How Broad is a Neutrino?
- Banks, Hannah et al
- arXiv:2209.11270CERN-TH-2022-152
 | A schematic Feynman diagram for a general neutrino propagation process. The double lines show the external states at the production and detection vertices. The elliptical blob symbolises the K\"all\'en-Lehmann propagator. In the case of canonical oscillations, this reduces to the usual Feynman propagator. |
 | The flow of probability around the ring of fermions for $N = 6$ sites and $q = 10^3$. The neutrino is initialised at $t=0$ in the active, $i = 1$ state and, as time evolves, may overlap with the other $N -1$ sites, before returning to a maximum of being detected in the $n =1$ state again after a time $T$. The probability that the system is in the $i^{\textnormal{th}}$ site on measurement after a time $t$ is shown in the main figure, in units of the cycle period $T$. The circular bar charts illustrate, to scale, the flow of probability around the sites, plotted in the same colours as in the main figure, at a number of instances. The inner and outer concentric dashed circles denote measurement probabilities of 0.5 and 1 respectively. |
 | : Comparison of 3-flavour oscillation probabilities generated by a density of states comprised of 3 top-hat functions with fractional breadths $\tilde{b}_i$ = 0.005, and a pseudo-Dirac density of states with masses $(M_1, M_2, M_3) = (1.23, 1.21, 1.39$) $\times 10^{-4} $eV, selected by performing a least squares fit to the top-hat probability distribution. The lower panel shows the fit residuals. |
 | : A plot of the spectral function $\rho({\mu^2})$ for these two models with the same parameters as in (a). Also shown is the triple $\delta$-function density of states corresponding to the canonical scenario. The heights of the top-hat functions relative to each other are plotted to scale but the vertical extent of the (formally infinite) $\delta$-functions for the pseudo-Dirac and conventional models are intended for illustrative purposes only. : Evaluation of the top-hat phenomenological ansatz defined in Sec.~\ref{subsec:Pheno} to capture the oscillation behaviour of pseudo-Dirac models as detailed in Sec.~\ref{subsec:PD}. |
 | : Comparison of 3-flavour oscillation probabilities generated by a density of states comprised of 3 top-hat functions with fractional breadths $\tilde{b}_i$ = 0.005, and a $N=10$ band density of states. The value of $q = 987.2$ was selected using a least squares fit to the top-hat probability distribution. |
 | Plots of the anti-electron neutrino survival probability as a function of $L/E$ for the 3-flavour top-hat density of states set up as defined in Sec.~\ref{subsec:Pheno} for the case where only one of the three states has a finite breadth, of fractional value $\tilde{b} = 0.03$ and the remaining two are $\delta$-functions. Also shown for comparison is the probability distribution for the standard scenario in which the density of states comprises of 3 $\delta$-functions ($b_i = 0$). |
 | Plots of the anti-electron neutrino survival probability as a function of $L/E$ for the 3-flavour top-hat density of states as defined in Sec.~\ref{subsec:Pheno} with $\tilde{b}_{1}=\tilde{b}_{2}=\tilde{b}_{3}=\tilde{b}$, for various values of $\tilde{b}$. The case $\tilde{b}_i = 0$ corresponds to the standard scenario in which the density of states is comprised of 3 $\delta$-functions. |
 | Oscillation probability for reactor antineutrinos as a function of $L/E$ for the standard three-neutrino case (grey) and including nonzero spectral-function breadths as indicated in the legend (blue). We shade the regions of $L/E$ probed by existing/future experiments Daya Bay (red), JUNO (purple), and KamLAND (green). |
 | Current constraints from KamLAND (blue), Daya Bay (green), and long-baseline $\nu_\mu$ disappearance measurements from T2K and NOvA (orange) at $1$, $2$, and $3\sigma$ CL (dotted, dashed and solid respectively) on the reduced breadths $b_i$, relative to the overall neutrino-masses-squared when we assume $m_1 = 10^{-2}$ eV. |
 | Expected future constraints by JUNO (purple) in the absence of a new-physics signal in the parameter space of $\tilde{b}_i$, compared against the current constraints from KamLAND (blue). Compared to Fig.~\ref{fig:CurrentWConstraints}, the data range here is so narrow that the constraints from Daya Bay, T2K, and NOvA do not appear. |