Understand
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 $\hat q_F$ which can also be expressed in a gauge invariant form and is given by the gluon distribution density in the nuclear medium.
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