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Title: Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N = 3 via the SU ( N ) analog of Wigner 6 - j symbols

Abstract

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 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 ( 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 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 × 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

Authors:
Publication Date:
Research Org.:
Univ. of Virginia, Charlottesville, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1559384
Alternate Identifier(s):
OSTI ID: 1598229
Grant/Contract Number:  
SC0007984
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 3; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Arnold, Peter. Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N = 3 via the SU ( N ) analog of Wigner 6 - j symbols. United States: N. p., 2019. Web. doi:10.1103/PhysRevD.100.034030.
Arnold, Peter. Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N = 3 via the SU ( N ) analog of Wigner 6 - j symbols. United States. doi:10.1103/PhysRevD.100.034030.
Arnold, Peter. Thu . "Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N = 3 via the SU ( N ) analog of Wigner 6 - j symbols". United States. doi:10.1103/PhysRevD.100.034030.
@article{osti_1559384,
title = {Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large- N QCD to N = 3 via the SU ( N ) analog of Wigner 6 - j symbols},
author = {Arnold, Peter},
abstractNote = {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-Nc limits, where Nc is the number of quark colors. In this paper, we show how one may remove the assumption of large Nc and so begin investigation of Nc=3 without soft-emission approximations. Treating finite Nc 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(Nc). Throughout, we make use of the multiple scattering (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 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 Nc=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 5×5 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},
doi = {10.1103/PhysRevD.100.034030},
journal = {Physical Review D},
number = 3,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}

Journal Article:
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DOI: 10.1103/PhysRevD.100.034030

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