At present time direct measurements of sin$^2(~\theta _{13})$ are derived from the reactor ${{\overline{\mathit \nu}}_{{{e}}}}$ disappearance at distances corresponding to the $\Delta {{\mathit m}}{}^{2}_{32}$ value, i.e. L $\sim{}$ 1km. Alternatively, limits can also be obtained from the analysis of the solar neutrino data and accelerator-based ${{\mathit \nu}_{{{\mu}}}}$ $\rightarrow$ ${{\mathit \nu}_{{{e}}}}$ experiments.

If an experiment reports sin$^2(2~\theta _{13})$ we convert the value to sin$^2(~\theta _{13})$.

VALUE ($ 10^{-2} $) CL% DOCUMENT ID TECN  COMMENT $\bf{ 2.19 \pm0.07}$ OUR AVERAGE  Error includes scale factor of 1.2. $2.80$ ${}^{+0.28}_{-0.65}$ 1 ABE 2023 F T2K Normal mass ordering $2.17$ $\pm0.063$ 2 AN 2023 DAYA DayaBay, Ling Ao/Ao II reactors $2.70$ $\pm0.37$ 3 DE-KERRET 2020 DCHZ Chooz reactors $2.22$ $\pm0.21$ $\pm0.37$ 4 SHIN 2020 RENO Yonggwang reactors $2.29$ $\pm0.18$ 5 BAK 2018 RENO Yonggwang reactors $1.81$ $\pm0.29$ 6 AN 2016 A DAYA DayaBay, Ling Ao/Ao II reactors • • We do not use the following data for averages, fits, limits, etc. • • $3.10$ ${}^{+0.30}_{-0.69}$ 1 ABE 2023 F T2K Inverted mass ordering $2.41$ $\pm0.45$ 7 ABRAHAO 2021 DCHZ Chooz reactors $2.200$ ${}^{+0.069}_{-0.062}$ 8 SALAS 2021 FIT Normal mass ordering, global fit $2.225$ ${}^{+0.064}_{-0.070}$ 8 SALAS 2021 FIT Inverted mass ordering, global fit $2.219$ ${}^{+0.062}_{-0.063}$ 9 ESTEBAN 2020 A FIT Normal mass ordering, global fit $2.238$ ${}^{+0.063}_{-0.062}$ 9 ESTEBAN 2020 A FIT Inverted mass ordering, global fit $<3.9$ 68 AGAFONOVA 2019 OPER $1.8$ ${}^{+2.9}_{-1.3}$ 10 ABE 2018 B SKAM 3${{\mathit \nu}}$ osc: normal mass ordering, ${{\mathit \theta}_{{{13}}}}$ free $0.8$ ${}^{+1.7}_{-0.7}$ 10 ABE 2018 B SKAM 3${{\mathit \nu}}$ osc: inverted mass ordering, ${{\mathit \theta}_{{{13}}}}$ free $2.188$ $\pm0.076$ 11 ADEY 2018 A DAYA DayaBay, LingAo/Ao II reactors $<12$ 90 12 AGAFONOVA 2018 A OPER OPERA: ${{\mathit \nu}_{{{e}}}}$ appearance $2.160$ ${}^{+0.083}_{-0.069}$ DE-SALAS 2018 FIT Normal mass ordering, global fit $2.220$ ${}^{+0.074}_{-0.076}$ DE-SALAS 2018 FIT Inverted mass ordering, global fit $2.09$ $\pm0.23$ $\pm0.16$ 13 SEO 2018 RENO Yonggwang reactors $2.7$ $\pm0.7$ 14 ABE 2017 F T2K Normal mass ordering, T2K only $2.149$ $\pm0.071$ $\pm0.050$ 15 AN 2017 A DAYA DayaBay, LingAo/Ao II reactors $2.25$ ${}^{+0.87}_{-0.86}$ 16 ABE 2016 B DCHZ Chooz reactors $2.09$ $\pm0.23$ $\pm0.16$ 17 CHOI 2016 RENO Yonggwang reactors $2.15$ $\pm0.13$ 18 AN 2015 DAYA DayaBay, Ling Ao/Ao II reactors $2.6$ ${}^{+1.2}_{-1.1}$ 19 ABE 2014 A DCHZ Chooz reactors $3.0$ ${}^{+1.3}_{-1.0}$ 20 ABE 2014 C T2K Inverted mass ordering $3.6$ ${}^{+1.0}_{-0.9}$ 20 ABE 2014 C T2K Normal mass ordering $2.3$ ${}^{+0.9}_{-0.8}$ 21 ABE 2014 H DCHZ Chooz reactors $2.3$ $\pm0.2$ 22 AN 2014 DAYA DayaBay, Ling Ao/Ao II reactors $2.12$ $\pm0.47$ 23 AN 2014 B DAYA DayaBay, Ling Ao/Ao II reactors $2.34$ $\pm0.20$ 24 FORERO 2014 FIT Normal mass ordering $2.40$ $\pm0.19$ 24 FORERO 2014 FIT Inverted mass ordering $2.18$ $\pm0.10$ 25 GONZALEZ-GARC.. 2014 FIT Normal mass ordering; global fit $2.19$ ${}^{+0.11}_{-0.10}$ 25 GONZALEZ-GARC.. 2014 FIT Inverted mass ordering; global fit $2.5$ $\pm0.9$ $\pm0.9$ 26 ABE 2013 C DCHZ Chooz reactors $2.3$ ${}^{+1.3}_{-1.0}$ 27 ABE 2013 E T2K Normal mass ordering $2.8$ ${}^{+1.6}_{-1.2}$ 27 ABE 2013 E T2K Inverted mass ordering $1.6$ ${}^{+1.3}_{-0.9}$ 28 ADAMSON 2013 A MINS Normal mass ordering $3.0$ ${}^{+1.8}_{-1.6}$ 28 ADAMSON 2013 A MINS Inverted mass ordering $<13$ 90 AGAFONOVA 2013 OPER OPERA: 3${{\mathit \nu}}$ $<3.6$ 95 29 AHARMIM 2013 FIT global solar: 3${{\mathit \nu}}$ $2.3$ $\pm0.3$ $\pm0.1$ 30 AN 2013 DAYA DayaBay, LIng Ao/Ao II reactors $2.2$ $\pm1.1$ $\pm0.8$ 31 ABE 2012 DCHZ Chooz reactors $2.8$ $\pm0.8$ $\pm0.7$ 32 ABE 2012 B DCHZ Chooz reactors $2.9$ $\pm0.3$ $\pm0.5$ 33 AHN 2012 RENO Yonggwang reactors $2.4$ $\pm0.4$ $\pm0.1$ 34 AN 2012 DAYA DayaBay, Ling Ao/Ao II reactors $2.5$ ${}^{+1.8}_{-1.6}$ 35 ABE 2011 FIT KamLAND + global solar $\text{< 6.1}$ 95 36 ABE 2011 FIT Global solar $1.3\text{ to }5.6 $ 68 37 ABE 2011 A T2K Normal mass ordering $1.5\text{ to }5.6 $ 68 38 ABE 2011 A T2K Inverted mass ordering $0.3\text{ to }2.3 $ 68 39 ADAMSON 2011 D MINS Normal mass ordering $0.8\text{ to }3.9 $ 68 40 ADAMSON 2011 D MINS Inverted mass ordering $8$ $\pm3$ 41 FOGLI 2011 FIT Global neutrino data $7.8$ $\pm6.2$ 42 GANDO 2011 FIT KamLAND + solar: 3${{\mathit \nu}}$ $12.4$ $\pm13.3$ 43 GANDO 2011 FIT KamLAND: 3${{\mathit \nu}}$ $3$ ${}^{+9}_{-7}$ 90 44 ADAMSON 2010 A MINS Normal mass ordering $6$ ${}^{+14}_{-6}$ 90 45 ADAMSON 2010 A MINS Inverted mass ordering $8$ ${}^{+8}_{-7}$ 46, 47 AHARMIM 2010 FIT KamLAND + global solar: 3${{\mathit \nu}}$ $\text{< 30}$ 95 46, 48 AHARMIM 2010 FIT global solar: 3${{\mathit \nu}}$ $\text{< 15}$ 90 49 WENDELL 2010 SKAM 3${{\mathit \nu}}$ osc.; normal $\mathit m$ ordering $\text{< 33}$ 90 49 WENDELL 2010 SKAM 3${{\mathit \nu}}$ osc.; inverted $\mathit m$ ordering $11$ ${}^{+11}_{-8}$ 50 ADAMSON 2009 MINS Normal mass ordering $18$ ${}^{+15}_{-11}$ 51 ADAMSON 2009 MINS Inverted mass ordering $6$ $\pm4$ 52 FOGLI 2008 FIT Global neutrino data $8$ $\pm7$ 53 FOGLI 2008 FIT Solar + KamLAND data $5$ $\pm5$ 54 FOGLI 2008 FIT Atmospheric + LBL + CHOOZ $\text{< 36}$ 90 55 YAMAMOTO 2006 K2K Accelerator experiment $\text{< 48}$ 90 56 AHN 2004 K2K Accelerator experiment $\text{< 36}$ 90 57 BOEHM 2001 Palo Verde react. $\text{< 45}$ 90 58 BOEHM 2000 Palo Verde react. $\text{< 15}$ 90 59 APOLLONIO 1999 CHOZ Reactor Experiment 1  ABE 2023F results are based on data collected between 2010 and 2020 in (anti)neutrino mode and include a neutrino beam exposure of $1.97 \times 10^{21}$ ($1.63 \times 10^{21}$) protons on target. 2  AN 2023 reports results derived from the complete data set collected by the Daya-Bay experiment, corresponding to 3158 days of operation, resulting in $5.55 \times 10^{6}{{\overline{\mathit \nu}}_{{{e}}}}$ candidate events. Solar oscillation parameters are fixed in the analysis to sin$^2({{\mathit \theta}_{{{12}}}})$ = $0.307$ $\pm0.013$, $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$ from PDG 2020. Supersedes ADEY 2018A. 3  DE-KERRET 2020 uses 481 days of data from single detector operation and also 384 days of data with both near and far detectors operating. A rate and shape analysis is performed on combined neutron captures on ${}^{}\mathrm {H}$ and ${}^{}\mathrm {Gd}$. Supersedes ABE 2016B. 4  SHIN 2020 uses the RENO detector and 1500 live days of data. The near (far) detector observed 567,690 (90,747) ${{\overline{\mathit \nu}}_{{{e}}}}$ candidate events with a delayed neutron capture on hydrogen. The extracted value of sin$^2{{\mathit \theta}_{{{13}}}}$ is consistent with the previous analysis with neutron capture on ${}^{}\mathrm {Gd}$ in BAK 2018. 5  BAK 2018 reports results of the RENO experiment using about 2200 live-days of data taken with detectors placed at 410.6 and 1445.7 m from reactors of the Hanbit Nuclear Power Plant. Supersedes SEO 2018. 6  AN 2016A uses data from the eight antineutrino detectors (404 days) and six antineutrino detectors (217 days) runs to determine the mixing parameter sin$^2(2{{\mathit \theta}_{{{13}}}})$ using the neutron capture on ${}^{}\mathrm {H}$ only. Supersedes AN 2014B. 7  ABRAHAO 2021 uses 865 days of data collected in both near and far detectors with at least one reactor in operation. The analysis is based on a background model independent approach, so called Reactor Rate Modulation, to determine the mixing angle ${{\mathit \theta}_{{{13}}}}$. Adding the background model reduces the uncertainty to 0.0041. Supersedes ABE 2016B. 8  SALAS 2021 reports results of a global fit to neutrino oscillation data available at the time of the Neutrino 2020 conference. 9  ESTEBAN 2020A reports results of a global fit to neutrino oscillation data available at the time of the Neutrino2020 conference. 10  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$^2{{\mathit \theta}_{{{12}}}}$ = $0.304$ $\pm0.014$. 11  ADEY 2018A reports results from analysis of 1958 days of data taking with the Daya-Bay experiment, with $3.9 \times 10^{6}{{\overline{\mathit \nu}}_{{{e}}}}$ candidates. The fit to the data gives $\Delta $m${}^{2}_{ee}$ = ($2.522$ ${}^{+0.068}_{-0.070}$) $ \times 10^{-3}$ eV${}^{2}$. Solar oscillation parameters are fixed in the analysis using the global averages, sin$^2({{\mathit \theta}_{{{12}}}})$ = $0.307$ ${}^{+0.013}_{-0.012}$, $\Delta $m${}^{2}_{21}$ = ($7.53$ $\pm0.18$) $ \times 10^{-5}$ eV${}^{2}$, from PDG 2018. Supersedes AN 2017A. 12  AGAFONOVA 2018A reports sin$^2(2{{\mathit \theta}_{{{13}}}})$ $<$ 0.43 at 90$\%$ C.L. The result on the sterile neutrino search in the context of 3+1 model is also reported. A 90$\%$ C.L. upper limit on sin$^2(2\theta _{{{\mathit \mu}} {{\mathit e}})}$ = $0.021$ for $\Delta $m${}^{2}_{41}{}\geq{}$ 0.1 eV${}^{2}$ is set. 13  SEO 2018 reports results of the RENO experiment using about 500 days of data, performing a rate and shape analysis. Compared to AHN 2012, a significant reduction of the systematic uncertainties is reported. A 3$\%$ excess of events near 5 MeV of the prompt energy is observed. SEO 2018 is a detailed description of the results published in CHOI 2016, which it supersedes. Superseded by BAK 2018. 14  Using T2K data only. For inverted mass ordering, all values of ${{\mathit \theta}_{{{13}}}}$ are ruled out at 68$\%$ CL. 15  AN 2017A reports results from combined rate and spectral shape analysis of 1230 days of data taken with the Daya Bay reactor experiment. The data set contains more than $2.5 \times 10^{6}$ inverse beta-decay events with neutron capture on ${}^{}\mathrm {Gd}$. A simultaneous fit to ${{\mathit \theta}_{{{13}}}}$ and $\Delta $m${}^{2}_{ee}$ is performed. Superseded by ADEY 2018A. 16  ABE 2016B uses 455.57 live days of data from a detector 1050 m away from two reactor cores of the Chooz nuclear power station, to determine the mixing parameter sin$^2(2{{\mathit \theta}_{{{13}}}})$. This analysis uses 7.15 reactor-off days for constraining backgrounds. A rate and shape analysis is performed on combined neutron captures on ${}^{}\mathrm {H}$ and ${}^{}\mathrm {Gd}$. Supersedes ABE 2014H and ABE 2013C. 17  CHOI 2016 reports results of the RENO experiment using about 500 days of data, performing a rate and shape analysis. Compared to AHN 2012, a significant reduction of the systematic uncertainties is reported. A 3$\%$ excess of events near 5 MeV of the prompt energy is observed. Supersedes AHN 2012. 18  AN 2015 uses all eight identical detectors, with four placed near the reactor cores and the remaining four at the far hall to determine the mixing angle $\theta _{13}$ using the ${{\overline{\mathit \nu}}_{{{e}}}}$ observed interaction rates with neutron capture on ${}^{}\mathrm {Gd}$ and energy spectra. The result corresponds to the exposure of $6.9 \times 10^{5}$ GW$_{th}$-ton-days. Superseded by AN 2017A. 19  ABE 2014A uses 467.9 live days of one detector, 1050 m away from two reactor cores of the Chooz nuclear power station, to determine the mixing parameter sin$^2(2 {{\mathit \theta}_{{{13}}}})$. The Bugey4 data (DECLAIS 1994) is used to constrain the neutrino flux. The data set includes 7.24 reactor-off days. A "rate-modulation" analysis is performed. Supercedes ABE 2012B. 20  ABE 2014C result is for ${{\mathit \nu}_{{{e}}}}$ appearance and assumes $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.4 \times 10^{-3}$ eV${}^{2}$, sin$^2( \theta _{23})$ = 0.5, and $\delta $ = 0. 21  ABE 2014H uses 467.9 live days of one detector, 1050 m away from two reactor cores of the Chooz nuclear power station, to determine the mixing parameter sin$^2(2 {{\mathit \theta}_{{{13}}}})$. The Bugey4 data (DECLAIS 1994) is used to constrain the neutrino flux. The data set includes 7.24 reactor-off days. A rate and shape analysis is performed. Superceded by ABE 2016B. 22  AN 2014 uses six identical detectors, with three placed near the reactor cores (flux-weighted baselines of 512 and 561 m) and the remaining three at the far hall (at the flux averaged distance of 1579 m from all six reactor cores) to determine the mixing angle $\theta _{13}$ using the ${{\overline{\mathit \nu}}_{{{e}}}}$ observed interaction rates with neutron capture on ${}^{}\mathrm {Gd}$ and energy spectra. Supersedes AN 2013 and superseded by AN 2015. 23  AN 2014B uses six identical anti-neutrino detectors with flux-weighted baselines of $\sim{}$500 m and $\sim{}$1.6 km to six power reactors. This rate analysis uses a 217-day data set and neutron capture on protons (not ${}^{}\mathrm {Gd}$) only. $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$= $2.32 \times 10^{-3}$ eV${}^{2}$ is assumed. Superseded by AN 2016A. 24  FORERO 2014 performs a global fit to neutrino oscillations using solar, reactor, long-baseline accelerator, and atmospheric neutrino data. 25  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 ($2.18$ ${}^{+0.10}_{-0.11}$) $ \times 10^{-2}$ eV${}^{2}$ for normal and ($2.19$ ${}^{+0.12}_{-0.10}$) $ \times 10^{-2}$ eV${}^{2}$ for inverted mass ordering. 26  ABE 2013C uses delayed neutron capture on hydrogen instead of on ${}^{}\mathrm {Gd}$ used previously. The physical volume is thus three times larger. The fit is based on the rate and shape analysis as in ABE 2012B. The Bugey4 data (DECLAIS 1994) is used to constrain the neutrino flux. Superseded by ABE 2016B. 27  ABE 2013E assumes maximal $\theta _{23}$ mixing and $\mathit CP$ phase $\delta $ = 0. 28  ADAMSON 2013A results obtained from ${{\mathit \nu}_{{{e}}}}$ appearance, assuming $\delta $ = 0, and sin$^2(2 \theta _{23})$ = 0.957. 29  AHARMIM 2013 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ fixed to $2.45 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data. AHARMIM 2013 global solar neutrino data include SNO's all-phases-combined analysis results on the total active ${}^{8}\mathrm {B}$ neutrino flux and energy-dependent ${{\mathit \nu}_{{{e}}}}$ survival probability parameters, measurements of ${}^{}\mathrm {Cl}$ (CLEVELAND 1998), ${}^{}\mathrm {Ga}$ (ABDURASHITOV 2009 which contains combined analysis with GNO (ALTMANN 2005 and Ph.D. thesis of F. Kaether)), and ${}^{7}\mathrm {Be}$ (BELLINI 2011A) rates, and ${}^{8}\mathrm {B}$ solar-neutrino recoil electron measurements of SK-I (HOSAKA 2006) zenith, SK-II (CRAVENS 2008) and SK-III (ABE 2011) day/night spectra, and Borexino (BELLINI 2010A) spectra. AHARMIM 2013 also reported a result combining global solar and KamLAND data, which is sin${}^{2}$(2 ${{\mathit \theta}_{{{13}}}}$) = ($9.1$ ${}^{+2.9}_{-3.1}$) $ \times 10^{-2}$. 30  AN 2013 uses six identical detectors, with three placed near the reactor cores (flux-weighted baselines of 498 and 555 m) and the remaining three at the far hall (at the flux averaged distance of 1628 m from all six reactor cores) to determine the ${{\overline{\mathit \nu}}_{{{e}}}}$ interaction rate ratios. Superseded by AN 2014. 31  ABE 2012 determines the ${{\overline{\mathit \nu}}_{{{e}}}}$ interaction rate in a single detector, located 1050 m from the cores of two reactors. A rate and shape analysis is performed. The rate normalization is fixed by the results of the Bugey4 reactor experiment, thus avoiding any dependence on possible very short baseline oscillations. The value of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ = $2.4 \times 10^{-3}$ eV${}^{2}$ is used in the analysis. Superseded by ABE 2012B. 32  ABE 2012B determines the neutrino mixing angle ${{\mathit \theta}_{{{13}}}}$ using a single detector, located 1050$~$m from the cores of two reactors. This result is based on a spectral shape and rate analysis. The Bugey4 data (DECLAIS 1994) is used to constrain the neutrino flux. Superseded by ABE 2014A. 33  AHN 2012 uses two identical detectors, placed at flux weighted distances of 408.56 m and 1433.99 m from six reactor cores, to determine the mixing angle ${{\mathit \theta}_{{{13}}}}$. This rate-only analysis excludes the no-oscillation hypothesis at 4.9 standard deviations. The value of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ = ($2.32$ ${}^{+0.12}_{-0.08}$) $ \times 10^{-3}$ eV${}^{2}$ was assumed in the analysis. Superseded by CHOI 2016. 34  AN 2012 uses six identical detectors with three placed near the reactor cores (flux-weighted baselines of 470 m and 576 m) and the remaining three at the far hall (at the flux averaged distance of 1648 m from all six reactor cores) to determine the mixing angle ${{\mathit \theta}_{{{13}}}}$ using the ${{\overline{\mathit \nu}}_{{{e}}}}$ observed interaction rate ratios. This rate-only analysis excludes the no-oscillation hypothesis at 5.2 standard deviations. The value of $\Delta {{\mathit m}^{2}}_{\mathrm {31}}$ = ($2.32$ ${}^{+0.12}_{-0.08}$) $ \times 10^{-3}$ eV${}^{2}$ was assumed in the analysis. Superseded by AN 2013. 35  ABE 2011 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ fixed to $2.4 \times 10^{-3}$ eV${}^{2}$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 2008A), Homestake, GALLEX/GNO, SAGE, and KamLAND data. This result implies an upper bound of sin$^2{{\mathit \theta}_{{{13}}}}<$ 0.059 (95$\%$ CL) or sin$^22{{\mathit \theta}_{{{13}}}}<$ 0.22 (95$\%$ CL). The normal neutrino mass ordering and CPT invariance are assumed. 36  ABE 2011 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ fixed to $2.4 \times 10^{-3}$ eV${}^{2}$, using solar neutrino data including Super-Kamiokande, SNO, Borexino (ARPESELLA 2008A), Homestake, and GALLEX/GNO data. The normal neutrino mass ordering is assumed. 37  The quoted limit is for $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.4 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = ${{\mathit \pi}}$/2, ${{\mathit \delta}}$ = 0, and the normal mass ordering. For other values of ${{\mathit \delta}}$, the 68$\%$ region spans from 0.03 to 0.25, and the 90$\%$ region from 0.02 to 0.32. 38  The quoted limit is for $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.4 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = ${{\mathit \pi}}$/2, ${{\mathit \delta}}$ = 0, and the inverted mass ordering. For other values of ${{\mathit \delta}}$, the 68$\%$ region spans from 0.04 to 0.30, and the 90$\%$ region from 0.02 to 0.39. 39  The quoted limit is for $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.32 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = ${{\mathit \pi}}$/2, ${{\mathit \delta}}$ = 0, and the normal mass ordering. For other values of ${{\mathit \delta}}$, the 68$\%$ region spans from 0.02 to 0.12, and the 90$\%$ region from 0 to 0.16. 40  The quoted limit is for $\Delta {{\mathit m}^{2}}_{\mathrm {32}}$ = $2.32 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = ${{\mathit \pi}}$/2, ${{\mathit \delta}}$ = 0, and the inverted mass ordering. For other values of ${{\mathit \delta}}$, the 68$\%$ region spans from 0.02 to 0.16, and the 90$\%$ region from 0 to 0.21. 41  FOGLI 2011 obtained this result from an analysis using the atmospheric, accelerator long baseline, CHOOZ, solar, and KamLAND data. Recently, MUELLER 2011 suggested an average increase of about 3.5$\%$ in normalization of the reactor ${{\overline{\mathit \nu}}_{{{e}}}}$ fluxess, and using these fluxes, the fitted result becomes $0.10$ $\pm0.03$. 42  GANDO 2011 report sin$^2{{\mathit \theta}_{{{13}}}}$ = $0.020$ $\pm0.016$. This result was obtained with three-neutrino fit using the KamLAND + solar data. 43  GANDO 2011 report sin$^2{{\mathit \theta}_{{{13}}}}$ = $0.032$ $\pm0.037$. This result was obtained with three-neutrino fit using the KamLAND data only. 44  This result corresponds to the limit of $<$0.12 at 90$\%$ CL for $\Delta {{\mathit m}}{}^{2}_{32}$ = $2.43 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = $\pi $/2, and $\delta $ = 0. For other values of $\delta $, the 90$\%$ CL region spans from 0 to 0.16. 45  This result corresponds to the limit of $<$0.20 at 90$\%$ CL for $\Delta {{\mathit m}}{}^{2}_{32}$ = $2.43 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = $\pi $/2, and $\delta $ = 0. For other values of $\delta $, the 90$\%$ CL region spans from 0 to 0.21. 46  AHARMIM 2010 global solar neutrino data include SNO's low-energy-threshold analysis survival probability day/night curves, SNO Phase III integral rates (AHARMIM 2008), Cl (CLEVELAND 1998), SAGE (ABDURASHITOV 2009), Gallex/GNO (HAMPEL 1999, ALTMANN 2005), Borexino (ARPESELLA 2008A), SK-I zenith (HOSAKA 2006), and SK-II day/night spectra (CRAVENS 2008). 47  AHARMIM 2010 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{{{\mathit 31}}}$ fixed to $2.3 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data and KamLAND data (ABE 2008A). $\mathit CPT$ invariance is assumed. This result implies an upper bound of sin$^2{{\mathit \theta}_{{{13}}}}<$ 0.057 (95$\%$ CL) or sin$^22{{\mathit \theta}_{{{13}}}}<$ 0.22 (95$\%$ CL). 48  AHARMIM 2010 obtained this result by a three-neutrino oscillation analysis with the value of $\Delta {{\mathit m}^{2}}_{{{\mathit 31}}}$ fixed to $2.3 \times 10^{-3}$ eV${}^{2}$, using global solar neutrino data. 49  WENDELL 2010 obtained this result by a three-neutrino oscillation analysis with one mass scale dominance ($\Delta $m${}^{2}_{21}$ = 0) using the Super-Kamiokande-I+II+III atmospheric neutrino data, and updates the HOSAKA 2006A result. 50  The quoted limit is for $\Delta {{\mathit m}}{}^{2}_{32}$ = $2.43 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = $\pi $/2, and $\delta $ = 0. For other values of $\delta $, the 68$\%$ CL region spans from 0.02 to 0.26. 51  The quoted limit is for $\Delta {{\mathit m}}{}^{2}_{32}$ = $2.43 \times 10^{-3}$ eV${}^{2}$, $\theta _{23}$ = $\pi $/2, and $\delta $ = 0. For other values of $\delta $, the 68$\%$ CL region spans from 0.04 to 0.34. 52  FOGLI 2008 obtained this result from a global analysis of all neutrino oscillation data, that is, solar + KamLAND + atmospheric + accelerator long baseline + CHOOZ. 53  FOGLI 2008 obtained this result from an analysis using the solar and KamLAND neutrino oscillation data. 54  FOGLI 2008 obtained this result from an analysis using the atmospheric, accelerator long baseline, and CHOOZ neutrino oscillation data. 55  YAMAMOTO 2006 searched for ${{\mathit \nu}_{{{\mu}}}}$ $\rightarrow$ ${{\mathit \nu}_{{{e}}}}$ appearance. Assumes 2 sin$^2(2\theta _{{{\mathit \mu}} {{\mathit e}}})$ = sin$^2(2\theta _{13})$. The quoted limit is for ${{\mathit \Delta}}{{\mathit m}}{}^{2}_{32}$ = $1.9 \times 10^{-3}$ eV${}^{2}$. That value of ${{\mathit \Delta}}{{\mathit m}}{}^{2}_{32}$ is the one-$\sigma $ low value for AHN 2006A. For the AHN 2006A best fit value of $2.8 \times 10^{-3}$ eV${}^{2}$, the sin$^2(2\theta _{13})$ limit is $<$ 0.26. Supersedes AHN 2004. 56  AHN 2004 searched for ${{\mathit \nu}_{{{\mu}}}}$ $\rightarrow$ ${{\mathit \nu}_{{{e}}}}$ appearance. Assuming 2 sin$^2(2 \theta _{{{\mathit \mu}_{{{e}}}}})$ = sin$^2(2 \theta _{13})$, a limit on sin$^2(2 \theta _{{{\mathit \mu}_{{{e}}}}})$ is converted to a limit on sin$^2(2 \theta _{13})$.The quoted limit is for ${{\mathit \Delta}}{{\mathit m}}{}^{2}_{32}$ = $1.9 \times 10^{-3}$ eV${}^{2}$. That value of ${{\mathit \Delta}}{{\mathit m}}{}^{2}_{32}$ is the one-${{\mathit \sigma}}$ low value for ALIU 2005. For the ALIU 2005 best fit value of $2.8 \times 10^{-3}$ eV${}^{2}$, the sin$^2(2 \theta _{13})$ limit is $<$ 0.30. 57  The quoted limit is for $\Delta \mathit m{}^{2}_{32}$ = $1.9 \times 10^{-3}$ eV${}^{2}$. That value of $\Delta \mathit m{}^{2}_{32}$ is the 1-${{\mathit \sigma}}$ low value for ALIU 2005. For the ALIU 2005 best fit value of $2.8 \times 10^{-3}$ eV${}^{2}$, the sin$^22 {{\mathit \theta}}_{13}$ limit is $<$ 0.19. In this range, the ${{\mathit \theta}}_{13}$ limit is larger for lower values of $\Delta \mathit m{}^{2}_{32}$, and smaller for higher values of $\Delta \mathit m{}^{2}_{32}$. 58  The quoted limit is for $\Delta \mathit m{}^{2}_{32}$ = $1.9 \times 10^{-3}$ eV${}^{2}$. That value of $\Delta \mathit m{}^{2}_{32}$ is the 1-${{\mathit \sigma}}$ low value for ALIU 2005. For the ALIU 2005 best fit value of $2.8 \times 10^{-3}$ eV${}^{2}$, the sin$^22 {{\mathit \theta}}_{13}$ limit is $<$ 0.23. 59  The quoted limit is for $\Delta \mathit m{}^{2}_{32}$ = $2.43 \times 10^{-3}$ eV${}^{2}$. That value of $\Delta \mathit m{}^{2}_{32}$ is the central value for ADAMSON 2008. For the ADAMSON 2008 1-$\sigma $ low value of $2.30 \times 10^{-3}$ eV${}^{2}$, the sin$^22 {{\mathit \theta}}_{13}$ limit is $<$ 0.16. See also APOLLONIO 2003 for a detailed description of the experiment.

Conservation Laws:

LEPTON FAMILY NUMBER

References