  Jet-associated deuteron production in $pp$ collisions at $\sqrt{s}=13$ TeV
and $p$-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV is studied in the coalescence
model by using the phase-space information of proton and neutron pairs from a
multiphase transport (AMPT) model at the kinetic freezeout. In the low
transverse momentum ($p_T$) region $p_T/A < 1.5$ GeV/$c$, where $A$ is the mass
number of a nucleus, the in-jet coalescence factor $B_2^\text{In-jet}$ for
deuteron production, given by the ratio of the in-jet deuteron number to the
square of the in-jet proton number, is found to be larger than the coalescence
factor $B_2$ in the medium perpendicular to the jet by a factor of about 10 in
$pp$ collisions and of 25 in $p-$Pb collisions, which are consistent with the
ALICE measurements at the LHC. Such large low-momentum enhancements mainly come
from coalescence of nucleons inside the jet with the medium nucleons.
Coalescence of nucleons inside the jet dominates deuteron production only at
the higher $p_T$ region of $p_T/A\gtrsim 4$ GeV/$c$, where both the yield ratio
$d/p$ of deuteron to proton numbers and the $B_2$ are also significantly larger
in the jet direction than in the direction perpendicular to the jet due to the
strong collinear correlation among particles produced from jet fragmentation.
Studying jet-associated deuteron production in relativistic nuclear collisions
thus opens up a new window to probe the phase-space structure of nucleons
inside jets.
