Precise measurements of $\Lambda$ hypernuclear binding energies are essential in understanding the interaction between $\Lambda$ and nucleons. Thanks to the recent progress of accurate theoretical calculations and cutting-edge experiments for $\Lambda$ hypernuclei around the light mass regions, the studies of the interaction of the hypernuclear medium have progressed well; for example, the effect of $\Lambda$-$\Sigma$ coupling and the $\Lambda$-N Charge Symmetry Breaking. Though recent $^3_\Lambda$H mass and lifetime results from the heavy-ion collision experiments have significantly impacted reconsidering the hypernuclear picture, more accurate measurements are necessary to discuss further.
We have developed a new technique "decay pion spectroscopy" to measure the $\Lambda$ binding energies of the hypernuclear ground states with an accuracy of better than 100 keV/$c^2$. In 2015, we successfully measured the $\Lambda$ binding energy of $^4_\Lambda$H by measuring the momentum of two-body decay pion from $^4_\Lambda$H with a resolution of $<$100 keV/$c$ in FWHM.
We applied the same spectroscopic technique to $^3_\Lambda$H by updating the target system and the energy calibration method. The physics data taking was already done in 2022, and the analysis is ongoing.
I will present the updated experiment and the latest analysis status. I will also introduce a plan for high-resolution spectroscopy of $\Lambda$ hypernuclei.