Neutrino oscillations in the front form of Hamiltonian dynamics

Abstract

Since future, precise theory of neutrino oscillations should include the understanding of the neutrino mass generation and a precise, relativistic description of hadrons, and observing that such a future theory may require Dirac's front form of Hamiltonian dynamics, we provide a preliminary front form description of neutrino oscillations using the Feynman--Gell-Mann--Levy version of an effective theory in which leptons interact directly with whole nucleons and pions, instead of with quarks via intermediate bosons. The interactions are treated in the lowest-order perturbative expansion in the coupling constants ${G}_{F}$ and ${F}_{\ensuremath{\pi}}$ in the effective theory, including a perturbative solution of the coupled constraint equations. Despite missing quarks and their binding mechanism, the effective Hamiltonian description is sufficiently precise for showing that the standard oscillation formula results from the interference of amplitudes with different neutrinos in virtual intermediate states. This holds provided that the inherent experimental uncertainties of preparing beams of incoming and measuring rates of production of outgoing particles are large enough for all of the different neutrino intermediate states to contribute as alternative virtual paths through which the long-baseline scattering process can manifest itself. The result that an approximate, effective front form theory reproduces the standard oscillation formula at the level of transition rates for currently considered long-baseline experiments---even though the space-time development of scattering is traced differently and the relevant interaction Hamiltonians are constructed differently than in the commonly used instant form of dynamics---has two implications. It shows that the common interpretation of experimental results is not the only one, and it opens the possibility of considering more precise theories taking advantage of the features of the front form that are not available in the instant form.