Probing dark-state electromagnetic form factors at future linear electron-positron colliders with polarized beams

TL;DR

This work probes the electromagnetic form factors of neutral dark-sector fermions using higher-dimensional operators that couple to the SM photon and Z boson, focusing on dim-5 magnetic/electric dipole moments and dim-6 anapole and charge radius. By studying mono-photon production at future polarized e^+e^- colliders (ILC and CLIC) and exploiting beam polarization to boost signal while suppressing neutrino backgrounds, the authors forecast sensitivities surpassing current bounds by up to two orders of magnitude. They implement a detailed event selection and statistically quantify reach via a χ^2 framework, while also assessing the perturbative unitarity and EFT validity limits, noting that dim-5 EFT remains reliable in most accessible regions whereas dim-6 EFT can be problematic at high energies. The results underscore the practical impact of beam polarization in enhancing dark-state sensitivity and provide guidance on the EFT applicability for interpreting potential signals at future linear colliders.

Abstract

We study the electromagnetic form factors of electrically neutral dark-sector particles in this paper. Concretely speaking, we focus on operators that can lead to interactions of fermionic dark states with the Standard-Model (SM) photon, including both dimension-5 (the magnetic and electric dipole moments) and dimension-6 (the anapole moment and charge radius) operators. Correspondingly, instead of the SM-photon form factors, we employ hypercharge gauge-field form factors that can induce additional couplings to the SM $Z$-boson. Utilizing the mono-photon production channel at future linear electron-positron colliders, the International Linear Collider (ILC) and the Compact Linear Collider (CLIC), we demonstrate that tuning beam polarization allows for simultaneous enhancement of signal-event rates and suppression of dominant SM background events, i.e.~neutrino-induced processes, and hence improvement of sensitivity reach. Our analysis reveals that ILC and CLIC can probe electromagnetic form factors of dark-sector particles up to about two orders of magnitude beyond existing experimental limits. We also estimate, at the order-of-magnitude level, the validity range of the effective-field-theory (EFT) approach we adopt, finding that for the dimension-5 operators the EFT remains valid in most of the parameter regions to which the ILC and CLIC can be sensitive, while it breaks down in the entire sensitivity region for the dimension-6 operators.

Figures (10)

• Figure 1: Feynman diagrams for the signal process $e^- e^+ \to \chi \bar{\chi} \gamma$ where the SM photon $\gamma$ is emitted from either the electron beam (left) or the positron beam (right). We omit the FSR-photon case, considering its negligible effects.
• Figure 2: Mono-photon signal cross sections as functions of $m_\chi$ at an $e^-e^+$ collider with $\sqrt{s} = 1$ TeV. The benchmark parameters are $d_\chi = \mu_\chi = 10^{-2}$ GeV$^{-1}$ and $a_\chi = b_\chi = 10^{-5}$ GeV$^{-2}$. The left (right) panel shows results for MDM and EDM (AM and CR). Line styles indicate different polarization configurations: solid $(0, 0)$ for ($P_{e^-} = 0\%$, $P_{e^+} = 0\%$), dashed $(-, +)$ for ($P_{e^-} = -100\%$, $P_{e^+} = +100\%$), and dot-dashed $(+, -)$ for ($P_{e^-} = +100\%$, $P_{e^+} = -100\%$). "SM" labels the curves for the irreducible SM background process $e^- e^+\to \nu \bar{\nu}\gamma$; see section \ref{['subsec:background']} for detail. In addition, we show in the lower parts of both panels the ratios of cross sections with the polarized beam setups to those with the unpolarized one; we note that the ratios for the MDM and EDM operators in the left panel (the AM and CR operators in the right panel) overlap with each other.
• Figure 3: Mono-photon signal cross sections as functions of $\sqrt{s}$ at an $e^-e^+$ collider, with $m_\chi$ fixed at 10 GeV. The format follows figure \ref{['fig:sig-mchi-1tev']}.
• Figure 4: Upper: The Feynman diagrams for the process $e^- e^+ \to \nu_\ell\bar{\nu}_\ell\gamma$, where $\nu_\ell=\nu_e,\nu_\mu,\nu_\tau$ are the SM neutrinos. Lower: The Feynman diagrams for the radiative Bhabha scattering $e^-e^+\to e^-e^+\gamma$. Diagrams with photon radiated by the positron are included in the physics analysis but not shown here.
• Figure 5: The scattering cross sections of the signal process with the EDM (upper left) and AM (upper right), and the neutrino-background process (lower), as functions of the incoming beams' polarizations $P_{e^\pm}$, with benchmark parameters $\sqrt{s} = 1\,\text{TeV}, m_\chi = 10\,\text{GeV}, d_\chi = 10^{-3}$ GeV$^{-1}$, and $a_\chi = 10^{-6}$ GeV$^{-2}$. The kinematic requirements on the photon as given in equation \ref{['eq:initial-cut']} are included. The yellow star in each plot marks the $(P_{e^-},P_{e^+})=(+80\%, -20\%)$ position corresponding to the polarization choice for each operator type that is predicted to have the largest signal-to-background cross-section ratio among all four possible helicity-orientations, cf. table \ref{['table:difpol-SM-sig-ILC']}.