Challenging the LyC-Ly$\alpha$ relation: strong Ly$\alpha$ emitters without LyC leakage at z $\sim$ 2.3

The escape fraction of LyC ionizing radiation ($f_{lyc}$) is crucial for understanding reionization, yet difficult to measure at $z \gtrsim 4$. Recently, studies have focused on calibrating indirect indicators of $f_{lyc}$ at $z \sim 0.3$, finding that $Ly\alpha$ is closely linked to it. What is still unclear is whether the LyC $-$ $Ly\alpha$ relation evolves with redshift, and if $Ly\alpha$ is truly applicable as an $f_{lyc}$ indicator during the reionization epoch. In this study, we investigate seven $-21 \lesssim M_{UV} \lesssim-19$ gravitationally lensed galaxies from the BELLS GALLERY Survey at $z\sim2.3$. Our targets have rest-frame $Ly\alpha$ equivalent widths between 40 \r{A} and 200 \r{A} and low dust content ($-2.4 \lesssim \beta \lesssim -2.0$), both indicative of high LyC escape. Surprisingly, direct estimates of $f_{lyc}$ using Hubble Space Telescope imaging with F275W and F225W reveal that our targets are not LyC emitters, with an absolute $f_{lyc} < 13 \%$ (assuming the median IGM transmission). The low $f_{lyc}$, coupled with the high $Ly\alpha$ equivalent width and escape fraction, could potentially be attributed to the redshift evolution of the neutral hydrogen column density and dust content, as well as covering fractions of optically thick gas below 1 in high redshift galaxies. Additionally, our analysis suggests that the emission for each lensed component is uniformly absorbed. Our results challenge the validity of the extrapolation of $z\sim0$ Ly$\alpha$-based LyC indirect estimators into the reionization epoch.