Chiral-scale perturbation theory about an infrared fixed point.

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].