Abstract
The pion electromagnetic form factor has been calculated for the first time from the solutions of the Bethe-Salpeter equation, obtained directly in Minkowski space by using the Nakanishi integral representation of the Bethe-Salpeter amplitude. The one-gluon exchange kernel contains as inputs the quark and gluon masses, as well as a scale parameter featuring the extended quark-gluon vertex. The range of variability of these parameters is suggested by lattice calculations. After presenting a very successful comparison with the existing data in the whole range of the momentum transfer, we show how inserting the light-front (LF) formalism in our approach allows to achieve further interesting results, like the evaluation of the LF valence form factor and a first investigation of the end-points effects.
Highlights
The pion electromagnetic form factor has been calculated for the first time from the solutions of the BetheSalpeter equation, obtained directly in Minkowski space by using the Nakanishi integral representation of the Bethe-Salpeter amplitude
Within our approach [21], based on the 4D Bethe-Salpeter equation (BSE) in Minkowski space and the Nakanishi integral representation (NIR) of the Bethe-Salpeter amplitude, we have evaluated the em form factor (FF) of the pion
In order to study the asymptotic behavior of the LF valence FF, we first observe that the rightmost contribution to Eq (12) can be disregarded since (i) κ⊥ · κ⊥ vanishes for γ → 0, precisely where the functions ψi are bigger, and (ii) the overall weight of the S = 1 configuration is smaller with respect to the S = 0 one
Summary
The pion electromagnetic form factor has been calculated for the first time from the solutions of the BetheSalpeter equation, obtained directly in Minkowski space by using the Nakanishi integral representation of the Bethe-Salpeter amplitude. The pion valence wave function contributes only with 70% [21] of the normalization, and to the charge (in impulse approximation).
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