Towards a Sub-percent Precision Measurement of $\sin^2\theta_{13}$ with Reactor Antineutrinos

Measuring the neutrino mixing parameter \ensuremath{\sin^2\theta_{13}} to the sub-percent precision level could be necessary in the next ten years for the precision unitary test of the PMNS matrix. In this work, we discuss the possibility of such a measurement with reactor antineutrinos. We find that a single liquid scintillator detector on a reasonable scale could achieve the goal. We propose to install a detector of $\sim10$\% energy resolution at about 2.0~km from the reactors with a JUNO-like overburden. The integrated luminosity requirement is about 150~${\rm kton}\cdot {\rm GW}\cdot {\rm year}$, corresponding to 4 years' operation of a 4~kton detector near a reactor complex of 9.2 GW thermal power like Taishan reactor. Unlike the previous $\theta_{13}$ experiments with identical near and far detectors, which can suppress the systematics especially the rate uncertainty by the near-far relative measurement and the optimal baseline is at the first oscillation maximum of about 1.8~km, a single-detector measurement prefers to offset the baseline from the oscillation maximum. At low statistics $\lesssim 10$~${\rm kton}\cdot {\rm GW}\cdot {\rm year}$, the rate uncertainty dominates the systematics, and the optimal baseline is about 1.3~km. At higher statistics, the spectral shape uncertainty becomes dominant, and the optimal baseline shifts to about 2.0~km. The optimal baseline keeps being $\sim 2.0$~km for an integrated luminosity up to $10^6$~${\rm kton}\cdot {\rm GW}\cdot {\rm year}$. We have assumed that the TAO experiment will improve our understanding of the spectral shape uncertainty, which gives the highest precision measurement of reactor antineutrino spectrum for neutrino energy in the range of 3--6~MeV. We find that the optimal baseline is $\sim 2.9$~km with a flat input spectral shape uncertainty provided by the future summation or conversion methods' prediction.