High energy constraints in the octet SS-PP correlator and resonance saturation at NLO in 1/Nc

Abstract

We study the octet SS − P P correlator within resonance chiral theory up to the oneloop level, i.e., up to next-to-leading order in the 1/N C expansion. We will require that our correlator follows the power behaviour prescribed by the operator product expansion at high euclidian momentum. Nevertheless, we will not make use of short-distance constraints from other observables. Likewise, the high-energy behaviour will be demanded for the whole correlator, not for individual absorptive channels. The amplitude is progressively improved by considering more and more complicated operators in the hadronic lagrangian. Matching the resonance chiral theory result with chiral perturbation theory at low energies produces the estimates L 8 (µ) SU (3) = (1.0±0.4)•10 −3 and C 38 (µ) SU (3) = (8±5)•10 −6 for µ = 770 MeV. The effect of alternative renormalization schemes is also discussed in the article.

Scalar and pseudoscalar correlators in Resonance Chiral Theory

“…between the determination from Ref. [10] and this work [1]. Thus, the S S − PP dispersive calculation carried out in Ref.…”

“…where the tiny contribution ǫ from the dimension four condensate [18] is usually neglected, as we do in the present work [1]. However, there are several caveats that may be raised to this kind of procedures since the truncation might, in principle, induce important uncertainties in the LEC determinations [19].…”

“…In general, there is a reduced knowledge on the spectrum at high energies and just the lightest resonances are moderately well known. Thus, one is forced in many cases to truncate the infinite tower of large-N C states and to work with a finite number of them or even within the single resonance approximation, as we did in the present work [1]. Still, one may think about interpolating this rational approximation between low-energies -ruled by χPT-and the deep Euclidean domain at p 2 → −∞ -governed by the OPE- [14].…”

“…In this talk 1 we discuss the results from a previous work on SS-PP correlator [1] together with some new estimates for the OZI suppressed difference of the SU(3) singlet and octet scalar correlators (S 1 S 1 − S 8 S 8 ) [2]. We will work with a chiral invariant action for the chiral pseudo-Goldstones and the meson resonances, namely, resonance chiral theory (RχT) [3,4].…”

“…First, the structure of the amplitude is constrained by imposing the power behaviour prescribed by the operator product expansion (OPE) for deep Euclidean momentum p 2 → −∞ [9]. After that, one is ready to go to the low-energy regime to make predictions on the χPT couplings [8], using the RχT expression as an interpolator between short and long distances [1]. The phenomenological determinations for the LEC L 8 (µ) and C 38 (µ), which rule the SS-PP correlator at long distances, were found in good agreement with previous results in the bibliography [8,10,11].…”