Examining scalar portal inelastic dark matter with lepton fixed-target experiments

Inelastic dark matter scenarios have attracted considerable attention in contemporary particle physics. In this study, we investigate the phenomenology of sub-GeV inelastic dark matter interacting via a lepton-specific scalar portal. By solving the Boltzmann equations, we obtain thermal target curves for several inelastic DM mass splittings in the sub-GeV mediator-mass range. We study the discovery potential of lepton fixed-target experiments, particularly NA64e, Light Dark Matter eXperiment (LDMX), and <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>NA</a:mi> <a:mrow> <a:mn>64</a:mn> <a:mi>μ</a:mi> </a:mrow> </a:mrow> </a:math> , via their missing-energy signatures. Our analysis focuses on the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ϕ</c:mi> </c:math> -strahlung process, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>l</e:mi> <e:mi>N</e:mi> <e:mo stretchy="false">→</e:mo> <e:mi>l</e:mi> <e:mi>N</e:mi> <e:mi>ϕ</e:mi> </e:math> , followed by the invisible decay of the scalar mediator into Majorana dark matter particles <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>ϕ</h:mi> <h:mo stretchy="false">→</h:mo> <h:msub> <h:mi>χ</h:mi> <h:mn>1</h:mn> </h:msub> <h:msub> <h:mi>χ</h:mi> <h:mn>2</h:mn> </h:msub> </h:math> . We use this channel to probe the mediator coupling to charged leptons of the Standard Model. For phenomenologically viable parameters of the inelastic dark matter scenario, we derive projected sensitivities for NA64e, LDMX, and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi>NA</k:mi> <k:mrow> <k:mn>64</k:mn> <k:mi>μ</k:mi> </k:mrow> </k:mrow> </k:math> , assuming that the boosted state <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>χ</m:mi> <m:mn>2</m:mn> </m:msub> </m:math> decays visibly via <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>χ</o:mi> <o:mn>2</o:mn> </o:msub> <o:mo stretchy="false">→</o:mo> <o:msub> <o:mi>χ</o:mi> <o:mn>1</o:mn> </o:msub> <o:msup> <o:mi>e</o:mi> <o:mo>+</o:mo> </o:msup> <o:msup> <o:mi>e</o:mi> <o:mo>−</o:mo> </o:msup> </o:math> outside the detector acceptance. Our results demonstrate the complementary roles of electron and muon beam experiments in exploring the sub-GeV inelastic dark matter sector interacting via a scalar portal.