Δ I = 1 / 2 rule for kaon decays derived from QCD infrared fixed point

Crewther, R. J.; Tunstall, Lewis (2015). Δ I = 1 / 2 rule for kaon decays derived from QCD infrared fixed point. Physical review. D - particles, fields, gravitation, and cosmology, 91(3) American Physical Society 10.1103/PhysRevD.91.034016

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This article gives details of our proposal to replace ordinary chiral SU(3)L×SU(3)R perturbation theory χPT3 by three-flavor chiral-scale perturbation theory χPTσ. In χPTσ, amplitudes are expanded at low energies and small u,d,s quark masses about an infrared fixed point αIR of three-flavor QCD. At αIR, the quark condensate ⟨q¯q⟩vac≠0 induces nine Nambu-Goldstone bosons: π,K,η, and a 0++ QCD dilaton σ. Physically, σ appears as the f0(500) resonance, a pole at a complex mass with real part ≲ mK. The ΔI=1/2 rule for nonleptonic K decays is then a consequence of χPTσ, with a KSσ coupling fixed by data for γγ→ππ and KS→γγ. We estimate RIR≈5 for the nonperturbative Drell-Yan ratio R=σ(e+e−→hadrons)/σ(e+e−→μ+μ−) at αIR and show that, in the many-color limit, σ/f0 becomes a narrow qq¯ state with planar-gluon corrections. Rules for the order of terms in χPTσ loop expansions are derived in Appendix A and extended in Appendix B to include inverse-power Li-Pagels singularities due to external operators. This relates to an observation that, for γγ channels, partial conservation of the dilatation current is not equivalent to σ-pole dominance.

Item Type:

Journal Article (Original Article)

Division/Institute:

10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)
08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Tunstall, Lewis

Subjects:

500 Science > 530 Physics

ISSN:

1550-7998

Publisher:

American Physical Society

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

17 Sep 2015 08:18

Last Modified:

21 Sep 2015 10:54

Publisher DOI:

10.1103/PhysRevD.91.034016

ArXiv ID:

1312.3319v4

BORIS DOI:

10.7892/boris.71593

URI:

https://boris.unibe.ch/id/eprint/71593

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