Chiral-scale perturbation theory about an infrared fixed point.
Files
Date
2013
Authors
Tunstall, Lewis Cristian
Editors
Advisors
Crewther, Rodney James
Young, Ross Daniel
Young, Ross Daniel
Journal Title
Journal ISSN
Volume Title
Type:
Thesis
Citation
Statement of Responsibility
Conference Name
Abstract
This work explores the infrared behaviour of the strong running coupling αs [s is subscript] in Quantum Chromodynamics (QCD).We propose that αs [s is subscript] runs non-perturbatively to an infrared fixed point αIR [IR is subscript] for three light quark flavours u, d, s . At the fixed point, we show that the quark condensate spontaneously breaks scale and chiral SU(3)L [L is subscript] ×SU(3)R [R is subscript] symmetry. Consequently, the low-lying spectrum contains nine pseudo-Nambu-Goldstone bosons: π,K ,η and a scalar-isoscalar QCD dilaton σ. We argue that σ may be identified with the ƒ₀(500) resonance, a pole at a complex mass with real part ≲ mK [K is subscript] . For low-energy expansions in αs [s is subscript] about αIR [IR is subscript], we replace chiral SU(3)L [L is subscript] × SU(3)R [R is subscript] perturbation theory with a new model-independent theory χPTσ [σ is subscript] based on approximate scale and chiral SU(3)L [L is subscript] × SU(3)R [R is subscript] symmetry. We examine the phenomenological consequences which arise from this framework by constructing effective Lagrangians which simulate strong, weak, and electromagnetic interactions. We also study the convergence properties of the effective theory, wherein we find that χPTσ [σ is subscript] converges much better than χPT₃ in the presence of both scalar-isoscalar channels and O(mK ) [K is subscript] extrapolations in momentum. We achieve this without spoiling the successful leading order predictions of χPT₃ elsewhere. In our phenomenological investigations, we show that the ΔI = 1/2 rule for non-leptonic K -decays emerges as a consequence of χPTσ [σ is subscript], with a KSσ [S is subscript] coupling fixed by data for γγ → ππ and KS → γγ [S is subscript]. This constitutes our most important result. We also apply the electromagnetic trace anomaly to QCD at the infrared fixed point and obtain the estimate RIR ≈ 5 [IR is subscript] for the non-perturbative Drell-Yan ratio R=σ(e⁺e⁻ → hadrons)/σ(e⁺e⁻ → μ⁺μ⁻) at αIR [IR is subscript].
School/Discipline
School of Chemistry and Physics
Dissertation Note
Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2013
Provenance
This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals
Copyright material removed from digital thesis. See print copy in University of Adelaide Library for full text.
Copyright material removed from digital thesis. See print copy in University of Adelaide Library for full text.