Soft charge form factor of the pion

Abstract

We identify the source of a discrepancy between pPft /long and FP'~~~,,,, found by Isgur and Llewellyn Smith. We find that the discrepancy disappears when virtual qq pair production for longitudinal-momentum transfers is included. Our result rectifies the discussion by Isgur and Llewellyn Smith of soft nonperturbative effects at presently available values of Q2. PACS Number(s): 13.40.Fn, ll.lO.St, 1 2 . 3 8 . B~ While perturbative Q C D ( P Q C D ) [l-51 is expected t o be a n adequate tool t o study the asymptotic Qoo behavior of hard exclusive reactions, doubts have been raised [6,71 a b o u t t h e applicability of P Q C D a t presently available Q'. Currently a strong disagreement continues a b o u t a scale of momentum transfers characteristic for the transition from the nonperturbative to perturbative regime. While some argue [8-141 t h a t the transition may take place for Q2 as low as 4-6 (GeV/c)', or a t some 15 (GeV/c)' [15], others maintain [16, 171 t h a t the transition should take place for much higher values of Q 2 , perhaps as high as 100 (GeV/c)'. Recently Isgur and Llewellyn Smith [16] (ILS) reexamined their original arguments [7] against the applications of P Q C D in exclusive processes a t presently available Q2.

Linking parton distributions to form factors and Compton scattering

“…An example is the Drell-Yan overlap formula [13] of the elastic form factor, for which Isgur and Llewellyn Smith [7] observed that different results are obtained in different reference frames. Sawicki [18] has shown the origin of this discrepancy: in certain reference frames there are overlap contributions which are not contained in the Drell-Yan formula; when they are taken into account Lorentz invariance is restored. We shall first review Sawicki's arguments [18,19] for the form factor and then investigate the case of Compton scattering.…”

“…Sawicki [18] has shown the origin of this discrepancy: in certain reference frames there are overlap contributions which are not contained in the Drell-Yan formula; when they are taken into account Lorentz invariance is restored. We shall first review Sawicki's arguments [18,19] for the form factor and then investigate the case of Compton scattering.…”

Pion-photon and photon-pion transition form factors in the light-cone formalism

“…Other choice of q µ will cause contribution from Z-graphs, and it should give the same result as that in the q + = 0 case if all graphs are taken into account [26]. Therefore some more complicated diagrams should be included.…”

Spacelike and timelike pion electromagnetic form factor and Fock state components within the light-front dynamics

“…It is worth noting that in the timelike region the full result for the pion form factor is always given by the pair-production process (''Z-diagram'') alone, independently of this approximation, while in the spacelike region only the ''Z-diagram'' contribution [14,19,21,22,27,41] survives for a massless pion [26]. The importance of the ''Z-diagram'' contribution to the electromagnetic current for q > 0 was also recently investigated in the context of the Bethe-Salpeter equation within the light-front quantization in Ref.…”