Resolving the atmospheric octant by an improved measurement of the reactor angle

Taking into account the current global information on neutrino oscillation parameters we forecast the capabilities of future long-baseline experiments such as DUNE and T2HK in settling the atmospheric octant puzzle. We find that a good measurement of the reactor angle ${\theta }_{13}$ plays a key role in fixing the octant of the atmospheric angle ${\theta }_{23}$ with such future accelerator neutrino studies.

Figure 1

Precision measurement of ${\theta }_{23}$ and ${\delta }_{CP}$ at $4\sigma$ ($\mathrm{\Delta }{\chi }^2=19.33$) confidence. Left (right) panels correspond to DUNE (T2HK). Differently shaded (colored) regions correspond to various errors associated with ${\sin }^2{\theta }_{13}$. The top panel uses the global fit in [3], while the bottom panel corresponds to the global fit in [5]. The star denotes the best fit point.

Figure 2

$4\sigma$ ($\mathrm{\Delta }{\chi }^2=19.33$) precision measurement of ${\theta }_{23}$. The left (right) panel is for DUNE (T2HK). Differently shaded regions correspond to various errors associated with ${\sin }^2{\theta }_{13}$. The thick dashed line represents the current best fit value from [3].

Figure 3

Octant discrimination potential as a function of the relative error on ${\sin }^2{\theta }_{13}$ for the true value of ${\delta }_{CP}^{\mathrm{TRUE}}=1.45\pi$. The left (right) panel represents the results for DUNE (T2HK). The red, green, blue and cyan curves delimit the ${\theta }_{23}$ “octant-blind” region corresponding to 2, 3, 4 and $5\sigma$ ($\mathrm{\Delta }{\chi }^2=4$, 9, 16, and 25 respectively) confidence.

Figure 4

Octant discrimination potential at $4\sigma$ ($\mathrm{\Delta }{\chi }^2=19.33$) confidence level in the $[{\sin }^2{\theta }_{23},{\delta }_{CP}]$ (true) plane. The red, green, blue and cyan curves delimit the octant-blind regions corresponding to 1.2%, 2.4%, 3.6% and 4.8% relative errors on ${\sin }^2{\theta }_{13}$.

Figure 5

Measurement of ${\theta }_{23}$ and ${\delta }_{CP}$ at $4\sigma$ ($\mathrm{\Delta }{\chi }^2=19.33$) confidence. The symbol “star” denotes ${\sin }^2{\theta }_{23}^{\mathrm{TRUE}}=0.441$ and ${\delta }_{CP}^{\mathrm{TRUE}}=1.45\pi$. Left (right) panels correspond to DUNE (T2HK). Differently shaded (colored) regions correspond to various errors associated with ${\sin }^2{\theta }_{13}$.