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Is the large uncertainty of $δ_{CP}$ fundamentally encoded in the neutrino quantum state?

Michela Ignoti, Claudia Frugiuele, Matteo G. A. Paris, Marco G. Genoni

Abstract

The precise measurement of the leptonic CP-violating phase $δ_{CP}$ remains one of the major open challenges in neutrino physics, as current experiments achieve only very limited accuracy. We address this issue through the lens of quantum estimation theory. A distinctive feature of neutrino oscillation experiments is that they cannot freely optimize the probe or measurement, since both are constrained by the production and detection of flavor eigenstates. We therefore examine whether the large uncertainty in $δ_{CP}$ originates from intrinsic reasons, either of the neutrino quantum state or of flavor measurements, or if it instead stems from experimental limitations. By comparing quantum and classical Fisher information, we demonstrate that the limited sensitivity to $δ_{CP}$ originates primarily from the information content of flavor measurements. Furthermore, we show that targeting the second oscillation maximum, as in the ESS$ν$SB proposal, substantially enhances $δ_{CP}$ information compared to experiments centered on the first maximum.

Is the large uncertainty of $δ_{CP}$ fundamentally encoded in the neutrino quantum state?

Abstract

The precise measurement of the leptonic CP-violating phase remains one of the major open challenges in neutrino physics, as current experiments achieve only very limited accuracy. We address this issue through the lens of quantum estimation theory. A distinctive feature of neutrino oscillation experiments is that they cannot freely optimize the probe or measurement, since both are constrained by the production and detection of flavor eigenstates. We therefore examine whether the large uncertainty in originates from intrinsic reasons, either of the neutrino quantum state or of flavor measurements, or if it instead stems from experimental limitations. By comparing quantum and classical Fisher information, we demonstrate that the limited sensitivity to originates primarily from the information content of flavor measurements. Furthermore, we show that targeting the second oscillation maximum, as in the ESSSB proposal, substantially enhances information compared to experiments centered on the first maximum.

Paper Structure

This paper contains 1 section, 14 equations, 2 figures.

Table of Contents

  1. Neutrino oscillations

Figures (2)

  • Figure 1: The effective QFI $H_{\nu,\overline{\nu}}(\delta_{CP})$ (green solid line) and the neutrino appearance probabilities $P(\nu_\mu \to \nu_e)$ (dashed bordeaux line) plotted as a function of $L/E$ and for $\delta_{CP}=\delta_{CP}^{(\mathrm{NO})}$. The two black points correspond to the value of the QFI for the experiments T2K/T2HK and ESS$\nu$SB, identified by considering the peak energy $E$ of the neutrino spectrum.
  • Figure 2: Classical effective FI corresponding to flavor detection $F_{\nu,\overline{\nu}}(\delta_{CP})$ as a function of the effective baseline $L/E$ and for different values of $\delta_{CP}$: black solid line, $\delta_{CP}=\delta_{CP}^{(\mathrm{NO})}$; red long-dashed line, $\delta_{CP}=90^\circ$; blue dash-dotted line , $\delta_{CP}=0^\circ$. The short-dashed green line corresponds to the effective QFI $H_{\nu,\overline{\nu}}(\delta_{CP})$, while the two black points correspond to the value of the FI for the experiments T2K/T2HK and ESS$\nu$SB. These have been identified by considering the peak energy $E$ of the neutrino spectrum.