Ab initio coupling of jets to collective flow in the opacity expansion approach

We calculate the leading corrections to jet momentum broadening and medium-induced branching that arise from the velocity of a moving medium at first order in opacity. These results advance our knowledge of jet quenching and demonstrate how it couples to the collective flow of the quark-gluon plasma in heavy-ion collisions. We also compute the leading corrections to jet momentum broadening due to transverse gradients of temperature and density. We find that the velocity effects lead to both anisotropic transverse momentum diffusion proportional to the medium velocity and anisotropic medium-induced radiation emitted preferentially in the direction of the flow. We isolate the relevant subeikonal corrections by working with jets composed of scalar particles with arbitrary color factors interacting with the medium by scalar QCD. Appropriate substitution of the color factors and light-front wave functions allow us to immediately apply the results to a range of processes including $q\to qg$ branching in real QCD. The resulting general expressions can be directly coupled to hydrodynamic simulations on an event-by-event basis to study the correlations between jet quenching and the dynamics of various forms of nuclear matter.

Figure 1

Diagrams contributing to jet broadening (a) and medium-induced radiation (b) of a quark jet in QCD at first order in opacity. Thick vertical lines denote all possible final-state cuts, and vertical gluons left dangling denote all possible attachments to partons in the jet at that point. Asymmetric diagrams have mirror conjugates which are not drawn explicitly.

Figure 2

Gluonic potential $a_i^{\mu a}(q)$ produced by medium particle $i$.

Figure 3

The Born-level amplitude $M_1$ (left) and double-Born amplitude $M_2$ (right) for transverse-momentum broadening in an external potential.

Figure 4

The coupling of jets to the medium velocity presented in this work. The transverse momentum of the jet is deflected in the direction of the medium velocity.

Figure 5

Elementary splitting vertex for the emission of scalar radiation from a scalar jet. We do not distinguish diagrammatically the color representations of the scalars, which may correspond to either choice in (a3).

Figure 6

The coupling of soft radiation to the medium velocity presented in this work. The medium-induced radiation is emitted preferentially in the direction of the medium velocity as schematically shown by the number of gluons along the direction of the flow in comparison to the “standard” symmetric unbent jet.

Figure 7

The initial-state scattering diagram denoted $R_1^A$.

Figure 8

The final-state scattering diagrams denoted $R_1^B$ and $R_1^C$.

Figure 9

Double-Born diagram denoted $R_{2,D}$ corresponding to initial-state scattering followed by final-state branching.

Figure 10

Left: double-Born diagram denoted $R_{2,E}$ corresponding to initial-state branching followed by final-state scattering on one of the daughter partons. Right: diagram denoted $R_{2,F}$ with scattering on the other daughter parton is obtained by the substitution $k\leftrightarrow (p-k)$ from $R_{2,E}$.

Figure 11

Double-Born diagram denoted $R_{2,G}$ corresponding to initial-state branching followed by final-state scattering on both of the daughter partons.

Figure 12

Double-Born diagrams denoted $R_{2,H},R_{2,I}$ in which the branching occurs between the double scattering.