From dimensional reduction to droplets

Understanding strong first-order phase transitions

David J. Weir [he/they] - Helsinki - davidjamesweir

This talk: saoghal.net/slides/d2d

Gravitational Wave Probes of Physics Beyond the Standard Model, July 2021

Temperature slice from a simulation by Daniel Cutting

Hot, red areas are shrinking droplets

  • How do droplets form?
  • What are the consequences for gravitational waves?

Particle physics model
$\Downarrow \mathcal{L}_{4\mathrm{d}}$
Dimensional reduction
$\Downarrow \mathcal{L}_{3\mathrm{d}}$
Phase transition parameters from lattice simulations
$\Downarrow \alpha, \beta, T_N, \ldots$
Real time cosmological simulations
$\Downarrow \Omega_\text{gw}(f)$
Cosmological GW background

Key parameters bridge the gap

Including:

  • $\alpha$, the phase transition strength
  • $\beta$, the inverse phase transition duration
  • $T_N$, the nucleation temperature

A "pipeline"

Particle physics model
$\Downarrow \mathcal{L}_{4\mathrm{d}}$
Dimensional reduction
$\Downarrow \mathcal{L}_{3\mathrm{d}}$
Phase transition parameters from lattice simulations

$\Downarrow \alpha, \beta, T_N, \ldots$
Real time cosmological simulations
$\Downarrow \Omega_\text{gw}(f)$
Cosmological GW background

My focus: extensions of the Standard Model

$$ \mathcal{L}_{4\mathrm{d}} = \mathcal{L}_\text{SM}[\text{SM fields}] + \mathcal{L}_\text{BSM}[\text{SM fields},\ldots ?] $$

SM electroweak phase transition

  • Process by which the Higgs 'switched on'
  • In the Standard Model it is a crossover
  • Possible in extensions that it would be first order
    ➥ colliding bubbles then make gravitational waves


SM electroweak phase diagram


arXiv:hep-ph/9605288 ; arXiv:hep-lat/9704013; arXiv:hep-ph/9809291

How? Dimensional reduction

  • At high $T$, system looks 3D at distances $\Delta x \gg 1/T$
  • Each step involves matching Green's functions in the effective and full theories to the desired order.
  • Handles the infrared problem, light fields can be studied on lattice. arXiv:hep-ph/9508379

Using the dimensional reduction

  • Simulate DR'ed 3D theory on lattice arXiv:hep-let/9510020
  • With DR, integrate out heavy new physics and recycle

When new physics is heavy

Benchmark: ● 4d PT vs ● 3d PT vs ● lattice

arXiv:1903.11604

How to get strong transitions?

Need light physics or dim-6 operators

arXiv:1903.11604

DR: $\Sigma$SM (triplet) example

Perturbation theory doesn't see the phase transition!

arXiv:2005.11332

Key points so far

  • Dimensional reduction + lattice simulations a well-proven method for studying BSM theories
  • Higher dimensional operators or light new physics needed for a strong phase transition
  • Should benchmark perturbation theory with DR + lattice, particularly for strong transitions

Particle physics model
$\Downarrow \mathcal{L}_{4\mathrm{d}}$
Dimensional reduction ✅
$\Downarrow \mathcal{L}_{3\mathrm{d}}$
Phase transition parameters from lattice simulations ✅
$\Downarrow \alpha, \beta, T_N, \ldots$
Real time cosmological simulations
$\Downarrow \Omega_\text{gw}(f)$
Cosmological GW background

Particle physics model
$\Downarrow \mathcal{L}_{4\mathrm{d}}$
Dimensional reduction ✅
$\Downarrow \mathcal{L}_{3\mathrm{d}}$
Phase transition parameters from lattice simulations ✅
$\Downarrow \alpha, \beta, T_N, \ldots$
Real time cosmological simulations
$\Downarrow \Omega_\text{gw}(f)$
Cosmological GW background

Out of equilibrium physics

  1. Bubbles nucleate and grow
  2. Expand in a plasma - create reaction fronts
  3. Bubbles + fronts collide $\Omega_\text{col}(f)$
  4. Sound waves left behind in plasma $\Omega_\text{sw}(f)$
  5. Shocks [$\rightarrow$ turbulence] $\rightarrow$ damping $\Omega_\text{turb}(f)$

Simulating weak transitions: $\alpha \ll 1$

Explore $\Omega_\text{sw}(f)$ with PTPlot.org

Model ⟶ ($T_*$, $\alpha_{T_*}$, $v_\mathrm{w}$, $\beta$) ⟶ this plot

[Here: $Z_2$-symmetric xSM points from arXiv:1910.13125]

But what about strong transitions?

  • Nonlinearities during the transition:
    • Generation of vorticity
    • Droplets
  • Nonlinearities after the transition:
    • Shocks
    • turbulence
  • Let's take a look at droplets

Strong simulation velocity slice

[$\alpha_{T_*} = 0.34$, $v_\mathrm{w} = 0.24$ (deflag.)], velocity $\mathbf{v}$

Walls slow, droplets form

At large $\alpha_{T_*}$ reheated droplets form in front of the walls

Isolated spherical droplets

In the spherical case, we can get a self-similar droplet. We see the same wall velocity slowdown:

Droplets may suppress GWs

Suppression compared to sound waves (redder = worse)

arXiv:1906.00480

Thanks

  • Students:
    Anna Kormu, Lauri Niemi, Satumaaria Sukuvaara, Essi Vilhonen
  • Postdocs:
    Daniel Cutting, Oliver Gould
  • Collaborators:
    Jonathan Kozaczuk, Mark Hindmarsh, Stephan Huber, Hiren Patel, Michael Ramsey-Musolf, Kari Rummukainen, Tuomas Tenkanen

What I want you to remember

  • Dimensional reduction, a valuable field theory tool
    $\Rightarrow$ test perturbative studies of phase transitions
  • Strong phase transitions: hot droplets slow completion
    $\Rightarrow$ also suppress GW production

Questions you can ask me

  • How accurate are bubble nucleation calculations?
  • What about the onset of shocks and turbulence?
  • What other physics could explain the GW suppression seen in strong transitions?