Medium-induced gluon emission via transverse and longitudinal scattering in dense nuclear matter

We study the medium-induced gluon emission from a hard quark jet traversing the dense nuclear matter within the framework of deep inelastic scattering off a large nucleus. We extend the previous work and compute the single gluon emission spectrum including both transverse and longitudinal momentum exchanges between the hard jet parton and the medium constituents. On the other hand, with only transverse scattering and using static scattering centers for the traversed medium, our induced gluon emission spectrum in the soft gluon limit reduces to the Gyulassy-Levai-Vitev one-rescattering-one-emission formula.

Figure 1

Leading twist contribution to the hadronic tensor.

Figure 2

A central-cut diagram which contributes to the twist-4 hadronic tensor: one rescattering on the radiated gluon in both the amplitude and the complex conjugate.

Figure 3

Two central-cut diagrams: one rescattering in both the amplitude and the complex conjugate.

Figure 4

Two central-cut diagrams: one rescattering in both the amplitude and the complex conjugate.

Figure 5

A central-cut diagram: one rescattering in both the amplitude and the complex conjugate.

Figure 6

A central-cut diagram: one rescattering in both the amplitude and the complex conjugate.

Figure 7

Two central-cut diagrams: one rescattering in both the amplitude and the complex conjugate.

Figure 8

Two non-central-cut diagrams: two rescatterings in the amplitude and zero in the complex conjugate (or vice versa).

Figure 9

Two non-central-cut diagrams: two rescatterings in the amplitude and zero in the complex conjugate (or vice versa).

Figure 10

Two non-central-cut diagrams: two rescatterings in the amplitude and zero in the complex conjugate (or vice versa).

Figure 11

Two non-central-cut diagrams: two rescatterings in the amplitude and zero in the complex conjugate (or vice versa).

Figure 12

Two non-central-cut diagrams: two rescatterings in the amplitude and zero in the complex conjugate (or vice versa).

Figure 13

Two non-central-cut diagrams: two rescatterings in the amplitude and zero in the complex conjugate (or vice versa).