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B. L. G. Bakker

Publications and source records attributed to B. L. G. Bakker.

At least 55 records · Page 3Linked to original sources
arXiv2002

Light-meson orbital excitations in the QCD string approach

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 $σ$ as the only parameter. The Regge slope $α'_L$ and the intercept $α_L(0)$ of the Regge L-trajectory for $\bar{M}(nL)$ are calculated analytically and turn out to be $α'_L = 0.80$ GeV${}^{-2}$ (for $L \leq 4$) and $α_L(0) = -0.34$, in good agreement with the experimental data: $α'_{L {\rm exp}} = 0.81 \pm 0.01$ GeV${}^{-2}$, $α_{L {\rm exp}}(0) = -0.30 \pm 0.02$. To obtain this strong agreement with the data the nonperturbative quark self-energy contributions to the meson masses must be taken into account, which appeared to be large and negative for small values of L, and are even for larger values of L important for a close fit. From the present analysis of the meson spectra the restriction $α_s \leq 0.40$ on the strong coupling is required.

hep-ph↗
arXiv2002

Light meson radial Regge trajectories

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 suppression and a favorable gain in the action, produced by holes, creates a new metastable (predecay) stage with a renormalized string tension which now depends on the separation r. This results in smaller values of the slope of the radial Regge trajectories, in good agreement with the analysis of experimental data in [Ref.3]

hep-ph↗
arXiv2002

Relativistic bound-state calculations in Light Front Dynamics

We calculated bound states in the quantum field theoretical approach. Using the Wick-Cutkosky model and an extended version of this model (in which a particle with finite mass is exchanged) we have calculated the bound states in the scalar case.

hep-ph↗
arXiv2001

Frame Dependence of Spin-One Angular Conditions in Light Front Dynamics

We elaborate the frame dependence of the angular conditions for spin-1 form factors. An extra angular condition is found in addition to the usual angular condition relating the four helicity amplitudes. Investigating the frame-dependence of the angular conditions, we find that the extra angular condition is in general as complicated as the usual one, although it becomes very simple in the $q^+ = 0$ frame involving only two helicity amplitudes. It is confirmed that the angular conditions are identical in frames that are connected by kinematical transformations. The high $Q^2$ behaviors of the physical form factors and the limiting behaviors in special reference frames are also discussed.

hep-ph↗
arXiv2001

Nonperturbative hyperfine contribution to the $b_1$ and $h_1$ meson masses

Due to the nonperturbative contribution to the hyperfine splitting the mass of the $n^1P_1$ state is strongly correlated with the center of gravity $M_{\rm cog}(n^3P_J)$ of the $n^3P_J$ multiplet: $M(n^1P_1)$ is less than $M_{\rm cog}(n^3P_J)$ by about 40 MeV (20 MeV) for the 1P (2P) state. For $b_1(1235)$ the agreement with experiment is reached only if $a_0(980)$ belongs to the $1^3P_J$ multiplet. The predicted mass of $b_1(2^1P_1)$ is $\approx 1620$ MeV. For the isoscalar meson a correlation between the mass of $h_1$(1170) $(h_1(1380))$ and $M_{cog}(1^3P_J)$ composed from light (strange) quarks also takes place.

hep-ph↗
arXiv2001

The scalar field-theoretical Coulomb problem

We analyze the fully relativistic, field-theoretical treatment of the scalar Coulomb problem. We work in a truncated Hilbert-Fock space containing the two-constituent states and the two-constituent-and-one-massless-exchange-particle states. Self-energy contributions are dominant for large values of the coupling constant. Using the covariant formulation of the self-energy does not alter these results significantly. Both the weak-coupling limit and the heavy-mass limit lead to the non-relativistic results.

hep-ph↗
arXiv2000

Short Range Linear Potential in 3D Lattice Compact QED

We study the static potential between electric charges in the finite temperature three dimensional compact gauge theory on the lattice. We show that in the deconfinement phase at small separations between the charges the potential contains a linearly rising piece which goes over into the Coulomb potential as the distance between the charges is increased. The linear potential is due to the gas of magnetic dipoles which are realized as monopole-antimonopole bound states.

hep-lat↗
arXiv2000

Techniques for solving bound state problems

We have used different methods to obtain the bound states of a Hamiltonian of a relativistic two scalar particle system in a local potential. The potentials we are interested in are binding and confining potentials, that are associated with particle exchange. The issues we concentrate on when comparing the different methods are ease of numerical implementation, accuracy and stability. To check our codes we have made use of several potentials for which the bound states are known in the nonrelativistic situation. Finally we calculate the bound states for the Yukawa potential in the relativistic situation and look at the collapse of the wave functions in this situation.

hep-ph↗
arXiv2000

Effective theory of NN interactions in a separable representation

We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation allows for the explicit solution of the Lippmann-Schwinger equation and a consistent renormalization procedure. The phase shifts in the $^1S_0$ channel are calculated to subleading order.

hep-ph↗
arXiv2000

Strong coupling constant from bottomonium fine structure

From a fit to the experimental data on the $b\bar{b}$ fine structure, the two-loop coupling constant is extracted. For the 1P state the fitted value is $α_s(μ_1) = 0.33 \pm 0.01(exp)\pm 0.02 (th)$ at the scale $μ_1 = 1.8 \pm 0.1$ GeV, which corresponds to the QCD constant $Λ^{(4)}(2-loop) = 338 \pm 30$ MeV (n_f = 4) and $α_s(M_Z) = 0.119 \pm 0.002. For the 2P state the value $α_s(μ_2) = 0.40 \pm 0.02(exp)\pm 0.02(th)$ at the scale $μ_2 = 1.02 \pm 0.2$ GeV is extracted, which is significantly larger than in the previous analysis of Fulcher (1991) and Halzen (1993), but about 30% smaller than the value given by standard perturbation theory. This value $α_s(1.0) \approx 0.40$ can be obtained in the framework of the background perturbation theory, thus demonstrating the freezing of $α_s$. The relativistic corrections to $α_s$ are found to be about 15%.

hep-ph↗
arXiv2000

Disentangling Intertwined Embedded States and Spin Effects in Light-Front Quantization

Naive light-front quantization, carried out by a light-front energy integration of covariant amplitudes, is not guaranteed to generate the corresponding Feynman amplitudes. In an explicit example we show that the nonvalence contribution to the minus-component of the EM current of a meson with fermion constituents has a persistent end-point singularity. Only after this term is subtracted, the result is covariant and satisfies current conservation. If the spin-1/2 constituents are replaced by spin zero ones, the singularity does not occur and the result is, without any adjustment, identical to the Feynman amplitude. Numerical estimates of valence and nonvalence contributions are presented for the cases of fermion and boson constituents.

hep-th↗
arXiv1999

Fine structure splittings of excited P and D states in charmonium

It is shown that the fine structure splittings of the $2 ^3P_J$ and $3 ^3P_J$ excited states in charmonium are as large as those of the $1^3P_J$ state if the same $α_s(μ)\approx 0.36$ is used. The predicted mass $M(2 ^3P_0)=3.84$ GeV appears to be 120 MeV lower that the center of gravity of the $2 ^3P_J$ multiplet and lies below the $D\bar D^*$ threshold. Our value of $M(2 ^3P_0)$ is approximately 80 MeV lower than that from the paper by Godfrey and Isgur while the differences in the other masses are $\la 20$ MeV. Relativistic kinematics plays an important role in our analysis.

hep-ph↗
arXiv1998

Entanglement of Fock-space expansion and covariance in light-front Hamiltonian dynamics

We investigate in a model with scalar ``nucleons'' and mesons the contributions of higher Fock states that are neglected in the ladder approximation of the Lippmann-Schwinger equation. This leads to a breaking of covariance, both in light-front and in instant-form Hamiltonian dynamics. The lowest Fock sector neglected has two mesons in the intermediate state and corresponds to the stretched box. First we show in a simplified example that the contributions of higher Fock states are much smaller on the light-front than in instant-form dynamics. Then we show for a scattering amplitude above threshold that the stretched boxes are small, however, necessary to retain covariance. For an off energy-shell amplitude covariance is not necessarily maintained and this is confirmed by our calculations. Again, the stretched boxes are found to be small.

hep-ph↗
arXiv1998

Equivalence of renormalized covariant and light-front perturbation theory: II. Transverse divergences in the Yukawa model

Light-front dynamics can only become a viable alternative to the covariant approach if doubts about its covariance can be taken away. As a minimal requirement we take that the physical quantities calculated with light-front perturbation theory are the same as those obtained using covariant perturbation theory. If this situation occurs, we use the word equivalent to characterize it. For quantities that involve the calculation of superficially convergent diagrams, proofs of equivalence exist. For some types of divergent diagrams the proof of equivalence is complicated. Longitudinal divergences were dealt with in Part I. (hep-ph/9702311). In Part II we deal with diagrams with transverse divergences. Our method is based on minus regularization, which is inspired on BPHZ regularization. In a calculation using numerical methods we show how to obtain a rotationally invariant amplitude for two triangle diagrams contributing to the decay of a scalar boson in the Yukawa model. It concludes our proof of equivalence of covariant and light-front perturbation theory.

hep-ph↗
arXiv1998

Equivalence of renormalized covariant and light-front perturbation theory: I. Longitudinal divergences in the Yukawa model

Light-front perturbation theory has been proposed as an alternative to covariant perturbation theory. Light-front perturbation theory is only acceptable if it produces invariant S-matrix elements. Doubts have been raised concerning the equivalence of light-front and covariant perturbation theory. One of the obstacles to a rigorous proof of equivalence is the occurrence of longitudinal divergences not present in covariant perturbation theory. We show in the case of the Yukawa model of fermions interacting with scalar bosons at the one-loop level how to deal with the longitudinal divergences. Invariant S-matrix elements are obtained using our method.

hep-ph↗
arXiv1998

Properties of Abelian Monopoles in SU(2) Lattice Gluodynamics

We discuss some properties of abelian monopoles in the Maximal Abelian projection of the SU(2) lattice gluodynamics. We show that in the maximal abelian projection abelian monopoles carry fluctuating electric charge and that the monopole currents are correlated with the magnetic and the electric parts of the SU(2) action density.

hep-lat↗