The LPM effect in sequential bremsstrahlung: from large-N QCD to N=3 via the SU(N) analog of Wigner 6-j symbols

Understand

Consider a high-energy parton showering as it traverses a QCD medium such as a quark-gluon plasma.

• Interference effects between successive splittings in the shower are potentially very important but have so far been calculated (even in idealized theoretical situations) only in soft emission or large-$N_{\rm c}$ limits, where $N_{\rm c}$ is the number of quark colors.
• In this paper, we show how one may remove the assumption of large $N_{\rm c}$ and so begin investigation of $N_{\rm c}{=}3$ without soft-emission approximations.
• Treating finite $N_{\rm c}$ requires (i) classifying different ways that four gluons can form a color singlet and (ii) calculating medium-induced transitions between those singlets, for which we find application of results for the generalization of Wigner 6-$j$ symbols from angular momentum to SU($N_{\rm c}$).