Quark structure of the pion and pion form factor

Abstract

We consider the pion structure in the region of low and moderately high momentum transfers: at low Q 2 , the pion is treated as a composite system of constituent quarks; at moderately high momentum transfers, Q 2 = 10 ÷ 25 GeV 2 , the pion form factor is calculated within perturbative QCD taking into account one-gluon hard exchange. Using the data on pion form factor at Q 2 < 3 GeV 2 and pion axial-vector decay constant, we reconstruct the pion wave function in the soft and intermediate regions. This very wave function combined with one-gluon hard scattering amplitude allows a calculation of the pion form factor in the hard region Q 2 = 10 ÷ 25 GeV 2 . A specific feature of the reconstructed pion wave function is a quasi-zone character of the qq-excitations. On the basis of the obtained pion wave function and the data on deep inelastic scattering off the pion, the valence quark distribution in a constituent quark is determined.

Publisher's Note: Pion form factor in QCD: From nonlocal condensates to next-to-leading-order analytic perturbation theory [Phys. Rev. D 70, 033014 (2004)]

“…But as argued originally in Refs. [18,23,115,116], and confirmed latter on in several works, for instance, in [21,25,28,29,79], the dominant contribution at low to moderate values of the momentum transfer Q 2 ≤ 10 GeV 2 originates mainly from the soft contribution that involves no hard-gluon exchanges and is attributed to the Feynman mechanism. At present there is no unique way to calculate this contribution from first principles at the partonic level.…”

“…It has been advocated in [18,20,21,23,25,42,67,79] that at momentum-transfer values probed experimentally so far, this latter contribution, though power suppressed because it behaves like 1/Q 4 for large Q 2 , dominates and mimics rather well the observed 1/Q 2 behavior. To account for this effect, we will include the soft contribution [25] (discussed in Sec.…”

Modeling electromagnetic form factors of light and heavy pseudoscalar mesons

“…In the DR approach, the electromagnetic form factors F em (q 2 ) are expressed by a double spectral representation (see references [10][11][12][13][14]),…”

“…It was applied to calculate light mesons form factors [11,12] and used to elucidate long-distance effects [13,14] in weak decays of heavy mesons. More recently the interplay between perturbative and nonperturbative regions in the pion electromagnetic form factor was discussed within the DR approach [15], where it was pointed out the dominance of the nonperturbative contribution up to rather high values of momentum transfers, going beyond a previous analysis performed up to intermediate values of momentum transfers within light-cone sum rule approach [16].…”

Constituent quarks, chiral symmetry, and chiral point of the constituent quark model

“…For the description of the mass spectrum of hadrons and their interactions at low momentum transfers, QCD-inspired constituent quark models (i.e., models based on constituent-quark degrees of freedom in which mesons appear asQQ bound states in a potential) proved to be quite successful [2,3]. Moreover, there are many pieces of evidence that the constituent-quark picture provides a good description not only of the mass spectrum of hadrons, but also of their interactions at not too large momentum transfers [4,5,6,7]. Just because of the proper description of the hadron mass spectrum, the Lagrangian of the constituent quark model cannot be chirally invariant (otherwise it would produce a chirally invariant spectrum of hadron states).…”