Quark Vertex Research Articles

Pion and kaon electromagnetic and gravitational form factors

A unified set of predictions for pion and kaon elastic electromagnetic and gravitational form factors is obtained using a symmetry-preserving truncation of each relevant quantum field equation. A key part of the study is a description of salient aspects of the dressed graviton + quark vertices. The calculations reveal that each meson’s mass radius is smaller than its charge radius, matching available empirical inferences; and meson core pressures are commensurate with those in neutron stars. The analysis described herein paves the way for a direct calculation of nucleon gravitational form factors.

Two-current correlations in the pion in the Nambu and Jona-Lasinio model

We present an analysis of two-current correlations for the pion in the Nambu–Jona-Lasinio model, with Pauli–Villars regularization. We provide explicit expressions in momentum space for two-current correlations corresponding to the zeroth component of the vector Dirac bilinear in the quark vertices, which has been evaluated on the lattice, thinking to applications in a high energy framework, as a step towards the calculation of pion double parton distributions. The numerical results show a remarkable qualitative agreement with recent lattice data. The factorization approximation into one-body currents is discussed based on previous evaluation of the relevant low energy matrix elements in the Nambu–Jona-Lasinio model, confirming the lattice result.

Double parton distributions in the pion in the Nambu\u2013Jona-Lasinio model

Two-parton correlations in the pion, a non perturbative information encoded in double parton distribution functions, are investigated in the Nambu–Jona-Lasinio model. It is found that double parton distribution functions expose novel dynamical information on the structure of the pion, not accessible through one-body parton distributions, as it happens in several estimates for the proton target and in a previous evaluation for the pion, in a light-cone framework. Expressions and predictions are given for double parton distributions corresponding to leading-twist Dirac operators in the quark vertices, and to different regularization methods for the Nambu–Jona-Lasinio model. These results are particularly relevant in view of forthcoming lattice data.

Krein regularization of quantum chromodynamics

In this paper, we use Krein regularization to study certain standard computations in quantum chromodynamics (QCD). In this method, the auxiliary modes[Formula: see text]— those with negative norms[Formula: see text]— are employed to calculate the quark self-energy, vacuum polarizations and vertex functions. We explicitly show that after making use of these modes and by taking into account the quantum metric fluctuation for the problems at hand, the conventional results can indeed be reproduced; but with the advantage of finite answers which require fewer mathematical procedures. An obvious merit of this approach is that the theory is naturally renormalized. The ultraviolet (UV) divergences disappear due to the presence of negative norm state, similar to the Pauli–Villars regularization method. We compare the answers of Krein regularization with the results of calculations which have been done in Hilbert space.

STRONG DECAYS OF FIRST RADIAL EXCITATIONS OF LIGHTEST VECTOR MESON STATES

In this work, we have employed Bethe–Salpeter equation (BSE) under Covariant Instantaneous Ansatz (CIA) to study strong decays of first radial excitations, ω(1420) and ρ(1450) of lightest vector mesons, ω(782) and ρ(770) respectively, through the processes: ω(1420)→ρ+π and ρ(1450)→ω+π. The main motivation for this work was our intention to resolve the problems involved in calculations of triangle quark-loop diagrams as pointed out earlier in Ref. 1 which appear in processes such as h→h'+h" and h→h'+γ (attempted recently) in BSE under CIA, which gives rise to complexities in amplitudes making calculations difficult. We explicitly show the mathematical procedure for handling the process, h→h'+h" involving three hadron–quark vertex functions, which is more involved than that for h→h'+γ and leads to decay widths which are in rough agreement with data.

The canonical transformation and massive CSW vertices for MHV-SQCD

The similarity of massive CSW scalar vertices and quark vertices can be understood using a kind of light-cone SUSY transformation presented in this paper. We also show that the canonical transformation generating the MHV-SQCD Lagrangian, can be fixed by applying this light-cone SUSY transformation to the canonical transformation for MHV-QCD obtained in paper arxiv:0805.0239. Most of the massive CSW vertices for SQCD can also be pinned down in this way.

Generalized structure of hadron–quark vertex function in Bethe–Salpeter framework: applications to leptonic decays of V-mesons

We employ the framework of the Bethe–Salpeter equation under a covariant instantaneous ansatz to study the leptonic decays of vector mesons. The structure of the hadron–quark vertex function Γ is generalized to include various Dirac covariants (other than iγ ⋅ ε) from their complete set. They are incorporated in accordance with a naïve power counting rule order-by-order in powers of the inverse of the meson mass. The decay constants for ρ, ω and ϕ mesons are calculated with the incorporation of leading-order covariants.

Isospin breaking in diagonal pion–nucleon coupling constant: QCD sum rule approach

Using the vacuum-to-pion matrix element of the correlation function of the interpolating fields of two nucleons, isospin splitting in the diagonal pion–nucleon coupling constant has been studied in the framework of the conventional QCD sum rule. The quark mass dependent terms, π0–η mixing and electromagnetic corrections to meson–quark vertices have been included as well. Some of the implications of the isospin splitting have also been discussed.

Examination of the strangeness contribution to the nucleon magnetic moment

We examine the nucleon strangeness magnetic moment ${\ensuremath{\mu}}_{s}$ with a lowest order meson cloud model. We observe that (1) strangeness in the nucleon is a natural requirement of the empirical relation ${\ensuremath{\mu}}_{p}∕{\ensuremath{\mu}}_{n}=\ensuremath{-}3∕2$, which favors an SU(3) octet meson cloud instead of merely the SU(2) pions. (2) In a consistent perturbative calculation, the quark vertex contribution to ${\ensuremath{\mu}}_{s}$ is divergently positive, the meson cloud contribution to ${\ensuremath{\mu}}_{s}$ is divergently negative, and the sum is convergent and negative. (3) In the rest frame of the nucleon, ${\ensuremath{\mu}}_{s}$ cannot be separated into a quark part and an antiquark part, neither can ${\ensuremath{\mu}}_{s}$ be calculated via the spin and orbital angular momentum of the strange quarks and antiquarks. (4) While the overall sign of ${\ensuremath{\mu}}_{s}$ is under debate, the spin part of ${\ensuremath{\mu}}_{s}$ (which is related to the strange quark tensor charge) is better known to be negative.

Strong two-body decays of light mesons

In this paper, we present results on strong two-body decay widths of light $q\bar q$ mesons calculated in a covariant quark model. The model is based on the Bethe-Salpeter equation in its instantaneous approximation and has already been used for computing the complete meson mass spectrum and many electroweak decay observables. Our approach relies on the use of a phenomenological confinement potential with an appropriate spinorial Dirac structure and 't Hooft's instanton--induced interaction as a residual force for pseudoscalar and scalar mesons. The transition matrix element for the decay of one initial meson into two final mesons is evaluated in lowest order by considering conventional decays via quark loops as well as Zweig rule violating instanton--induced decays generated by the six--quark vertex of 't Hooft's interaction; the latter mechanism only contributes if all mesons in the decay have zero total angular momentum. We show that the interference of both decay mechanisms plays an important role in the description of the partial widths of scalar and pseudoscalar mesons.

Radiative corrections to the quark–gluon-Reggeized quark vertex in QCD

This paper is devoted to the calculation of quark–gluon-Reggeized quark effective vertex in perturbative QCD in the next-to-leading order. The case of QCD with massive quarks is considered. This vertex has a number of applications, in particular, the result can be used for determination of the next-to-leading correction to the massive Reggeized quark trajectory.

γ★γ→ π0 transition and asymptotics of γ★γ and γ★γ★ transitions of unflavored pseudoscalar mesons

For the spacelike momenta k of the virtual photon γ ★, the π 0( p) γ ★( k) γ( k ′) transition form factor is considered in the coupled Schwinger–Dyson and Bethe-Salpeter approach in conjunction with the generalized impulse approximation using the dressed quark–photon–quark vertices of the Ball–Chiu and Curtis-Pennington type. These form factors are compared with the ones predicted by the vector meson dominance, operator product expansion, QCD sum rules, and the perturbative QCD for the large spacelike transferred momenta k. The most important qualitative feature of the asymptotic behavior, namely the 1/ k 2 dependence, is in our approach obtained in the model-independent way. Again model-independently, our approach reproduces also the Adler–Bell–Jackiw anomaly result for the limit of both photons being real. For the case of one highly virtual photon, we find in the closed form the asymptotic expression which is then easily generalized both to the case of other unflavored pseudoscalar mesons P 0= π 0, η 8, η 0, η c , η b , and to the case of arbitrary virtuality of the other photon.

Screening of mass singularities and finite soft-photon production rate in hot QCD

The production rate of a soft photon from a hot quark-gluon plasma is computed to leading order at logarithmic accuracy. The canonical hard-thermal-loop resummation scheme leads to logarithmically divergent production rate due to mass singularities. We show that these mass singularities are screened by employing the effective hard-quark propagator, which is obtained through resummation of one-loop self-energy part in a self-consistent manner. The damping-rate part of the effective hard-quark propagator, rather than the thermal-mass part, plays the dominant role of screening mass singularities. Diagrams including photon--(hard-)quark vertex corrections also yield leading contribution to the production rate.

Search for new mechanism of CP violation through tau decay and semileptonic decay of hadrons

If CP is violated in any decay process involving leptons it will signify the existense of a new force (called the X boson) responsible for CP violation that may be the key to understanding matter-antimatter asymmetry in the universe. We discuss the signatures of CP violation in (1) the decay of tau lepton, and (2) the semileptonic decay of $\pi$, K, D, B and t particles by measuring the polarization of the charged lepton in the decay. We discuss how the coupling constants and their phases of the coupling of the X boson to 9 quark vertices and 3 lepton vertices can be obtained through 12 decay processes.

COMPLEXITY OF HADRONIC AMPLITUDES VIA QUARK LOOPS

The structure of hadronic transition amplitudes h→h′+h″ via quark triangle loops is investigated in terms of hadron quark vertex functions [Formula: see text], using for illustration the case of the ρ→ππ transition. A Bethe-Salpeter model based on the Covariant-Instantaneity-Ansatz (CIA) for its kernel which provides an exact interconnection between the 3D and 4D forms the BS wave function, determines the structure [Formula: see text]. The nonlocality feature inherent in the vertex function causes the imaginary part of gρππ calculated from the loop integral to be generally different from its dispersion relation value which would be obtained from analyticity of gρππ in the ρ-mass. Pending a proper understanding of this nonlocality (associated with confining interactions) only the real part of gρππ is found unambiguous while the imaginary part is model-dependent.

A HADRON–QUARK VERTEX FUNCTION: INTERCONNECTION BETWEEN 3D AND 4D WAVE FUNCTIONS

The interrelation between the 4D and 3D forms of the Bethe–Salpeter equation (BSE) with a kernel [Formula: see text] which depends on the relative four-momenta, [Formula: see text] orthogonal to Pμ is exploited to obtain a hadron–quark vertex function of the Lorentz-invariant form [Formula: see text]. The denominator function [Formula: see text] is universal and controls the 3D BSE, which provides the mass spectra with the eigenfunctions [Formula: see text]. The vertex function, directly related to the 4D wave function Ψ which satisfies a corresponding BSE, defines a natural off-shell extension over the whole of four-momentum space, and provides the basis for the evaluation of transition amplitudes via appropriate quark-loop digrams. The key role of the quantity [Formula: see text] in this formalism is clarified in relation to earlier approaches, in which the applications of this quantity had mostly been limited to the mass shell (q · P = 0). Two applications (fP values for [Formula: see text] and Fπ for π0 → γγ) are sketched as illustrations of this formalism, and attention is drawn to the problem of complex amplitudes for bigger quark loops with more hadrons, together with the role of the [Formula: see text] function in overcoming this problem.

An exact calculation of the flavour-changing quark-photon vertex

An exact calculation of the sd γ vertex in the unitary gauge is presented, and its applications are considered. It is found that flavour-changing radiative decays of strange hyperons appear to be explainable in terms of flavour-changing quark vertices involving either a photon or a gluon emission. But the CP-violating effects in such decays are estimated to be too small to be measurable. The exact expression for the sd γ vertex improves the old estimate for the neutron electric dipole moment to 10 −33 e cm. The possibility of bare top flavour production from e + e − → t c or e − u → e − t is shown to be very unlikely.

Infrared structure of non-abelian gauge theories: Comments on perturbation theory calculations

Perturbation theory calculations of infrared behavior in quantum chromodynamics (QCD) have been made using different renormalization schemes. In this paper we compare these calculations as well as the various renormalization group type equations which have been suggested to govern the infrared behavior of the quark vertex function in QCD.

Fine structure in non-Abelian gauge theories

Fine-structure effects of purely non-Abelian origin are isolated and evaluated for quark-antiquark bound states in a general massless non-Abelian gauge theory. The relevant kernels are identified by studying the threshold power singularities of the quark-antiquark scattering amplitude. The non-Abelian fine structure is shown to consist of (a) an $O({{\ensuremath{\alpha}}_{s}}^{3})$ contribution ascribable to the (spatial) momentum dependence of the effective Coulomb-gluon---quark coupling, which is larger than the $O({{\ensuremath{\alpha}}_{s}}^{2})$ Coulomb energy for a wide range of ${\ensuremath{\alpha}}_{s}$, and (b) $O({{\ensuremath{\alpha}}_{s}}^{4})$ contributions comparable to the usual Abelian fine structure. A way is suggested of improving the threshold expansion to avoid the breakdown associated with logarithmic singularities piling up in higher order: In this approach the spin-independent fine structure is reasonably given by the Breit-Fermi interaction with a phenomenological potential, taken together with the purely non-Abelian contributions computed previously. The Breit-Fermi formula cannot be taken seriously for the hyperfine structure, however: Transverse- and Coulomb-gluon exchanges seem to be associated with different effective couplings. In addition, there are Pauli-type contributions to the transverse-gluon---quark vertex which involve logarithmic singularities. The threshold expansion is expected to be directly and unambiguously applicable, however, for threshold bound states of sufficiently heavy quarks (say, ${m}_{q}\ensuremath{\gtrsim}15$ GeV), should such exist.

Applications of the reggeon calculus to dual models

The reggeon calculus devised by Polkinghorne to study the j-plane structure of hybrid graphs is utilised to investigate the orientable non-planar dual loop. A hybrid model with quark vertices is also studied and the calculus extended to deal with a dual reggeon triangle graph which contributes to the asymptotic behaviour of a simple production process. Finally the results from single dual loops are expressed in terms of a reggeon operator calculus.