Gluon jet function at three loops in QCD

We present here the first result on the three-loop gluon jet function in perturbative QCD. Using the three-loop coefficient functions [J. A. M. Vermaseren, A. Vogt, and S. Moch, Nucl. Phys. B724, 3 (2005)., G. Soar, S. Moch, J. A. M. Vermaseren, and A. Vogt, Nucl. Phys. B832, 152 (2010).] for deep-inelastic scattering via the exchange of a virtual photon that couples to quarks or a scalar that couples to gluons and employing the KG equation, renormalization group invariance and factorization theorem, we obtain both the quark and the gluon jet functions up to the three-loop level. The former agrees with the recent result [R. Bruser, Z. L. Liu, and M. Stahlhofen, Phys. Rev. Lett. 121, 072003 (2018).]. These jet functions being universal ingredients in the SCET framework, will play an important role in the phenomenological studies at the Large Hadron Collider, such as resummation of jet observables and also in N-jettiness subtraction method.