Sensitivity potential to a light flavor-changing scalar boson with DUNE and NA64$\mu$

In this work, we report on the sensitivity potential of complementary muon-on-target experiments to new physics using a scalar boson benchmark model associated with charged lepton flavor violation. The NA64$\mu$ experiment at CERN uses a 160-GeV energy muon beam with an active target to search for excess events with missing energy and momentum as a probe of new physics. At the same time, the proton beam at Fermilab, which is used to produce the neutrino beam for the Deep Underground Neutrino Experiment (DUNE) will also produce a high-intensity muon beam dumped in an absorber. Combined with the liquid Argon Near Detector, the system could be used to search for similar scalar boson particles with a lower energy but higher intensity beam. We find that both NA64$\mu$ and DUNE could cover new, unexplored parts of the parameter space of the same benchmark model, providing a complementary way to search for new physics.