Virtual neutrino propagation at short baselines

Abstract

Within a covariant perturbative field-theoretical approach, the wave-packet modified neutrino propagator is expressed as an asymptotic expansion in powers of dimensionless Lorentz- and rotation-invariant variables. The expansion is valid at high energies and short but macroscopic space-time distances between the vertices of the proper Feynman macrodiagram. In terms of duality between the propagator and the effective neutrino wave packet, at short times and distances, neutrinos are deeply virtual and move quasi-classically. In the lowest-order approximation, this leads to the classical inverse-square dependence of the modulus squared flavor transition amplitude and related neutrino-induced event rate from distance L between the source and detector, and the above-mentioned asymptotics results in the corrections to the classical behavior represented by powers of $$L^2$$ L 2 . This is very different from the long-baseline regime, where similar corrections are given by an asymptotic expansion in inverse powers of $$L^2$$ L 2 . However, in both short- and long-baseline regimes, the main corrections lead to a decrease in number of neutrino events.

Neutrino oscillations as a single Feynman diagram

“…With this at hand and properly normalizing the initial and final states (25) we derived the flavor conversion Master Formula for differential rate of the process (8) valid under the approximation m m E i k 2 2  n . For the particular process (33) we demonstrated that the presented approach leads to a probability formula for ν μ → ν e neutrino oscillation corrected with respect to the conventional one by terms ∼m k /E ν , which can be large for heavy neutrino quasi degenerate states.…”

“…Nevertheless, this happens under certain reasonable approximations, so that in the rest frame of the target neutron we arrive at G p + in (35). They both give the rate of the same process (33), while the conventional approach (35) assumes factorization of the process (33) in the three separate steps (34). We find that both results coincide in structure if we interpret as the QFT oscillation probability the expression…”

“…In the proposed QFT approach, we apply equation (24) for the process (33). In this case we have Here, P π ≡ (E π , p π ), P n ≡ (E n , p n ), P p ≡ (E p , p p ), P μ ≡ (E μ , p μ ), P e ≡ (E e , p e ), and…”

“…One of them resorts to the representation of oscillating neutrinos in the form of wave packets [18][19][20][21][22][23][24]. This idea was further developed in a series of papers [25][26][27][28][29][30][31][32][33]. Although the quantum mechanical wave-packet approach is a significant improvement to the standard plane-wave treatment, it also suffers from drawbacks.…”