Transverse-momentum-dependent parton distribution function and jet transport in a nuclear medium

We show that the gauge-invariant transverse-momentum-dependent (TMD) quark distribution function can be expressed as a sum of all higher-twist collinear parton matrix elements in terms of a transport operator. From such a general expression, we derive the nuclear broadening of the transverse-momentum distribution. Under the maximal two-gluon correlation approximation, in which all higher-twist nuclear multiple parton correlations with the leading nuclear enhancement are given by products of twist-two nucleon parton distributions, we find the nuclear transverse-momentum distribution as a convolution of a Gaussian distribution and the nucleon TMD quark distribution. The width of the Gaussian, or the mean total transverse-momentum broadening squared, is given by the path integral of the quark transport parameter (q) over cap (F) which can also be expressed in a gauge-invariant form and is given by the gluon distribution density in the nuclear medium. We further show that contributions from higher-twist nucleon gluon distributions can be resummed under the extended adjoint two-gluon correlation approximation and the nuclear transverse-momentum distribution can be expressed in terms of a transverse-scale-dependent quark transport parameter or gluon distribution density. We extend the study to hot medium and compare to dipole model approximation and N = 4 supersymmetric Yang-Mills (SYM) theory in the strong coupling limit. We find that multiple gluon correlations become important in the strongly coupled system such as N = 4 SYM plasma.