# $\delta$, $\boldsymbol CP$ violating phase INSPIRE search

Measurements of $\delta$ come from atmospheric and accelarator experiments looking at ${{\mathit \nu}_{{e}}}$ appearance. We encode values between 0 and 2$\pi$, though it is equivalent to use $\text{-}\pi$ to $\pi$.
VALUE (${{\mathit \pi}}$ rad) CL% DOCUMENT ID TECN  COMMENT
$\bf{ 1.36 \pm0.17}$ OUR AVERAGE
$0.0$ ${}^{+1.3}_{-0.4}$ 1
 2019
NOVA Normall mass ordering, octant II for ${{\mathit \theta}_{{23}}}$
$1.33$ ${}^{+0.45}_{-0.51}$ 2
 2018 B
SKAM Normal mass ordering, ${{\mathit \theta}_{{13}}}$ constrained
$1.40$ $\pm0.20$ 3
 2018 G
T2K Normal mass ordering, ${{\mathit \theta}_{{13}}}$ constrained
• • • We do not use the following data for averages, fits, limits, etc. • • •
$1.33$ ${}^{+0.46}_{-0.53}$ 4
 2018 B
SKAM 3${{\mathit \nu}}$ osc: normal mass ordering, ${{\mathit \theta}_{{13}}}$ free
$1.22$ ${}^{+0.76}_{-0.67}$ 4
 2018 B
SKAM 3${{\mathit \nu}}$ osc: inverted mass ordering, ${{\mathit \theta}_{{13}}}$ free
$1.33$ ${}^{+0.48}_{-0.53}$ 2
 2018 B
SKAM 3${{\mathit \nu}}$ osc: inverted mass ordering, ${{\mathit \theta}_{{13}}}$ constrained
$1.54$ ${}^{+0.14}_{-0.12}$ 95 3
 2018 G
T2K Inverted mass ordering, ${{\mathit \theta}_{{13}}}$ constrained
$1.21$ ${}^{+0.91}_{-0.30}$ 5
 2018
NOVA Normal mass ordering, octant II for ${{\mathit \theta}_{{23}}}$
$1.46$ ${}^{+0.56}_{-0.42}$ 5
 2018
NOVA Normal mass order; octant I for ${{\mathit \theta}_{{23}}}$
$1.32$ ${}^{+0.21}_{-0.15}$
 2018
FIT Normal mass ordering, global fit
$1.56$ ${}^{+0.13}_{-0.15}$
 2018
FIT Inverted mass ordering, global fit
$1.45$ ${}^{+0.27}_{-0.26}$ 6
 2017 F
T2K Normal mass ordering
$1.54$ ${}^{+0.22}_{-0.23}$ 6
 2017 F
T2K Inverted mass ordering
$1.50$ ${}^{+0.53}_{-0.57}$ 7
 2017 B
NOVA Inverted mass ordering; ${{\mathit \theta}_{{23}}}$ in octant II
$0.74$ ${}^{+0.57}_{-0.93}$ 7
 2017 B
NOVA Normal mass ordering; ${{\mathit \theta}_{{23}}}$ in octant II
$1.48$ ${}^{+0.69}_{-0.58}$ 7
 2017 B
NOVA Normal mass ordering; ${{\mathit \theta}_{{23}}}$ in octant I
$\text{ 0.0 to 0.1, 0.5 to 2.0}$ 90 8, 7
 2016
NOVA Inverted mass ordering
$0.0\text{ to }2.0$ 90 8
 2016
NOVA Normal mass ordering
$\text{ 0 to 0.15, 0.83 to 2}$ 90
 2015 D
T2K Normal mass ordering
$1.09\text{ to }1.92$ 90
 2015 D
T2K Inverted mass ordering
$0.05\text{ to }1.2$ 90 9
 2014
MINS Normal mass ordering
$1.34$ ${}^{+0.64}_{-0.38}$
 2014
FIT Normal mass ordering
$1.48$ ${}^{+0.34}_{-0.32}$
 2014
FIT Inverted mass ordering
$1.70$ ${}^{+0.22}_{-0.39}$ 10
 2014
FIT Normal mass ordering; global fit
$1.41$ ${}^{+0.35}_{-0.34}$ 10
 2014
FIT Inverted mass ordering; global fit
$\text{ 0 to 1.5 or 1.9 to 2}$ 90 11
 2013 A
MINS Normal mass ordering
1  ACERO 2019 is based on a sample size of $1.33 \times 10^{20}$ protons on target with combined antineutrino and neutrino data. Supersedes ACERO 2018 .
2  ABE 2018B uses 328 kton$\cdot{}$years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the three parameters, $\Delta$m${}^{2}_{32}$, sin$^2{{\mathit \theta}_{{23}}}$, and $\delta$, while the solar parameters and sin$^2{{\mathit \theta}_{{23}}}$ are fixed to $\Delta$m${}^{2}_{21}$= ($7.53$ $\pm0.18$) $\times 10^{-5}$ eV${}^{2}$, sin$^2{{\mathit \theta}_{{12}}}$ = $0.304$ $\pm0.014$, and sin$^2{{\mathit \theta}_{{13}}}$ = $0.0219$ $\pm0.0012$.
3  ABE 2018G confidence intervals are marginalized over both mass orderings. Normal order preferred with a posterior probability of 87$\%$. The 1-sigma result for normal mass ordering used in the average was provided by the experiment via private communications. Supersedes ABE 2017F.
4  ABE 2018B uses 328 kton$\cdot{}$years of Super-Kamiokande I-IV atmospheric neutrino data to obtain this result. The fit is performed over the four parameters, $\Delta$m${}^{2}_{32}$, sin$^2{{\mathit \theta}_{{23}}}$, sin$^2{{\mathit \theta}_{{13}}}$, and $\delta$, while the solar parameters are fixed to $\Delta$m${}^{2}_{21}$= ($7.53$ $\pm0.18$) $\times 10^{-5}$ eV${}^{2}$ and sin$^2{{\mathit \theta}_{{12}}}$ = $0.304$ $\pm0.014$.
5  ACERO 2018 performs a joint fit to the data for ${{\mathit \nu}_{{\mu}}}$ disappearance and ${{\mathit \nu}_{{e}}}$ appearance. The overall best fit favors normal mass ordering and ${{\mathit \theta}_{{23}}}$ in octant II. No 1$\sigma$ confidence intervals are presented for the inverted mass ordering scenarios. Superseded by ACERO 2019 .
6  ABE 2017F confidence intervals are obtained using a frequentist analysis including ${{\mathit \theta}_{{13}}}$ constraint from reactor experiments. Bayesian intervals based on Markov Chain Monte Carlo method are also provided by the authors. Superseded by ABE 2018G.
7  Errors are projections of 68$\%$ C.L. curve of $\delta _{CP}$ vs. sin$^2{{\mathit \theta}_{{23}}}$.
8  ADAMSON 2016 result is based on a data sample with $2.74 \times 10^{20}$ protons on target. The likelihood-based analysis observed 6 ${{\mathit \nu}_{{e}}}$ events with an expected background of $0.99$ $\pm0.11$ events.
9  ADAMSON 2014 result is based on three-flavor formalism and ${{\mathit \theta}_{{23}}}>{{\mathit \pi}}$/4. Likelihood as a function of $\delta$ is also shown for the other three combinations of hierarchy and ${{\mathit \theta}_{{23}}}$ octants; all values of $\delta$ are allowed at 90$\%$ C.L.
10  GONZALEZ-GARCIA 2014 result comes from a frequentist global fit. The corresponding Bayesian global fit to the same data results are reported in BERGSTROM 2015 as 68$\%$ CL intervals of $1.24 - 1.94$ for normal and $1.15 - 1.77$ for inverted mass ordering.
11  ADAMSON 2013A result is based on ${{\mathit \nu}_{{e}}}$ appearance in MINOS and the calculated sin$^2(2{{\mathit \theta}_{{23}}})$ = 0.957,${{\mathit \theta}_{{23}}}>{{\mathit \pi}}$/4, and normal mass hierarchy. Likelihood as a function of$\delta$ is also shown for the other three combinations of hierarchy and ${{\mathit \theta}_{{23}}}$ octants; all values of $\delta$ are allowed at 90$\%$ C.L.
Conservation Laws:
 $\mathit CP$ INVARIANCE
References:
 ACERO 2019
PRL 123 151803 First Measurement of Neutrino Oscillation Parameters using Neutrinos and Antineutrinos by NOvA
 ABE 2018G
PRL 121 171802 Search for CP Violation in Neutrino and Antineutrino Oscillations by the T2K Experiment with $2.2\times10^{21}$ Protons on Target
 ABE 2018B
PR D97 072001 Atmospheric neutrino oscillation analysis with external constraints in Super-Kamiokande I-IV
 ACERO 2018
PR D98 032012 New constraints on oscillation parameters from $\nu_e$ appearance and $\nu_\mu$ disappearance in the NOvA experiment
 DE-SALAS 2018
PL B782 633 Status of neutrino oscillations 2018: 3$\sigma$ hint for normal mass ordering and improved CP sensitivity
 ABE 2017F
PR D96 092006 Measurement of Neutrino and Antineutrino Oscillations by the T2K Experiment Including a New Additional Sample of ${{\mathit \nu}_{{e}}}$ Interactions at the Far Detector
PRL 118 231801 Constraints on Oscillation Parameters from νe Appearance and ${{\mathit \mu}_{{\nu}}}$ Disappearance in NOvA
PR D91 072010 Measurements of Neutrino Oscillation in Appearance and Disappearance Channels by the T2K Experiment with $6.6 \times 10^{20}$ Protons on Target
PRL 112 191801 Combined Analysis of ${{\mathit \nu}_{{\mu}}}$ Disappearance and ${{\mathit \nu}_{{\mu}}}\rightarrow{{\mathit \nu}_{{e}}}$ Appearance in MINOS using Accelerator and Atmospheric Neutrinos
JHEP 1411 052 Updated Fit to Three Neutrino Mixing: Status of Leptonic $\mathit CP$ Violation