Unitarity bounds and sum rules in the SMEFT

Abstract

We present a comprehensive reassessment of perturbative unitarity bounds in the dimension-six Standard Model Effective Field Theory, exploiting a new formalism based on spinor-helicity techniques to derive partial-wave unitarity bounds for generic $N \to M$ scattering amplitudes. We find that, in several cases, these theoretical constraints are already competitive with, or even stronger than, the corresponding experimental bounds for energy scales above a few TeV. This is especially the case for four-fermion operators under realistic flavor assumptions, where unitarity bounds can be further strengthened by exploiting sum rules.

Figures (4)

• Figure 1: Parameter space allowed by unitarity bounds in the plane of Wilson coefficients in the single-flavor limit. In the last two plots, we also show the dependence on the relative complex phases $\mathrm{arg}(C_{quqd}^{(1)}/C_{quqd}^{(8)})$ and $\mathrm{arg}(C_{\ell equ}^{(1)}/C_{\ell equ}^{(3)})$.
• Figure 2: Parameter space allowed by unitarity bounds (blue) and spinning sum rules in the cases of scalar (orange) and vector (green) dominance, in the single-flavor limit. The missing plot for the Wilson coefficients $C_{qd}^{(1,8)}$ is identical to that of $C_{qu}^{(1,8)}$.
• Figure 3: Minimum energy scales $E_*$ at which the unitarity bounds in Table \ref{['tab:UniBounds']} are violated for each purely bosonic Wilson coefficient in Celada:2024mcf, using the 95% CL marginalized intervals from linear (blue) and quadratic (orange) fits.
• Figure 4: (Left) Experimental and unitarity constraints on the Wilson coefficients of the operators $O_{\varphi q}^{(1)} = \sum_{p=1,2}i(\varphi^\dagger \overset{\leftrightarrow}{D}{}_\mu \varphi)(\overline q_p \gamma^\mu q_p)$ and $O_{\varphi q}^{(3)} = \sum_{p=1,2}i(\varphi^\dagger \overset{\leftrightarrow}{D}{}_\mu^I \varphi)(\overline q_p \sigma^I \gamma^\mu q_p)$. Experimental limits correspond to $95\%$ CL marginalized intervals Celada:2024mcf. (Middle) Experimental and unitarity constraints on the Wilson coefficients of the operators $O_{Qq}^{1,8} = \sum_{p=1,2}(\overline q_3 \gamma_\mu T^A q_3)(\overline q_p \gamma^\mu T^A q_p)$ and $O_{Qq}^{3,8} = \sum_{p=1,2}(\overline q_3 \gamma_\mu T^A \sigma^I q_3)(\overline q_p \gamma^\mu T^A \sigma^I q_p)$. Experimental limits correspond to $68\%$ CL and are derived from a quadratic fit Brivio:2019ius. Here, the sum rules select the region where $C_{Qq}^{1,8}-(1\pm 2)C_{Qq}^{3,8}$ are positive (negative) for scalar (vector) completions. (Right) Experimental and unitarity constraints on the Wilson coefficients of the operators $[O_{\ell q}^{(1)}]_{3333} = (\overline \ell_3 \gamma^\mu \ell_3)(\overline q_3 \gamma_\mu q_3)$ and $[O_{\ell q}^{(3)}]_{3333} = (\overline \ell_3 \gamma^\mu \sigma^I \ell_3)(\overline q_3 \gamma_\mu \sigma^I q_3)$. Experimental limits correspond to $68\%$ CL Allwicher:2023shc.