Quantum-gravity effects on a Higgs-Yukawa model Astrid Eichhorn - PowerPoint PPT Presentation

Quantum-gravity effects on a Higgs-Yukawa model Astrid Eichhorn University of Heidelberg with Aaron Held and Jan Pawlowski September 22, 2016 ERG 2016, ICTP, Trieste

Motivation: Observational tests of quantum gravity

Motivation: Observational tests of quantum gravity Problem: It’s tough to probe the microscopic structure of spacetime directly Idea: Let’s devise ``indirect’’ tests using low-energy data

Motivation: Observational tests of quantum gravity Problem: It’s tough to probe the microscopic structure of spacetime directly Idea: Let’s devise ``indirect’’ tests using low-energy data Analogy: What is the microscopic structure of honey?

Motivation: Observational tests of quantum gravity Problem: It’s tough to probe the microscopic structure of spacetime directly Idea: Let’s devise ``indirect’’ tests using low-energy data Analogy: What is the microscopic structure of honey? It’s about 1/3 glucose, 1/3 fructose and 1/3 water It’s about molecules 1/2 fructose and 1/2 water molecules A B

Motivation: Observational tests of quantum gravity Problem: It’s tough to probe the microscopic structure of spacetime directly Idea: Let’s devise ``indirect’’ tests using low-energy data Analogy: What is the microscopic structure of honey? It’s about 1/3 glucose, 1/3 fructose and 1/3 water It’s about molecules 1/2 fructose and 1/2 water molecules A B low-energy data: viscosity of honey (measurement at scales >> molecular scale; calculable from microscopic model) m atched by model A

Motivation: Observational tests of quantum gravity Problem: It’s tough to probe the microscopic structure of spacetime directly Idea: Let’s devise ``indirect’’ tests using low-energy data Analogy: What is the microscopic structure of honey? It’s about 1/3 glucose, 1/3 fructose and 1/3 water It’s about molecules 1/2 fructose and 1/2 water molecules A B low-energy data: viscosity of honey (measurement at scales >> molecular scale; calculable from microscopic model) matched by model A

Motivation: Observational tests of quantum gravity Problem: It’s tough to probe the microscopic structure of spacetime directly Idea: Let’s devise ``indirect’’ tests using low-energy data Analogy: What is the microscopic structure of honey? It’s about 1/3 glucose, 1/3 fructose and 1/3 water It’s about molecules 1/2 fructose and 1/2 water molecules A B low-energy data: viscosity of honey (measurement at scales >> molecular scale; calculable from microscopic model) matched by model A

Motivation: Observational tests of quantum gravity Problem: It’s tough to probe the microscopic structure of spacetime directly Idea: Let’s devise ``indirect’’ tests using low-energy data Analogy: What is the microscopic structure of honey? No ``smoking-gun’’ signal for any particular QG model, It’s about 1/3 glucose, 1/3 fructose and 1/3 water It’s about molecules but: could rule out models this way! 1/2 fructose and 1/2 water molecules A B low-energy data: viscosity of honey (measurement at scales >> molecular scale; calculable from microscopic model) matched by model A

Motivation: Why matter & quantum gravity? Observational viability of quantum gravity models: - must reduce to GR in classical limit probes of dynamical gravity regime: experimental challenge

Motivation: Why matter & quantum gravity? Observational viability of quantum gravity models: - must reduce to GR in classical limit probes of dynamical gravity regime: experimental challenge - must accommodate all observed matter degrees of freedom example: chiral (i.e., light) fermions X asymptotic safety 7 causal sets: X LQG (in truncation) fermions ??? [A.E., Gies ’11; [Barnett, Smolin ‘15] [Gambini, Pullin ‘15] Meibohm, Pawlowski ‘15] minimally coupled SM matter fields compatible with asymptotic safety in simple truncation [Dona, A.E., Percacci ’13]

Motivation: Why matter & quantum gravity? Observational viability of quantum gravity models: - must reduce to GR in classical limit probes of dynamical gravity regime: experimental challenge - must accommodate all observed matter degrees of freedom example: chiral (i.e., light) fermions X asymptotic safety 7 causal sets: X LQG (in truncation) fermions ??? [A.E., Gies ’11; [Barnett, Smolin ‘15] [Gambini, Pullin ‘15] Meibohm, Pawlowski ‘15] minimally coupled SM matter fields compatible with asymptotic safety in simple truncation [Dona, A.E., Percacci ’13] - must be consistent with the properties of matter at low energies (charges, interaction strengths, masses….)

Motivation: Why matter & quantum gravity? Observational viability of quantum gravity models: - must reduce to GR in classical limit probes of dynamical gravity regime: experimental challenge - must accommodate all observed matter degrees of freedom example: chiral (i.e., light) fermions X asymptotic safety 7 causal sets: X LQG (in truncation) fermions ??? [A.E., Gies ’11; [Barnett, Smolin ‘15] [Gambini, Pullin ‘15] Meibohm, Pawlowski ‘15] minimally coupled SM matter fields compatible with asymptotic safety in simple truncation [Dona, A.E., Percacci ’13] - must be consistent with the properties of matter at low energies (charges, interaction strengths, masses….) Higgs discovery: Standard Model consistent up to high scales →

Implications of the Higgs discovery only for narrow window of values of Higgs masses can we reach high scales without requiring new physics M H = λ · 246 GeV V [ H ] = λ H 4 λ triviality k vacuum stability [Ellis et al. ‘09] [Ellis et al. ‘09]

Implications of the Higgs discovery only for narrow window of values of Higgs masses can we reach high scales without requiring new physics M H = λ · 246 GeV V [ H ] = λ H 4 λ triviality k vacuum stability [Ellis et al. ‘09] Does gravity provide UV completion for the SM?

A window into Planck-scale physics at the electroweak scale 1.0 g 3 y t low-energy data 0.8 constrains g 2 0.6 SM couplings high-energy physics g 1 0.4 0.2 Λ y b 0.0 10 10 10 12 10 14 10 16 10 18 10 20 10 2 10 4 10 6 10 8 RGE scale Μ in GeV [Butazzo et al. ‘13] It’s about 1/3 glucose, 1/3 fructose and 1/3 It’s about water 1/2 fructose and 1/2 water A B low-energy data: viscosity of honey: matched by model A

Higgs sector & quantum gravity V [ H 2 ] 1.0 h H 2 + λ H 4 Γ k = ... + m 2 g 3 y t X 0.8 y q H ¯ q R q L + .. + q SM couplings g 2 0.6 g 1 0.4 0.2 m in TeV Λ → M top ≈ 173 GeV y t ( M Pl ) ≈ 0 . 4 y b 0.0 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 y b ( M Pl ) ≈ 0 → M bottom ≈ 4 GeV [Buttazzo et al. ‘13] RGE scale Μ in GeV

Higgs sector & quantum gravity 1.0 assume: g 3 y t 0.8 no new physics below M Planck SM couplings g 2 0.6 g 1 → quantum gravity must allow 0.4 0.2 m in TeV Λ → M top ≈ 173 GeV y t ( M Pl ) ≈ 0 . 4 y b 0.0 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 y b ( M Pl ) ≈ 0 → M bottom ≈ 4 GeV [Buttazzo et al. ‘13] RGE scale Μ in GeV

Higgs sector & quantum gravity 1.0 assume: g 3 y t 0.8 no new physics below M Planck SM couplings g 2 0.6 g 1 → quantum gravity must allow 0.4 0.2 m in TeV Λ → M top ≈ 173 GeV y t ( M Pl ) ≈ 0 . 4 y b 0.0 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 y b ( M Pl ) ≈ 0 → M bottom ≈ 4 GeV [Buttazzo et al. ‘13] RGE scale Μ in GeV 1.0 g 2 : UV- attractive (relevant): 0.5 any value can be reached in IR 0.0 g 2 g 1 : UV- repulsive (irrelevant): - 0.5 IR-value fixed - 1.0 - 0.5 0.0 0.5 1.0 g 1 → Irrelevant couplings in the Higgs sector could allow predictions

Yukawa coupling in quantum gravity

Yukawa coupling in quantum gravity toy model of the Higgs-Yukawa sector coupled to gravity: Γ k = Z φ Z d 4 x p g g µ ν ∂ µ φ∂ ν φ + i Z ψ Z d 4 x p g ¯ Z d 4 x p g φ ¯ ψ / r ψ + i y ψψ 2 1 Z d 4 x √ g ( R − 2 λ ) + S gf − 16 π G N

Yukawa coupling in quantum gravity toy model of the Higgs-Yukawa sector coupled to gravity: Γ k = Z φ Z d 4 x p g g µ ν ∂ µ φ∂ ν φ + i Z ψ Z d 4 x p g ¯ Z d 4 x p g φ ¯ ψ / r ψ + i y ψψ 2 1 Z d 4 x √ g ( R − 2 λ ) + S gf A.E., A. Held, J. Pawlowski ‘16 − 16 π G N see also Zanusso, Zambelli, Vacca, Percacci, ’09 Oda, Yamada ‘15 quantum-gravity effects on Yukawa coupling (Functional Renormalization Group)

Yukawa coupling in quantum gravity α = 1 , β = 1 β y = ( η φ / 2 + η ψ ) y + 60 − 5 η φ − 6 η ψ y 3 + G y 32 + η ψ 480 π 2 10 π β G = 2 G − G 2 43 6 π + ... A.E., A. Held, J. Pawlowski ‘16

Yukawa coupling in quantum gravity for α = 1 , β = 1 β y = ( η φ / 2 + η ψ ) y + 60 − 5 η φ − 6 η ψ y 3 + G y 32 + η ψ 480 π 2 10 π β G = 2 G − G 2 43 6 π + ... A.E., A. Held, J. Pawlowski ‘16 1.0 0.8 G > 0 fixed point at , y = 0 → 0.6 G 0.4 0.2 0.0 - 1.0 - 0.5 0.0 0.5 1.0 y

Yukawa coupling in quantum gravity α = 1 , β = 1 β y = ( η φ / 2 + η ψ ) y + 60 − 5 η φ − 6 η ψ y 3 + G y 32 + η ψ 480 π 2 10 π β G = 2 G − G 2 43 UV repulsive 6 π + ... A.E., A. Held, J. Pawlowski ‘16 1.0 UV attractive 0.8 G > 0 fixed point at , y = 0 → 0.6 G 0.4 0.2 0.0 - 1.0 - 0.5 0.0 0.5 1.0 y