We investigate the specific angular momentum (sAM) $ j(<r)$ profiles of intermediate redshift ($0.4<z<1.4$) star-forming galaxies (SFGs) in the relatively unexplored regime of low masses (down to $M_starsim 10^8$M$_{odot}$) and small sizes (down to $R_{rm e}sim 1.5$ kpc) and characterize the sAM scaling relation and its redshift evolution. We have developed a 3D methodology to constrain sAM profiles of the star-forming gas using a forward modeling approach with galpak{} that incorporates the effects of beam smearing, yielding the intrinsic morpho-kinematic properties even with limited spatial resolution data. Using mock observations from the TNG50 simulation, we find that our 3D methodology robustly recovers the SFR-weighted $j(<r)$ profiles down to low effective signal-to-noise ratio (SNR) of $gtrapprox3$. We apply our methodology blindly to a sample of 494 OII{}-selected SFGs in the MUSE Ultra Deep Field (UDF) 9~arcmin$^2$ mosaic data, covering the unexplored $8<log M_*/$M$_{odot}<9$ mass range. We find that the (SFR-weighted) sAM relation follows $jpropto M_star^{alpha}$ with an index $alpha$ varying from $alpha=0.3$ to $alpha=0.5$, from $log M_star/$M$_{odot}=8$ to $log M_*/$M$_{odot}=10.5$. The UDF sample supports a redshift evolution consistent with the $(1+z)^{-0.5}$ expectation from a Universe in expansion. The scatter of the sAM sequence is a strong function of the dynamical state with $log j|_{M_*}propto 0.65 times log(V_{rm max}/sigma)$ where $sigma$ is the velocity dispersion at $2 R_{rm e}$. In TNG50, SFGs also form a $j-M_{star}-(V/sigma)$ plane but correlates more with galaxy size than with morphological parameters. Our results suggest that SFGs might experience a dynamical transformation before their morphological transformation to becoming passive via either merging or secular evolution.
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