A Combined Study of the Pion’s Static Properties and form Factors

We study consistently the pion’s static observables and the elastic and γ* γ → π ⁰ transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the γ* γ → π ⁰ form factor at large q ², yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40 % smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data.     

Deuteron structure and diffractive deuteron-nucleus interaction

A nonrelativistic deuteron wave function involving the D-wave state and having a correct asymptotic behavior is constructed on the basis of the experimentally measured deuteron charge form factor G _C(q) and deuteron structure function A(q). The differential cross section for elastic deuteron-nucleus scattering is calculated by using this wave function and is found to agree with experimental data at an energy of 110 MeV. Integrated cross sections for various processes involving deuteron-nucleus interactions are also calculated. The distribution in the emission angle of the center of mass of the neutron-proton system produced in the diffractive dissociation of 110-MeV deuterons in the field of ²⁰⁸Pb nuclei is obtained.     

A non-perturbative calculation of the infrared limit of the axial gauge gluon propagator (I)

We describe a non-perturbative study of the infrared behavior of the axial gauge gluon propagator based on the Dyson equation and Ward identities. We conclude that the propagator Δ_μν(q) displays a q^?4 singularity in the infrared limit, and that consequently the axial gauge running coupling constant g_A²)(q) displays a q^?2 singularity in the same limit. The only assumption necessary to obtain this conclusion is that the transverse part of the triple-gluon vertex function does not dominate the longitudinal part in the infrared regime.     

Inclusive heavy-flavor production from nuclei

We describe a light-cone wave function formulation for hadroproduction of heavy-flavors at high energies. At moderate values ofx _F heavy-flavor production can be viewed as a diffractive excitation of heavy quark-antiquark Fock states, present in the interacting gluon from the projectile. The approach developed here is well suited to address coherence effects in heavy-quark production from nuclei at small values ofx _t?0.1·A ^?1/3.     

Behaviour of the proton-proton total cross section at ISR energies in the reggeon calculus

We study the behaviour of σ^pp_T at ISR energies in the Reggeon calculus with a bare triple Pomeron coupling non vanishing at q² = 0. The parameters are determined from elastic and inclusive data. A sizable increase of σ_T with s can only be obtained when the bare Pomeron intercept is such that the renormalized Pomeron singularity is above one, in the forward direction.     

Form factors,threshold relations,and large angle elastic scattering of pions

The form factor F(q²) of the pion in a simple core model is investigated, together with the deep inelastic electroproduction structure function, F₂(ω). A relation between these two, analagous to the Drell-Yan-West relation for nucleons, is derived and it is found that F₂ is related to either the form factor or the square of the form factor depending on how rapidly F(q²) ultimately falls with momentum transfer. The unitarity equation and its implications for this kind of threshold relation are discussed. The simple core model is also applied to elastic large angle ππ scattering.     

The deuteron wave function at short range and the triton

It is shown that if one assumes something between zero and the prediction of the scaling model with dipole fit for the neutron electric form factor, then a variety of short-range behaviour for the deuteron wave function is consistent with existing experimental data on the deuteron electric form factor. This still relatively wide latitude for the inner deuteron wave function, consistent with existing experimental electromagnetic data, gives rise to an off-shell variation of approximately 1.2 MeV in the triton binding energy with a fixed ¹S₀ interaction and a P_D varying from 4.5 to 6.5 %. Interactions with greater densities of matter at short range bind the triton more strongly and closer to the experimental value. An off-shell variation of 0.7 MeV is obtained with a fixed p_d and singlet interaction. However, a single measurement of the deuteron tensor polarization at about q² = 20 fm^?2 would severely restrict this variation.     

Off-shell effects in quasielastic electron nucleus scattering

Using the Ward-Takahashi identity, on-shell condition, bound Dirac equation and off-shell expansion, a reduced version of half off-shell virtual photon nucleon vertex has been suggested. The vertex are decomposed into several different order terms: the on-shell terms, first and second off-shell terms. The off-shell behaviour of the form factors is discussed in the one meson loop model. Using the reduced vertex and parametrized off-shell form factors the quasielastic response functions are calculated for several nuclei at ¦q¦–k_f and for⁵⁶Fe at large ¦q¦ up to 1.14 GeV/c and at ?q²=0.9 (GeV/c)². The Coulomb sums are evaluated and a comparison of the theoretical prediction with data is given. The off-shell electron nucleon cross section is calculated and compared with the “cc1” off-shell extrapolation.     

Bounds for Kℓ3 decay parameters

The extremum of the integral ∫^∞f(x) ‖F (x)‖² dx is determined for the case when the values taken by the function F (x)¹ at three points are known. The result is applied to the K_?3 problem, the function F (x) being replaced by the form factor f₊(q²)+f₋(q²)q²(m_K²−m_π²) of the divergence of the strangeness changing vector current.     

Range,light-cone dominance and scaling at low Q2 in electroproduction

The analysis of light cone singularities is used to connect the y · P, or range, dependence of the current correlation function with the Q² dependence of the inelastic electroproduction structure functions. We study for what regions of the Q², ν plane and for what y · P dependence the leading light-cone singularity dominates contributions from less singular terms with the same y · P dependence. When the leading singularity can be shown to dominate for a particular region of Q² and ν, we study whether this implies scaling for νW₂ in that kinematic region. It is shown that a division of the current correlation function into short and long range contributions is fundamentally ambiguous and not related to scaling at low Q². Short range terms which are shown to be light-cone dominated for all Q² so long as ν → ∞, are found but are shown not to scale at low Q² and to be indistinguishable from corrections to long range terms which produce the leading Regge behavior. We show that leading Regge terms may receive contributions far away from the light cone for small virtual photon mass, but that light-cone dominance and scaling are recovered when the photon mass is taken very large.     

Spin structure of the pion in a light-cone representation

The spin structure of the pion is discussed by transforming the wave function for the pion in the naive quark model into a light-cone representation. It is shown that there are higher helicity (λ ₁+λ ₂=±1) states in the full light-cone wave function for the pion besides the ordinary helicity (λ ₁+λ ₂=0) component wave functions as a consequence from the Melosh rotation relating spin states in light-front dynamics and those in instantform dynamics. Some low energy properties of the pion, such as the electromagnetic form factor, the charged mean square radius, and the weak decay constant, could be interrelated in this representation with reasonable parameters.     

Vertex QCD sum rules,quark model and pion wave function

It is shown that the predictions of the QCD sum rules (SR) and the quark model for the low energy pion wave function can be reconciled within the so-called vertex SR in exclusive kinematics. In contrast to the standard procedure, non-singular terms asx→0 in correlation functions are summed up by means of the conformal symmetry arguments. The soft contribution into the pion form factor is argued to dominate at least up toQ ²～4–6 GeV²     

Light-cone expansions,the parton model and virtual γγ scattering

It is shown that it is sufficient to use the light-cone algebra of currents and the algebra of bilocal operators to find the asymptotic behaviour of the γγ scattering amplitude when one (or two) of the photon masses q_1,2² is large, and for an arbitrary value of the energy squared s = (q₁+q₂)². A general form of this asymptotic behaviour is obtained. The box-diagram is dominant over the wide region in $\text{s(μ}{}^2\text{« s « q}{}_1{}^2\text{q}{}_2{}^2\text{/μ}{}^2\text{,μ ～ 1}\text{GeV}\text{)}$ and so the asymptotic amplitude is known completely. It is shown that the parton model of the type of ref.[8] gives the same predictions for the asymptotic behaviour of the γγ amplitude.     

The Sudakov form factor beyond the leading logarithmic approximation

We present the general form of the asymptotic behavior of the massless electron-photon vetex function in quantum electrodynamics in the limit whereq ², the virtual mass of the photon, becomes large. All the logarithms inq ² are taken into account, whereas inverse powers ofq ² are neglected. In contradistinction to previous investigations we consider the off-shell vertex function and work in the Feynman gauge. Extensive use is made of the α-representation of Feynman integrals.     

Universal power law for the energy spectrum of breaking Riemann waves

The universal power law for the spectrum of one-dimensional breaking Riemann waves is justified for the simple wave equation. The spectrum of spatial amplitudes at the breaking time t = t _b has an asymptotic decay of k ^?4/3, with corresponding energy spectrum decaying as k ^?8/3. This spectrum is formed by the singularity of the form (x ? x _b )^1/3 in the wave shape at the breaking time. This result remains valid for arbitrary nonlinear wave speed. In addition, we demonstrate numerically that the universal power law is observed for long time in the range of small wavenumbers if small dissipation or dispersion is taken into account in the viscous Burgers or Korteweg-de Vries equations.