Gravitational waves from a dilaton-induced, first-order QCD phase transition

Abstract

We show that a `QCD dilaton' field, whose vacuum expectation value sets the strong coupling, can render the Quantum Chromodynamic (QCD) confinement transition first-order. The QCD dilaton is cosmologically attracted to a false vacuum at weak coupling in the early universe. Quantum tunnelling towards the true vacuum triggers prompt chiral symmetry breaking and confinement of QCD, leading to detonating bubbles of the hadronic phase. We find that plasma sound waves produced by this dilaton-induced, first-order QCD phase transition generate a stochastic gravitational wave signal strikingly similar to the recently detected gravitational wave background from Pulsar Timing Arrays. We briefly comment on how this theory can be probed through collider experiments and cosmology.

Figures (5)

• Figure 1: Left: The dilaton potential, $V_{\rm eff}(\phi)$, at different temperatures. The values of the potential are rescaled for visual clarity. For $T\sim100~\mathrm{TeV}\gg m_\phi$ the minimum is located in between the tree-level vacua. As temperature drops ($T\sim \mathcal{O}({\color{blue}1})~\mathrm{GeV}\ll m_\phi$), the minimum moves towards the $\phi_{\rm FV}$ while a local minimum emerges near $\phi_{\rm TV}$. When temperature corrections become unimportant, $\phi_{\rm TV}$ becomes the global minimum. Right: Schematic contour plot for the two-field potential, $V_{\rm tot}(\chi, \phi)$ for $T_{\rm QCD}^{\rm FV}<T<T_{\rm QCD}^{\rm TV}$.
• Figure 2: Gravitational wave spectra from a dilaton-induced QCD PT overlaid with NANOGrav 15-year free-spectrum constraints (two shades of gray violins). The red curve corresponds to the best-fit spectrum to the 14 lowest-frequency bins (darker gray). For more information, see the main text.
• Figure S1: Gravitational wave spectra from a dilaton-induced QCD PT overlaid with NANOGrav 15-year free-spectrum constraints (gray violins), including the contribution from bubble wall collisions. Solid lines show the spectra in the regime where the energy is carried by bubble walls, while dashed lines correspond to the regime where the energy is converted into sound waves, for comparison. The solid red curve corresponds to the best fit.
• Figure S2: The fit of the QCD pressure as provided by the HotQCD collaboration HotQCD:2014kol, for $T>T_{\rm QCD}=154$ MeV, normalised over the ideal gas pressure $\mathcal{P}_{\rm SB}=p_{\rm id}T^4$.
• Figure S3: The diagonal panels show the marginalised 1D distributions, while the off-diagonal panel displays the 2D contours at $1\sigma$ and $2\sigma$ credibility levels for sound wave (blue) and runaway wall (red) scenarios. Raw data for this figure is available at dataset.