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We present ionized gas kinematics for 681 galaxies at $z\sim 1.4-3.8$ fromthe MOSFIRE Deep Evolution Field survey, measured using models which accountfor random galaxy-slit misalignments together with structural parametersderived from CANDELS Hubble Space Telescope (HST) imaging. Kinematics and sizesare used to derive dynamical masses. Baryonic masses are estimated from stellarmasses and inferred gas masses from dust-corrected star formation rates (SFRs)and the Kennicutt-Schmidt relation. We measure resolved rotation for 105galaxies. For the remaining 576 galaxies we use models based on HST imagingstructural parameters together with integrated velocity dispersions andbaryonic masses to statistically constrain the median ratio of intrinsicordered to disordered motion, $V/\sigma_{V,0}$. We find that $V/\sigma_{V,0}$increases with increasing stellar mass and decreasing specific SFR (sSFR).These trends may reflect marginal disk stability, where systems with higher gasfractions have thicker disks. For galaxies with detected rotation we assesstrends between their kinematics and mass, sSFR, and baryon surface density($\Sigma_{\mathrm{bar},e}$). Intrinsic dispersion correlates most with$\Sigma_{\mathrm{bar},e}$ and velocity correlates most with mass. By comparingdynamical and baryonic masses, we find that galaxies at $z\sim 1.4-3.8$ arebaryon dominated within their effective radii ($R_E$), with Mdyn/Mbaryonincreasing over time. The inferred baryon fractions within $R_E$,$f_{\mathrm{bar}}$, decrease over time, even at fixed mass, size, or surfacedensity. At fixed redshift, $f_{\mathrm{bar}}$ does not appear to vary withstellar mass but increases with decreasing $R_E$ and increasing$\Sigma_{\mathrm{bar},e}$. For galaxies at $z\geq2$, the median inferred baryonfractions generally exceed 100%. We discuss possible explanations and futureavenues to resolve this tension.

The MOSDEF Survey: Kinematic and Structural Evolution of Star-Forming Galaxies at $1.4\leq z\leq 3.8$