Phenomenology of relaxion-Higgs mixing

TL;DR

This work shows that relaxion dynamics generically end at a CP-violating point, inducing a mixing with the Higgs and yielding a broad relaxion mass range from sub-eV to GeV. The authors derive the relaxion-Higgs mixing and couplings, and map a comprehensive set of constraints from laboratory experiments, cosmology, and astrophysics, including fifth-force tests, beam dumps, rare meson decays, LEP/LHC Higgs data, and cosmological distortions, highlighting that the backreaction scale Lambda_br is tightly constrained in large regions of parameter space. They also analyze clockwork (multiaxion) UV completions and show mild tuning issues that push toward lower cutoffs, connecting experimental bounds to theoretical space. Overall, the paper provides a unified framework for testing Higgs portal relaxions across vast mass and coupling ranges and demonstrates that present data already probe large portions of the viable theory space, with future experiments like SHiP, NA62, and PIXIE offering further reach. The results urge reconsideration of high-scale relaxion scenarios in light of the combined experimental constraints and CP-violating signatures.

Abstract

We show that the relaxion generically stops its rolling at a point that breaks CP leading to relaxion-Higgs mixing. This opens the door to a variety of observational probes since the possible relaxion mass spans a broad range from sub-eV to the GeV scale. We derive constraints from current experiments (fifth force, astrophysical and cosmological probes, beam dump, flavour, LEP and LHC) and present projections from future experiments such as NA62, SHiP and PIXIE. We find that a large region of the parameter space is already under the experimental scrutiny. All the experimental constraints we derive are equally applicable for general Higgs portal models. In addition, we show that simple multiaxion (clockwork) UV completions suffer from a mild fine tuning problem, which increases with the number of sites. These results favour a cut-off scale lower than the existing theoretical bounds.

Figures (6)

• Figure 1: Relaxion properties: (a) The relaxion mass $m_{\phi}$ as a function of $\Lambda_{{\rm br} }$ for different values of $f$, where the vertical gray line indicates $\Lambda_{{\rm br} }^{*}$ that maximizes $m_{\phi}$ for each $f$. Here $\Lambda_{\rm br }^{\rm{max} }$ is the upper bound on $\Lambda_{{\rm br} }$ arising from the requirement of a non-tachyonic $\phi$ in Eq. (\ref{['tach']}) for $\sin (\phi_0/f)=1/\sqrt{2}$. (b) The lifetime $\tau_{\phi}$ also depending on $m_{\phi}$ and $\sin^2\theta$ with thresholds (vertical gray lines) and example values of $\tau_{\phi}$ (horizontal gray lines). The lifetime for any other $\sin^2\theta$ value can be obtained from the $\sin^2\theta=1$ line using $\tau_\phi\sim 1/\sin^2\theta$.
• Figure 2: Constraints on the relaxion-Higgs mixing $\sin^2\theta$ for light relaxions with $m_{\phi}$ between $10^{-16}\,\textrm{GeV}$ and $10^{-7}\,\textrm{GeV}$. Fifth-force experiments (orange) probe the lightest mass range via the equivalence principle (labelled as EqP), the inverse square law (ISqL) and the Casimir effect (Casimir). Contours of constant $\Lambda_{\rm br}$ (gray) for $\Lambda_{\rm br}=0.99\Lambda_{\rm br }^{\rm{max} } \simeq 104\,\textrm{GeV}$ (gray, thick, solid) and $\Lambda_{\rm br}=5\,\textrm{GeV}$ (gray, dashed). Here $\Lambda_{\rm br }^{\rm{max} }$ is the upper bound on $\Lambda_{{\rm br} }$ arising from the requirement of a non-tachyonic $\phi$ in Eq. (\ref{['tach']}) for $\sin (\phi_0/f)=1/\sqrt{2}$. Contours of constant $f=M_{\rm{Pl} } , 10^{16}\,\textrm{GeV}, 10^{14}\,\textrm{GeV}$ (black, solid). The light gray region below the dotted gray line corresponds to trans-Planckian field excursions $\Delta\phi>M_{\rm{Pl} }$ for $\Lambda=2\,\textrm{TeV}$.
• Figure 3: Constraints on the relaxion-Higgs mixing $\sin^2\theta$ for relaxions with $m_{\phi}$ between MeV and 5 GeV. The laboratory probes include: proton beam dump experiments (red for CHARM, light red for the projected sensitivity for SHIP and SeaQuest), $K$-meson decays (blue, our conservative projection from NA62 in a lighter shade of blue), $B$-meson decays (turquoise), LHC search for $h\rightarrow 4 \mu$ (light blue) and LEP (green). Astrophysical and cosmological probes include the Supernova 1987a (pale violet, labelled as SN), $\eta_b$ (orange) and $N_{\text{eff}}$( pink). Contours for $\Lambda_{\rm br}=0.99\Lambda_{\rm br }^{\rm{max} } \simeq 104\,\textrm{GeV}$ (gray, thick, solid), $\Lambda_{\rm br}= 10 \,\textrm{GeV}$ (gray, dashed), $f/\,\textrm{GeV}=10^6, 10^4, 125$ (black, solid) are presented. Here $\Lambda_{\rm br }^{\rm{max} }$ is the upper bound on $\Lambda_{{\rm br} }$ arising from the requirement of a non-tachyonic $\phi$ in Eq. (\ref{['tach']}) for $\sin (\phi_0/f)=1/\sqrt{2}$. The vertical light gray line corresponds to the contour for the relaxion mass at the muon threshold; the yellow contour corresponds to $c \tau =2$ m and the purple one to $\tau = 1$ s.
• Figure 4: Constraints on the relaxion-Higgs mixing $\sin^2\theta$ for relaxions with $m_{\phi}$ between $5\,\textrm{GeV}$ and $90\,\textrm{GeV}$ from LEP and the LHC: 4-fermion final states from Higgs strahlung at LEP (green, labelled as LEP hZ); Higgs decays to NP with $\textrm{BR}(h \rightarrow\rm{NP})\leq20\%$ at the LHC (purple, solid) as well as a projection for $\textrm{BR}(h \rightarrow\rm{NP})\leq10\%$ (purple, dashed); explicit searches for $h\rightarrow\phi\phi$ with final states $4\tau$ (dark blue, dotted, $m_{\phi}<10\,\textrm{GeV}$, Run 3 projection) and $2\mu2b$ (dark blue, dotted, $m_{\phi}>25\,\textrm{GeV}$, Run 3 projection). Contours for $\Lambda_{{\rm br} }=120$ GeV (gray, dashed for $j=2$; brown, dashed for $j=1$), $f=m_h$ and $f=1\,\textrm{TeV}$ (black for $j=2$, brown for $j=1$).
• Figure 5: Cosmological and astrophysical bounds on $\sin^2\theta$ and $m_{\phi}$ from $100$ eV to $0.3\,\textrm{GeV}$: globular cluster via coupling to electrons (blue) or coupling to photons (turquoise), supernova 1987a (light blue), extragalactic background light (EBL, yellow), CMB $y$-distortion (light green) and $\mu$-distortion (green), entropy injection $\Delta S/S$ bounded by the baryon-to-photon ratio $\eta_B$ (orange) and by $N_{\rm{eff} }$ (pink), BBN (red). The green dotted lines represent the projection for the sensitivity of of PIXIE to CMB distortions.The light gray band indicates the possible range of $\sin^2\theta$ for $j=1$, i.e. the QCD case. The gray lines (from top to bottom) are contours of constant $\Lambda_{\rm br}=0.99\Lambda_{\rm br }^{\rm{max} }$ (thick, solid), and $1\,\textrm{GeV}$ (dashed). Here $\Lambda_{\rm br }^{\rm{max} }$ is the upper bound on $\Lambda_{{\rm br} }$ arising from the requirement of a non-tachyonic $\phi$ in Eq. (\ref{['tach']}) for $\sin (\phi_0/f)=1/\sqrt{2}$. The black lines (from left to right) are contours of constant $f=10^{10}\,\textrm{GeV}, 10^6\,\textrm{GeV}$ (thin) and $f=m_h$ (thick).