# The Daya Bay Experiment

Post-publication activity

Curator: Miao He

## Introduction

The study of neutrinos is an extremely active field within elementary particle physics. Neutrinos are elementary particles in the Standard Model and come in three types of flavors, known as $$\nu_e$$, $$\nu_\mu$$ and $$\nu_\tau$$. In the Standard Model, neutrinos are massless. However, we now know that neutrinos have mass and that the neutrino flavor states are superpositions of three mass eigenstates $$\nu_1$$, $$\nu_2$$ and $$\nu_3$$. As the neutrino travels through space (in vacuum or in matter), one flavor can change into another due to quantum interference between the mass eigenstates. This phenomenon is known as neutrino oscillation or neutrino mixing, and its observation in the late 1990s was the first indication that the neutrino flavor states are massive. The amplitude of the oscillation is connected with three mixing angles $$\theta_{12}$$, $$\theta_{23}$$ and $$\theta_{13}$$ in what is now known as the neutrino standard model. The oscillation frequencies are determined by the difference of squared neutrino masses, $$\Delta m^2_{ji}=\Delta m^2_{j}-\Delta m^2_{i}$$. The Daya Bay Reactor Neutrino Experiment was designed to study the oscillation of neutrinos coming from nuclear reactors and in 2012 was the first experiment to conclusively determine that $$\theta_{13}$$ is non-zero. It has provided the most precise measurement of $$\theta_{13}$$ to date.

## The third mixing angle $$\theta_{13}$$

The mixing angles $$\theta_{12}$$ and $$\theta_{23}$$ were measured over a decade ago, while $$\theta_{13}$$ was only poorly known prior to the Daya Bay results. It was constrained by a $$\sin^22\theta_{13}<0.17$$ limit from the CHOOZ reactor experiment. Measurements by T2K and MINOS using muon neutrino beams and the Double Chooz reactor experiment indicated that $$\theta_{13}$$ could be non-zero. Subsequently, Daya Bay and then the RENO reactor experiment showed conclusively that $$\theta_{13}$$ was non-zero. $$\theta_{13}$$ is not only a fundamental parameter of nature, but is also connected experimentally to the lepton Charge-Parity (CP) violation phase, which may explain the abundance of matter over antimatter in the Universe. A zero $$\theta_{13}$$ will make it impossible to measure the CP phase through neutrino oscillation.

## Measuring $$\theta_{13}$$ with reactor antineutrinos

A reactor is a powerful neutrino source which comes free to the physicists who wish to study the neutrino's properties. This makes it a very attractive neutrino source for an experiment. A reactor core releases electron antineutrinos, $$\overline{\nu}_{e}$$, via $$\beta$$-decay of the fission products of four main isotopes, $$^{235}$$U, $$^{239}$$Pu, $$^{238}$$U, $$^{241}$$Pu. The neutrino energy is mostly below 10 MeV. Since the 1950s, reactor experiments have played a critical role in the study of neutrino physics, from the discovery of the antineutrino, to the first observation of reactor antineutrino disappearance. The importance of the reactor antineutrino continues to grow, since it provides an unambiguous measurement of $$\theta_{13}$$, free from matter-induced or CP violation effects.

For reactor-based experiments, $$\theta_{13}$$ can be extracted from the survival probability of the electron antineutrino $$\overline{\nu}_{e}$$ at distances of a few kilometers from the reactor, $P_{\overline{\nu}_e\rightarrow\overline{\nu}_e} = 1 - \cos^4\theta_{13}\sin^2 2\theta_{12}\sin^2\Delta_{21} - \sin^2 2\theta_{13}(\cos^2\theta_{12}\sin^2\Delta_{31} + \sin^2\theta_{12}\sin^2{\Delta_{32}}),$ where $$\Delta_{ji}\equiv\Delta m^2_{ji}({\rm eV}^2)[L(m)/E(MeV)]$$, $$L$$ is the distance between the neutrino source and the detector (baseline) and $$E$$ is the neutrino energy. Past neutrino experiments found $$\Delta m_{21}^2 \ll \left|\Delta m_{31}^2\right| \approx \left|\Delta m_{32}^2\right|$$. The maximum oscillation driven by $$\Delta m_{21}^2$$ appears at around 60 kilometers, while $$\Delta m_{31}^2$$ dominates the oscillation at distances on the order of a kilometer.

Figure 1: Reactor electron antineutrino signal in the gadolinium doped liquid scintillator. Higher energy and shorter capture time on gadolinium improve the background rejection of naturally occurring radioactivity.

Antineutrinos with energy greater than 1.8 MeV are detected via the inverse $$\beta$$-decay (IBD) reaction: $\overline{\nu}_{e} + p \to e^{+} + n.$ The positron carries most of the antineutrino energy and rapidly annihilates with an electron producing a prompt signal with energy ranging from 1 MeV to 12 MeV. The neutron, after thermalizing, captures on a gadolinium (Gd) or hydrogen (H) nucleus (in the liquid-scintillator detectors of Daya Bay), producing a delayed signal with an energy of approximately 8 MeV (capture on Gd) or 2 MeV (capture on H) at a time on the order of tens to hundreds of microseconds after the prompt signal from the positron. The correlation between the energy and the time, as well as the spatial separation, between the prompt and delayed signals, provides a distinctive $$\overline{\nu}_{e}$$ signature. Figure 1 describes this process pictorially and shows the energy correspondence.

The number of detected antineutrinos $$N_{\rm det}$$ is given by $N_{\rm det}=\frac{N_{\rm p}}{4\pi L^2}\int{\epsilon\sigma P_{\rm sur}(E,L,\theta_{13})S dE},$ where $$N_{\rm p}$$ is the number of free protons in the target, $$L$$ is the distance of the detector from the reactor, $$E$$ is the antineutrino energy, $$\epsilon$$ is the efficiency of detecting an antineutrino, $$\sigma$$ is the total cross section of the IBD process, $$P_{\rm sur}$$ is the antineutrino survival probability, that depends on the value of $$\sin^2 2\theta_{13}$$, and $$S$$ is the antineutrino energy spectrum from the reactor.

It is clear from this equation that we need to know the absolute antineutrino flux $$S$$ and the absolute detector efficiency, $$\epsilon$$, in order to measure $$\sin^2 2\theta_{13}$$. Experimentally, it is a challenge to control systematic uncertainties to the sub-percent level, especially for reactor-related uncertainties from the fission process and operational conditions. However, the systematic uncertainties can be greatly suppressed, or totally eliminated, when two detectors are positioned at two different baselines. The detector closer to the reactor core is primarily used to establish the flux and energy spectrum of the antineutrinos. In this approach, the value of $$\sin^2 2\theta_{13}$$ can be measured by comparing the antineutrino flux and energy distribution observed with the far detector to those observed at the near detector.

For a single reactor core and single near and far detectors, the ratio of the number of antineutrino events with energy between $$E$$ and $$E+dE$$ detected at distance $$L_f$$ (far detector) from the reactor core to that at a distance $$L_n$$ (near detector) is given by $\frac{N_{\rm f}}{N_{\rm n}}= \left (\frac{N_{\rm p,f}}{N_{\rm p,n}}\right ) \left (\frac{L_{\rm n}}{L_{\rm f}}\right)^2 \left (\frac{\epsilon_{\rm f}}{\epsilon_{\rm n}}\right ) \left [\frac{P_{\rm sur}(E,L_{\rm f},\theta_{13})}{P_{\rm sur}(E,L_{\rm n},\theta_{13})}\right],$ where $$N_{\rm p,f}$$ and $$N_{\rm p,n}$$ refer to the number of target protons at the far and near sites, respectively. With identical detectors, the relative detector efficiency ($$\epsilon_{\rm f} / \epsilon_{\rm n}$$) can be determined more precisely than the absolute efficiency. Hence, the detector-related systematic uncertainty in this approach is also greatly reduced.

The Daya Bay experiment employed a new idea to further reduce detector related systematic uncertainties by using multiple modules at each site. In this case, the absolute detector efficiency is cancelled by the near-far configuration and the relative difference between detectors is reduced by $$1/\sqrt{N}$$, where $$N$$ is the number of identical detectors at each site. The Daya Bay experiment implements this strategy by deploying two functionally identical modules at each of two sites near the reactor cores, and four detectors at a far site.

## The Daya Bay collaboration

The Daya Bay international collaboration consists of 41 institutes, mainly from China and the US but also from Europe and South-America. Around 250 collaborators contribute to the experiment. The full list of institutions is given here.

## Experiment site

Figure 2: Layout of the Daya Bay experiment. The dots represent reactor cores, labeled as D1, D2, L1, L2, L3 and L4. Each pair of cores forms a Nuclear Power Plant (NPP). The three NPPs, Daya Bay, Ling Ao, and Ling Ao-II are between the Daya Bay coast and 400 m high mountains inland. Eight antineutrino detectors (ADs) were installed in three experimental halls (EHs). Additional halls were used for filling the detectors (LS Hall) or processing the water (Water Hall) for the experimental hall water pools. The ADs were assembled in the Surface Assembly Building (SAB) before being moved underground.

The Daya Bay nuclear power complex is located on the southern coast of China, 55 kilometers to the northeast of Hong Kong and 45 kilometers to the east of Shenzhen. It consists of three nuclear power plants with each of them consisting of two reactor cores. All six cores are functionally identical, pressurized water reactors of 2.9 GW thermal power. The last core started commercial operation on August 7, 2011.

The Daya Bay experimental facility (Figure 2) consists of surface facilities, three underground experimental halls, and two additional underground utility halls known as the Liquid Scintillator Hall (LS Hall) and the Water Hall. Each experimental hall contains a water pool instrumented to detect Cherenkov radiation, either two or four antineutrino detectors (ADs) installed inside the water pool, and modules containing four layers of resistive plate chambers (RPCs) over the top of the pool. Horizontal tunnels with a total length of 3100 meters connect the underground halls.

The mountain contour over the tunnels and experimental halls was carefully surveyed as well as the position of the detectors. The distances between each detector and the reactor cores were thus determined to a precision of 18 mm. Approximate values of the vertical overburden in terms of meter-water-equivalent (mwe) for each hall and their distances to each nuclear power plant are given in Table 1. At full thermal power, each AD in EH1 is expected to observe about 800 IBD events per day where the neutron is captured by a Gd nucleus.

Table 1. Vertical overburden, muon rate, average muon energy of three experimental halls and their distances in meters to the Daya Bay, Ling Ao, and Ling Ao-II Nuclear Power Plants.
Site Overburden (mwe) $$R_\mu(Hz/m^2)$$ $$<E\mu>(GeV)$$ Distance to Daya Bay (m) Distance to Ling Ao (m) Distance to Ling Ao-II (m)
EH1 250 1.27 57 360 860 1310
EH2 265 0.95 58 1350 480 530
EH3 860 0.056 137 1910 1540 1550

## The Antineutrino detectors

Figure 3: Schematic for a Daya Bay antineutrino detector.

Each AD has three nested cylindrical volumes separated by concentric acrylic vessels as shown in Figure 3. The innermost volume holds gadolinium-doped liquid scintillator that serves as the antineutrino target. The middle volume is called the $$\gamma$$-catcher and is filled with un-doped liquid scintillator for detecting $$\gamma$$-rays that escape the target volume. The $$\gamma$$-catcher increases the containment of photon energy, thus improving the energy resolution and reducing the uncertainties in the antineutrino detection efficiency. The outermost volume is constructed of stainless steel and contains mineral oil to provide optical homogeneity and to shield the inner volumes from radiation originating, for example, from the photo-multiplier tubes (PMTs) or the stainless steel. There are 192 20-cm PMTs within the mineral oil volume. The PMT surface is 20 cm from the middle volume. A single coaxial cable is used to supply positive high voltage and transmit the PMT signal to the front-end electronics. There are two optical reflectors at the top and bottom of the outer acrylic vessel that is incorporated in order to increase the optical acceptance of photons. The use of the reflectors allows us to reduce the number of PMTs by a factor of two. Three automated calibration units (ACU-A, ACU-B, and ACU-C) are mounted at the top of the stainless steel tank. Each ACU contains a LED, as well as two sealed capsules with radioactive sources that can be lowered individually into the gadolinium-doped liquid scintillator along either the centerline, the inner edge, or in the un-doped liquid scintillator (see Figure 3). Table 2 contains detailed parameters for each component.

Besides the detector components shown in Figure 3 and Table 2, six 5-cm PMTs, three at the top and three at the bottom of the AD, are installed to monitor the attenuation length of the Gd-LS and LS via optical windows on the reflective panels. A mineral oil clarity device is installed on the AD lid to monitor the attenuation length of the mineral oil by detecting blue LED light reflected from a retroreflector at the bottom of the AD. The AD is also instrumented with two CMOS cameras and temperature sensors to monitor the liquid levels.

Table 2. Components and parameters of the antineutrino detector.
Detector components Position Parameters
Inner acrylic vessel Inner volume 3.1 m$$\times$$3.1 m, 18 mm thick.
Outer acrylic vessel Middle volume 4 m$$\times$$4 m, 10 mm thick.
Stainless steel tank Outer volume 5 m$$\times$$5 m, 12 mm thick.
Two reflective panels At the top and bottom of the outer acrylic vessel 4.6 m diameter, 2 cm thick.
PMTs In the mineral oil 20 cm diameter (Hamamatsu R5912). The gain is set to $$1\times10^7$$.
Liquid scintillator In the outer acrylic vessel Composition: linear alkylbenzene + 3 g/L PPO + 15 mg/L bis-MSB. 21 ton. 0.859 g/mL.
Gadolinium-doped liquid scintillator In the inner acrylic vessel Same as liquid scintillator except 0.1% gadolinium by weight. 20 ton. 0.860 g/mL.
Mineral oil In the stainless steel tank 37 ton. 0.851 g/mL.
Automated calibration units ACUA: on the central axis of the detector
ACUB: at a radius of 135.00 cm
ACUC: at a radius of 177.25 cm
Calibration sources:
• LED
• 2$$\times$$511 keV $$\gamma$$, 10 Hz
• $$^{60}$$Co, 1.17 + 1.33 MeV $$\gamma$$, 100 Hz
• $$^{241}$$Am–$$^{13}$$C, neutron, 0.7 Hz

## The Muon system

Figure 4: Schematic for the Daya Bay Near Hall (EH1) including the ADs, water shields, and RPCs. The ADs are separated by 1 m.

The muon system consists of a RPC tracking device and an active water shield (Figure 4, Table 3). The water shield consists of two optically separated regions known as the inner and outer water shields. Each region operates as an independent water Cherenkov detector instrumented with PMTs. The water shield has multiple purposes. It detects muons that can produce spallation neutrons or other cosmogenic backgrounds in the ADs. The pool also moderates neutrons and attenuates $$\gamma$$-rays produced in the rock and other structural materials in and around the experimental halls. The water pool is designed so that there is at least 2.5 m of water surrounding each AD in every direction. The PMTs are distributed between the inner and outer zones that are optically divided using Tyvek ® sheets. Each pool is outfitted with a light-tight cover with dry-nitrogen flowing underneath.

Each water pool is covered with an array of RPC modules. RPCs are gaseous particle detectors that consist of two resistive planar electrodes separated by a gas gap. A RPC module in Daya Bay is constructed from four layers of bare RPCs. Each readout plane has eight readout strips and the four planes are arranged in alternating (X-Y) orientations. Each hall has a RPC gas system with a mixture of argon, freon (R134a), isobutane, and SF6. In addition, two RPC modules were specially installed about two meters above the RPC array in each experimental hall to form RPC telescopes. Muons that pass through both the telescope and the main RPC array can be tracked with good angular resolution.

Table 3. Components and parameters of the muon system.
EH1 EH2 EH3
Water pool
Resistance 18 M$$\Omega$$-cm
Volume 1200 ton 1200 ton 1950 ton
Number of PMTs 288 288 384
Resistive plate chambers
Dimensions of a module 2.17 m$$\times$$2.20 m$$\times$$8 cm
Number of layers in a module 4
Dimensions of a readout strip 26 cm$$\times$$2.10 m
Number of readout strips in a layer 8
Gas composition Argon:Freon(R134a):isobutene:SF6 = 65.5:30.0:4.0:0.5
Number of modules 6$$\times$$9+2 6$$\times$$9+2 9$$\times$$9+2

## Electronics and data acquisition

Figure 5: Block diagram outlining the PMT readout electronics.

The RPC readout consists of 32-channel front-end cards mounted on the detector modules, as well as a trigger module and a readout module that resides in a VME crate. The RPC electronics employs a self-triggering scheme and reads out a digital hit map of the over-threshold channels along with a GPS time-stamp for the trigger.

The data acquisition (DAQ) architecture is designed as a multilevel system using embedded Linux, advanced commercial computers and distributed network technology. It is modeled after the BESIII and ATLAS DAQ systems. It receives data fragments from each VME crate and assembles events, merging and sorting, by trigger time-stamp, the events from various crates. The DAQ system also provides an interactive interface for the electronics, trigger and calibration systems. Run control is flexible and configurable, allowing global operation of all detector systems or operation of sub-sets of detectors whenever debugging or commissioning is required.

The Daya Bay Detector Control System (DCS) monitors and controls the experimental hardware and environment. It monitors a wide array of detector parameters, including AD liquid levels, temperatures, humidity and air pressure, RPC high voltages, as well as photomultiplier high voltages and currents. It measures gas flow and pressures in the gas purification system and in the gas storage system. In addition, the DCS monitors environmental parameters and auxiliary systems, such as the electronics crates' operational status, Radon gas concentration inside and outside of the experiment hall, additional temperatures during the detector preparation and the status of the water pool system.

## Offline software and data processing

Figure 6: Offline data processing and monitoring

The Daya Bay offline software was developed in the framework of Gaudi. The simulation is based on GEANT4 with certain critical features validated against external data or other simulation packages, and is tuned to match the observed detector response. Reconstruction algorithms have been developed to reconstruct the energy and the vertex of the antineutrino event from the charge pattern of the PMTs. The detector-related parameters and calibration constants needed by the reconstruction are stored in an offline central database with a number of mirror sites located at different institutes. An alternative Lightweight Analysis Framework was designed and implemented to improve the analysis efficiency.

Figure 6 shows the flowchart of the offline data processing. An automated system ensures real-time delivery of raw data and databases to offline. Data are transferred to the Institute of High Energy Physics (IHEP) in Beijing and Lawrence Berkeley National Laboratory (LBNL) in the US as central storage and processing facilities, and then distributed to other institutions for validation and analysis. A Performance Quality Monitoring system (PQM) runs onsite, using fast reconstruction algorithms and analysis modules to monitor the physics performance with a latency of around 40 minutes. Data processing, using the full reconstruction and the latest calibration constants, takes place as soon as the data reach IHEP or LBNL and is processed in real time. The generated detector monitoring plots are published and archived through an Offline Data Monitoring system (ODM) with a latency of around 3 hours. The extracted data quality information is filled in a dedicated database for long-term monitoring. Physics production takes place one or two times per year according to the requirement of the physics analysis, using the validated and frozen calibration constants and reconstruction algorithms. It also contains event tagging and filtering and provides both the full data sample and different reduced samples to improve the efficiency of the data analysis.

## Operation and performance

Figure 7: History of Daya Bay operation, accumulated reactor antineutrinos and measurements of $$\theta_{13}$$. The three-month gap in 2012 corresponds to the installation of the last two ADs. Each result of $$\theta_{13}$$ is located at the time of the publication, and the vertical length corresponds to the 1-$$\sigma$$ uncertainty. The point in October 2014 uses the hydrogen capture sample (nH) while the others use gadolinium capture samples.

The Daya Bay experiment started taking data with three near detectors and three far detectors in 2011. The last two ADs were installed in Summer 2012 and the full experiment has been in operation since October of 2012. The antineutrino candidates have been accumulated steadily, with a rate of about 0.7 million in the near detectors and 0.1 million in the far detectors per year (Figure 7).

Regular data taking typically includes a 48 hours physics run followed by a pedestal run and an electronics diagnostic run. The data from each of the three halls is recorded in separate runs using a universal clock to record begin/end run times. The typical trigger rate for a physics run is 1.3 kHz for EH1, 1.0 kHz for EH2, and 0.6 kHz for EH3, with the variation between halls driven by the different overburden and muon rate at each hall. Pedestal runs and electronics diagnostic runs give additional information regarding the detector status for the corresponding physics runs. About 320 raw data files, 1 GB per file, are generated per day and transferred to the computing farms. Weekly radioactive source and LED pulser calibrations are also performed. Detector live time for recording antineutrino events was greater than 95%, with the majority of the down time dedicated to calibrations.

Figure 8: Various gamma sources are used to calibrate the energy response in the detector. The nonlinear response of the electronics has been removed from these data points and the residual non-linearity comes from the quenching effect and the contribution from the Cherenkov light in the liquid scintillator.

Detector calibrations, both weekly and longer dedicated studies, are essential for controlling the detector systematics. ADs are calibrated periodically using the automated calibration units on the lid of each detector. The $$^{60}$$Co, $$^{68}$$Ge and $$^{241}$$Am–$$^{13}$$C sources are used to calibrate the energy response of the detector. Low intensity LED runs, combined with single photoelectron hit data from physics runs, are used to continuously monitor the PMT gain and timing. During the shutdown in Summer 2012, additional dedicated calibration runs were performed in some of the ADs, using various sources, in order to provide more energy points in the antineutrino energy range. Figure 8 shows all of the calibration gamma sources and the detector energy nonlinearity. A manual calibration system was installed in AD1 after the water had been drained, which allowed us to deploy a combined source of $$^{60}$$Co and $$^{238}$$Pu–$$^{13}$$C to any position of the gadolinium doped liquid scintillator. This provided a performance study over the full detector volume. At the same time, two of the $$^{241}$$Am–$$^{13}$$C sources were removed from each detector in EH3, to reduce backgrounds from $$^{241}$$Am–$$^{13}$$C neutrons.

The number of photoelectrons collected by the PMTs was found to be around 160 per MeV of visible energy in each AD, and the energy resolution was $$(7.5/\sqrt{E(MeV)}+0.9)\%$$. The relative energy scale uncertainty between ADs, one of the major components of the overall detector systematics, was determined to be 0.2% by comparing the reconstructed energies of various calibration reference points in each AD. The relative difference between neutron capture time in the various ADs was found to be less than 0.2μs, which translated to a 0.1% relative uncertainty in the Gd concentration in the detectors. Other differences between ADs gave negligible contribution to the systematics. The numbers of IBD candidates, after background subtraction, were compared between ADs. Using all data up to the end of 2013, the measured ratio of the IBD rates in EH1 (AD1/AD2) is 0.981±0.004, agreeing well within error to the expected value of 0.982. The same is true for EH2, where the measured ratio of AD3/AD8 is 1.019±0.004, consistent with the expectation 1.012. The expected ratio deviates from 1 because of the slight differences in baselines and detector target masses between the various ADs. The inner water shield (IWS) and outer water shield (OWS) efficiencies were studied using muons going through an AD. The muon rate is about 20 Hz in EH1, 15 Hz in EH2 and 1 Hz in EH3, with essentially 100% detection efficiency. The mean IWS efficiency is 99.98±0.01%, and the mean OWS efficiency is larger than 97% for all three halls. The true OWS efficiency is even higher because of muons that deposit energy in the ADs and stop there or in the IWS, either without traversing the OWS at all, or by traversing only a short path in the OWS.

## Physics results

Figure 9: Ratio of measured versus expected signal in each detector using the first 55 days of data, assuming no oscillation. The error bar is the uncorrelated uncertainty of each AD, including statistical, detector-related, and background-related uncertainties. The expected signal is corrected with the best-fit normalization parameter. Reactor and survey data were used to compute the flux-weighted average baselines. The oscillation survival probability at the best-fit value is given by the smooth curve. The AD4 and AD6 data points are displaced by -30 and +30 m for visual clarity. The $$\chi^2$$ versus $$\sin^{2}2\theta_{13}$$ is shown in the inset.

The first physics result of the Daya Bay experiment was released on 8 March 2012. Using the first 55 days of data collected in the six-AD operation period, 10416 reactor antineutrinos were observed at the far hall. Comparing with the prediction based on the near-hall measurements, a deficit of 6.0% in the antineutrino rate was found. A rate-only analysis yielded $$\sin^{2}2\theta_{13}=0.092\pm0.016({\rm stat.})\pm0.005({\rm syst.})$$. The neutrino mixing angle $$\theta_{13}$$ was found to be non-zero, with a significance of 5.2 standard deviations. The same analysis was extended to 139 days of data and this improved the statistical uncertainty to 0.010.

A measurement of the energy dependence of antineutrino disappearance at the Daya Bay experiment was reported using 217 days of data taken in six ADs. A combined rate and spectra analysis improved the measurement of $$\theta_{13}$$ to $$\sin^{2}2\theta_{13}=0.090^{+0.008}_{-0.009}$$, and the first direct measurement of the neutrino mass-squared difference $$|\Delta m^{2}_{\mathrm{ee}}|=2.59^{+0.19}_{-0.20}\times10^{-3} {\rm eV}^2$$ was obtained. $$|\Delta m^{2}_{\mathrm{ee}}|$$ is defined as $$\sin^2\Delta_{ee} \equiv \cos^2\theta_{12}\sin^2\Delta_{31}+\sin^2\theta_{12}\sin^2{\Delta_{32}}$$. This value of $$|\Delta m^{2}_{\mathrm{ee}}|$$ is consistent with $$|\Delta m^{2}_{\mu\mu}|$$ measured by muon neutrino disappearance, supporting the three-flavor oscillation model.

The preliminary results of electron antineutrino disappearance using the fully-constructed Daya Bay experiment was reported in June 2014. Including data collected in all eight ADs by the end of 2013, we obtained a factor of 3.6 increase in total exposure. The increased statistics and improvements in calibration, background, and analysis methods halved the uncertainties in the estimates of $$\sin^{2}2\theta_{13}$$ and $$|\Delta m^{2}_{\mathrm{ee}}|$$. A reactor model-independent comparison of the relative antineutrino rates and energy spectra between detectors gives $$\sin^{2}2\theta_{13}=0.084\pm0.005$$, and $$|\Delta m^{2}_{\mathrm{ee}}|=2.44^{+0.10}_{-0.11}\times10^{-3} {\rm eV}^2$$.

Figure 10: (Preliminary) Allowed regions in the $$|\Delta m^{2}_{\mathrm{ee}}|$$ vs. $$\sin^{2}2\theta_{13}$$ plane at the $$68.3\%$$, $$95.5\%$$ and $$99.7\%$$ confidence levels. The black dot represents the best fit oscillation parameters. The adjoining panels show the dependence of $$\Delta \chi^{2}$$ on $$|\Delta m^2_{\mathrm{ee}}|$$ (right) and $$\sin^{2}2\theta_{13}$$ (top).

Neutrons produced in the IBD reaction and captured on hydrogen (nH) provide an independent tag of reactor antineutrino events. A new event selection was implemented to improve the signal to background ratio and the selected nH sample was about 65% of the size of the gadolinium capture (nGd) sample. The systematics were reevaluated and found to be largely independent to the nGd analysis. An analysis of the rate of the nH events in the six-AD period gave a measurement of $$\sin^{2}2\theta_{13}$$ consistent with the nGd's result, and it independently rules out a zero $$\theta_{13}$$ at 4.6 standard deviations.

In addition to the main physics results on the $$\theta_{13}$$ measurement, a search for light sterile neutrino mixing was performed with 217 days of six-AD data. The unique configuration of multiple baselines makes it possible to test for oscillations to a fourth (sterile) neutrino in the $$10^{-3} {\rm eV}^2<|\Delta m^{2}_{41}|<0.3 {\rm eV}^2$$ range. The relative spectral distortion due to the disappearance of electron antineutrinos was found to be consistent with that of the three-flavor oscillation model. It yields the world’s most stringent limits on $$\sin^{2}2\theta_{14}$$ in the $$|\Delta m^{2}_{41}|<0.1 {\rm eV}^2$$ region. With at least three more years of additional data, the sensitivity to $$\sin^{2}2\theta_{14}$$ is expected to improve by a factor of two for most $$\Delta m^{2}_{41}$$ values.

Table 4. Measurements of $$\sin^{2}2\theta_{13}$$ by Daya Bay
Dataset (days) Sample Rate analysis Rate and spectrum analysis References
55 Gadolinium capture 0.092$$\pm$$0.017 PRL 108, 171803
139 Gadolinium capture 0.089$$\pm$$0.011 CPC 37, 011001
217 Gadolinium capture 0.089$$\pm$$0.009 0.090$$^{+0.008}_{-0.009}$$ RPL 112, 061801
Hydrogen capture 0.083$$\pm$$0.018 PRD 90, 071101(R)
621 Gadolinium capture 0.085$$\pm$$0.006 0.084$$\pm$$0.005 Preliminary

## Perspective

Daya Bay will continue taking data until the end of 2017, and the expected precision on both $$\sin^{2}2\theta_{13}$$ and $$|\Delta m^{2}_{\mathrm{ee}}|$$ are estimated to be about 3%. In addition, Daya Bay is working on a precision measurement of the reactor antineutrino flux and spectrum, measurements of cosmogenic neutrons and isotopes, studies of supernova neutrinos and on non-standard interactions.