Drag-induced radiative energy loss from semihard heavy quarks

The case of gluon bremsstrahlung off a heavy quark in extended nuclear matter is revisited within the higher twist formalism. In particular, the in-medium modification of “semihard” heavy quarks is studied, where the momentum of the heavy quark is larger but comparable to the mass of the heavy quark $(p\gtrsim M)$. In contrast to all prior calculations, where the gluon emission spectrum is entirely controlled by the transverse momentum diffusion parameter $\left(\widehat{q}\right)$, both for light and heavy quarks, in this work, we demonstrate that the gluon emission spectrum for a heavy quark (unlike that for light flavors) is also sensitive to $\widehat{e}$, which so far has been used to quantify the amount of light-cone drag experienced by a parton. This mass dependent effect, due to the non-light-like momentum of a semihard heavy quark, leads to an additional energy loss term for heavy quarks, while resulting in a negligible modification of light flavor (and high energy heavy flavor) energy loss. This result can be used to estimate the value of this subleading nonperturbative jet transport parameter $\left(\widehat{e}\right)$ from heavy flavor suppression in ultrarelativistic heavy-ion collisions.

Figure 1

Gluon bremsstrahlung by heavy quark. External legs with green blobs are on shell, while off-shell internal legs have either a red blob or a blue blob. Lines with blue blobs are in-medium Glauber gluons. Red and blue blobs with (without) an additional dark ring indicate spacelike (timelike) off shell.

Figure 2

A representative single gluon emission diagram, where gluon emission is induced by single scattering. This is a symmetric diagram with scattering off the final produced quark. Three separate cuts, denoted as central, left, and right are indicated by the dashed lines.

Figure 3

Central, left and right cuts for ${\mathcal{C}}_{11}$.

Figure 4

Single possible central cut for ${\mathcal{C}}_{22}$.

Figure 5

Central and left cuts for ${\mathcal{C}}_{12}$.

Figure 6

Central and right cuts for ${\mathcal{C}}_{21}$.

Figure 7

Central, left and right cuts for ${\mathcal{C}}_{33}$.

Figure 8

Central, left and right cuts for ${\mathcal{C}}_{13}$.

Figure 9

Central, left and right cuts for ${\mathcal{C}}_{31}$.

Figure 10

Central and right cuts for ${\mathcal{C}}_{23}$.

Figure 11

Central and left cuts for ${\mathcal{C}}_{32}$.

Figure 12

Single possible right cut for ${\mathcal{C}}_{01}$.

Figure 13

Single possible left cut for ${\mathcal{C}}_{10}$.