Nucleon form factors and distribution amplitudes in QCD

Abstract

We derive light-cone sum rules for the electromagnetic nucleon form factors including the next-to-leading-order corrections for the contribution of twist-three and twist-four operators and a consistent treatment of the nucleon mass corrections. The essence of this approach is that soft Feynman contributions are calculated in terms of small transverse distance quantities using dispersion relations and duality. The form factors are thus expressed in terms of nucleon wave functions at small transverse separations, called distribution amplitudes, without any additional parameters. The distribution amplitudes, therefore, can be extracted from the comparison with the experimental data on form factors and compared to the results of lattice QCD simulations. A selfconsistent picture emerges, with the three valence quarks carrying 40% : 30% : 30% of the proton momentum.

Light-Cone Sum Rule Approach for Baryon Form Factors

“…The shape of the resulting distribution amplitudes is plotted in figure 7. Table 1 LCSR (ABO1) and LCSR (ABO2) refer to the two models ABO1 and ABO2 extracted in [23]. The values of the normalization of the leading and next-to-leading twist distribution amplitudes fN /λ1 and the first order shape parameter of the leading distribution amplitude, ϕ10 and ϕ11 have been fixed before fitting to the experimental data.…”

“…a consistent and practical renormalization scheme for three-quark operators was developed [25] 2. expressions for matrix elements of operators with non light-like distance in terms of distribution amplitudes were derived [23] 3. next to leading order corrections both for twist 3 and 4 were calculated [23] 4. the kinematic contributions to higher twist distribution amplitudes, the so called Wandzura-Wilczek contributions, were taken into account [26] 5. off light-cone corrections (x 2 -corrections) to leading twist distribution amplitudes were recalculated [23] 6. the leading twist distribution amplitude was expanded up to second order [23] These advances allowed for the first time to make quantitative statements on the shape of the nucleon and N * distribution amplitude based on experimental data. The extracted shape parameters for the nucleon and N * with lattice results for comparison are given in table 1 and 2.…”

“…The difference in the shape parameters between the two fits can be seen as a measure for the induced deviation. We have illustrated the separate variation of the Borel-parameter in figure 6 of [23]. Fourth, the factorization scale dependence increases with increasing momentum transfer Q 2 .…”

Advances in QCD sum-rule calculations

“…Many sum-rule analyses of the baryon elastic and transition form factors have been presented in the recent years (see e.g. [49][50][51][52] and references therein). With a few exceptions (e.g.…”

“…With a few exceptions (e.g. [49]), these calculations are based on the leading-order O(1) correlation functions and use the traditional approaches to fix the effective thresholds, usually neglecting the τ-and Q 2 -dependence of the latter. These analyses are expected to provide reasonable ball-park estimates for the form factors; however, in most of the cases, the estimates of the OPE-errors (related to the uncertainties of the QCD parameters, to the missing radiative corrections, and in particular to a strong dependence on the scale µ) and the systematic errors, related to the adopted procedures of fixing the effective continuum thresholds) are not done properly.…”