The standard model is not complete in that we don't know what the mass term of the neutrino is, if it is Dirac or Majorana or some combination. There's the mysterious absence of the right-handed neutrino which is a good candidate for the "dark matter" particle. This is not "physics beyond the standard model" but "a missing piece of the standard model". There is at least one major secret inside the neutrino and Occam's razor makes that a good candidate for explaining the missing mass and maybe even the matter-antimatter asymmetry.