Pion form factor at spacelike momentum transfers from local-duality QCD sum rule

Abstract

We study the pion form factor in a broad range of spacelike momentum transfers within the local-duality version of QCD sum rules. We make use of the recently calculated two-loop double spectral density of the AV A correlator including O(1) and O(αs) terms, which allows us to give predictions for the pion form factor and to study the interplay between the nonperturbative and perturbative contributions to the pion form factor without any reference to the pion distribution amplitude. Our results demonstrate the dominance of the nonperturbative contribution to the form factor up to relatively large values of the momentum transfer: namely, the nonperturbative O(1) term, which provides the 1/Q 4 power correction, gives more than half of the pion form factor in the region Q 2 ≤ 20 GeV 2 .

Pseudoscalar-Meson Form Factors: A Fresh Look by QCD Sum Rules

“…Our model interpolates between the large-Q 2 asymptote and the empirical low-Q 2 behaviour of s eff (Q 2 ) [1] (Fig. 1).…”

“…We analyze the dependences on the involved momentum transfer squared Q 2 of the elastic form factor F π (Q 2 ) of the charged pion and of the form factor F πγ (Q 2 ) describing the transition π 0 ↔ γ γ * of the neutral pion to a real and a virtual photon by dispersive QCD sum rules deduced from vacuum expectation values of products of the three adequate interpolating or electromagnetic currents [1,2]. In the limit of local duality (LD) [3] the sum rules relate the form factors to dispersion integrals over perturbatively deducible spectral densities.…”

“…1). Figure 1: Naive LD modelling (BLM) [1] of the exact effective threshold for F π (Q 2 ) fixed by experiment [7].…”

“…2). The Q 2 behaviour of the elastic pion form factor F π (Q 2 ) obtained [8] by Brodsky and de Téramond (BT'2008), Grigoryan and Radyushkin (GR'2008), and Bakulev, Pimikov, and Stefanis (BPS'2009) Regarding pseudoscalar-meson transition form factors, LD sum rules perform satisfactorily for (η, η ′ , η c ) ↔ γ γ * but do not reproduce a BABAR claim [9] of Q 2 F πγ (Q 2 ) rising with Q 2 beyond the LD asymptote √ 2 f π [1,2] (Fig. 3); confident in our approach, we feel that this mismatch casts some doubt on the BABAR measurement.…”

Modeling electromagnetic form factors of light and heavy pseudoscalar mesons

“…A recent calculation of the pion form factor within the dispersion relation approach including O(α S ) QCD perturbative contribution [15], showed in a model independent way that the nonperturbative part stays above 50% for Q 2 ≤ 20 GeV 2 . The nonperturbative part is compatible with a pion wave function close to the asymptotic one, with a momentum scale given by the effective continuum threshold that determines to a great extent their results for the form factor.…”