Behavior Of Form Factors Research Articles

Transition to Perturbative QCD

We review the Jefferson Lab program concerning the interplay between hadronic and underlying quark degrees of freedom in exclusive reactions. Much of the program was initially based on predictions from perturbative QCD (pQCD) concerning scaling of reaction cross sections, helicity conservation, and asymptotic behavior of form factors. Although much of the data do not follow simple pQCD expectations, some observables scale better than expected. Generally, the underlying dynamics are best understood with nonperturbative quark models, but the elastic deuteron form factors provide an example of the success of hadronic models to high momentum transfer.

Rigorous pion electromagnetic form factor behavior in the spacelike region

Precise experimental information on ${\ensuremath{\sigma}}_{\text{tot}}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$ is transferred into the spacelike region by taking advantage of the analyticity. As a result, rigorous pion electromagnetic form factor behavior in spacelike region is obtained. The latter is compared with some existing model predictions.

Low-[formula omitted] scaling behavior of the form-factor ratios for the [formula omitted]-transition

We address the issue of the scaling behavior of the nucleon electromagnetic form factors (FFs). We propose a consistent Lagrangian of the electromagnetic NΔ(1232)-interaction possessing all the internal symmetries of the spin-32 baryon resonance, point and gauge invariance. The point and gauge invariant FFs may exhibit quasi-scaling behavior—while the FFs do not reach asymptotic scaling domain, the ratios thereof do. The hypothesis of the quasi-scaling is in good agreement with the experimental data available at Q2⩾0.4 GeV2.

Tests of Universality of Baryon Form Factors in Holographic QCD

We describe a new exact relation for large $N_c$ QCD for the long-distance behavior of baryon form factors in the chiral limit, satisfied by all 4D semi-classical chiral soliton models. We use this relation to test the consistency of the structure of two different holographic models of baryons.

Analyticity in a Phenomenology of Electro-Weak Structure of Hadrons

Analyticity in a Phenomenology of Electro-Weak Structure of HadronsThe utility of an application of the analyticity in a phenomenology of electro-weak structure of hadrons is demonstrated in a number of obtained new and experimentally verifiable results. With this aim first the problem of an inconsistency of the asymptotic behavior of VMD model with the asymptotic behavior of form factors of baryons and nuclei is solved generally and a general approach for determination of the lowest normal and anomalous singularities of form factors from the corresponding Feynman diagrams is reviewed. Then many useful applications by making use of the analytic properties of electro-weak form factors and amplitudes of various electromagnetic processes of hadrons are carried out.

QUARK COUNTING RULES: OLD AND NEW APPROACHES

I discuss the subject of powerlike asymptotic behavior of hadronic form factors in pre-QCD analyses of soft (Feynman/Drell-Yan) and hard (West) mechanisms, and also recent derivation of 1/Q2 asymptotics of meson form factors in AdS/QCD. At the end, I briefly comment on "light-front holography" ansatz.

CHIRAL SYMMETRY AND HOLOGRAPHIC MODELS OF THE BARYON: TESTING HOLOGRAPHIC MODELS OF THE BARYON WITH MODEL-INDEPENDENT RELATIONS

A model-independent relation for the long-distance behavior of baryon form factors in the large Nc and chiral limits is introduced and used to probe the consistency of various models of the baryon including recently proposed holographic models. This relation is satisfied by the Skyrme model and all other 4D semiclassical chiral soliton models. The "bottom-up" Pomarol-Wulzer holographic model which treats baryons as 5D Skyrmions also satisfies the relation. However, the "top down" holographic model treating baryons as instantons in the Sakai-Sugimoto model fails to satisfy the relation. This failure can ultimately be traced to the imposition of a scale separation in the model between the curvature scale and the KK scale; such a scale separation has no counterpart in QCD.

Model independent pion electromagnetic form factor behavior in the space-like region

Very precise data on σ tot ( e + e − → π + π − ) recently measured by radiative return in Frascati and simultaneously the corrected Novosibirsk CMD-2 and SND data are transferred using the analyticity into the space-like region. As a result a rigorous pion electromagnetic form factor behavior is obtained, which is compared with AdS/QCD model predictions and existing data from electroproduction on proton.

ON PERTURBATIVE QCD OF HARD AND SOFT PROCESSES

We discuss some problems concerning the application of perturbative QCD to high energy processes. In particular for hard processes, we analyze higher order and higher twist corrections. It is argued that these effects are of great importance for understanding the behaviour of pion electromagnetic form factor at moderately large momentum transfers. For soft processes, we show that summing the contributions of the lowest twist operators leads to a Regge-like amplitude.

On the electromagnetic form factors of hadrons in the time-like region near threshold

Hadron electromagnetic form factor in the time-like region at the boundary of the physical region is considered. The energy behavior of the form factor is shown to be determined by the strong hadron–antihadron interaction. We propose a simple phenomenological model of the h h ¯ interaction that describes the form factor behaviour in the region where scattering length approximation fails and estimate on its basis imaginary part of the scattering lengths (volumes) for Λ Λ ¯ , Λ Σ ¯ 0 ( Λ ¯ Σ 0 ) , Σ 0 Σ ¯ 0 and D ∗ D ∗ ¯ from present experimental data. The developed approach enables us to analyze the existence of baryon–antibaryon ( B B ¯ ) near threshold resonances. The experiments to extract detailed information on the near threshold B B ¯ interaction from hadron form factor energy behavior are suggested.

Model Independent Tests of Skyrmions and Their Holographic Cousins

We describe a new exact relation for large Nc QCD for the long-distance behavior of baryon form factors in the chiral limit. This model-independent relation is used to test the consistency of the structure of several baryon models. All 4D semiclassical chiral soliton models satisfy the relation, as does the Pomarol-Wulzer holographic model of baryons as 5D Skyrmions. However, remarkably, we find that the holographic model treating baryons as instantons in the Sakai-Sugimoto model does not satisfy the relation.

Contribution of meson-exchange currents to the electromagnetic structure of the deuteron at high momentum transfers

The leading term of the asymptotic expansion of the contributions of the πNN and ρπγ processes to the electromagnetic form factors of the deuteron at high momentum transfers is calculated. The resulting asymptotic behavior is compared with experimental data obtained at the Thomas Jefferson Laboratory. Constraints on the functional dependence of meson-nucleon vertex functions that ensure a correct asymptotic behavior of deuteron form factors are discussed.

Asymptotic behavior of the deuteron form factors in the two-nucleon model and electron scattering experiments at GeV energies at JLab

Using the instant form dynamics of Poincar\'e invariant quantum mechanics and the modified relativistic impulse approximation proposed previously, we calculate asymptotic behavior of electromagnetic form factors for the deuteron considered as a two-nucleon system. We show that today, experimentation on elastic $\mathit{ed}$ scattering has reached the asymptotic regime. We also estimate the possible range of momentum transfer in which the quark degrees of freedom will possibly be seen in future JLab experiments. The explicit relation between the behavior of the deuteron wave function at $r=0$ and the form factors asymptotic behavior is obtained, and the conditions of wave functions that give the asymptotic behavior predicted by QCD and quark counting rules are formulated.

Vector mesonω−ϕmixing and their form factors in the light-cone quark model

The vector meson $\omega$-$\phi$ mixing is studied in two alternative scenarios with different numbers of mixing angles, i.e., the one-mixing-angle scenario and the two-mixing-angle scenario, in both the octect-singlet mixing scheme and the quark flavor mixing scheme. Concerning the reproduction of experimental data and the $Q^2$ behavior of transition form factors, one-mixing-angle scenario in the quark flavor scheme performs better than that in the octet-singlet scheme, while the two-mixing-angle scenario works well for both mixing schemes. The difference between the two mixing angles in the octet-singlet scheme is bigger than that in the quark flavor scheme.

SEMILEPTONIC B(Bs, Bc) DECAYS IN THE LIGHT-CONE QCD SUM RULES

Semileptonic B(Bs, Bc) decays are investigated systematically in the light-cone QCD sum rules. Special emphasis is put on the LCSR calculation on weak form factors with an adequate chiral current correlator, which turns out to be particularly effective to control the pollution by higher twist components of spectator mesons. The result for each channel depends on the distribution amplitude of the the producing meson. The leading twist distribution amplitudes of the related heavy mesons and charmonium are worked out by a model approach in the reasonable way. A practical scenario is suggested to understand the behavior of weak form factors in the whole kinematically accessible ranges. The decay widths and branching ratios are estimated for several B(Bc) decay modes of current interest.

Phenomenological insight into the space-like proton elastic form factor using the deuteron impulse approximation

The analysis of the JLab proton polarization data on the ratio {mu}{sub p}G{sub Ep}(t)/G{sub Mp}(t) in the framework of the unitary and analytic model of nucleon electromagnetic structure implicates surprising nondipole behavior of the proton electric form factor G{sub Ep}(t) in the space-like region with the zero around the momentum transfer squared value t=-Q{sup 2}=-13 GeV{sup 2}. This result differs from the unpolarized cross-section measurements giving the dipole behavior of G{sub Ep}(t) by means of the Rosenbluth technique. Recent investigations demonstrate that inclusion of a two-photon mechanism could solve the problem, which plays an important role for the unpolarized cross section, but it is negligible for the polarization ratio. Here, investigating a size of a difference in a prediction of the deuteron elastic structure functions A(t),B(t) by both, the nondipole and the old dipole, behaviors of G{sub Ep}(t) in space-like region through the nonrelativistic impulse approximation, we have come to the conclusion that the two-photon mechanism plays much less of a role for the unpolarized electron-deuteron elastic scattering than for the unpolarized electron-proton elastic scattering.

Q2-evolution of nucleon-to-resonance transition form factors in a QCD-inspired vector-meson-dominance model

We adopt the vector-meson-dominance approach to investigate ${Q}^{2}$-evolution of $NR$-transition form factors ($N$ denotes nucleon and $R$ an excited resonance) in the first and second resonance regions. The developed model is based upon conventional $\ensuremath{\gamma}NR$-interaction Lagrangians, introducing three form factors for spin-$3/2$ resonances and two form factors for spin-$1/2$ nucleon excitations. Lagrangian form factors are expressed as dispersionlike expansions with four or five poles corresponding to the lowest excitations of the mesons $\ensuremath{\rho}(770)$ and $\ensuremath{\omega}(782)$. Correct high-${Q}^{2}$ form-factor behavior predicted by perturbative QCD is due to phenomenological logarithmic renormalization of electromagnetic coupling constants and linear superconvergence relations between the parameters of the meson spectrum. The model is found to be in good agreement with all the experimental data on ${Q}^{2}$-dependence of the transitions $N\ensuremath{\Delta}(1232)$, $NN(1440)$, $NN(1520)$, $NN(1535)$. We present fit results and model predictions for high-energy experiments proposed by JLab. Besides, we make special emphasis on the transition to perturbative domain of $N\ensuremath{\Delta}(1232)$ form factors.

Implications of the JLab proton polarization data for the behavior of strange nucleon form factors

Special eight-resonance unitary and analytic model of nucleon electromagnetic structure is used to analyze, first the classical proton form factor data obtained by the Rosenbluth technique and then also the contradicting JLab proton polarization data on the ratio $\mu_p G_{Ep}(Q^2)/G_{Mp}(Q^2)$ with the aim to investigate a manifestation of the latter on the strange nucleon form factors behaviour.

Asymptotic behavior of nucleon electromagnetic form factors in time-like region

We study the asymptotic behavior of the ratio of Pauli and Dirac electromagnetic nucleon form factors, $F_2/F_1$, in time-like region for different parametrizations built for the space-like region. We investigate how fast the ratio $F_2/F_1$ approaches the asymptotic limits according to the Phragm\`en-Lindel\"of theorem. We show that the QCD-inspired logarithmic behavior of this ratio results in very far asymptotics, experimentally unachievable. This is also confirmed by the normal component of the nucleon polarization, $P_y$, in $e^++e^-\to N+\bar{N}$ (in collisions of unpolarized leptons), which is a very interesting observable, with respect to this theorem. Finally we observe that the 1/Q parametrization of $F_2/F_1$ contradicts this theorem.

Finite temperature pion vector form factors in chiral perturbation theory

We discuss the thermal behaviour of the pion vector form factors and calculate them in one-loop chiral perturbation theory. The perturbative result is used to analyze the T-dependent electromagnetic pion charge radius, obtaining a rough estimate of the deconfinement critical temperature. Imposing thermal unitarity, we generate the ρ resonance pole for the form factor in the center of mass frame. The ρ peak height in the modulus of the form factor decreases for increasing temperature, while its width increases and the peak position is slightly shifted downwards for T≃150 MeV. These results point in the direction suggested by many analysis of dilepton production data in relativistic heavy ion collisions.