The idea that dark matter forms part of a larger dark sector is very intriguing, given the high degree of complexity of the visible sector. In this paper, we discuss lepton jets as a promising signature of an extended dark sector. As a simple toy mod
el, we consider an $mathcal{O}(text{GeV})$ DM fermion coupled to a new $U(1)$ gauge boson (dark photon) with a mass of order GeV and kinetically mixed with the Standard Model photon. Dark matter production at the LHC in this model is typically accompanied by collinear radiation of dark photons whose decay products can form lepton jets. We analyze the dynamics of collinear dark photon emission both analytically and numerically. In particular, we derive the dark photon energy spectrum using recursive analytic expressions, using Monte Carlo simulations in Pythia, and using an inverse Mellin transform to obtain the spectrum from its moments. In the second part of the paper, we simulate the expected lepton jet signatures from radiating dark matter at the LHC, carefully taking into account the various dark photon decay modes and allowing for both prompt and displaced decays. Using these simulations, we recast two existing ATLAS lepton jet searches to significantly restrict the parameter space of extended dark sector models, and we compute the expected sensitivity of future LHC searches.
Lensing peaks have been proposed as a useful statistic, containing cosmological information from non-Gaussianities that is inaccessible from traditional two-point statistics such as the power spectrum or two-point correlation functions. Here we exami
ne constraints on cosmological parameters from weak lensing peak counts, using the publicly available data from the 154 deg$^2$ CFHTLenS survey. We utilize a new suite of ray-tracing N-body simulations on a grid of 91 cosmological models, covering broad ranges of the three parameters $Omega_m$, $sigma_8$, and $w$, and replicating the Galaxy sky positions, redshifts, and shape noise in the CFHTLenS observations. We then build an emulator that interpolates the power spectrum and the peak counts to an accuracy of $leq 5%$, and compute the likelihood in the three-dimensional parameter space ($Omega_m$, $sigma_8$, $w$) from both observables. We find that constraints from peak counts are comparable to those from the power spectrum, and somewhat tighter when different smoothing scales are combined. Neither observable can constrain $w$ without external data. When the power spectrum and peak counts are combined, the area of the error banana in the ($Omega_m$, $sigma_8$) plane reduces by a factor of $approx2$, compared to using the power spectrum alone. For a flat $Lambda$ cold dark matter model, combining both statistics, we obtain the constraint $sigma_8(Omega_m/0.27)^{0.63}=0.85substack{+0.03 -0.03}$.
