Ultraviolet complete model of large N thermal QCD

Chen, Fang; Chen, Long; Dasgupta, Keshav; Mia, Mohammed; Trottier, Olivier

doi:10.1103/PhysRevD.87.041901

Considermore » 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_{c}

limits, where

N_{c}

is the number of quark colors. In this paper, we show how one may remove the assumption of large

N_{c}

and so begin investigation of

N_{c} = 3

without soft-emission approximations. Treating finite

N_{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_{c})

. Throughout, we make use of the multiple scattering (

\hat{q}

) approximation for high-energy partons crossing quark-gluon plasmas, and we find that this approximation is self-consistent only if the transverse-momentum diffusion parameter

\hat{q}

for different color representations satisfies Casimir scaling (even for strongly coupled, and not just weakly coupled, quark-gluon plasmas). We also find that results for

N_{c} = 3

depend, mathematically, on being able to calculate the propagator for a coupled nonrelativistic quantum harmonic oscillator problem in which the spring constants are operators acting on a five-dimensional Hilbert space of internal color states. Those spring constants are represented by constant

5 \times 5

matrices, which we explicitly construct. We are unaware of any closed form solution for this type of harmonic oscillator problem, and we discuss prospects for using numerical evaluation

Title: Ultraviolet complete model of large $N$ thermal QCD

Citation Formats

Title: Ultraviolet complete model of large N thermal QCD

Citation Formats

Title: Ultraviolet complete model of large $N$ thermal QCD