Bernard Bakker

Vrije Universiteit Amsterdam | VU · Department of Physics and Astronomy

The masses of excited charmed mesons are shown to decrease by $\sim (50-150)$~MeV due to a flattening of the confining potential at large distances, which effectively takes into account open decay channels. The scale of the mass shifts is similar to that in charmonium for $\psi(4660)$ and $\chi_{c0}(4700)$. The following masses of the first excitat...

The spectra of heavy quarkonia are studied in two approaches: with the use of the Afonin-Pusenkov representation of the Regge trajectories for the squared excitation energy E2(nl) (ERT) and using the relativistic Hamiltonian with the universal interaction. The parameters of the ERTs are extracted from the experimental masses and in both cases, bott...

The spectrum of the \(s\bar{s}\) mesons is studied performing a phenomenological analysis of the Regge trajectories defined for the excitation energies. For the \(\phi (3\,^3S_1)\) state the mass \(M(\phi (3S))=2100(20)\) MeV and the leptonic width \(\varGamma _{ee}(\phi (3S))=0.27(2)\) keV are obtained, while the mass of the \(2\,^3D_1\) state, \(...

The dynamical picture of a quark-antiquark interaction in light mesons, which provides linearity of radial and orbital Regge trajectories (RT), is studied with the use of the relativistic string Hamiltonian with flattened confining potential (CP) and taking into account three negative corrections: the gluon-exchange, the self-energy, and the string...

We discuss the electroproduction of a pseudoscalar (0−+) meson or a scalar (0++) meson off the scalar target. The most general formulation of the differential cross section for the 0−+ or 0++ meson process involves only one or two hadronic form factors, respectively, on a scalar target. The Rosenbluth-type separation of the differential cross secti...

The number of Compton form factors of a scalar hadron is known to be three. It may be expected that depending on the structure of that hadron, it may occur that in some kinematical regimes the observables are only sensitive to one dominant form factor. Here we show in a particular kinematic situation that one may perform an experiment that unequivo...

The spectrum of the $s\bar s$ mesons is studied performing a phenomenological analysis of the Regge trajectories defined for the excitation energies. For the $\phi(3 ^3S_1)$ state the mass $M(\phi(3S))=2100(20)$ MeV and the leptonic width $\Gamma_{ee}(\phi(3S))=0.27(2)$ keV are obtained, while the mass of the $2 ^3D_1$ state, $M(\phi(2 ^3D_3))=2180...

The dynamical picture of a quark-antiquark interaction in light mesons, which provides linearity of radial and orbital Regge trajectories (RT), is studied with the use of the relativistic string Hamiltonian with flattened confining potential and taking into account the self-energy and string corrections. Due to the flattening effect both slopes, $\...

We discuss the electroproduction of scalar ($0^{++}$) or pseudoscalar ($0^{-+}$) meson production off the scalar target. The most general formulation of the differential cross section for the $0^{-+}$ or $0^{++}$ meson production process involves only one or two hadronic form factors, respectively, on a scalar target. The Rosenbluth type separation...

The leptonic widths of high $\psi$-resonances are calculated in a coupled-channel model with unitary inelasticity, where analytical expressions for mixing angles between $(n+1)\,^3S_1$ and $n\,^3D_1$ states and probabilities $Z_i$ of the $c\bar c$ component are derived. Since these factors depend on energy (mass), different values of mixing angles...

Current conservation is a vital condition in electrodynamics. We review the literature concerning the ways to ensure that the formalism used in calculating amplitudes for the scattering of charged particles is in compliance with current conservation. For the case of electron scattering off a scalar and a spin-1/2 target as well as Compton scatterin...

Using deeply virtual Compton scattering as a tool to study the structure of hadrons in an exclusive process, one expresses the amplitudes in terms of invariant quantities: the Compton form factors. In this paper the sensitivity of the hadronic part of the cross section to the Compton form factors is determined.

It is shown that two physical phenomena are important for high excitations: (i) the screening of the universal gluon-exchange potential and (ii) the flattening of the confining potential owing to creation of quark loops, and both effects are determined quantitatively. Taking the first effect into account, we predict the masses of the ground states...

When deeply virtual Compton scattering is used as a tool to study the structure of hadrons in an exclusive process, one way to analyze this process is to express the amplitudes in terms of generalized parton distributions (GPDs). The definition of the latter quantities requires a special kinematics, that cannot always be realized in experiments. Th...

Radiative decays of $X(3872)$ are studied in single-channel approximation (SCA) and in the coupled-channel (CC) approach, where the decay channels $D\bar D^*$ are described with the string breaking mechanism. In SCA the transition rate $\tilde{\Gamma}_2=\Gamma(2\,{}^3P_1 \rightarrow \psi\gamma)=71.8$~keV and large $\tilde{\Gamma}_1=\Gamma(2\,{}^3P_...

An outstanding goal of physics is to find solutions that describe hadrons in the theory of strong interactions, Quantum Chromodynamics (QCD). For this goal, the light-front Hamiltonian formulation of QCD (LFQCD) is a complementary approach to the well-established lattice gauge method. LFQCD offers access to the hadrons' nonperturbative quark and gl...

We study the universal static potential V st(r) and the force, which are fully determined by two fundamental parameters: the string tension σ = 0.18 ± 0.02 GeV2 and the QCD constants ΛMS̄(nf) taken from pQCD, while the infrared (IR) regulator M B is taken from the background perturbation theory and expressed via the string tension. The vector coupl...

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the...

Four-fermion operators have been utilized in the past to link the quark-exchange processes in the interaction of hadrons with the effective meson-exchange amplitudes. In this presentation, we apply the similar idea of Fierz rearrangement to the electromagnetic processes and focus on the electromagnetic form factors of nucleon and electron. We expla...

With the acceptance of QCD as the fundamental theory of strong interactions, one of the basic problems in the analysis of nuclear phenomena became how to consistently account for the effects of the underlying quark/gluon structure of nucleons and nuclei. Besides providing more detailed understanding of conventional nuclear physics, QCD may also poi...

Deeply virtual Compton scattering has been proposed as a tool to study the structure of hadrons in an exclusive process. The Compton-scattering amplitude can be expressed in terms of scalar quantities, the Compton form factors. Their number depends on the spin of the target as well as the virtuality of the incoming and outgoing photons. For high va...

During the 22nd European Few-Body Conference, a session was devoted to a panel discussion on the future of few-body physics. The panel members were Charlotte Elster, Jaume Carbonell, Evgeny Epelbaum, Nasser Kalantar-Nayestanaki, and Jean-Marc Richard. The session was chaired by Ben Bakker. After presentations by the panel members, several topics we...

An outstanding goal of physics is to find solutions that describe hadrons in the theory of strong interactions, Quantum Chromodynamics (QCD). For this goal, the light-front Hamiltonian formulation of QCD (LFQCD) is a complementary approach to the well-established lattice gauge method. LFQCD offers access to the hadrons' nonperturbative quark and gl...

Four-fermion operators have been utilized in the past to link the quark-exchange processes in the interaction of hadrons with the effective meson-exchange amplitudes. In this paper, we apply the similar idea of a Fierz rearrangement to the electromagnetic processes and focus on the electromagnetic form factors of the nucleon and the electron. We ex...

We study the universal static potential $V_{\rm st}(r)$ and the force, which are fully determined by two fundamental parameters: the string tension $\sigma=0.18\pm 0.02$ GeV$^2$ and the QCD constants $\Lambda_{\bar{\rm MS}}(n_f)$, taken from pQCD, while the infrared (IR) regulator $M_{\rm B}$ is taken from the background perturbation theory and exp...

We review the interface between the current theoretical framework based on generalized parton distributions (GPDs) and experimental measurements of deeply virtual Compton scattering (DVCS) observables. We find that the present theoretical framework needs to be extended to cover the current and future DVCS experiments. The current formulation is bas...

Four-fermion operators have been utilized in the past to link the quarkexchange processes in the interaction of hadrons with the effective mesonexchange amplitudes. In this paper, we apply the similar idea of Fierz rearrangement to the electromagnetic processes and focus on the electromagnetic form factors of nucleon and electron. We explain the mo...

We show that there are two reasons why the partial width for the transition Γ1(Υ(3S)→γ+χb1(1P)) is suppressed. First, the spin-averaged matrix element I(3S|r|1PJ)̅ is small, being equal to 0.023 GeV-1 in our relativistic calculations. Secondly, the spin-orbit splittings produce relatively large contributions, giving I(3S|r|1P2)=0.066 GeV-1, while d...

Radiative decays of X(3872) with JPC=1++ are studied in the coupled-channel approach, where the cc̅ states are described by the relativistic string Hamiltonian, while for the decay channels DD* a string-breaking mechanism is used. Within this method a sharp peak and correct mass shift of the 23P1 charmonium state just to the D0D*0 threshold was alr...

Light-front dynamics(LFD) plays an important role in the analyses of relativistic few-body systems. As evidenced from the recent studies of generalized parton distributions (GPDs) in hadron physics, a natural framework for a detailed study of hadron structures is LFD due to its direct application in Minkowski space as well as its distinct feature o...

Generalized Parton Distributions (GPDs) in Deeply Virtual Compton Scattering (DVCS) have been widely recognized and used as a useful tool to explore the quark and gluon structure of the target hadrons. However, we recently pointed out treacherous kinematic issues in analyzing DVCS in terms of GPDs. We present our key findings in the simplest possib...

Whether the kinematics includes the hard transverse photon momenta or not makes a dramatic difference in computing deeply virtual Compton scattering in terms of the widely used reduced operators that define generalized parton distributions. Our tree-level complete deeply virtual Compton scattering amplitude including the lepton current plays the ro...

Virtual Compton scattering (VCS) can be used to explore the structure of hadrons. In the domain of large energy and momentum transfers, VCS is complementary to deep-inelastic scattering. If the kinematics is collinear, generalized parton distributions (GPDs) are widely used to describe VCS. This formulation satisfies electromagnetic gauge invarianc...

The masses of higher $D(nL)$ and $D_s(nL)$ excitations are shown to decrease due to the string contribution, originating from the rotation of the QCD string itself: it lowers the masses by 45 MeV for $L=2 (n=1)$ and by 65 MeV for $L=3 (n=1)$. An additional decrease $\sim 100$ MeV takes place if the current mass of the light (strange) quark is used...

Whether the kinematics includes the hard transverse photon momenta or not makes a dramatic difference in computing deeply virtual Compton scattering (DVCS) in terms of the widely used reduced operators that define generalized parton distributions (GPDs). We present a tree-level complete DVCS amplitude including the lepton current which plays the ro...

Calculations in light-front quantization are sometimes found to lead to singularities that are not present in the corresponding manifestly covariant treatment. We give some examples that were found in the framework of perturbation theory, but must also occur in nonperturbative calculations. In the case of anomalies, regularization-scheme dependence...

Hyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the $B_q$ (q=n,s) mesons are shown to be in full agreement with experiment if a universal coupling $\alpha_{HF}=0.310$ is taken in perturbative spin-spin potential. It gives $M(B^*)-M(B)=45.7(3)$ MeV...

A universal description of the hyperfine splittings (HFS) in bottomonium and the B{sub q} (q=n, s, c) mesons is obtained with a universal strong coupling constant {alpha}{sub s}({mu})=0.310 in a spin-spin potential. Other characteristics are calculated within the field correlator method, taking the freezing value of the strong coupling independent...

Compton scattering provides a unique tool for studying hadron structure. In contrast to elastic electron scattering, which provides information about the hadron’s structure in terms of form factors, Compton scattering is more versatile, as the basic process is the coupling of two electro-magnetic currents. Therefore, the hadronic structure can be d...

In deeply virtual Compton scattering (DVCS) it is found that in some kinematics angular momentum is not conserved if the amplitudes are calculated in terms of widely used reduced operators. Consequently, those kinematics will lead to the wrong analysis of experimental data in terms of generalized parton distributions. Contrary to common lore, the c...

Deeply virtual Compton scattering is proposed as a way to probe hadronic matter beyond generalized parton distributions. In this paper, it is argued that depending on the kinematics used, some singularities may occur that render the connection between the experimental data and the generalized parton distributions problematic.

We discuss the issue of extracting the generalized parton distribution (GPD) from deeply virtual Compton scattering (DVCS). We focus our discussion on the fermion propagator between the two photons in the handbag diagram taking the well-known kinematics frequently used in the light-front dynamics (LFD). We compare the results between the full calcu...

We put forward a proposal for a benchmark calculation of the deuteron form factors. The purpose of the benchmark is to define more accurately what we mean by 'relativistic effects'. A first step to that goal is made here: We define a model Lagrangean in the spirit of the Walecka model, namely one having only a scalar meson σ, and a vector one, ω. I...

We discuss the issue of kinematics in computing deeply virtual Compton scattering (DVCS) in terms of the widely used reduced operators that define generalized parton distributions (GPDs). Analyzing the complete tree level Compton scattering process which includes the lepton part of the amplitude, we find a dramatic difference in the result dependin...

A universal description of the hyperfine splittings (HFS) in bottomonium and the $B_q (q=n,s,c)$ mesons is obtained with a universal strong coupling constant $\alpha_s(\mu)=0.305(2)$ in a spin-spin potential. Other characteristics are calculated within the Field Correlator Method, taking the freezing value of the strong coupling independent of $n_f...

The dielectron widths of ψ(4040), ψ(4160), and ψ(4415), and their ratios are shown to be in good agreement with experiment, if in all cases the S-D mixing with a large mixing angle θ ≅ 34° is taken. Arguments are presented why continuum states give small contributions to the wave functions at the origin. We find that the Y (4360) resonance, conside...

The dielectron widths of $\Upsilon(nS) (n=1,...,7)$ and vector decay constants are calculated using the Relativistic String Hamiltonian with a universal interaction. For $\Upsilon(nS) (n=1,2,3)$ the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For $\Upsilon(10580)$ and $\Upsilon(11020)$ a good agreeme...

The possibility to observe new bottomonium states with $J^{PC}= 1^{--}$ in the region $10.7-11.1$ GeV is discussed. The analysis of the di-electron widths shows that the $(n+1)^3S_1$ and $n^3D_1$ states ($n\geq 3$) may be mixed with a rather large mixing angle, $\theta\sim30^\circ$ and this effect provides the correct values of $\Gamma_{ee}(\Upsilo...

Heavy-light mesons masses and decay constants are calculated within the framework of the field correlator model. Good agreement is obtained with the experimental data.

Since Dirac wrote his famous article on forms of relativistic dynamics, it has been realized that the front form, or light-front dynamics, is ideally suited for the solution of the bound state problem in quantum field theory. Still, it is useful to know what the other forms are and what makes the front form so well-adapted to non-perturbative probl...

There exist several types of monopole - like topological defects in Electroweak theory. We investigate properties of these objects using lattice numerical methods. The intimate connection between them and the dynamics of the theory is established. We find that the density of Nambu monopoles cannot be predicted by the choice of the initial parameter...

It is shown that a 25(20)% difference between the decay constants fDs f_{D_s } (fBsf_{B_s} ) and f D (f B ) occurs due to large differences in the pole masses of the s and d(u) quarks. The values η D = fDs f_{D_s } /f D ∼ 1.23(15), recently observed in the CLEO experiment, and η B = fBs f_{B_s } /f B ∼ 1.20, obtained in unquenched lattice QCD,...

Deeply virtual Compton scattering has been recognized as a tool to obtain information about hadronic wave functions from experimental data. Light-front dynamics provides boost-invariant and process-independent wave functions, which makes it the preferred theoretical tool to analyze those data. The purpose of the present work is to apply it to a mod...

The hyperfine splittings in heavy quarkonia are studied in a model-independent way using experimental data on dielectron widths. Relativistic correlations are taken into account together with the smearing of spin-spin interaction. The radius of smearing is fixed by known G/ψ−η c(1S), ψ(2S)−η c′(2S) splittings, which appears to be small, r ss ≅ 0.06...

We investigated numerically properties of Nambu monopoles in lattice Electroweak theory at realistic values of $\alpha$ and $\theta_W$. Our choice of parameters of lattice Lagrangian corresponds to large values of the Higgs boson mass $M_H > 2 M_W$. We find that the density of Nambu monopoles cannot be predicted by the choice of the initial paramet...

We considered the lattice electroweak theory at realistic values of $\alpha$ and $\theta_W$ and for large values of the Higgs mass. We investigated numerically the properties of topological objects that are identified with quantum Nambu monopoles. We have found that the action density near the Nambu monopole worldlines exceeds the density averaged...

The Yukawa model is discussed in Light-Front Dynamics. Different types of singularities that may occur are mentioned. Two cases are treated in detail: The fermion self energy and the box diagram.

It is shown that a 25(20)% difference between the decay constants $f_{D_s}(f_{B_s})$ and $f_D(f_B)$ occurs due to large differences in the pole masses of the $s$ and $d(u)$ quarks. The values $\eta_D =f_{D_s}/f_D\approx 1.23(15)$, recently observed in the CLEO experiment, and $\eta_B=f_{B_s}/f_B\approx 1.20$, obtained in unquenched lattice QCD, can...

Meson Green's functions and decay constants $f_{\Gamma}$ in different channels $\Gamma$ are calculated using the Field Correlator Method. Both, spectrum and $f_\Gamma$, appear to be expressed only through universal constants: the string tension $\sigma$, $\alpha_s$, and the pole quark masses. For the $S$-wave states the calculated masses agree with...

The hyperfine splittings in heavy quarkonia are studied using new experimental data on the di-electron widths. The smearing of the spin spin interaction is taken into account, while the radius of smearing is fixed by the known J/ψ-η(1S) and ψ(2S)-ηc‧(2S) splittings and appears to be small, r≈0.06 fm. Nevertheless, even with such a small radius an e...

Light-front dynamics(LFD) plays an important role in hadron phenomenology. Last few years, however, it has been emphasized that treacherous points such as zero-mode contributions should be taken into account for successful LFD applications to hadron phenomenology. We discuss examples of treacherous points and present new progresses made last few ye...

We present a light-front calculation of the box diagram in Yukawa theory. The covariant box diagram is finite for the case of spin-1/2 constituents exchanging spin-0 particles. In light-front dynamics, however, individual time-ordered diagrams are divergent. We analyze the corresponding light-front singularities and show the equivalence between the...

The relativistic string Hamiltonian is used to calculate the masses and decay constants of $B_q$ mesons: they appear to be expressed through onlythree fundamental values: the string tension $\sigma $, $\alpha_s$, and the quark pole masses. The values $f_B =186 $ MeV, $f_{B_s}= 222$ MeV are calculated while $f_{B_c}$ depends on the $c$-quark pole ma...

In light-front dynamics singularites may appear in time-ordered amplitudes that are absent in the manifestly covariant treatment of a system described by the same Lagrangian. Examples are discussed for the case of the Yukawa model. It is shown that both instantaneous contributions to the fermion propagator and higher Fock components are needed to r...

We consider the lattice realization of the Standard Model with an additional Z6 symmetry. Numerical simulations were performed on the asymmetric lattice, which corresponds to the finite temperature theory. Our choice of parameters corresponds to large Higgs masses (MH>90GeV). The phase diagram was investigated and has been found to be different fro...

The precision measurement of the hyperfine splitting, ΔHF(1P, c-c) = M cog(xcJ) — M(h c), in the Fermilab-E835 and CLEO experiments allows one to determine the gluonic condensate G 2 with high accuracy if the gluonic correlation length T g is fixed. In our calculations, the negative value of ΔHF = −0.5 ± 0.4 MeV, as in the E835 experiment, is obtai...

Light-front dynamics(LFD) plays an important role in hadron phenomenology as evidenced from recent development of generalized parton distributions and other quantities involving hadrons. For successful LFD applications to hadron phenomenology, however, treacherous points such as zero-mode contributions should be taken into account. For a concrete e...

We discuss a treacherous point in light-front dynamics (LFD) which should be taken into account to restore complete equivalence with the manifestly covariant formalism. We present examples that require an inclusion of the arc contribution in the light-front energy contour integration in order to achieve the equivalence between the LFD result and th...

Sum rules, relating the total angular momentum of a nucleon to the spin and orbital angular momentum carried by its constituents, are interesting and important in understanding the internal structure of the nucleon. In a much cited paper, Jaffe and Manohar stressed the subtleties involved in deriving general angular momentum sum rules. As they poin...

An additional Z symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently [Phys. Lett. B 583 (2004) 379]. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In [Yad. Fiz. (2005)] we have reported our results on the numerical simulation of the electroweak sector of the mo...

Light-front dynamics (LFD) is like sweeping dirt to a corner to make the rest of the space clean. This feature allows many practical applications of LFD to the phenomenology of particle physics. To strengthen the practicality of LFD, however, it is necessary to check where the dirt is piled and to find ways to handle the associate complications. In...

In the calculation of the anomalous magnetic moment of W± bosons, we discuss vector anomalies occurring in the fermion loop that spoil the predictive power of the theory. While the previous analyses were limited to using essentially the manifestly covariant dimensional regulation method, we extend the analysis using both the manifestly covariant fo...

An additional Z 6 symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently. It has a singular nature and is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In this paper, we report our resu...

The precision measurement of the hyperfine splitting $\Delta_{\rm HF} (1P, c\bar c)=M_{\rm cog} (\chi_{cJ}) - M(h_c) = -0.5 \pm 0.4$ MeV in the Fermilab--E835 experiment allows to determine the gluonic condensate $G_2$ with high accuracy if the gluonic correlation length $T_g$ is fixed. In our calculations the negative value of $\Delta_{\rm HF} = -...

Agreement with the measured electronic widths of the resonances ψ(4040), ψ(4415) and Υ(11 019) is shown to be obtained if two effects are taken into account: (i) a flattening of the confining potential at distances r ≳ 1.2 fm, which gives a drop in the leptonic widths of high excitations of about 10-20%, but does not affect low-lying states, and (i...

Our purpose is to calculate relativistic bound states in a quantum filed theoretical approach. We work in the Yukawa model and first calculate the bound-state equation in the ladder approximation. We discuss why this is not a complete treatment and what possibilities there are to extend this equation.

In the calculation of the anomalous magnetic moment of $W^\pm$ bosons, we discuss vector anomalies occuring in the fermion loop that spoil the predictive power of the theory. While the previous analyses were limited to using essentially the manifestly covariant dimensional regularization method, we extend the analysis using both the manifestly cova...

We present a study of the tensorial structure of the hadronic matrix elements of the angular momentum operators $\bm{J}$. Well known results in the literature are shown to be incorrect, and we have taken pains to derive the correct expressions in three different ways, two involving explicit physical wave packets and the third, totally independent,...

From the fact that the nonperturbative self-energy contribution $C_{\rm SE}$ to the heavy meson mass is small: $C_{\rm SE}(b\bar{b})=0$; $C_{\rm SE}(c\bar{c})\cong -40$ MeV \cite{ref.01}, strong restrictions on the pole masses $m_b$ and $m_c$ are obtained. The analysis of the $b\bar{b}$ and the $c\bar{c}$ spectra with the use of relativistic (strin...

The $b\bar b$ spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings $\Delta_1= \Upsilon({\rm 1D})-\chi_b({\rm 1P})$ and other splittings are very sensitive to the QCD constant $\Lambda_V(n_f)$ which oc...

The hyperfine splitting for the $2S$ charmonium state is calculated and the predicted number is ${$\Delta${}}_{\mathrm{HF}}(2S)=57\ifmmode\pm\else\textpm\fi{}8\mathrm{MeV},$ being by derivation the lower bound of this splitting. It results in $M({$\eta${}}_{c}(2S))=3630\ifmmode\pm\else\textpm\fi{}8\mathrm{MeV},$ which is smaller by two standard dev...

We study the transition form factors between pseudoscalar and vector mesons using a covariant fermion field theory model in $(3+1)$ dimensions. Performing the light-front calculation in the $q^+ =0$ frame in parallel with the manifestly covariant calculation, we note that the suspected nonvanishing zero-mode contribution to the light-front current...

We found an additional symmetry hidden in the fermion and Higgs sectors of the Standard Model. It is connected to the centers of the SU(3) and SU(2) subgroups of the gauge group. A lattice regularization of the whole Standard Model is constructed that possesses this symmetry.

Form factors are extracted form current matrix elements. In a light-front calculation based on a simple field-theoretical model, we show that care must be exercised in the choice of the current components and the reference frame, lest the extracted form factors are unreliable.

Using the Wick-Cutkosky model and an extended version (massive exchange) of it, we have calculated the bound states in a quantum field theoretical approach. In the light-front formalism we have calculated the bound-state mass spectrum and wave functions. Using the Terent'ev transformation we can write down an approximation for the angular dependenc...

We consider the SU(2) lattice gauge model and investigate numerically the continuum limit of the simple center vortices which are singular configurations of the gauge fields. We found that the vortices remain alive in the continuum theory. Also we investigate the Creutz ratio and found that for all β it vanishes for those field configurations which...

A new physical mechanism is suggested to explain the universal depletion of high meson excitations. It takes into account the appearance of holes inside the string world sheet due to $q\bar{q}$ pair creation when the length of the string exceeds the critical value $R_1 \simeq 1.4$ fm. It is argued that a delicate balance between large $N_c$ loop su...

In the framework of the QCD string approach it is shown that the spin-averaged masses $\bar{M}(nL)$ of all low-lying light mesons are well described using the string tension $\sigma$ as the only parameter. The Regge slope $\alpha'_L$ and the intercept $\alpha_L(0)$ of the Regge L-trajectory for $\bar{M}(nL)$ are calculated analytically and turn out...

We study the form factors of vector mesons using a covariant fermion field theory model in $(3+1)$ dimensions. Performing a light-front calculation in the $q^+ =0$ frame in parallel with a manifestly covariant calculation, we note the existence of a nonvanishing zero-mode contribution to the light-front current $J^+$ and find a way of avoiding the...