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

Abstract

Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/N C expansion. Imposing the correct QCD short-distance constraints, one fixes the amplitude in terms of the pion decay constant F and resonance masses. Its low momentum expansion determines then the corresponding O(p 4 ) and O(p 6 ) low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence. At µ 0 = 0.77 GeV, we obtain L 9 (µ 0 ) = (7.9 ± 0.4) · 10 −3 and C 88 (µ 0 ) − C 90 (µ 0 ) = (−4.6 ± 0.4) · 10 −5 .

Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality

“…Among the estimates of the subleading scaling for various resonance parameters, G V is the most reliable one, since it can be directly derived by requiring a proper high-energy behavior of the partial wave amplitudes, which are the key input in the study of semilocal duality. In addition, this constraint has also been confirmed in different processes, as already discussed above [40,46,93,94,97]. It turns out that the large N C condition Eq.…”

“…Of course, the values at large N C are not accessible directly by experiment and can be ascertained only through theoretical considerations. In the past decades, great progress along this line has been achieved in the analyses of short distance constraints of two-and threepoint Green functions, form factors, decays, and scattering within RT [22,33,46,67,[91][92][93][94].…”

“…This relation was also derived from the high-energy constraint of the pion vector form factor at tree level [67]. An updated study of the vector form factor at the one-loop level [93] revealed a new version for the constraint:…”

Oblique S and T constraints on electroweak strongly-coupled models with a light Higgs

“…We can profit from the experience acquired in low-energy QCD, where a thorough investigation of RχT at the one-loop level has been performed in recent years [127][128][129][130][131][132][133][134][135], bringing an improved understanding of the resonance dynamics. In particular, we make use of the procedure developed to compute the low-energy constants of χPT at NLO through a matching with RχT [127][128][129][130][131]. The estimation of S in strongly-coupled electroweak models is equivalent to the calculation of L 10 in χPT [130], whereas the calculation of T is similar to the determination of f 2 π ± − f 2 π 0 in χPT.…”

“…As shown in refs. [129][130][131], the dispersive approach that we adopt avoids all technicalities associated with the renormalization procedure, allowing for a much more transparent understanding of the underlying physics.…”