Pion light-cone distribution amplitude from the pion electromagnetic form factor

Abstract

We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor F π ðQ 2 Þ and the integrated modulus of the timelike form factor. For F π ðQ 2 Þ, the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients a 2;4;6;::. (Gegenbauer moments) from this equation, employing the measured pion timelike form factor. For the exploratory fit we use the data of the BABAR collaboration. The results definitely exclude the asymptotic twist-2 distribution amplitude. Also the model with a single a 2 ≠ 0 is disfavored by the fit. Considering the models with a n>2 ≠ 0, we find that the fitted values of the second and fourth Gegenbauer moments cover the intervals a 2 ð1 GeVÞ ¼ ð0.22-0.33Þ, a 4 ð1 GeVÞ ¼ ð0.12-0.25Þ. The higher moments starting from a 8 are consistent with zero, albeit with large uncertainties. The spacelike pion form factor obtained in two different ways, from the dispersion relation and from the light-cone sum rule, agrees, within uncertainties, with the measurement by the Jefferson Lab F π collaboration.

The D∗Dπ and B∗Bπ couplings from light-cone sum rules

“…Our Model 2 is of a different origin and is based on the comparison of the LCSR for the pion electromagnetic form factor [50] with the experimental data. We use the results of the recent analysis [51], where a dispersion relation and the data in the timelike region are used to reproduce the pion form factor in the spacelike region. These results are then used to fit the LCSR form factor calculated to the twist-2 NLO accuracy including the subleading twist-4,6 terms.…”

“…The simplest option is to adopt a truncated Gegenbauer expansion with a relatively large positive a 4 (1 GeV) and small a n>4 . A pion DA with such a pattern of Gegenbauer moments at µ = 1 GeV: a 2 = 0.135 ± 0.032 (the rescaled value (5.4)) and a 4 = 0.218 ± 0.059, a n>4 = 0, was used in [51] (see the second line in the table IV there) among other models fitting the LCSR for the pion electromagnetic form factor to the timelike form factor data. According to (5.2), the resulting midpoint value is ϕ π (1/2, µ = 1 GeV) = 1.81 ± 0.18.…”

QCD-based estimates of direct CP asymmetry in charm decays

“…, s) at s → ∞, which is a manifestation of the local quark-hadron duality. To demonstrate that the approximation (19) is valid for simpler hadronic matrix elements such as the pion electromagnetic form factor, we refer to [9], where the absolute values of the pion timelike and spacelike form factors (the former measured and the latter calculated from a dedicated LCSR) are compared. We observe that local…”

Cross-link relations between $π$ and $ρ$-meson channels and the QCD vacuum

“…( 22) before averaging, i.e. Φ2(M 2 ), whereas the upper thinner (blue) line denotes its upper limit [27] (see Appendix B).…”