Towards a consistent estimate of the chiral low-energy constants

Abstract

Guided by the large-N C limit of QCD, we construct the most general chiral resonance Lagrangian that can generate chiral low-energy constants up to O(p 6 ). By integrating out the resonance fields, the low-energy constants are parametrized in terms of resonance masses and couplings. Information on those couplings and on the low-energy constants can be extracted by analysing QCD Green functions of currents both for large and small momenta. The chiral resonance theory generates Green functions that interpolate between QCD and chiral perturbation theory. As specific examples we consider the V A P and S P P Green functions.

The vector form factor at the next-to-leading order in 1/N C : chiral couplings L9(μ) and C88(μ) − C90(μ)

“…To comply with this requirement we will only consider operators constructed with chiral tensors of O(p 2 ); interactions with higher-order chiral tensors tend to violate the asymptotic short-distance behaviour prescribed by QCD [6,14]. Likewise, it has been shown in some cases that resonance operators with higher number of derivatives can be simplified into terms with less derivatives, terms without resonances and operators that contribute to other hadronic amplitudes, by means of the equations of motion and convenient meson field redefinitions [7,9,11,12,13,19]. 1 In ref.…”

“…This corresponds to the tree approximation of some local Lagrangian, being meson loops suppressed by higher powers of 1/N C [4]. Resonance Chiral Theory (RχT) provides an appropriate framework to incorporate these massive mesonic states within a chiral invariant phenomenological Lagrangian [7,8,9]. The operators of the RχT action are constructed such that they remain unchanged under flavour transformations U(3) L ⊗ U(3) R .…”

“…Some O(p 6 ) LECs have been also estimated in this way, by studying appropriate sets of Green functions (see ref. [9] and references therein). All the required terms in the RχT Lagrangian that may contribute to the O(p 6 ) LECs at LO in 1/N C were classified in ref.…”

“…All the required terms in the RχT Lagrangian that may contribute to the O(p 6 ) LECs at LO in 1/N C were classified in ref. [9].…”

Odd sector of QCD

“…One possibility how to gain an insight into them is to use the phenomenology above the domain of ChPT applicability (∼ 1 GeV). The first attempt of systematic description of the active degrees of freedom of the low-lying meson resonances with spin ≤ 1 was provided in [5] for NLO and in [6] for NNLO, in both cases for even intrinsic parity sector. This effort was concluded in [7] also for the anomalous sector.…”