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

Quantum-gravity effects

• n a Higgs-Yukawa model

Astrid Eichhorn University of Heidelberg September 22, 2016 ERG 2016, ICTP, Trieste

with Aaron Held and Jan Pawlowski

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 molecules It’s about 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 molecules It’s about 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 molecules It’s about 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 molecules It’s about 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 molecules It’s about 1/2 fructose and 1/2 water molecules

A B

No ``smoking-gun’’ signal for any particular QG model, but: could rule out models this way! 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
• must accommodate all observed matter degrees of freedom

probes of dynamical gravity regime: experimental challenge example: chiral (i.e., light) fermions

asymptotic safety

(in truncation)

[A.E., Gies ’11; Meibohm, Pawlowski ‘15]

X

LQG

[Gambini, Pullin ‘15]

X 7

[Barnett, Smolin ‘15]

causal sets: fermions ???

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
• must accommodate all observed matter degrees of freedom

(charges, interaction strengths, masses….)

• must be consistent with the properties of matter at low energies

probes of dynamical gravity regime: experimental challenge example: chiral (i.e., light) fermions

asymptotic safety

(in truncation)

[A.E., Gies ’11; Meibohm, Pawlowski ‘15]

X

LQG

[Gambini, Pullin ‘15]

X 7

[Barnett, Smolin ‘15]

causal sets: fermions ???

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
• must accommodate all observed matter degrees of freedom

→

Higgs discovery: Standard Model consistent up to high scales

(charges, interaction strengths, masses….)

• must be consistent with the properties of matter at low energies

probes of dynamical gravity regime: experimental challenge example: chiral (i.e., light) fermions

asymptotic safety

(in truncation)

[A.E., Gies ’11; Meibohm, Pawlowski ‘15]

X

LQG

[Gambini, Pullin ‘15]

X 7

[Barnett, Smolin ‘15]

causal sets: fermions ???

minimally coupled SM matter fields compatible with asymptotic safety in simple truncation

[Dona, A.E., Percacci ’13]

Implications of the Higgs discovery

V [H] = λ H4

triviality vacuum stability

[Ellis et al. ‘09]

k λ

MH = λ · 246 GeV

• nly for narrow window of values of

Higgs masses can we reach high scales without requiring new physics

[Ellis et al. ‘09]

Implications of the Higgs discovery

k λ

V [H] = λ H4

triviality vacuum stability

MH = λ · 246 GeV

• nly for narrow window of values of

Higgs masses can we reach high scales without requiring new physics

[Ellis et al. ‘09]

Does gravity provide UV completion for the SM?

A window into Planck-scale physics at the electroweak scale

102 104 106 108 1010 1012 1014 1016 1018 1020 0.0 0.2 0.4 0.6 0.8 1.0 RGE scale Μ in GeV SM couplings g1 g2 g3 yt Λ yb

[Butazzo et al. ‘13]

low-energy data: viscosity of honey: matched by model A

It’s about 1/3 glucose, 1/3 fructose and 1/3 water It’s about 1/2 fructose and 1/2 water

A B low-energy data constrains high-energy physics

Higgs sector & quantum gravity

102 104 106 108 1010 1012 1014 1016 1018 1020 0.0 0.2 0.4 0.6 0.8 1.0 RGE scale Μ in GeV SM couplings g1 g2 g3 yt Λ yb m in TeV

→ Mtop ≈ 173 GeV

yt(MPl) ≈ 0.4 yb(MPl) ≈ 0 → Mbottom ≈ 4 GeV

[Buttazzo et al. ‘13]

V [H2]

Γk = ... + m2

hH2 + λH4

+ X

q

yqH ¯ qRqL + ..

Higgs sector & quantum gravity

102 104 106 108 1010 1012 1014 1016 1018 1020 0.0 0.2 0.4 0.6 0.8 1.0 RGE scale Μ in GeV SM couplings g1 g2 g3 yt Λ yb m in TeV

assume: no new physics below MPlanck → quantum gravity must allow → Mtop ≈ 173 GeV

yt(MPl) ≈ 0.4 yb(MPl) ≈ 0 → Mbottom ≈ 4 GeV

[Buttazzo et al. ‘13]

Higgs sector & quantum gravity

102 104 106 108 1010 1012 1014 1016 1018 1020 0.0 0.2 0.4 0.6 0.8 1.0 RGE scale Μ in GeV SM couplings g1 g2 g3 yt Λ yb m in TeV

assume: no new physics below MPlanck → quantum gravity must allow → Mtop ≈ 173 GeV

• 0.5

0.0 0.5 1.0

• 1.0
• 0.5

0.0 0.5 1.0 g1 g2

g2: UV- attractive (relevant):

any value can be reached in IR

g1: UV- repulsive (irrelevant):

IR-value fixed

→ Irrelevant couplings in the Higgs sector could allow predictions

yt(MPl) ≈ 0.4 yb(MPl) ≈ 0 → Mbottom ≈ 4 GeV

[Buttazzo et al. ‘13]

Yukawa coupling in quantum gravity

Yukawa coupling in quantum gravity

toy model of the Higgs-Yukawa sector coupled to gravity:

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ − 1 16πGN Z d4x√g (R − 2λ) + Sgf

Yukawa coupling in quantum gravity

toy model of the Higgs-Yukawa sector coupled to gravity:

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

quantum-gravity effects on Yukawa coupling (Functional Renormalization Group)

− 1 16πGN Z d4x√g (R − 2λ) + Sgf

A.E., A. Held, J. Pawlowski ‘16 see also Zanusso, Zambelli, Vacca, Percacci, ’09 Oda, Yamada ‘15

Yukawa coupling in quantum gravity

βG = 2G − G2 43 6π + ... βy = (ηφ/2 + ηψ)y + 60 − 5ηφ − 6ηψ 480π2 y3 + G y 32 + ηψ 10π

A.E., A. Held, J. Pawlowski ‘16

α = 1, β = 1

Yukawa coupling in quantum gravity

fixed point at ,

y = 0

→

• 1.0
• 0.5

0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 y G

βG = 2G − G2 43 6π + ...

G > 0

βy = (ηφ/2 + ηψ)y + 60 − 5ηφ − 6ηψ 480π2 y3 + G y 32 + ηψ 10π

A.E., A. Held, J. Pawlowski ‘16

for α = 1, β = 1

Yukawa coupling in quantum gravity

fixed point at ,

y = 0

→

• 1.0
• 0.5

0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 y G

βG = 2G − G2 43 6π + ...

G > 0

βy = (ηφ/2 + ηψ)y + 60 − 5ηφ − 6ηψ 480π2 y3 + G y 32 + ηψ 10π UV attractive UV repulsive

A.E., A. Held, J. Pawlowski ‘16

α = 1, β = 1

Yukawa coupling in quantum gravity

fixed point at ,

y = 0

→

• 1.0
• 0.5

0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 y G

βG = 2G − G2 43 6π + ...

G > 0

βy = (ηφ/2 + ηψ)y + 60 − 5ηφ − 6ηψ 480π2 y3 + G y 32 + ηψ 10π UV attractive UV repulsive

A.E., A. Held, J. Pawlowski ‘16

α = 1, β = 1

y(MPl) ≈ 0 prediction (within toy model):

Yukawa coupling in quantum gravity

fixed point at ,

y = 0

→

• 1.0
• 0.5

0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 y G

βG = 2G − G2 43 6π + ...

G > 0

βy = (ηφ/2 + ηψ)y + 60 − 5ηφ − 6ηψ 480π2 y3 + G y 32 + ηψ 10π UV attractive y(MPl) ≈ 0 prediction (within toy model): UV repulsive

A.E., A. Held, J. Pawlowski ‘16

gauge dependence:

• J. Meibohm, J. Pawlowski,
• M. Reichert ‘15

Dona, A.E., Percacci ‘13 w. graviton ``mass” parameter from fluctuation calc.

α = 1, β = 1

Fµ = ¯ Dνhν

µ − 1 + β

4 ¯ Dµh

Becker, Reuter ‘14

102 104 106 108 1010 1012 1014 1016 1018 1020 0.0 0.2 0.4 0.6 0.8 1.0 RGE scale Μ in GeV SM couplings g1 g2 g3 yt Λ yb m in TeV

Yukawa coupling in quantum gravity

fixed point at ,

y = 0

→

• 1.0
• 0.5

0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 y G

βG = 2G − G2 43 6π + ...

G > 0

βy = (ηφ/2 + ηψ)y + 60 − 5ηφ − 6ηψ 480π2 y3 + G y 32 + ηψ 10π UV attractive → Mtop ≈ 173 GeV

yt(MPl) ≈ 0.4 yb(MPl) ≈ 0

→ Mbottom ≈ 4 GeV

[Buttazzo et al. ‘13]

UV repulsive

A.E., A. Held, J. Pawlowski ‘16

α = 1, β = 1

y(MPl) ≈ 0 prediction (within toy model):

Beyond canonical power counting

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

Can canonical interaction terms capture the full dynamics

• f matter

in quantum gravity?

Beyond canonical power counting

A.E., H. Gies ‘11 A.E. ‘12

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

Can canonical interaction terms capture the full dynamics

• f matter

in quantum gravity?

matter-gravity interaction vertices from kinetic term

generate new momentum-dependent matter self-interactions

Beyond canonical power counting

A.E., H. Gies ‘11 A.E. ‘12

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

Can canonical interaction terms capture the full dynamics

• f matter

in quantum gravity?

matter-gravity interaction vertices from kinetic term

• 0.5

0.5 1.0 1.5 2.0 2.5 ρ (matter self-coupling)

• 3
• 2
• 1

1 2 βρ

without gravity with gravity: interacting at fixed point

generate new momentum-dependent matter self-interactions

Beyond canonical power counting

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

A.E., A. Held, J. Pawlowski ‘16

Beyond canonical power counting

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

A.E., A. Held, J. Pawlowski ‘16

X1− k4 Z

x

pg ⇥ ¯ ψγµrνψ (rν ¯ ψ)γµψ

• ∂µφ∂νφ

⇤ + X2− k4 Z

x

pg ⇥ ¯ ψγµrµψ (rµ ¯ ψ)γµψ

• ∂νφ∂νφ

⇤

vertices depend on momenta of the matter fields:

Beyond canonical power counting

• 250
• 200
• 150
• 100
• 50

X

• 250
• 200
• 150
• 100
• 50

50 100 b X

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

A.E., A. Held, J. Pawlowski ‘16

X1− k4 Z

x

pg ⇥ ¯ ψγµrνψ (rν ¯ ψ)γµψ

• ∂µφ∂νφ

⇤ + X2− k4 Z

x

pg ⇥ ¯ ψγµrµψ (rµ ¯ ψ)γµψ

• ∂νφ∂νφ

⇤

= 1 √ 2 (χ1− + χ2−)

G=0 G=3 G=6

vertices depend on momenta of the matter fields:

strong gravity fluctuations appear incompatible with existence

• f fixed point in matter sector

Beyond canonical power counting

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

A.E., A. Held, J. Pawlowski ‘16

1 2 3 4 5 6 7 g 0.01 0.1 1 10 100 1000 Abs@ X 2 -

* D

X1− k4 Z

x

pg ⇥ ¯ ψγµrνψ (rν ¯ ψ)γµψ

• ∂µφ∂νφ

⇤ + X2− k4 Z

x

pg ⇥ ¯ ψγµrµψ (rµ ¯ ψ)γµψ

• ∂νφ∂νφ

⇤

vertices depend on momenta of the matter fields:

strong gravity fluctuations appear incompatible with existence

• f fixed point in matter sector

G

Beyond canonical power counting

Γk = Zφ 2 Z d4xpg gµν∂µφ∂νφ + i Zψ Z d4xpg ¯ ψ / rψ + i y Z d4xpgφ ¯ ψψ

A.E., A. Held, J. Pawlowski ‘16

strong gravity fluctuations appear incompatible with existence

• f fixed point in matter sector

X1− k4 Z

x

pg ⇥ ¯ ψγµrνψ (rν ¯ ψ)γµψ

• ∂µφ∂νφ

⇤ + X2− k4 Z

x

pg ⇥ ¯ ψγµrµψ (rµ ¯ ψ)γµψ

• ∂νφ∂νφ

⇤

vertices depend on momenta of the matter fields:

‡

1 2 3 4 5

• 1.0
• 0.5

0.0 0.5 1.0 g m h

2

fixed-point values (w/o from )

Meibohm, Pawlowksi, Reichert ‘15

χi−

ηψ,φ

but: critical interaction strength not exceeded (within truncation)

G

→ joint fixed point

Conclusions

• properties of the matter sector offer observational

consistency tests for quantum gravity

• microscopic model must admit all observed

properties of matter (values of masses etc)

• toy model of Higgs sector coupled to asymptotically safe

quantum gravity:

gravity does not exceed critical strength for fixed-point annihilation in Yukawa sector

y(MPl) ≈ 0 Outlook: Realistic Yukawa sector (top-bottom asymmetry) → → → momentum-dependent scalar-fermion

interactions