Form Of Relativistic Quantum Mechanics Research Articles

An estimation of non-valence contributions to form factors of heavy-light mesons

We study the influence of non-valence quark-pair contributions in weak transition form factors of heavy-light mesons. Form factors are first calculated for spacelike momentum transfers in a reference frame where such contributions are suppressed. Analytic continuation to the timelike region and a comparison with the direct decay calculation, done with pure valence degrees of freedom, provides an estimate of the role that quark-pair contributions may play. We use the point form of relativistic quantum mechanics, which is particularly useful when treating heavy-light systems.

Weak transition form factors of heavy-light pseudoscalar mesons for space- and timelike momentum transfers

Weak $B^-\rightarrow D^0, \pi^0$ and $D^-\rightarrow {K}^0, \pi^0$ transition form factors are described in both the space- and time-like momentum transfer regions, within a constituent-quark model. Neutrino-meson scattering and semileptonic weak decays are formulated within the point form of relativistic quantum mechanics to end up with relativistic invariant process amplitudes from which meson transition currents and form factors are extracted in an unambiguous way. For space-like momentum transfers, form factors depend on the frame in which the $W M M^\prime$ vertex is considered. Such a frame dependence is expected from a pure valence-quark picture, since a complete, frame independent description of form factors is supposed to include non-valence contributions. The most important of such contributions are the $Z$-graphs, which are, however, suppressed in the infinite-momentum frame ($q^2<0$). On the other hand, they can play a significant role in the Breit frame ($q^2<0$) and in the direct decay calculation ($q^2>0$), as a comparison with the infinite-momentum-frame form factors (analytically continued to $q^2>0$) reveals. Numerical results for the analytically continued infinite-momentum-frame form factors agree very well with lattice data in the time-like momentum transfer region and the experimental value for the slope of the $F^+_{B\rightarrow D}$ transition form factor at zero recoil is reproduced satisfactorily. These predictions satisfy heavy-quark-symmetry constraints and their $q^2$ dependence is well approximated by a pole fit, reminiscent of a vector-meson-dominance-like decay mechanism. We discuss how such a decay mechanism can be accommodated within an extension of our constituent-quark model, by allowing for a non-valence component in the meson wave functions. We also address the question of wrong cluster properties inherent in the Bakamjian-Thomas formulation.

On the Microscopic Structure of {varvec{pi }}NN, {varvec{pi }}N{varvec{Delta }} and {varvec{{pi }Delta Delta }} Vertices

We use a hybrid constituent-quark model for the microscopic description of pi N N, pi N Delta and pi Delta Delta vertices. In this model quarks are confined by an instantaneous potential and are allowed to emit and absorb a pion, which is also treated as dynamical degree of freedom. The point form of relativistic quantum mechanics is employed to achieve a relativistically invariant description of this system. Starting with an SU(6) spin-flavor symmetric wave function for N_0 and Delta _0, i.e. the eigenstates of the pure confinement problem, we calculate the strength of the pi N_0 N_0, pi N_0 Delta _0 and pi Delta _0 Delta _0 couplings and the corresponding vertex form factors. Interestingly the ratios of the resulting couplings resemble strongly those needed in purely hadronic coupled-channel models, but deviate significantly from the ratios following from SU(6) spin-flavor symmetry in the non-relativistic constituent-quark model.

Electroweak properties ofρ-meson in the instant form of relativistic quantum mechanics

Charge and magnetic radii, magnetic and quadrupole moments of the ρ -meson are calculated in framework of the developed by authors version of the instant form of relativistic quantum mechanics with fixed number of particles (IF RQM). The calculations are performed with different wave functions of quarks in the ρ -meson and using the so- called modified impulse approximation (MIA). The electromagnetic characteristics of ρ -meson are obtained without fitting parameters. The value of the magnetic moment coincides with available experimental data: μρ = 2.1 ± 0.5 e /2Mρ .

Poincaré-invariant constituent quark model for light mesons: capabilities and constraints

We present a brief survey of some results on electroweak properties of com- posite systems that are obtained in the frameworks of our version of the instant form of relativistic quantum mechanics (RQM). Our approach describes well the π- and the ρ- mesons in wide range of momentum transfers Q 2 . At large Q 2 the obtained pion form factor asymptotics coincides with that of QCD predictions. The method permits to per- form analytic continuation of pion form factor to complex plane of momentum transfers that is in accordance with predictions of quantum field theory.

Describing radiation decay using the instant form of relativistic quantum mechanics

For a transition between states with different total angular momentum values, we develop a method for constructing an electromagnetic current operator that satisfies the Lorentz-covariance and current-conservation conditions. Our method is realized in the framework of an instant form of relativistic quantum mechanics using the general method of relativistic parameterization of matrix elements of local operators. We illustrate the method by calculating the radiation decay of a ρ-meson into a pion. In the modified impulse approximation, we obtain an analytic expression for the transition form factor of this process in the form of an integral representation of dispersion type. Results of the numerical calculation agree with the results of calculating the light-front dynamics and with the model of vector meson dominance.

Elastic electron-deuteron scattering within a relativistic potential model

Elastic electron-deuteron scattering was considered in the point form of relativistic quantum mechanics. Observables of this process and the dependence of the deuteron form factors on the 4-momentum transfer Q up to 8 fm−1 were calculated. The nucleon-nucleon potentials used in the calculations included the Nijmegen potentials NijmI and NijmII, the Bonn potential CD-Bonn, and the Moscow potential involving forbidden states. A parametrization of the nucleon form factors that complies with present-day experimental results was used as input data. The results of the calculations that employ all of the above potential types describe experimental data at least up to Q ≈ 5 fm−1.

Hadron Structure Within the Point Form of Relativistic Quantum Mechanics

We present an outline of recent developments in the field of hadron form-factor calculations within constituent-quark models using the point form of relativistic quantum mechanics. Our method to calculate currents and form factors is exemplified by means of the weak B → D transition. We present results for weak B → D transition form factors in the space- and the time-like momentum-transfer region. We discuss how wrong cluster properties, which one has to deal with when employing relativistic quantum mechanics, affect these form factors and we estimate the role non-valence, Z-graph contributions may play for decay kinematics.

EFFECTIVE DEGREES OF FREEDOM IN LOW-ENERGY QUANTUM CHROMODYNAMICS

Confinement and spontaneous breaking of chiral symmetry are assumed to generate the governing degrees of freedom of low-energy quantum chromodynamics. On this basis a relativistic constituent-quark model is constructed and formulated along an invariant mass operator within Poincaré-invariant quantum mechanics. The model is effectively applied to the spectroscopy of all known baryons of flavors u, d, s, c and b. The mass-operator eigenstates are furthermore tested with regard to the baryon electromagnetic and axial form factors. Through using the point form of relativistic quantum mechanics, these observables are obtained in a manifestly covariant manner. For all light and strange baryon ground states the electroweak structures are reproduced either in good agreement with phenomenology or, if no experimental data exist, in consistency with results available from lattice quantum chromodynamics. It is concluded that the relativistic constituent-quark model, relying on {QQQ} Fock states only, provides a universal framework for the description of low-energy baryons. The most important ingredients are spontaneous chiral-symmetry breaking and strict relativistic invariance.

Electroweak form factors of heavy-light mesons: A relativistic point-form approach

We present a general relativistic framework for the calculation of the electroweak structure of heavy-light mesons within constituent-quark models. To this aim the physical processes in which the structure is measured, i.e., electron-meson scattering and semileptonic weak decays, are treated in a Poincar\'e-invariant way by making use of the point form of relativistic quantum mechanics. The electromagnetic and weak meson currents are extracted from the $1\mathrm{\text{\ensuremath{-}}}\ensuremath{\gamma}$- and $1\mathrm{\text{\ensuremath{-}}}W$-exchange amplitudes that result from a Bakamjian-Thomas type mass operator for the respective systems. The covariant decomposition of these currents provides the electromagnetic and weak (transition) form factors. Problems with cluster separability, which are inherent in the Bakamjian-Thomas construction, are discussed and it is shown how to keep them under control. It is proved that the heavy-quark limit of the electroweak form factors leads to one universal function, the Isgur-Wise function, confirming that the requirements of heavy-quark symmetry are satisfied. A simple analytical expression is given for the Isgur-Wise function and its agreement with a corresponding front-form calculation is verified numerically. Electromagnetic form factors for ${B}^{\ensuremath{-}}$ and ${D}^{+}$ and weak $B\ensuremath{\rightarrow}{D}^{(*)}$ decay form factors are calculated with a simple harmonic-oscillator wave function and heavy-quark symmetry breaking due to finite masses of the heavy quarks is discussed.

RQM description of PS meson form factors, constraints from space-time translations and underlying dynamics

The role of Poincar\'e covariant space-time translations is investigated in the case of the pseudoscalar-meson charge form factors. It is shown that this role extends beyond the standard energy-momentum conservation, which is accounted for in all relativistic quantum mechanics calculations. It implies constraints that have been largely ignored until now but should be fulfilled to ensure the full Poincar\'e covariance. The violation of these constraints, which is more or less important depending on the form of relativistic quantum mechanics that is employed, points to the validity of using a single-particle current, which is generally assumed in calculations of form factors. In short, these constraints concern the relation of the momentum transferred to the constituents to the one transferred to the system. How to account for the related constraints, as well as restoring the equivalence of different relativistic quantum mechanics approaches in estimating form factors, is discussed. Some conclusions relative to the underlying dynamics are given in the pion case.

Three-particle model of the pion-nucleon system

A relativistic, three-particle model of the pion-nucleon system is constructed in the instant form of relativistic quantum mechanics using the Bakamjian-Thomas procedure. The model space includes subspaces for the nucleon $(N)$, the resonances $\ensuremath{\Delta}={P}_{33}(1232)$, ${P}_{11}(1440)$, ${D}_{13}(1520)$, ${S}_{11}(1535)$, and ${S}_{31}(1620)$, as well as $\ensuremath{\pi}N$, $\ensuremath{\pi}\ensuremath{\Delta}$, $\ensuremath{\eta}N$, and $\ensuremath{\pi}\ensuremath{\pi}N$ subspaces. The model specifies a Poincar\'e invariant mass operator that includes vertex interactions that couple the various subspaces, as well as renormalization terms. Projection operator techniques are used to reduce the equations arising from this mass operator to a set of three-dimensional Lippmann-Schwinger integral equations that couple only the $\ensuremath{\pi}N$, $\ensuremath{\pi}\ensuremath{\Delta}$, and $\ensuremath{\eta}N$ channels. After a partial wave analysis these three-dimensional equations simplify to three coupled, one-dimensional integral equations for each partial wave. The mass operator interactions are derived from effective, hadronic Lagrangians that introduce a set of coupling constants. Cutoff functions are introduced to take into account the nonelementary nature of the particles in the model. These cutoff functions introduce a set of cutoff masses. The coupling constants, cutoff masses, and bare baryon masses are determined by fitting to a partial wave analysis of pion-nucleon elastic scattering up to a c.m. energy of $W=1550$ MeV.

Exclusive electrodisintegration of the deuteron within the point form of relativistic quantum mechanics

The process of exclusive deuteron electrodisintegration is considered within the point form of relativistic quantum mechanics. Relevant calculations are performed on the basis of the Nijmegen and Moscow nucleon-nucleon potentials, the latter involving forbidden states. Final-state interaction is taken into account. For either type of the potentials used, the results of the calculations describe well experimental data at final-neutron momenta p n of up to 500 MeV/c.

Vector mesons in a relativistic point-form approach

We apply the point form of relativistic quantum mechanics to develop a Poincare invariant coupled-channel formalism for two-particle systems interacting via one-particle exchange. This approach takes the exchange particle explicitly into account and leads to a generalized eigenvalue equation for the Bakamjian-Thomas type mass operator of the system. The coupling of the exchange particle is derived from quantum field theory. As an illustrative example we consider vector mesons within the chiral constituent quark model in which the hyperfine interaction between the confined quark-antiquark pair is generated by Goldstone-boson exchange. We study the effect of retardation in the Goldstone-boson exchange by comparing with the commonly used instantaneous approximation. As a nice physical feature we find that the problem of a too large $\rho$-$\omega$ splitting can nearly be avoided by taking the dynamics of the exchange meson explicitly into account.

Validity of the one-body current for the calculation of form factors in the point form of relativistic quantum mechanics

Form factors are calculated in the point form of relativistic quantum mechanics for the lowest energy states of a system made of two scalar particles interacting via the exchange of a massless boson. They are compared to the exact results obtained by using solutions of the Bethe-Salpeter equation which are well known in this case (Wick-Cutkosky model). The relevance of the comparison is examined by considering other relativistic quantum-mechanics approaches where results are known or have been obtained recently. Deficiencies of the point-form approach together with the single-particle current are emphasized. They point to quite sizeable contributions of two-body currents. These ones are required to fulfil current conservation in any case and to reproduce the high momentum transfer behaviour expected from the Born amplitude.

Poincaré-Invariant Coupled-Channel Models for Meson Photoproduction

A general procedure for constructing Poincare-invariant mass operators in a helicity basis is presented. The procedure is developed in the framework of the instant form of relativistic quantum mechanics, but it can be easily extended to other forms. The method is used to extend a previously developed Poincare-invariant coupled-channel model for the pion-nucleon system to include a photon-nucleon channel. This makes it possible to carry out calculations on photoproduction from nucleons that satisfy exactly the requirements of special relativity. Methods are given for deriving potentials that couple the photon-nucleon channel to the pion-nucleon channel. These potentials are invariant under gauge transformations of the photon's polarization vector. Amplitudes obtained by solving the Lippmann-Schwinger equations that arise from the Poincare-invariant mass operators satisfy unitarity, and hence Watson's theorem for photoproduction amplitudes. The methods presented can also be used to develop models for the photoproduction of \(\) and \(\) mesons, as well as vector mesons.

Relativistic model of two-quark composite systems

Relativistic two-particle composite quark systems are described in the framework of the instant form of relativistic quantum mechanics. A correct description of the spin properties of such composite systems, including relativistic spin rotation is obtained.

Dirac’s form of relativistic quantum mechanics

It is shown that Dirac’s ’’instant form’’ dynamics provides a theoretical framework in which models of relativistic quantum mechanics can be constructed. The convariant harmonic oscillator formalism discussed in previous papers is shown to be such a model. Dirac’s ’’point’’ and ’’front’’ forms are shown to generate a space-time geometry convenient for describing Lorentz deformation properties of relativistic extended hadrons.