2 )) t ( ) 1 = Graviton three-point function: (Flow of g and λ 3 ) t = Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

25 Phase diagram F 1 : UV fixed point F 2 : Gaußian fixed point F 3 : IR fixed point N. Christiansen, B. Knorr, J. Meibohm, J. Pawlowski, MR (2015) Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

26 Inclusion of matter Is the UV fixed point stable under inclusion of matter? Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

27 Inclusion of matter Is the UV fixed point stable under inclusion of matter? Generating action: (with N s scalars and N f fermions) S = S EH + d 4 x g ψ i / ψ i + 1 d 4 x gg µν µ ϕ j ν ϕ j 2 with i = 1,..., N f and j = 1,..., N s ( Γ (hh) k,matter = N s 1 2 ( 2N f ) ) Γ (hhh) k,matter = N s 1 2 2N f Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

28 Inclusion of scalars g λ 3 µ N strunc N s R(θ 1) R(θ 2) R(θ 3) N sstab N s ηh (k2 ) ηc (k2 ) ηh (0) η c (0) N strunc N s Reliability bound on truncation N strunc 21.5 Loss of an attractive UV fixed point N sstab 42.6 Complete loss of the UV fixed point N smax 66.4 J. Meibohm, J. Pawlowski, MR (2015) Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

29 Inclusion of fermions g λ 3 µ R(θ 1) R(θ 2) R(θ 3) ηh(k 2 ) ηc(k 2 ) ηψ(k 2 ) ηh(0) ηc(0) ηψ(0) N f N f N f Reliable attractive UV fixed point for all N f J. Meibohm, J. Pawlowski, MR (2015) Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20

30 Summary and Outlook Working hypothesis: The Standard Model + gravity is valid up to arbitrary high energy scales Asymptotic safety is a promising route towards a UV completion of the Standard Model Many indications that asymptotic safety works in gravity coupled to simple matter systems Further research Investigation of the stability of the Higgs potential Coupling the whole Standard Model to gravity Manuel Reichert (Heidelberg University) UV completion of the SM 15. December / 20