Transverse Spin Transfer of $\Lambda$ and $\overline{\Lambda}$ Hyperons in Polarized $p$+$p$ Collisions at $\sqrt{s} = 200$ GeV at RHIC-STAR

The transverse spin transfer, $D_{TT}$, of $\Lambda$ and $\overline{\Lambda}$ hyperons in $p$+$p$ collisions is expected to be sensitive to the $s$ and $\bar{s}$ quark transversity distributions in the proton and to the transversely polarized fragmentation functions. The STAR experiment has published the first measurement of the transverse spin transfer of $\Lambda$ and $\overline{\Lambda}$ hyperons in transversely polarized $p$+$p$ collisions at $\sqrt{s}$ = 200 GeV within pseudo-rapidity $|\eta| < 1.2$ and for the transverse momenta up to 8 GeV/$c$ based on the data taken in 2012. In 2015, a data sample of $p$+$p$ collisions at $\sqrt{s}$ = 200 GeV, about two times larger than the 2012 data, was collected. This contribution presents the preliminary results of the transverse spin transfer, $D_{TT}$, of $\Lambda$ and $\overline{\Lambda}$ hyperon versus transverse momentum and fractional momentum of the hyperon within a jet, based on 2015 data.