Universal correlation between CP phase $$\delta$$ and the non-unitarity $$\alpha$$ parameter phases
The non-unitarity of the neutrino mixing matrix is a problem related with a more fundamental question about the origin of the neutrino mass. After a brief discussion on the questions ``why do we need model-independent framework for unitarity test?'', we show interesting properties present in the oscillation probabilities of neutrinos propagating in matter with non-unitarity. That is, (1) partial unitarity and (2) universal phase correlation. %To illuminate these points, we formulate a perturbative framework with the two expansion parameters $$\epsilon \equiv \Delta m^2_{21} / \Delta m^2_{31}$$ and $$\alpha$$ matrix elements. The complex triangular $$\alpha$$ matrix is introduced through the definition of $$3 \times 3$$ non-unitary flavor mixing matrix $$N$$ as %\begin{eqnarray} N &=& \left( \bf{1} - \alpha \right) U = \left\{ \bf{1} - \left[ \begin{array}{ccc}\alpha_{ee} & 0 & 0 \\\alpha_{\mu e} & \alpha_{\mu \mu} & 0 \\\alpha_{\tau e} & \alpha_{\tau \mu} & \alpha_{\tau \tau} \\\end{array}\right] \right\}U \label{alpha-matrix-def}\end{eqnarray}%where $$U$$ is the unitary MNS mixing matrix, and hence $$\alpha$$ characterizes the size and the flavor dependence of unitarity violation (UV)\footnote{%%%%%%%%%%%%%Despite that in the physics literature UV usually means ``ultraviolet'', we use UV in this manuscript as an abbreviation for ``unitarity violation'' or ``unitarity violating''.}~~caused by new physics (NP) at low- or high-scales.~~~~The point (1) above essentially means that despite non-unitary mixing, neutrino evolution must be unitary because the three active neutrinos span a complete state space of neutral leptons. The {\em phase correlation} mentioned in the point (2) refers an intriguing property that the complex $$\alpha$$ parameters and $$\nu$$Standard Model CP phase $$\delta$$ always come into the oscillation probabilities in a correlated way, $$e^{- i \delta } \alpha_{\mu e}$$, $$\alpha_{\tau e}$$, and $$e^{i \delta} \alpha_{\tau \mu}$$, universally in all the oscillation channels. The physical meaning of this result is briefly discussed. }
- Research Organization:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- DOE Contract Number:
- AC02-07CH11359
- OSTI ID:
- 1958454
- Report Number(s):
- FERMILAB-CONF-18-833-V; oai:inspirehep.net:1770706
- Journal Information:
- PoS, Vol. NuFACT2018
- Country of Publication:
- United States
- Language:
- English
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