Significance of classically forbidden regions for short baseline neutrino experiments

Classically forbidden regions ($\mathtt{CFRs}$) are common to both non-relativistic quantum mechanics, and to relativistic quantum field theory. It is known since 2001 that $\mathtt{CFR}$ contributes roughly sixteen percent of energy to the ground state of a simple harmonic oscillator (Adunas G. Z. et al., Gen. Relativ. Gravit., 33 (2001) 183). Similarly, quantum field theoretic arguments yield a non-zero amplitude for a massive particle to cross the light cone (that is, into the $\mathtt{CFR}$). The signs of these amplitudes are opposite for fermions and antifermions. This has given rise to an erroneous conclusion that amplitude to cross the lightcone is identically zero. This is true as long as a measurement does not reveal the considered object to be a particle or antiparticle. However, neutrino oscillation experiments do measure a neutrino $\nu$, or an antineutrino $\bar\nu$. Here we show that in the context of neutrino oscillations these observations have the potential to resolve various short baseline anomalies for a sufficiently light lowest mass eigenstate. In addition, we make a concrete prediction for the upcoming results to be announced later this year by JSNS$^2$.