Behavior Of Form Factors Research Articles

Excitation spectrum of planar spin-½ Heisenbergxxzchains

We present analytic weak-coupling and numerical finite-chain results for the dynamic form factor associated with the out-of-plane fluctuations at zero temperature and zero field. The dynamic form factor associated with the in-plane fluctuations is treated numerically only. In the ferromagnetic regime, the dominant features are traced back to particle-hole pair continua and the associated bound states. With the approach toward the isotropic ferromagnet, the resonance associated with the bound state of the particle-hole pairs gradually exhausts the spectrum, corresponding in this limit to the magnon peak. In the antiferromagnetic regime, the spectrum is dominated by the particle-hole pair continuum. The analytic results for the dynamic form factor associated with the out-of-plane fluctuations reproduce and extend the well-known properties of the continuum model to leading order in the coupling constant. As expected from the relation between the six-vertex model and the $\mathrm{xxz}$ chain, these properties include singular behavior of dynamic form factors depending continuously on the coupling constant.

Asymptotic behavior of the Sudakov form factor in quantum chromodynamics

In this paper we give an algorithm to compute the asymptotic behavior of the on-shell quark form factor in the limit of large momentum transfer (Sudakov form factor) in Abelian and non-Abelian gauge theories. We ignore terms which are suppressed by a power of momentum transfer, but keep all nonleading logarithms of the momentum transfer and all powers of the coupling constant.

The asymptotic behaviour of form factors

Similar to the method of S.A. Anikin and O.I. Zavialov a modified renormalization procedure is applied to the already renormalized current operator. This allows the derivation of an identity for the coefficient functions of this operator and the proof of new renormalization group equations. These equations are applied to the theory and the electromagnetic form factor of quarks in QCD. In the last case the one-loop approximation gives the leading behaviour exp(− clnln Q 2ln Q 2) for large euclidean values of the momentum transfer Q 2 = − q 2 at the external electromagnetic vertex. If the leading logarithmic terms ( g 2ln 2 Q 2) n are extracted from this result, then the behaviour exp(− g 2 c′ln 2 Q 2) is obtained. Whereas the first result is modified by contributions from two-loop calculations, the result concerning the leading logarithmic terms does not change.

Proton’s opacity in a dual model

We study the optical properties of the proton in high-energy scattering by Fourier-Bessel analysing a duality-motivated model for elastic diffraction. Central opacity and edge effects are related to the large- and small-|t| behaviours of the scattering amplitude which in our model are governed by a logarithmic and a square-root behaviour of the trajectory function. We show that the power-behaved large-|t| tail of the scattering amplitude plays a nonnegligible role in determining the proton opacity. A connection between the proton opaqueness and the behaviour of the form factors is established and the role of diffraction dissociation is discussed.

Study of the reaction e +e − → K S0K L0 in the total energy range 1.4–2.18 GeV and interpretation of the K + and K 0 form factors

The e +e − → K S 0K L 0 cross section has been measured between 1400 and 2180 MeV. About 58 K S 0K L 0 events were in the magnetic detector DM1 at the Orsay storage ring DCI. The charged and neutral kaon form factor behaviour suggests the existence of a new isoscalar vector meson at 1.65 GeV.

Exclusive processes in perturbative quantum chromodynamics

We present a systematic analysis in perturbative quantum chromodynamics (QCD) of large-momentum-transfer exclusive processes. Predictions are given for the scaling behavior, angular dependence, helicity structure, and normalization of elastic and inelastic form factors and large-angle exclusive scattering amplitudes for hadrons and photons. We prove that these reactions are dominated by quark and gluon subprocesses at short distances, and thus that the dimensional-counting rules for the power-law falloff of these amplitudes with momentum transfer are rigorous predictions of QCD, modulo calculable logarithmic corrections from the behavior of the hadronic wave functions at short distances. These anomalous-dimension corrections are determined by evolution equations for process-independent meson and baryon "distribution amplitudes" $\ensuremath{\varphi}({x}_{i}, Q)$ which control the valence-quark distributions in high-momentum-transfer exclusive reactions. The analysis can be carried out systematically in powers of ${\ensuremath{\alpha}}_{s}({Q}^{2})$, the QCD running coupling constant. Although the calculations are most conveniently carried out using light-cone perturbation theory and the light-cone gauge, we also present a gauge-independent analysis and relate the distribution amplitude to a gauge-invariant Bethe-Salpeter amplitude.

Asymptotic behavior of the proton electromagnetic form factor with pion exchanges in the ladder approximation

The asymptotic behavior of the proton electromagnetic form factor due to virtual pion exchanges is studied by restricting to a class of ladder diagrams. We set up an off-mass-shell integral equation for the modified proton-proton-photon vertex due to virtual pion exchanges by summing up an infinite number of ladder diagrams. This integral equation is converted into a set of coupled differential equations involving Lorentz-invariant amplitudes. From the solutions of the differential equations it is found that the usual form factor is modified by a factor $\mathrm{exp}{[\ensuremath{-}\frac{1}{2}\ifmmode\pm\else\textpm\fi{}(\frac{1}{2}){(1\ensuremath{-}\frac{{g}^{2}}{{\ensuremath{\pi}}^{2}})}^{\frac{1}{2}}]\mathrm{ln}t}$ at large momentum transfers, where $g$ is the pion-nucleon coupling constant.

Factorization and asymptotic behaviour of pion form factor in QCD

We outline an all-orders, all-logarithms proof of the factorization theorem for the pion electromagnetic form factor in QCD. The proof is based on the analysis of the large momentum behaviour of Feynman diagrams in a parametric representation.

Asymptotic behavior of the pion electromagnetic form factor in a new phase representation

Asymptotic behavior of the pion electromagnetic form factor in a new phase representation

Asymptotic behavior of composite-particle form factors and the renormalization group

Composite-particle form factors are studied in the limit of large momentum transfer $Q$. It is shown that in models with spinor constituents and either scalar or guage vector gluons, the meson electromagnetic form factor factorizes at large ${Q}^{2}$ and is given by independent light-cone expansions on the initial and final meson legs. The coefficient functions are shown to satisfy a Callan-Symanzik equation. When specialized to quantum chromodynamics, this equation leads to the asymptotic formula of Brodsky and Lepage for the pion electromagnetic form factor. The nucleon form factors ${G}_{M}({Q}^{2})$, ${G}_{E}({Q}^{2})$ are also considered. It is shown that momentum flows which contribute to subdominant logarithms in ${G}_{M}({Q}^{2})$ vitiate a conventional renormalization-group interpretation for this form factor. For large ${Q}^{2}$, the electric form factor ${G}_{E}({Q}^{2})$ fails to factorize, so that a renormalization-group treatment seems even more unlikely in this case.

Anomalous dimensions of three-quark operators

We exhibit in a simple notation the composite operators of lowest twist with baryon quantum numbers and compute their anomalous dimensions. These operators contribute to the leading large- Q 2 behavior of baryon form factors.

Experimental behaviour of the P-wave isovector ππ phase shift and the pion form factor left hand cut contribution

By using the experimental data on the P-wave isovector ππ phase shift δ 1 1 the importance of the pion form factor left hand cut contribution of the second Riemann sheet is investigated. Starting with the pion form factor phase representation, finding the suitable parametrization of the phase shift δ 1 1 and calculating the corresponding integral in the pion c.m. momentum plane, one zero and two poles are found on the negative imaginary axis. The appearance of these poles and zero reveals that the contribution of the left hand cut of the second Riemann sheet to the pion form factor behaviour at the elastic region is nonnegligible.

Asymptotic behavior of the Sudakov form factor

The asymptotic behavior of the form factor in quantum electrodynamics is calculated in case the photon has a mass. The technique used takes into account all logarithms in ${q}^{2}$ but neglects inverse powers of ${q}^{2}$. The result is essentially that found by Sudakov. In order to obtain this result the large-$n$ behavior of ${\ensuremath{\gamma}}_{n}$ is obtained.

Charge screening and mass spectrum in abelian gauge theories

We give a rigorous proof confiriming a statement of Swieca on a connection between the charge and the mass spectrum in Abelian gauge theories. Our argument is based on a detailed analysis of the momentum-space behavior of form factors in the absence of local charge-carrying fields.

Physical basis for minimal time-energy uncertainty relation

A physical basis for the minimal time-energy uncertainty relation is formulated from basic high-energy hadronic properties such as the resonance mass spectrum, the form factor behavior, and the peculiarities of Feynman's parton picture. It is shown that the covariant oscillator formalism combines covariantly this time-energy uncertainty relation with Heisenberg's space-momentum uncertainty relation. A pictorial method is developed to describe the spacetime distribution of the localized probability density.

Asymptotic behaviour of weak formfactors within QCD

The highq2-behaviour of the six weak nucleon (quasi-)elastic formfactors as calculated from lowest order (two-gluon exchange) in QCD is presented. The expressions are also parametrized in the usual way by dipole (triplepole) formulae.

Charge form factors of nuclei in the alpha cluster model

The analysis of the form factors of elastic and inelastic electron scattering from 12C, 16O, 20Ne, 24Mg, 28Si, 32S and 40Ca has been performed in the framework of the alpha cluster model (the Brink model). Trial nucleon functions of s-states relative to the clustering centres are calculated for both the Gaussian and exponential asymptotic behaviour. An ambiguity of the model has been shown in the description of the observed form factors of p-shell nuclei. An interpretation is given for peculiarities of the form factor behaviour at high momentum transfers which can be described only by using trial functions of the exponential asymptotic form. Information concerning the nature of nuclear alpha clustering in the ground and excited states has been obtained.

Pion form factor and its asymptotic behaviour

A simple phenomenological formula is constructed, consistent with the basic principles, providing a definite freedom in the choice of asymptotic behaviour and reflecting all experimentally known features of the pion form factor. The formula is used to test the asymptotic behaviour of the pion form factor both in spacelike and timelike regions simultaneously. The present experimental data require the fall-off ∼t −2, which differs from the quark model prediction.

Electromagnetic effects in precision analyses of the low-energy neutron-proton interaction data

Detailed calculations in the frame of a potential model fitted precisely to the low-energy neutron-proton (deuteron and scattering) experimental data show that the corrections introduced into measurable quantities by electromagnetic interactions are relatively as important as the hadronic contributions from nucleon isobars. The unknown behaviour of the nucleon electromagnetic form factors at high momentum transfers affects only the details of the comparison, at least when constraints provided by current quark-parton models are imposed. But the ignorance of the explicit value of the nucleon hadronic mass is found to generate, in attempts at phenomenological extraction from the data of hadronic values for the np physical quantities, uncertainties as large as the contributions from the isobar channels themselves.

Connection between the asymptotic behavior of electromagnetic form factors and the singularities of their Fourier transforms

Connection between the asymptotic behavior of electromagnetic form factors and the singularities of their Fourier transforms