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 m H ❂ 125 ✿ 15 ✝ 0 ✿ 24GeV ❁ m Landau ❂ 175GeV max

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 ✡ DM h 2 ✘ 3 ✂ 10 � 27 cm 3 s � 1 WIMP relic density ❤ ✛ v rel ✐

✦ ❂ ✚ ❂ WIMP Dark Matter weakly interacting massive particles ✡ DM h 2 ✘ 3 ✂ 10 � 27 cm 3 s � 1 WIMP relic density ❤ ✛ v rel ✐ reduced Hubble constant h ❂ H 0 ❂ ✭ 100kms � 1 Mpc � 1 ✮

WIMP Dark Matter weakly interacting massive particles ✡ DM h 2 ✘ 3 ✂ 10 � 27 cm 3 s � 1 WIMP relic density ❤ ✛ v rel ✐ reduced Hubble constant h ❂ H 0 ❂ ✭ 100kms � 1 Mpc � 1 ✮ WIMP ‘miracle’ WIMPs are cold i.e. ✦ ❂ p ✚ ❂ 0

Connections to the Standard Model

Connections to the Standard Model ✑ ✁ ✏ E Fermion(s), scalar(s), vector boson(s) M fermions ✥ ❬ 3 ❂ 2 ❪ scalars ✣ ❬ 1 ❪ vectors A ✖ ❬ 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 ✕ H ✤ ❖ DM H ② H ✮ Higgs Portal coupling: 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 ✕ H ✤ ❖ DM H ② H ✮ Higgs Portal coupling: 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 Asymptotic Safety Freedom Scale invariance at a Gaussian Scale invariance at a non- fixed point ensures a free (per- Gaussian fixed point ensures a turbatively renormalizable) UV safe (non-perturbatively renor- theory malizable) UV theory

Asymptotic Safety conjecture ■ Fact: Einstein-Hilbert action is perturbatively non-renormalizable in d=4 ’t Hooft & Veltman 1974, Goroff & Sagnotti 1985 ❘ d d x ♣ g ❬ � R ✰ 2 ✄❪ 1 S EH ❂ 16 ✙ G ❬ G ❪ ❂ ❬ M ❪ 2 � d ■ Non-perturbatively renormalizable? ✦ Asymptotic Safety scenario Weinberg 1976

FRG Macroscopic Action Microscopic Action Scale-dependent Effective Action ✏ ✑ � 1 � ✭ 2 ✮ k ❅ k � k ❂ 1 2 STr ✰ ❘ k k ❅ k ❘ k k Wetterich ’93

Critical Exponents Classification of flow around fixed point g ✄ ☞ ❅ t g i ❂ ☞ i ✭ g ✄ ✮✰ P ☞ g n ❂ g ✄ ✭ g j � g ✄ j ✮✰ ✁✁✁ ✙ P ❅☞ i ☞ j M ij ✍ g j j ❅ g j ❂ 0 eigenvalue Solution of RG eq. ✏ k ✑ � ✒ I i ✰ P g i ✭ k ✮ ❂ g ✄ I C I V I ✄ i

✤ ✣ ✕ ✣ ✣ ✕ ✤ ✤ ✮ ❬ ✕ ✣ ❪ ❂ ❬ ✕ ✤ ❪ ❂ A Higgs Portal in Asymptotic Safety ✕ H ✤ ❖ DM H ② H Higgs Portal coupling:

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

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

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

Effective Action � k ❂� EH k ✰� matter k ❘ d 4 x ♣ g ❬ � R ✰ 2 ✄❪✰ S gf ✰ S gh 1 � EH k ❬ g ❪❂ 16 ✙ G ❤ ✐ ❘ d 4 x ♣ g V ✭ ✣❀✤ ✮✰ Z k ❀✣ 2 g ✖✗ ❅ ✖ ✣❅ ✗ ✣ ✰ Z k ❀✤ � matter 2 g ✖✗ ❅ ✖ ✤❅ ✗ ✤ ❬ ✣❀✤ ❪❂ k with m 2 m 2 2 ✣ 2 ✰ ✕ ✣ 8 ✣ 4 ✰ ✕ ✣✤ 8 ✤ 2 ✣ 2 ✰ 2 ✤ 2 ✰ ✕ ✤ 8 ✤ 4 V ✭ ✣❀✤ ✮❂ ✣ ✤

✮ Fixed points g ✄ ✮ ❂ 0 All beta functions vanish: ☞ i ✭ ❡ Fixed point indicates scale-invariant regime This work: Gaussian matter-fixed point, i.e. m 2 ✣ ✄ ❂ m 2 ✤ ✄ ❂ ✕ ✣ ✄ ❂ ✕ ✤ ✄ ❂ ✕ ✣✤ ✄ ❂ 0

Fixed points g ✄ ✮ ❂ 0 All beta functions vanish: ☞ i ✭ ❡ Fixed point indicates scale-invariant regime This work: Gaussian matter-fixed point, i.e. m 2 ✣ ✄ ❂ m 2 ✤ ✄ ❂ ✕ ✣ ✄ ❂ ✕ ✤ ✄ ❂ ✕ ✣✤ ✄ ❂ 0 ✮ Expected by shift symmetry

θ λ Λ Λ 2.0 η h = 0 η h =- 2 1.5 η h = 1 1.0 θ m 0.5 0.0 - 0.5 - 1.0 - 1.0 - 0.8 - 0.6 - 0.4 - 0.2 0.0 0.2 0.4 ˜ * 0.0 η h = 1 η h =- 2 - 0.5 η h = 0 - 1.0 - 1.5 - 2.0 - 2.0 - 1.5 - 1.0 - 0.5 0.0 0.5 1.0 ˜ *

20 15 ˜ * G 10 5 0 - 1.0 - 0.8 - 0.6 - 0.4 - 0.2 0.0 0.2 0.4 ˜ * Λ

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 ✒ m 2 ❃ 0 ✒ m 2 ❁ 0 -Gravitational Dark Matter -Gravitational Dark Matter -Misalignment Mechanism -Misalignment Mechanism + Resurgence mechanism

✒ ✕ ❁ 0 Decoupled dark sector ✒ m 2 ❃ 0 ✒ m 2 ❁ 0 -Gravitational Dark Matter -Gravitational Dark Matter -Misalignment Mechanism -Misalignment Mechanism + Resurgence mechanism

✮ ❁ � ❂ ❴ ❂ ■ ✏ ✑ ■ ✮ � ✣ ✙ ✭ ✮ ✙ ❂ ❖ ✭ ✮ ■ ❀ Thermal Gravitational Dark Matter? hGk B T ✮ 2 ✘ ✭ k B T ✮ 2 ❂ M 4 ■ Cross-section: ❤ ✛ v ✐ ✘ ✭✖ P

Thermal Gravitational Dark Matter? hGk B T ✮ 2 ✘ ✭ k B T ✮ 2 ❂ M 4 ■ Cross-section: ❤ ✛ v ✐ ✘ ✭✖ P ✮ Cross-section supressed for k B T ❁ M P ■ Interaction rate � vs. Expansion of the universe H ❂ ❴ a ❂ a ✏ ✑ 3 H ✙ G 2 M P ✭ k B T ✮ 3 ✙ ■ ✮ � ✣ T 10 32 K ■ T max ❀ universe ❂ ❖ ✭ 10 29 K ✮

Misalignment Mechanism ■ Spatially homogeneous, but time-dependent initial field value ✤ 1 ✭ t ✮ ✢ 0 ✤ ✰ m 2 ✤ ✰ 3 H ❴ ⑧ ✤ ✤ ❂ 0 Note: m ✤ ✻ ❂ m ✤ ✭ T ✮ ■ Not so early Early universe ( H ✢ m ✤ ) universe ( H ✜ m ✤ ) Cross-over 3 H ✭ T ✤ ✮ ❂ m ✤