A Higgs Portal in Asymptotic Safety? Johannes Lumma based on work - - PowerPoint PPT Presentation

A Higgs Portal in Asymptotic Safety?

Johannes Lumma

based on work with Astrid Eichhorn, Yuta Hamada and Masatoshi Yamada Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

November 14, 2017

Buttazzo et al. (2014), arxiv: 1307.3536

Gabrielli et al. (2014), arxiv: 1309.6632

mH ❂ 125✿15✝0✿24GeV❁mLandau

max

❂ 175GeV

Standard Model possibly valid up to the Planck scale But What about Beyond Standard Model (BSM) phenomena?

(Neutrino masses ✫ oscillations, Dark Matter, bayron asymmetry✿✿✿)

Standard Model possibly valid up to the Planck scale But What about Beyond Standard Model (BSM) phenomena?

(Neutrino masses ✫ oscillations, Dark Matter, bayron asymmetry✿✿✿)

Outline

■ General basics of Dark Matter ■ ■ ■ ■

Outline

■ General basics of Dark Matter ■ WIMP Dark Matter ■ ■ ■

Outline

■ General basics of Dark Matter ■ WIMP Dark Matter ■ Connections to the Standard Model ■ ■

Outline

■ General basics of Dark Matter ■ WIMP Dark Matter ■ Connections to the Standard Model ■ Higgs Portal to the Dark sector ■

Outline

■ General basics of Dark Matter ■ WIMP Dark Matter ■ Connections to the Standard Model ■ Higgs Portal to the Dark sector ■ Compatibility with Asymptotic Safety

Dark Matter basics

Dark Matter basics

■ Baryonic Matter only makes up 5% of the energy density of

the universe

■ ■

■ ■ ■ ■

Dark Matter basics

■ Baryonic Matter only makes up 5% of the energy density of

the universe

■ Particle? primordial Black Holes? MOND? ■

■ ■ ■ ■

Dark Matter basics

■ Baryonic Matter only makes up 5% of the energy density of

the universe

■ Particle? primordial Black Holes? MOND? ■ BUT we know there is something

■ ■ ■ ■

Dark Matter basics

■ Baryonic Matter only makes up 5% of the energy density of

the universe

■ Particle? primordial Black Holes? MOND? ■ BUT we know there is something

■ Galaxy rotation curves ■ Gravitational Lensing ■ Hot Gas ■ Bullet Cluster

Dark Matter basics

■ Baryonic Matter only makes up 5% of the energy density of

the universe

■ Particle? primordial Black Holes? MOND? ■ BUT we know there is something

■ Galaxy rotation curves ■ Gravitational Lensing ■ Hot Gas ■ Bullet Cluster

WIMP Dark Matter

weakly interacting massive particles WIMP relic density ✡DMh2 ✘ 3✂1027cm3s1

❤✛vrel✐

❂ ❂✭

• ✮

✦ ❂ ✚ ❂

WIMP Dark Matter

weakly interacting massive particles WIMP relic density ✡DMh2 ✘ 3✂1027cm3s1

❤✛vrel✐

reduced Hubble constant h ❂ H0❂✭100kms1Mpc1✮ ✦ ❂ ✚ ❂

WIMP Dark Matter

weakly interacting massive particles WIMP relic density ✡DMh2 ✘ 3✂1027cm3s1

❤✛vrel✐

reduced Hubble constant h ❂ H0❂✭100kms1Mpc1✮ WIMP ‘miracle’ WIMPs are cold i.e. ✦ ❂ p

✚ ❂ 0

Connections to the Standard Model

Connections to the Standard Model

Fermion(s), scalar(s), vector boson(s)

✏ E

M

✑✁

fermions ✥ scalars ✣ vectors A✖ ❬3❂2❪ ❬1❪ ❬1❪ We must include all operators allowed by symmetries! renormalizable operators are relevant in an EFT framework

Higgs Portal to the Dark Side

Higgs Portal to the Dark Sector

Silvera & Zee 1985, McDonald 1994, Burgess 2001

QFT tells us that we must include all operators allowed by symmetries ✮ Higgs Portal coupling: ✕H✤❖DMH ②H If ❖DM ❂ ✣2, ❬✕H✤❪ ❂ 0 ✦

Higgs Portal to the Dark Sector

Silvera & Zee 1985, McDonald 1994, Burgess 2001

QFT tells us that we must include all operators allowed by symmetries ✮ Higgs Portal coupling: ✕H✤❖DMH ②H If ❖DM ❂ ✣2, ❬✕H✤❪ ❂ 0 ✦ Might be relevant in the IR

Higgs Portal to the Dark Sector

Assume a scalar singlet Dark Matter candidate Constraints from direct detection experiments, indirect detection experiments and collider experiments

Can Quantum Gravity provide an explanation?

Asymptotic Safety & the FRG

Asymptotic Freedom

Scale invariance at a Gaussian fixed point ensures a free (per- turbatively renormalizable) UV theory

Asymptotic Freedom

Scale invariance at a Gaussian fixed point ensures a free (per- turbatively renormalizable) UV theory

Asymptotic Safety

Scale invariance at a non- Gaussian fixed point ensures a safe (non-perturbatively renor- malizable) UV theory

Asymptotic Safety conjecture

■ Fact: Einstein-Hilbert action is perturbatively

non-renormalizable in d=4

’t Hooft & Veltman 1974, Goroff & Sagnotti 1985

SEH ❂

1 16✙G

❘ ddx♣g❬R ✰2✄❪

❬G❪ ❂ ❬M❪2d

■ Non-perturbatively renormalizable? ✦ Asymptotic Safety

scenario

Weinberg 1976

FRG

Microscopic Action Macroscopic Action Scale-dependent Effective Action k❅kk ❂ 1

2STr

✏

✭2✮

k

✰❘k

✑1

k❅k❘k

Wetterich ’93

Critical Exponents

Classification of flow around fixed point g✄

❅tgi ❂ ☞i ✭g✄✮✰ P

j

❅☞i ❅gj

☞ ☞ ☞gn❂g✄✭gj g✄j ✮✰✁✁✁ ✙ P

j Mij ✍gj

❂ 0

Solution of RG eq.

gi✭k✮ ❂ g✄

i ✰ P I CI V I i

✏k

✄

✑✒I eigenvalue

A Higgs Portal in Asymptotic Safety

Higgs Portal coupling: ✕H✤❖DM H ②H ✤ ✣ ✕✣✣ ✕✤✤ ✮ ❬✕✣❪ ❂ ❬✕✤❪ ❂

A Higgs Portal in Asymptotic Safety

Higgs Portal coupling: ✕H✤❖DM H ②H singlet scalar field ✤ ✣ ✕✣✣ ✕✤✤ ✮ ❬✕✣❪ ❂ ❬✕✤❪ ❂

A Higgs Portal in Asymptotic Safety

Higgs Portal coupling: ✕H✤❖DM H ②H singlet scalar field ✤ singlet scalar field ✣ ✕✣✣ ✕✤✤ ✮ ❬✕✣❪ ❂ ❬✕✤❪ ❂

A Higgs Portal in Asymptotic Safety

Higgs Portal coupling: ✕H✤❖DM H ②H singlet scalar field ✤ singlet scalar field ✣ Consider also ✕✣✣4 and ✕✤✤4 ✮ ❬✕✣❪ ❂ ❬✕✤❪ ❂ 0

Effective Action

k ❂EH

k ✰matter k

EH

k ❬g❪❂ 1 16✙G

❘ d4x♣g❬R ✰2✄❪✰Sgf ✰Sgh

matter

k

❬✣❀✤❪❂

❘ d4x♣g ❤

V ✭✣❀✤✮✰ Zk❀✣

2 g✖✗❅✖✣❅✗✣✰ Zk❀✤ 2 g✖✗❅✖✤❅✗✤

✐

with V ✭✣❀✤✮❂

m2

✣

2 ✣2 ✰ ✕✣ 8 ✣4 ✰ ✕✣✤ 8 ✤2✣2 ✰ m2

✤

2 ✤2 ✰ ✕✤ 8 ✤4

Fixed points

All beta functions vanish: ☞i✭❡ g✄✮ ❂ 0 Fixed point indicates scale-invariant regime This work: Gaussian matter-fixed point, i.e. m2

✣✄ ❂ m2 ✤✄ ❂ ✕✣✄ ❂ ✕✤✄ ❂ ✕✣✤✄ ❂ 0

✮

Fixed points

All beta functions vanish: ☞i✭❡ g✄✮ ❂ 0 Fixed point indicates scale-invariant regime This work: Gaussian matter-fixed point, i.e. m2

✣✄ ❂ m2 ✤✄ ❂ ✕✣✄ ❂ ✕✤✄ ❂ ✕✣✤✄ ❂ 0

✮ Expected by shift symmetry

ηh= 0 ηh=-2 ηh= 1

• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.0 0.2 0.4

• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0

Λ ˜* θm

ηh= 0 ηh=-2 ηh= 1

• 2.0
• 1.5
• 1.0
• 0.5

0.0 0.5 1.0

• 2.0
• 1.5
• 1.0
• 0.5

0.0

Λ ˜* θλ

• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.0 0.2 0.4 5 10 15 20 Λ ˜* G ˜*

Potential phenomenological implications

■ Portal coupling irrelevant in the entire gravitational

parameter space ✮ Non-thermal productions mechanisms

■ Gravitational Dark Matter ■ Misalignment Mechanism

✒✕ ❁ 0 Decoupled dark sector ✒m2 ❃ 0 ✒m2 ❁ 0

• Gravitational Dark Matter
• Misalignment Mechanism

+ Resurgence mechanism

• Gravitational Dark Matter
• Misalignment Mechanism

✒✕ ❁ 0 Decoupled dark sector ✒m2 ❃ 0 ✒m2 ❁ 0

• Gravitational Dark Matter
• Misalignment Mechanism

+ Resurgence mechanism

• Gravitational Dark Matter
• Misalignment Mechanism

Thermal Gravitational Dark Matter?

■ Cross-section: ❤✛v✐ ✘ ✭✖

hGkBT✮2 ✘ ✭kBT✮2❂M 4

P

✮ ❁

■

• ❂ ❴ ❂

■ ✮ ✣ ✙

✭ ✮ ✙

✏ ✑

■ ❀

❂ ❖✭ ✮

Thermal Gravitational Dark Matter?

■ Cross-section: ❤✛v✐ ✘ ✭✖

hGkBT✮2 ✘ ✭kBT✮2❂M 4

P

✮ Cross-section supressed for kBT ❁ MP

■ Interaction rate vs. Expansion of the universe H ❂ ❴

a❂a

■ ✮ ✣ H ✙ G2MP ✭kBT✮3 ✙

✏

T 1032K

✑3

■ Tmax❀universe ❂ ❖✭1029K✮

Misalignment Mechanism

■ Spatially homogeneous, but time-dependent initial field

value ✤1✭t✮ ✢ 0

■

⑧ ✤✰3H ❴ ✤✰m2

✤✤ ❂ 0

Note: m✤ ✻❂ m✤✭T✮ Early universe (H ✢ m✤) Not so early universe (H ✜ m✤) Cross-over 3H✭T✤✮ ❂ m✤

Misalignment Mechanism

■ Spatially homogeneous, but time-dependent initial field

value ✤1✭t✮ ✢ 0

■

⑧ ✤✰3H ❴ ✤✰m2

✤✤ ❂ 0

Note: m✤ ✻❂ m✤✭T✮ Determine the dark matter mass m✤

✮

✚✤✭

✤✮

✭

✤✮ ❂ ✚✤✭

✮ ✭ ✮

Misalignment Mechanism

■ Spatially homogeneous, but time-dependent initial field

value ✤1✭t✮ ✢ 0

■

⑧ ✤✰3H ❴ ✤✰m2

✤✤ ❂ 0

Note: m✤ ✻❂ m✤✭T✮ Determine the dark matter mass m✤

✮ Consider

✚✤✭T✤✮ s✭T✤✮ ❂ ✚✤✭T0✮ s✭T0✮

Misalignment Mechanism

■ Spatially homogeneous, but time-dependent initial field

value ✤1✭t✮ ✢ 0

■

⑧ ✤✰3H ❴ ✤✰m2

✤✤ ❂ 0

Note: m✤ ✻❂ m✤✭T✮ Determine the dark matter mass m✤

✮ Consider

✚✤✭T✤✮ s✭T✤✮ ❂ ✚✤✭T0✮ s✭T0✮ Measured by Planck Collaboration

Misalignment Mechanism

■ Spatially homogeneous, but time-dependent initial field

value ✤1✭t✮ ✢ 0

■

⑧ ✤✰3H ❴ ✤✰m2

✤✤ ❂ 0

Note: m✤ ✻❂ m✤✭T✮ Determine the dark matter mass m✤

✮ Consider

✚✤✭T✤✮ s✭T✤✮ ❂ ✚✤✭T0✮ s✭T0✮ Measured by Planck Collaboration ✚✤✭T✤✮ ✘ 1

2m2 ✤✤2 1

✭

✤✮ ✘ ✤

Misalignment Mechanism

■ Spatially homogeneous, but time-dependent initial field

value ✤1✭t✮ ✢ 0

■

⑧ ✤✰3H ❴ ✤✰m2

✤✤ ❂ 0

Note: m✤ ✻❂ m✤✭T✮ Determine the dark matter mass m✤

✮ Consider

✚✤✭T✤✮ s✭T✤✮ ❂ ✚✤✭T0✮ s✭T0✮ Measured by Planck Collaboration ✚✤✭T✤✮ ✘ 1

2m2 ✤✤2 1

s✭T✤✮ ✘ T 3

✤

Misalignment Mechanism

Recall: Cross-over temperature 3H✭T✤✮ ❂ m✤ ✦ Solve for T✤

✮

✤ ✘

• ✒

✤

✓

Misalignment Mechanism

Recall: Cross-over temperature 3H✭T✤✮ ❂ m✤ ✦ Solve for T✤

✮ m✤ ✘ 1020 eV

✒

1017 GeV ✤1

✓4

✒✕ ❁ 0 Decoupled dark sector ✒m2 ❃ 0 ✒m2 ❁ 0

• Gravitational Dark Matter
• Misalignment Mechanism

+ Resurgence mechanism

• Gravitational Dark Matter
• Misalignment Mechanism

❡

❂ ❡

✄

✁✒

★

✄

✒✕ ❁ 0 Decoupled dark sector ✒m2 ❃ 0 ✒m2 ❁ 0

• Gravitational Dark Matter
• Misalignment Mechanism

+ Resurgence mechanism

• Gravitational Dark Matter
• Misalignment Mechanism

❡

m2 ❂ ❡ m2

k

✄

✁✒

★

need cut-off ✄

✒✕ ❁ 0 Decoupled dark sector ✒m2 ❃ 0 ✒m2 ❁ 0

• Gravitational Dark Matter
• Misalignment Mechanism

+ Resurgence mechanism

• Gravitational Dark Matter
• Misalignment Mechanism

❡

m2 ❂ ❡ m2

k

✄

✁✒

★

need cut-off ✄

Resurgence Mechanism

Masatoshi Yamada & Christof Wetterich 2017

■ ✒m2 ❁ 0 ✦ need cut-off ■ How to choose a clever cut-off?

log

✏

k MPl

✑

log

✏

MPl MPl

✑

❂ 1

m2 k 2

m✤Pl MPl ✘ 1047 ✏ MPl ✤1

✑4

m2

✤

k 2

✤ ❂ 1

log

✏ k✤

MPl

✑

✒

m

✙ 2 ✒ ❁

log

✏

k MPl

✑

log

✏

MPl MPl

✑

❂ 1

m2 k 2

m✤Pl MPl ✘ 1047 ✏ MPl ✤1

✑4

m2

✤

k 2

✤ ❂ 1

log

✏ k✤

MPl

✑

✒

m

✙ 2 ✒

m

❁

✒✕ ❁ 0 Decoupled dark sector ✒m2 ❃ 0 ✒m2 ❁ 0

• Gravitational Dark Matter
• Misalignment Mechanism

+ Resurgence mechanism

• Gravitational Dark Matter
• Misalignment Mechanism

❡

❂ ❡

✄

✁✒

★

✒✕ ❁ 0 Decoupled dark sector ✒m2 ❃ 0 ✒m2 ❁ 0

• Gravitational Dark Matter
• Misalignment Mechanism

+ Resurgence mechanism

• Gravitational Dark Matter
• Misalignment Mechanism

❡

m2 ❂ ❡ m2

k

✄

✁✒

★

fundamental asymptotic safety

Conclusions

■ Dark sector decoupled from Standard Model ■ Non-thermal dark matter production mechanisms needed

(e.g. Misalignment mechanism)

■ Two regimes ✭✒2 m ❃ 0❀✒2 m ❁ 0✮