Phenomenology with a recoil-free jet axis: TMD fragmentation and the jet shape

We study the phenomenology of recoil-free jet axes using analytic calculations and Monte Carlo simulations. Our focus is on the average energy as function of the angle with the jet axis (the jet shape), and the energy and transverse momenta of hadrons in a jet (TMD fragmentation). We find that the dependence on the angle (or transverse momentum) is governed by a power law, in contrast to the double-logarithmic dependence for the standard jet axis. The effects of the jet radius, jet algorithm, angular resolution and grooming are investigated. TMD fragmentation is important for constraining the structure of the proton through semi-inclusive deep-inelastic scattering. These observables are also of interest to the LHC, for example to constrain $\alpha_s$ from precision jet measurements, or probe the quark-gluon plasma in heavy-ion collisions.