Pion Vertex Research Articles

Limit on the pion distribution amplitude

The pion distribution amplitude (DA) can be related to the fundamental QCD Greenʼs functions as a function of the quark self-energy and the quark–pion vertex, which in turn are associated with the pion wave function through the Bethe–Salpeter equation. Considering the extreme hard asymptotic behavior in momentum space allowed for a pseudoscalar wave function, which is limited by its normalization condition, we compute the pion DA and its second moment. From the resulting amplitude, representing the field theoretical upper limit on the DA behavior, we calculate the photon–pion transition form factor . The resulting upper limit on the pion transition form factor is compared with existing data published by CLEO, BaBar and Belle Collaborations.

ππcontribution to the QCD sum rules for the light tetraquark

We perform a QCD sum rule analysis for the ${f}_{0}$ light tetraquark taking into account the contribution arising from the two pion intermediate state. With the interpolating currents of the different chiral combinations of scalar and pseudoscalar diquarks, it is demonstrated that the interpolating current with maximum chirality has a large coupling to the two pion state, but the current with zero chirality interacts only weekly with this state. Taking into account the form factor in the ${f}_{0}$-two pion vertex, it is shown that the ${f}_{0}$ coupling to the two pion state leads to an increase of the lightest tetraquark mass by a value of about 100 MeV. The analysis of the resulting sum rule shows that the $\ensuremath{\sigma}({f}_{0}(600))$-meson state might be treated as the four-quark bound state in the instanton field which has a rather strong coupling to the two pion state.

Nonforward parton distributions of the pion within an effective single instanton approximation

We develop a relativistic quark model for pion structure, which incorporates the nontrivial structure of the vacuum of quantum chromodynamics as modelled by instantons. Pions are bound states of quarks and the strong quark–pion vertex is determined from an instanton induced effective Lagrangian. The interaction of the constituents of the pion with the external electromagnetic field is introduced in gauge invariant form. The parameters of the model, i.e., effective instanton radius and constituent quark mass, are obtained from the vacuum expectation values of the lowest dimensional quark and gluon operators and the low-energy observables of the pion. We apply the formalism to the calculation of the pion form factor by means of the isovector nonforward parton distributions and find agreement with the experimental data.

Strong decays and Adler selfconsistency condition in two-dimensional QCD

Strong mesonic decays are studied in the framework of the 't Hooft model for the two-dimensional QCD in the axial gauge. Special attention is payed to the processes with pions in the final state involved and the low energy theorems have been checked including the “Adler zero”. It is demonstrated explicitly that in the chiral limit any three-meson decay amplitude with at least one pion vertex vanishes identically for any values of the external momenta. Ward identities for the dressed vector and axial-vector currents vertices are identified and their relationship to the pionic vertex are discussed.

Constraints on the self-consistent relativistic Fermi-sea particle formalism in the quantum hadrodynamical model.

The self-consistent relativistic Fermi-sea particle formalism in the quantum hadrodynamics is discussed in terms of properties of conserving approximations. The relativistic Dirac-Hartree-Fock approximation (\ensuremath{\sigma}, \ensuremath{\omega}, \ensuremath{\rho}, and \ensuremath{\pi}), for example, is examined from the point of view of the Hugenholtz--Van-Hove theorem and thermodynamics as a check for internal consistency. These two conditions sufficient for constructing conserving approximations are strict constraints on modification and simplification of the Fermi-sea particle approximations and should be used in order to define consistent quasiparticle approximations. It is shown that the pion vertex and retardation which enters through exchange corrections prevent conserving properties to be maintained in the Dirac-Hartree-Fock approximation, and this suggests a careful analysis of self-consistency in the relativistic formalism when correlation effects are considered. The relativistic Fermi-sea particle approximations can be defined uniquely when both constraints are incorporated into self-consistency of the approximations.

The six pion amplitude to fourth order in momenta

The six pion function is determined to fourth order in momenta and the pion mass using a generalized non-linear sigma model. All arbitrariness in the amplitude is shown to come from the four pion vertex, namely four parameters (or only one if we wish for an algebraically dual form).

Pion vertex functions from the spurion model and Veneziano formula

F r o m the Veneziano formula (1) for the process pr: -> ST:, where the spurion S carries the q u a n t u m numbers of the vacumn, NAMIKI and 0I~BA (~) were able to obtain an expression for the pion vec tor form factor . This was achieved by taking the l imit of the ampl i tude whel~ the f o u r m o m e n t u m of the spurion te~ds to zero a t a fixed value of t. The resu l tan t Venez ianotype ve r t ex funct ion looks like

On the renormalization of the linearσ-model

The problem of the renormalization of theσ-model with nucleons is considered. Following the general lines of Lee’s approach, explicit formulas are given for the relevant physical quantities as well as for the renormalization constants in the one-loop approximation. The pion decay constant and the nucleon pion vertex are evaluated.

Renormalization of the σ-model

We consider the renormalization of the σ-model in the absence of the baryon fields. The model is characterized by three parameters. In order that the current algebra and the partially conserved axial vector current condition are valid in the renormalized σ-model, it is necessary that all divergences of the theory may be absorbed in two constants, the mass and the coupling constant, and no new ad-hoc parameters be introduced to remove divergences. A perturbation method is presented, in which the lowest order gives rise to the usual results of the current algebra (or chiral dynamics). It is shown that indeed all divergences can be absorbed into the redefinitions of the mass parameter and the one coupling constant. This is achieved by demonstrating the existence of an intermediate renormalization (wherein the counter terms are precisely those of a chiral symmetric theory) which makes the theory finite. As a consequence, the mass difference between the scalar and pseudoscalar particles is finite and all the three point and four point couplings are expressible in terms of one parameter. The vacuum expectation value of the scalar σ field is given by a non-linear equation. A consistent treatment of this equation is outlined in detail, and the equation is shown to be finite and well-defined after the intermediate renormalization. The possibility of the spontaneous breakdown of the chiral symmetry, through the non-vanishing vacuum expectation value of the σ-field even when the Lagrangian is chiral invariant, is described and the Goldstone theorem is verified up to the second order in perturbation expansion. The treatment of the axial vector current - pion vertex (such as appears in the pion decay), which contains a linear divergence not encountered in the S-matrix expansion, is detailed. We relate the pion decay constant to the vacuum expectation value of the renormalized σ field in all orders of perturbation theory.

Radiative corrections to pion production in e+-e− collisions

Radiative corrections to the processes e−-e−→n pions are evaluated in relation to the planned colliding beam experiments. A theorem is proved which shows the possibility of separating experimentally the contribution of theγ-n pion vertex from the contribution of the 2γ-n pion vertex.