Longitudinal double spin asymmetry of $π^{\pm}$-tagged jet, $Λ$, $\overlineΛ$, and $K_S^0$ in polarized $p+p$ collisions at $\sqrt{s}=200$ $\rm{GeV}$ at STAR

Understanding the origin of the proton spin is one of the most fundamental and challenging questions in QCD. Much progress has been made since the first surprising result by the EMC experiment in the late 1980s. However, the helicity distributions of strange quarks and anti-quarks inside the proton are still not well constrained by the experimental data. Measurement of the longitudinal double spin asymmetry $A_{LL}$ of the inclusive jets tagged with a $\pi^{\pm}/\pi^-$ carrying high jet momentum fraction, $z$, in $p+p$ collisions can provide further constraints on the gluon helicity distribution in the proton. In addition, the $A_{LL}$ of $\Lambda$, $\overline{\Lambda}$ and $K_S^0$ in the longitudinally polarized $p+p$ collisions may shed light on the strange quark and anti-quark helicity distributions. In this contribution, we report the preliminary results on the $A_{LL}$ measurements of inclusive jets tagged with a high-$z$ $\pi^{\pm}$, and the $\Lambda$, $\overline{\Lambda}$ and $K_S^0$. We utilize the longitudinally polarized $p+p$ collisions at $\sqrt{s}=200$ $\rm{GeV}$ collected by the STAR experiment with an integrated luminosity of about 52 $\rm{pb^{-1}}$.