Higgs decays to four leptons to $\mathcal{O}(1/Λ^4)$ in SMEFT

TL;DR

This work develops a complete SMEFT analysis up to $\mathcal{O}(1/\Lambda^4)$ for Higgs decays to four leptons, including squares of dimension-six operators and interference with dimension-eight operators. The authors provide an analytic, spinor-helicity treatment using geoSMEFT to derive the full amplitudes for $h\to \ell\bar{\ell}(Z\to \ell'\bar{\ell'})$ and $h\to \ell\bar{\nu}_{\ell}\nu_{\ell'}\bar{\ell'}$, decomposing the results into angular $J$-functions and SMEFT-order structures. They identify that the fully reconstructible four-lepton channel predominantly exhibits SM-like angular distributions with notable photon-pole enhancements from SMEFT operators such as $Q_{HW}^{(6)}$, while dimension-eight effects are generally subdominant unless operator coefficients are large. In the non-reconstructible semileptonic channel, new angular dependencies appear at $\mathcal{O}(1/\Lambda^4)$ but are challenging to extract in hadron collider environments, though lepton colliders could access these effects more cleanly. Overall, the work clarifies which SMEFT operators imprint detectable patterns in Higgs decays to four leptons and provides a framework for interpreting future precision measurements in these channels.

Abstract

We study the decays $h \to \ell \bar{\ell} \left(Z \to \ell' \bar{\ell'}\right)$ and $h\to\ell\barν_\ellν_{\ell'}\bar{\ell'}$ within the SMEFT framework and including effects up to $\mathcal O(1/Λ^4)$, where $Λ$ is the new physics scale suppressing higher dimensional operators. To work to this order, we must include the square of dimension-six operators and the interference of dimension-eight operators with the Standard Model. We study angular asymmetries and other differential decay observables and determine which are most sensitive to $\mathcal O(1/Λ^4)$ effects. While new kinematic structures arising in higher dimensional operators have the potential to induce novel angular dependency, we find this does not occur for $h\to\ell\bar{\ell}\left(Z\xrightarrow{}\ell'\bar{\ell'}\right)$. For $h \to \ell \barν_\ell ν_{\ell'} \bar{\ell'}$, new angular dependencies do arise at $\mathcal O(1/Λ^4)$, though they require a fully reconstructible (meaning we can go to the Higgs rest frame) final state. For non-reconstructible final states such as $\ell \barν_\ell ν_{\ell'} \bar{\ell'}$, we must study Higgs production and decay together with the appropriate observables, which we find obscures the new angular effects.

Figures (12)

• Figure 1: Topologies for $h\to\ell\bar{\ell}\left(Z\to\ell'\bar{\ell'}\right)$
• Figure 2: Topologies for $h \to \ell \bar{\nu}_\ell \nu_{\ell'} \bar{\ell'}$
• Figure 3: Dimension 6 SMEFT operators' contribution to $\mathcal{A}_\phi^{(4)}$. The solid black lines represent the SM with all Wilson coefficients set to zero. The other curves represent the operator's contribution by setting it's respective Wilson coefficient to the indicated value, taking $\Lambda=1\, \text{TeV}$, and all other Wilson coefficients are set to zero. In figure (a) we considered interference terms and squared terms of $Q_{HW}^{(6)}$, while in figure (b) we have only considered the interference of $Q_{HW}^{(6)}$.
• Figure 4: Dimension 6 SMEFT operators' contribution to $d\Gamma/ds$. The solid black lines represent the SM with all Wilson coefficients set to zero. The other curves represent the operator's contribution by setting it's respective Wilson coefficient to the indicated value, taking $\Lambda=1\, \text{TeV}$, and all other Wilson coefficients are set to zero. Notice in figure (d), solid lines represent positive values of the Wilson coefficients, and dashed lines represent negative values.
• Figure 5: Dimension 6 SMEFT operators' contribution to $A_\theta^{(2)}$ and $A_\Delta^{(2)}$. The solid black lines represent the SM with all Wilson coefficients set to zero. The other curves represent the operator's contribution by setting it's respective Wilson coefficient to the indicated value, taking $\Lambda=1\, \text{TeV}$, and all other Wilson coefficients are set to zero. In figures (a) and (b) we compare the dipole contribution to $A_\theta^{(2)}$ and $A_\Delta^{(2)}$, respectively. Since for non-dipole operators $A_\Delta^{(2)}=A_\theta^{(2)}$, in figure (c) we only show the operators' contribution to $A_\theta^{(2)}$ .