  We study the transverse momentum distribution of hadrons within jets, where
the transverse momentum is defined with respect to the standard jet axis. We
consider the case where the jet substructure measurement is performed for an
inclusive jet sample $pp\to\text{jet}+X$. We demonstrate that this observable
provides new opportunities to study transverse momentum dependent fragmentation
functions (TMDFFs) which are currently poorly constrained from data, especially
for gluons. The factorization of the cross section is obtained within Soft
Collinear Effective Theory (SCET), and we show that the relevant TMDFFs are the
same as for the more traditional processes semi-inclusive deep inelastic
scattering (SIDIS) and electron-positron annihilation. Different than in SIDIS,
the observable for the in-jet fragmentation does not depend on TMD parton
distribution functions which allows for a cleaner and more direct probe of
TMDFFs. We present numerical results and compare to available data from the
LHC.
