Abstract
In this work, higher-derivative corrections of the non-linear sigma model of both even and odd intrinsic-parity sectors are systematically studied, focusing on ordered amplitudes of flavor scalars in massless limit. It should correspond to a theory known as chiral perturbation theory (ChPT) without external sources and with only single-trace operators. We briefly overview its formal development and apply new S-matrix methods to its amplitude constructions. The bottom-up analysis of the tree-level amplitudes of different orders and multiplicities focuses on the formal structure of general ChPT. Possible theoretical simplifications based on the Kleiss-Kuijf and Bern-Carrasco-Johansson relations are presented. Finally, in the same context, the comparison with the so-called Z-function, which is connected with string theory, is also discussed.
Highlights
This canonical choice is not the only option, and different possibilities were studied and confronted with experiments [3,4,5,6,7,8]
It should correspond to a theory known as chiral perturbation theory (ChPT) without external sources and with only single-trace operators
In the first part of this work, we have summarized the canonical forms of the ChPT Lagrangian as constructed using the symmetric breaking pattern H × H → H with unitary group H of degree Nf
Summary
We will mainly summarize the present status of the chiral Lagrangian in its two respective sectors: of the even and of the odd intrinsic parity. Sectors reflects specific symmetry properties of QCD, namely the chiral symmetry in the chiral limit (light quarks are massless), parity and charge conjugation, in combination with the general properties of quantum field theory (e.g. Hermiticity or CPT invariance). As mentioned in the introduction we will be focusing only on the single trace operators. This enables to define the cyclically ordered stripped vertices Vn(p1, . We will briefly discuss the singlet part of the theory, i.e. for example, in the three-flavor case, the difference between the nonet and octet multiplet
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