  The origin and impact of outflows on proto-planetary disks and planet
formation are key open questions. DG Tau B, a Class I protostar with a
structured disk and a striking rotating conical CO outflow, recently identified
with ALMA as one of the best MHD disk wind candidate, is an ideal target for
studying these phenomena. Our aim is to analyse the outflow components
intermediate between the fast axial jet and the wider molecular CO outflow to
discriminate between the different scenarios at their origin
(irradiated/shocked disk wind or swept-up material). Using observations from
JWST NIRSpec-IFU, NIRCam and SINFONI/VLT, we investigate the morphology,
kinematics and excitation conditions of H$_2$ emission lines of the red-shifted
outflow lobe. We find an onion-like structure of the outflows with increasing
temperature, velocity and collimation towards the flow axis. The red-shifted
H$_2$ emission reveals a narrow conical cavity nested inside the CO outflow and
originating from the inner disk regions (< 6 au). The H$_2$ shell exhibits a
constant vertical velocity ($\simeq$22 km/s), twice faster that of the CO flow
and an average mass flux of $\dot{M}$(H$_2$) = 3e-11 M$_\odot$/yr significantly
lower than the jet and CO values, suggesting low H$_2$ abundance. The global
layered structure of the H$_2$/CO outflows is consistent with an MHD disk wind
scenario, with the hot H$_2$ possibly tracing an inner dense photodissociation
layer of the wind coming from a launching radius in the disk of 0.2-0.4 au.
Further analysis, including MIRI observations will provide additional insights
into the H$_2$ excitation mechanisms and the origin of the layered outflows
observed in DG Tau B.
