Recent results of Daya Bay Experiment

. The Daya Bay reactor neutrino experiment aimed to precisely measure the least known mixing angle θ 13 . In March 2012, Daya Bay announced the non-zero value with more than 5 σ . With more statistics, less background and better control of systematics, the Daya Bay experiment is continuously improving the precision of sin 2 2 θ 13 as well as the e ﬀ ective neutrino mass squared di ﬀ erences. In this paper, I will report the recent oscillation results, which are the most precise measurement of the oscillation parameter θ 13 and | ∆ m 2 ee | . With 1230 days of data, sin 2 2 θ 13 is measured to be [8 . 41 ± 0 . 27(stat.) ± 0 . 19(syst.)] × 10 − 2 , and | ∆ m 2 ee | = [2 . 50 ± 0 . 06(stat.) ± 0 . 06(syst.)] × 10 − 3 eV 2 with χ 2 / NDF = 232 . 6 / 263. An independent measurement with the inverse beta decay neutron captured on hydrogen will also be presented. ,


Introduction
Using the PMNS matrix U PMNS , a neutrino with flavor α can be expressed as a combination of the mass eigenstates of neutrino.
where α = e, µ, τ for flavor eigenstates, and i = 1, 2, 3 for mass eigenstates. In the three-flavor model, U PMNS is commonly parameterized with three mixing angles (θ 12 , θ 23 , and θ 13 ) and the CP-violating phase δ CP . Of these mixing angles, θ 13 is the least known. Solar and long baseline reactor experiments have measured θ 12 [1,2] and atmospheric and accelerator experiments measured θ 23 [3,4]. Previous short baseline reactor and accelerator neutrino experiments found no evidence of reactor antineutrino disappearance, but limited the value of θ 13 to be less than 10 degree at 90% confidence level. The remain unknowns in neutrino oscillation include the mass hierarchy of neutrino and the CP phase. A non-zero value for θ 13 makes it possible to measure the unknowns. And the magnitude of θ 13 is the signpost for future experiments to determine the neutrino mass hierarchy and to search for neutrino CP-violation.
Of this method, sensitivity to neutrino oscillation depends on relative uncertainties between detectors, including the number of target protons N p , the baseling L and the detecting efficiency. Three experiments were constructed based on this technique, Daya Bay [5], RENO [6], and Double CHOOZ [9]. In March 2012, Daya Bay reported the discovery of the non-zero θ 13 [5]. and then be confirmed by the other two experiments [6,9]. The large value of θ 13 has allowed the measurement of ∆m ee from the oscillation of the neutrino energy spectrum. The experiment is located in the Daya Bay nuclear power station in ShenZhen, which is in the south of China, and about 55 km away from Hong Kong. Figure 1 shows the layout of the experiment. There are 6 reactor cores with a total power of 17.4 GW th (giga walts), and three experimental halls (The Daya Bay near site, LingAo near site and the far site) with 8 operating detectors , the total target mass of the detectors is 160 ton. The coordinates of each detector and reactor can be found in [19]. Th e coordinates were detected using GPS, and the uncertainties of the coordinates were 18mm. Details of the experimental layout can be found in [10].

The Daya Bay Experiment
In the experimental hall, a water cerenkov detector and the resistive plate chambers are used to tag muons, two identical designed antineutrino detectors(AD) are mounted in each near experimental hall, and 4 identical ADs were mounted in the far hall [17].
Each AD is constructed as a nested three zone structure, as shown in Figure 2. The inner most is the 3-meter acrylic tank, containing 20 tons of gadolinium loaded liquid scintillator(GdLS), which is the antineutrino target. In the 4-meter acrylic tank, it contains 22 tons of normal liquid scintillator (LS), with a function of gamma catcher. The outermost is the buffer shielding. Three automatic calibration units (ACU-A, ACU-B, ACU-C) were mounted on the top of each AD for detector calibration. 192 PMTs are used to collect photons. Details of the antineutrino detector can refer to [17]  The experiment started the data taking in Dec 2011, with the operating of 6 AD. The 8AD data taking period started in October 2012. Last year, we published the 621 days data result which combined the 6-AD and 8-AD period data [10], and the 1230 days data result will be published soon.

Energy Calibration
To do the energy calibration, the first step is to do the PMT gain calibration. There are two methods for PMT gain calibration, one is based on the single photoelectron from the PMT dark noise, and the other is based on the weekly deployment of LED. The second step is the energy calibration, both the calibration sources as well as the spallation neutrons were used for energy calibration.
The AD-to-AD relative energy scale was also measured using 13 different calibration sources, including both deployed and naturally occurred sources. The calibration sources include 68 Ge, 60 Co and AmC neutron sources; Neutrons from IBD and muon spallation captured both on H and Gd were used. Signals generated by natural radioactivity including α decays and γ rays from 40 K and 208 Tl were also compared between detectors. Figure 3 shows the comparison of the mean reconstructed energy between the ADs for these 13 various sources. Error bars in the figure are statistical only, and relative energy scale uncertainty for all calibration sources were less than 0.2%. The 8 MeV n-Gd capture γ peaks from Am-C sources were used to define the energy scale of each detector.
The energy model of Daya Bay experiment include the nonlinearity from liquid scintillator and the readout electronics. The energy model was built based on various γ peaks and continuous 12 B beta spectrum. This model was also validated using independent calibration data, include the Michel electron, the β+γ continuous spectra from Bi and Tl decays, and the Compton scattering electron data. Figure 4 shows the energy model, which the uncertainty band corresponds to the model consistent with the calibration data within 68% C.L. The prominent nonlinearity below 4 MeV was attributed to scintillator light yield (from ionization quenching and Cherenkov light production) and the charge response of the electronics. Gamma rays from both deployed and intrinsic sources as well as spallation 12

Event selection
Antineutrinos are detected via inverse beta decay (IBD), which provides two time-correlated signals of specific energies. The first, or prompt signal is produced by positron. The delayed signal is neutron, which can be captured on Gd or H. If it was captured on Gd, the capture time is about 30 us, and the excited Gd will release ∼8MeV of γ rays. If it was captured on H, the capture time is about 200us, and releasing ∼2.2MeV γ rays. To select IBD events, the PMT flashers are removed which are instrumental backgrounds [11]. Then the coincidence cut is applied, with the prompt energy between 0.7 and 12 MeV, the delayed energy between 6 and 12MeV. The coincidence time cut was applied as more than 1us and less than 200us. The combined efficiency was estimated to be 80.6%. The absolute efficiencies and their correlated uncertainties were canceled when comparing the ratio of signals in the far versus near detectors. Therefore, only the uncorrelated uncertainties were considered. The uncorrelated uncertainty of detection efficiency was estimated to be 0.13% [10]. There are five main backgrounds including the accidentals, the fast neutrons, the 9 Li/ 8 He, 13 C(α,n) 16 O, and the background from the calibration source 241 Am-13 C. The uncertainty of these backgrounds were limited to 0.2% for each experimental hall. In summary, the backgrounds were estimated to contribute 1.8% to the sample from EH1, 1.5% to EH2, and 2.0% to EH3. And the uncertainties of background were 0.2%, 0.15% and 0.2% for the three experimental hall, respectively. The upper panel of Figure 5 shows the positron energy spectra distribution in EH3, and compared the experimental data to prediction assuming no oscillation. The estimated background are barely visible as can be seen from the figure. The ratios of the data to predictions assuming no oscillation are shown in the lower panel of figure 5, to highlight the spectral distortion. The distortion of the energy spectra is consistent with oscillation, which allowed to measure ∆m ee .
With the 1230 days of data, over 2.8 million IBD candidates were obtained. This is double statistics of the result we published with 621 days data in 2015. Figure 6 shows the survival probability versus L/E for the three experimental hall using the 1230 days of data. The points are the ratios of the observed antineutrino spectra to expectation assuming no oscillation. The solid line is the expectation using the best estimates of the two parameters, sin 2 2θ 13 an |∆ ee |. Error bars are statistical only. < E ν > was obtained using the estimated detector response, while L e f f was calculated by equating the actual  flux to an effective antineutrino flux using a single baseline. And all the three experimental halls were consistent with the oscillation hypnosis.  Double CHOOZ [8], and consistent with the GeV-scale accelerator experiments like T2K [13], MINOS [12] and NOvA [14], and consistent with the atmospheric experiments like supreK [15] and Icecube [16]. ∆m 2 32 is 2.45 × 10 −3 eV 2 when consider normal hierarchy. While −2.55 × 10 −3 eV 2 when consider inverted mass hierarchy.

Oscillation results
6 Independent measurement of θ 13 using nH An independent measurement of sin 2 2θ 13 has been measured via the detection of IBDs tagged by neutron capture on hydrogen (nH) by Daya Bay experiment. The background of nH analysis is higher, the neutron capture time (200ms) is longer, and the energy neutron captured on hydrogen is lower (2.2MeV). To meet these challenges, new analysis approaches have been developed. Based on the rate deficit observed at the far-site detectors for the 6-AD period, a value of sin 2 2θ 13 = 0.071 ± 0.011 is extracted. The result is shown in Figure 8, which is consistent with the result obtained in the nGd analysis. Details of the nH analysis can refer to [18]

Summary
In this article, I present the latest results of the oscillation analysis from Daya Bay Experiment. With 1230 days of data, the most precise measurement of sin 2 2θ 13 and |∆m 2 ee | are given Independent measurement sin 2 2θ 13 using neutron captured on hydrogen with 631-day of data is also presented. sin 2 2θ 13 = 0.071 ± 0.011.