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Accelerating classical systems that couple to a fermion-antifermion pair at the microscopic level can radiate pairs of fermions and lose energy in the process. In this work, we derive the generalization of the Larmor formula for fermion pair radiation. We focus on the case of a point-like classical source in an elliptical orbit that emits fermions through vector and scalar mediators. Ultra-light fermion emission from such systems becomes relevant when the mass of the mediator is larger than the frequency of the periodic motion. This enables us to probe regions of the parameter space that are inaccessible in on-shell bosonic radiation. We apply our results to pulsar binaries with mediators that couple to muons and neutrinos. Using current data on binary period decays, we extract bounds on the parameters of such models. 

A bstract The Standard Model predicts a long-range force, proportional to $$ {G}_F^2/{r}^5 $$ G F 2 / r 5 , between fermions due to the exchange of a pair of neutrinos. This quantum force is feeble and has not been observed yet. In this paper, we compute this force in the presence of neutrino backgrounds, both for isotropic and directional background neutrinos. We find that for the case of directional background the force can have a 1 /r dependence and it can be significantly enhanced compared to the vacuum case. In particular, background effects caused by reactor, solar, and supernova neutrinos enhance the force by many orders of magnitude. The enhancement, however, occurs only in the direction parallel to the direction of the background neutrinos. We discuss the experimental prospects of detecting the neutrino force in neutrino backgrounds and find that the effect is close to the available sensitivity of the current fifth force experiments. Yet, the angular spread of the neutrino flux and that of the test masses reduce the strength of this force. The results are encouraging and a detailed experimental study is called for to check if the effect can be probed. 

A bstract We analyze the New Physics sensitivity of a recently proposed method to measure the CP-violating $$ \mathcal{B} $$ B ( K S → μ + μ − ) ℓ =0 decay rate using K S − K L interference. We present our findings both in a model-independent EFT approach as well as within several simple NP scenarios. We discuss the relation with associated observables, most notably $$ \mathcal{B} $$ B ( K L → π 0 $$ \nu \overline{\nu} $$ ν ν ¯ ). We find that simple NP models can significantly enhance $$ \mathcal{B} $$ B ( K S → μ + μ − ) ℓ =0 , making this mode a very promising probe of physics beyond the standard model in the kaon sector.