(B) Three-neutrino mixing parameters

$\delta $, $\mathit CP$ violating phase

INSPIRE   PDGID:
S067DEL
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
$\bf{ 1.23 \pm0.21}$ OUR AVERAGE  Error includes scale factor of 1.3.  See the ideogram below.
$0.82$ ${}^{+0.27}_{-0.87}$ 1, 2
ACERO
2022
NOVA Normal mass ordering, octant II for ${{\mathit \theta}_{{23}}}$, ${{\mathit \theta}_{{13}}}$ constrained
$1.40$ ${}^{+0.22}_{-0.18}$ 3
ABE
2020F
 T2K Normal mass ordering
$1.33$ ${}^{+0.45}_{-0.51}$ 4
ABE
2018B
 SKAM Normal mass ordering, ${{\mathit \theta}_{{13}}}$ constrained
• • We do not use the following data for averages, fits, limits, etc. • •
$1.52$ ${}^{+0.30}_{-0.41}$ 1, 5
ACERO
2022
NOVA Inverted mass ordering, octant II for ${{\mathit \theta}_{{23}}}$, ${{\mathit \theta}_{{13}}}$ constrained
$1.08$ ${}^{+0.13}_{-0.12}$ 6
SALAS
2021
FIT Normal mass ordering, global fit
$1.58$ ${}^{+0.15}_{-0.16}$ 6
SALAS
2021
FIT Inverted mass ordering, global fit
$1.09$ ${}^{+0.15}_{-0.13}$ 7
ESTEBAN
2020A
 FIT Normal mass ordering, global fit
$1.57$ ${}^{+0.14}_{-0.17}$ 7
ESTEBAN
2020A
 FIT Inverted mass ordering, global fit
$0.0$ ${}^{+1.3}_{-0.4}$ 8
ACERO
2019
NOVA Normall mass ordering, octant II for ${{\mathit \theta}_{{23}}}$
$1.33$ ${}^{+0.46}_{-0.53}$ 9
ABE
2018B
 SKAM 3${{\mathit \nu}}$ osc: normal mass ordering, ${{\mathit \theta}_{{13}}}$ free
$1.22$ ${}^{+0.76}_{-0.67}$ 9
ABE
2018B
 SKAM 3${{\mathit \nu}}$ osc: inverted mass ordering, ${{\mathit \theta}_{{13}}}$ free
$1.33$ ${}^{+0.48}_{-0.53}$ 4
ABE
2018B
 SKAM 3${{\mathit \nu}}$ osc: inverted mass ordering, ${{\mathit \theta}_{{13}}}$ constrained
$1.40$ $\pm0.20$ 10
ABE
2018G
 T2K Normal mass ordering, ${{\mathit \theta}_{{13}}}$ constrained
$1.54$ ${}^{+0.14}_{-0.12}$ 95 10
ABE
2018G
 T2K Inverted mass ordering, ${{\mathit \theta}_{{13}}}$ constrained
$1.21$ ${}^{+0.91}_{-0.30}$ 11
ACERO
2018
NOVA Normal mass ordering, octant II for ${{\mathit \theta}_{{23}}}$
$1.46$ ${}^{+0.56}_{-0.42}$ 11
ACERO
2018
NOVA Normal mass order; octant I for ${{\mathit \theta}_{{23}}}$
$1.32$ ${}^{+0.21}_{-0.15}$
DE-SALAS
2018
FIT Normal mass ordering, global fit
$1.56$ ${}^{+0.13}_{-0.15}$
DE-SALAS
2018
FIT Inverted mass ordering, global fit
$1.45$ ${}^{+0.27}_{-0.26}$ 12
ABE
2017F
 T2K Normal mass ordering
$1.54$ ${}^{+0.22}_{-0.23}$ 12
ABE
2017F
 T2K Inverted mass ordering
$1.50$ ${}^{+0.53}_{-0.57}$ 13
ADAMSON
2017B
 NOVA Inverted mass ordering; ${{\mathit \theta}_{{23}}}$ in octant II
$0.74$ ${}^{+0.57}_{-0.93}$ 13
ADAMSON
2017B
 NOVA Normal mass ordering; ${{\mathit \theta}_{{23}}}$ in octant II
$1.48$ ${}^{+0.69}_{-0.58}$ 13
ADAMSON
2017B
 NOVA Normal mass ordering; ${{\mathit \theta}_{{23}}}$ in octant I
$\text{ 0.0 to 0.1, 0.5 to 2.0}$ 90 14, 13
ADAMSON
2016
NOVA Inverted mass ordering
$0.0\text{ to }2.0 $ 90 14
ADAMSON
2016
NOVA Normal mass ordering
$\text{ 0 to 0.15, 0.83 to 2}$ 90
ABE
2015D
 T2K Normal mass ordering
$1.09\text{ to }1.92 $ 90
ABE
2015D
 T2K Inverted mass ordering
$0.05\text{ to }1.2 $ 90 15
ADAMSON
2014
MINS Normal mass ordering
$1.34$ ${}^{+0.64}_{-0.38}$
FORERO
2014
FIT Normal mass ordering
$1.48$ ${}^{+0.34}_{-0.32}$
FORERO
2014
FIT Inverted mass ordering
$1.70$ ${}^{+0.22}_{-0.39}$ 16
GONZALEZ-GARC..
2014
FIT Normal mass ordering; global fit
$1.41$ ${}^{+0.35}_{-0.34}$ 16
GONZALEZ-GARC..
2014
FIT Inverted mass ordering; global fit
$\text{ 0 to 1.5 or 1.9 to 2}$ 90 17
ADAMSON
2013A
 MINS Normal mass ordering
1  ACERO 2022 uses data from Jun 29, 2016 to Feb 26, 2019 ($12.5 \times 10^{20}$ POT) and Feb 6, 2014 to Mar 20, 2020 ($13.6 \times 10^{20}$ POT). Results for normal and inverted mass ordering, and ${{\mathit \theta}_{{23}}}$ octant I and II are presented. Supersedes ACERO 2019 .
2  For the octant I (lower octant), the 68$\%$ CL allowed region is discontinuous, and all delta values are allowed at 90$\%$ CL.
3  ABE 2020F results are based on data collected between 2009 and 2018 in (anti)neutrino mode and include a neutrino beam exposure of $1.49 \times 10^{21}$ ($1.64 \times 10^{21}$) protons on target. For inverted mass ordering, the quoted result is $1.56$ ${}^{+0.15}_{-0.17}$ $\pi $ rad. Supersedes ABE 2018G.
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 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$^2{{\mathit \theta}_{{13}}}$ = $0.0219$ $\pm0.0012$.
5  The inverted mass ordering is rejected at 1.0 $\sigma $. The quoted error bars are based on the local best-fit point.
6  SALAS 2021 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.
7  ESTEBAN 2020A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference.
8  ACERO 2019 is based on a sample size of $1.33 \times 10^{20}$ protons on target with combined antineutrino and neutrino data. Superseded by ACERO 2022 .
9  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$^2{{\mathit \theta}_{{12}}}$ = $0.304$ $\pm0.014$.
10  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.
11  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 .
12  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.
13  Errors are projections of 68$\%$ C.L. curve of $\delta _{CP}$ vs. sin$^2{{\mathit \theta}_{{23}}}$.
14  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.
15  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.
16  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.
17  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.

           $\delta $, $\mathit CP$ violating phase (${{\mathit \pi}}$ rad)
Conservation Laws:
$\mathit CP$ INVARIANCE
References:
ACERO 2022
PR D106 032004 Improved measurement of neutrino oscillation parameters by the NOvA experiment
SALAS 2021
JHEP 2102 071 2020 global reassessment of the neutrino oscillation picture
ABE 2020F
NAT 580 339 Constraint on the matter?antimatter symmetry-violating phase in neutrino oscillations
Also
PR D103 112008 Improved constraints on neutrino mixing from the T2K experiment with $\mathbf{3.13\times10^{21}}$ protons on target
ESTEBAN 2020A
JHEP 2009 178 The fate of hints: updated global analysis of three-flavor neutrino oscillations
ACERO 2019
PRL 123 151803 First Measurement of Neutrino Oscillation Parameters using Neutrinos and Antineutrinos by NOvA
ABE 2018B
PR D97 072001 Atmospheric neutrino oscillation analysis with external constraints in Super-Kamiokande I-IV
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
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
Also
PR D98 019902 (errat.) Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of $\nu_e$ interactions at the far detector
ADAMSON 2017B
PRL 118 231801 Constraints on Oscillation Parameters from νe Appearance and ${{\mathit \mu}_{{\nu}}}$ Disappearance in NOvA
ADAMSON 2016
PRL 116 151806 First easurement of Electron Neutrino Appearance in NOvA
ABE 2015D
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
ADAMSON 2014
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
FORERO 2014
PR D90 093006 Neutrino Oscillations Refitted
GONZALEZ-GARCIA 2014
JHEP 1411 052 Updated Fit to Three Neutrino Mixing: Status of Leptonic $\mathit CP$ Violation
ADAMSON 2013A
PRL 110 171801 Electron Neutrino and Antineutrino Appearance in the Full MINOS Data Sample