Positivity and partial wave unitarity bounds on ALP theories via amplitude methods

TL;DR

This work develops a comprehensive, first-principles bound analysis for Axion-Like Particles (ALPs) within an effective field theory framework extending up to dimension 8. Utilizing on-shell spinor-helicity techniques, it constructs an angular-momentum basis for $N\to M$ scattering and derives complete partial-wave unitarity bounds, including crucial coupled-channel effects that arise from energy-growing derivative ALP interactions. It concurrently computes a full set of positivity bounds for dimension-8 operators and elucidates their interplay with unitarity constraints, with several results testable in SMEFT contexts and UV-mpecified extensions. The study then applies these theoretical bounds to phenomenology, showing that unitarity can substantially constrain non-resonant ALP searches at colliders, dimension-5 and dimension-7 couplings in lepton processes, and weak-violating ALP interactions in rare decays, providing a framework that tightly links high-energy theoretical consistency to experimental probes.

Abstract

We derive the complete set of partial wave unitarity bounds on the most general Axion-Like Particle (ALP) effective interactions up to dimension 8 in the limit of large center-of-mass energy. Exploiting a recently developed formalism based on spinor-helicity techniques, we discuss the unitarity bounds for $N \to M$ (with $N, M \geq 2$) scattering amplitudes that can be relevant for ALP searches at colliders or in a variety of rare processes. Moreover, we compute positivity bounds on ALP interactions, emphasizing their complementarity with partial wave unitarity bounds. As a byproduct, we show that our results can be used to infer new positivity constraints in the Standard Model Effective Field Theory.

Figures (11)

• Figure 1: Plots of the boundaries of the parameter space allowed by the partial wave unitarity bounds in Eq. \ref{['eq:PWUB_d5_phiX2']} in the ${\newline}^{5}\!{{C}}^{}_{\phi B^2}$--${\newline}^{5}\!{{C}}^{}_{\phi W^2}$ plane (left panel) and in the ${\newline}^{5}\!{{C}}^{}_{\phi F^2}$--${\newline}^{5}\!{{C}}^{}_{\phi Z^2}$ plane (right panel) for different values of $| {\newline}^{5}\!{{C}}^{}_{\phi G^2} |$. The Wilson coefficients ${\newline}^{5}\!{{C}}^{}_{\phi F^2}$ and ${\newline}^{5}\!{{C}}^{}_{\phi Z^2}$ are defined as ${\newline}^{5}\!{{C}}^{}_{\phi F^2} = c^2_W \, {\newline}^{5}\!{{C}}^{}_{\phi B^2} + s^2_W\, {\newline}^{5}\!{{C}}^{}_{\phi W^2}$ and ${\newline}^{5}\!{{C}}^{}_{\phi Z^2} = s^2_W \, {\newline}^{5}\!{{C}}^{}_{\phi B^2} + c^2_W\, {\newline}^{5}\!{{C}}^{}_{\phi W^2}$ (where $s_W$ and $c_W$ are the sine and cosine of the weak mixing angle) and mediate the interactions of the ALP with photons and $Z$ bosons, respectively: $\mathcal{L} \supset {\newline}^{5}\!{{C}}^{}_{\phi F^2} \, \phi \, F_{\mu\nu}\widetilde{F}^{\mu\nu} + {\newline}^{5}\!{{C}}^{}_{\phi Z^2} \, \phi \, Z_{\mu\nu}\widetilde{Z}^{\mu\nu}$.
• Figure 2: Summary of the marginalized partial wave unitarity bounds on the Wilson coefficients associated with the dimension-5 and -6 ALP operators.
• Figure 3: Parameter space allowed by partial wave unitarity bounds in Eqs. \ref{['eq:PWUB_d7_phipsi2HD2_1']}--\ref{['eq:PWUB_d7_phipsi2HD2_2']} associated with the dimension-7 operators ${\newline}^{7}\!{{Q}}^{(1)pr}_{k}$ and ${\newline}^{7}\!{{Q}}^{(2)pr}_{k}$, with $k=\phi \ell e H,\phi qu H,\phi qd H$ and $p,r=1,2,3$. The imaginary parts of the Wilson coefficients are taken to be zero.
• Figure 4: Summary of the marginalized partial wave unitarity bounds on the Wilson coefficients associated with the dimension-7 ALP operators.
• Figure 5: Summary of the marginalized partial wave unitarity bounds on the Wilson coefficients associated with the dimension-8 ALP operators.