This Letter reports the first measurement of the oscillation amplitude and frequency of reactor antineutrinos at Daya Bay via neutron capture on hydrogen using 1958 days of data. With over 3.6 million signal candidates, an optimized candidate selection, improved treatment of backgrounds and efficiencies, refined energy calibration, and an energy response model for the capture-on-hydrogen sensitive region, the relative νe rates and energy spectra variation among the near and far detectors gives sin 2 2θ13 = 0.0759 +0.0050 −0.0049 and ∆m 2 32 = (2.72 +0.14 −0.15 )× 10 −3 eV 2 assuming the normal neutrino mass ordering, and ∆m 2 32 = (−2.83 +0.15 −0.14 )×10 −3 eV 2 for the inverted neutrino mass ordering. This estimate of sin 2 2θ13 is consistent with and essentially independent from the one obtained using the capture-on-gadolinium sample at Daya Bay. The combination of these two results yields sin 2 2θ13 = 0.0833 ± 0.0022, which represents an 8% relative improvement in precision regarding the Daya Bay full 3158-day capture-on-gadolinium result.

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This Letter presents results of a search for the mixing of a sub-eV sterile neutrino with three active neutrinos based on the full data sample of the Daya Bay Reactor Neutrino Experiment, collected during 3158 days of detector operation, which contains 5.55 × 10 6 reactor νe candidates identified as inverse beta-decay interactions followed by neutron-capture on gadolinium. The analysis benefits from a doubling of the statistics of our previous result and from improvements of several important systematic uncertainties. No significant oscillation due to mixing of a sub-eV sterile neutrino with active neutrinos was found. Exclusion limits are set by both Feldman-Cousins and CLs methods. Light sterile neutrino mixing with sin 2 2θ14 ≳ 0.01 can be excluded at 95% confidence level in the region of 0.01 eV 2 ≲ |∆m 2 41 | ≲ 0.1 eV 2 . This result represents the world-leading constraints in the region of 2 × 10 −4 eV 2 ≲ |∆m 2 41 | ≲ 0.2 eV 2 .

Recently, further reduction on normal forms of differential equations leading to the simplest normal forms (SNFs) has received considerable attention. However, the computation of the SNF has been mainly restricted to systems which do not contain perturbation parameters (unfolding), since the computation of the SNF with unfolding is much more complicated than that of the SNF without unfolding. From the practical point of view, only the SNF with perturbation (bifurcation) parameters is useful in analysing physical or engineering problems. It is shown that the SNF with unfolding cannot be obtained using only near-identity transformation. Additional transformations such as time and parameter rescaling need to be introduced. An efficient computational method is presented for computing the algebraic equations that can be used to find the SNF. A physical example is given to show the applicability of the new method.

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