Precise Measurement of $^{216}$Po Half-life with Exact Parent-daughter Pairing in PandaX-4T

We report a precise measurement of $^{216}\rm Po$ half-life using the PandaX-4T liquid xenon time projection chamber (TPC). $^{220}\rm Rn $, emanating from a $^{228}\rm Th $ calibration source, is injected to the detector and undergoes successive $α$ decays, first to $^{216}\rm Po$ and then to $^{212}\rm Pb$. PandaX-4T detector measures the 5-dimensional (5D) information of each decay, including time, energy, and 3-dimensional positions. Therefore, we can identify the $^{220}\rm Rn $ and $^{216}\rm Po$ decay events and pair them exactly to extract the lifetime of each $^{216}\rm Po$. With a large data set and high-precision $^{220}\rm $Rn-$^{216}\rm $Po pairing technique, we measure the $^{216}\rm Po$ half-life to be $143.7\pm0.5$ ms, which is the most precise result to date and agrees with previously published values. The leading precision of this measurement demonstrates the power of 5D calorimeter and the potential of exact parent-daughter pairing in the xenon TPC.