Constraint on the solar $\Delta m^2$ using 4,000 days of short baseline reactor neutrino data

There is a well known 2$\sigma$ tension in the measurements of the solar $\Delta m^2$ between KamLAND and SNO/Super-KamioKANDE. Precise determination of the solar $\Delta m^2$ is especially important in connection with current and future long baseline CP violation measurements. Reference \cite{Seo:2018rrb} points out that currently running short baseline reactor neutrino experiments, Daya Bay and RENO, can also constrain solar $\Delta m^2$ value as demonstrated by a GLoBES simulation with a limited systematic uncertainty consideration. In this work, the publicly available data, from Daya Bay (1,958 days) and RENO (2,200 days) are used to constrain the solar $\Delta m^2$. Verification of our method through $\Delta m^2_{ee}$ and $\sin^2 \theta_{13}$ measurements is discussed in Appendix A. Using this verified method, reasonable constraints on the solar $\Delta m^2$ are obtained using above Daya Bay and RENO data, both individually and combined. We find that the combined data of Daya Bay and RENO set an upper limit on the solar $\Delta m^2$ of 18 $\times 10^{-5}$ eV$^2$ at the 95% C.L., including both systematic and statistical uncertainties. This constraint is slightly more than twice the KamLAND value. As this combined result is still statistics limited, even though driven by Daya Bay data, the constraint will improve with the additional running of this experiment.