Return of the CHAMPs: A clockwork portal to charged dark matter

TL;DR

The paper proposes a clockwork portal to realize charged dark matter (CHAMP) in a controlled, natural framework. By extending the SM hypercharge to a chain of $U(1)$ factors and localizing the SM fields at one end while the CHAMP lives at the other, the CHAMP acquires an effective millicharge $\epsilon e$ suppressed as $\epsilon \sim Y_\chi q^{-N}$ without fine-tuning. The dark matter relic abundance is achieved through a tower of heavy $Z'$ bosons that mediate annihilation, with the correct density predominantly produced via resonant annihilation when $m_\chi \approx m_{Z'}/2$, and additional channels like $Z'_k Z'_l$ and $Z'_k \phi_n$ opening up at higher masses. The model respects electroweak precision constraints and current collider bounds while pushing direct-detection rates below current sensitivity through clockwork cancellations; it remains testable via future collider searches for multi-$Z'$ resonances and anticipated MeV gamma-ray observations, with a plausible UV interpretation in a five-dimensional bulk picture. Overall, the clockwork portal provides a robust, falsifiable route to a TeV-scale CHAMP dark matter candidate with distinctive experimental signatures.

Abstract

While Dark Matter (DM) is conventionally assumed to be chargeless, the possibility of a charged massive particle (CHAMP) as the DM particle remains alive. With phenomenological constraints on the charge being very severe, such a scenario is often sought to be dismissed, citing naturalness. We demonstrate here that such a (mini)charged DM can be realized within the clockwork paradigm, without the need to invoke unnaturally small parameters. The model is examined against constraints, theoretical and experimental, and the phenomenologically admissible parameter space is delineated. Several intriguing tests, at the LHC as well as at future direct and indirect detection experiments, are pointed out.

Figures (6)

• Figure 1: A schematic representation of the two-step symmetry breaking pattern in the model. The first row represents the extended hypercharge construction. In the second row, the individual blobs indicate the exponentially falling (site-dependent) charge under $U(1)_{CW}$. Similarly, in the third row, this translates into the strength of the photon couplings following EWSB (sans the overall gauge couplings).
• Figure 2: Bounds from $Z$-pole observables in the $(q,f)$ parameter space for fixed $N=25$ at the $68 \%$ CL. The region to the above each curve is allowed. The black dashed curve corresponds to the constraint from the $Z$-boson decay width, the blue solid curve arises from the oblique parameter $T$ (we have taken $T= 0.01 \pm 0.12$ParticleDataGroup:2024cfk), and the green dashed curve represents the constraint from the electron left-right asymmetry. The red vertical line indicates the lower bound on $q$ for the given $N$, as required by direct detection limits on fractionally charged DM (discussed in the next section).
• Figure 3: Variation of $\mathcal{P}_k$ for $\chi \bar{\chi} \rightarrow e^- e^+$ ( i.e$Y_L=-0.5, Y_R=-1.0$ and taken $Y_\chi=1.0$), given by \ref{['eq:prop2k']} corresponding to different $Z'_k$ states for $q = 3.0$ and $f = 3000~\text{GeV}$, shown for two different cases: (a) $N = 20$ and (b) $N = 50$. The blue dots represent the individual contributions (in picobarns) from each $Z'_k$, while the red line denotes the summed contribution, which exhibits a pronounced cancellation effect.
• Figure 4: Plot of $R_k$ for the individual $Z'_k$ modes, where $R_k$ denotes the dilepton production rate mediated by each $Z'_k$ relative to the $Z$ boson.
• Figure 5: Comparison of $R_5$ (scaled by $1928~\mathrm{pb}$), as defined in Eq. \ref{['eq:dilepratio']}, for two benchmark values $q=3$ (blue dashed curve) and $q=4$ (green dashed curve) for $N=25$, with the 95% CL observed and expected limits from CMS dilepton searches at $\sqrt{s}=13~\mathrm{TeV}$ and $L=137~\mathrm{fb}^{-1}$. The blue bands denote the uncertainty, with the darker (lighter) shaded region corresponding to the 68% (95%) confidence level.