arXiv subjects

B. L. G. Bakker

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

At least 37 records · Page 2Linked to original sources

arXiv2008

Lattice study of monopoles in the Electroweak theory

We investigated numerically properties of Nambu monopoles in lattice Electroweak theory at realistic values of $α$ and $θ_W$. 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 parameters of Electroweak theory and should be considered as the new external parameter of the theory. We also investigate the difference between the versions of Electroweak theory with the gauge groups $SU(2)\otimes U(1)$ and $SU(2)\otimes U(1)/Z_2$. We do not detect any difference at $α\sim {1/128}$. However, such a difference appears in the strong coupling region and is related to the properties of monopoles constructed of the hypercharge field.

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arXiv2007

Decay constants of the heavy-light mesons from the field correlator method

Meson Green's functions and decay constants $f_Γ$ in different channels $Γ$ are calculated using the Field Correlator Method. Both, spectrum and $f_Γ$, appear to be expressed only through universal constants: the string tension $σ$, $α_s$, and the pole quark masses. For the $S$-wave states the calculated masses agree with the experimental numbers within $\pm 5$ MeV. For the $D$ and $D_s$ mesons the values of $f_{\rm P} (1S)$ are equal to 210(10) and 260(10) MeV, respectively, and their ratio $f_{D_s}/f_D$=1.24(3) agrees with recent CLEO experiment. The values $f_{\rm P}(1S)=182, 216, 438$ MeV are obtained for the $B$, $B_s$, and $B_c$ mesons with the ratio $f_{B_s}/f_B$=1.19(2) and $f_D/f_B$=1.14(2). The decay constants $f_{\rm P}(2S)$ for the first radial excitations as well as the decay constants $f_{\rm V}(1S)$ in the vector channel are also calculated. The difference of about 20% between $f_{D_s}$ and $f_D$, $f_{B_s}$ and $f_B$ directly follows from our analytical formulas.

hep-ph↗

arXiv2006

Masses and decay constants of B_q mesons in the QCD string approach

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 $σ$, $α_s$, 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 mass used, namely $f_{B_c}=440 (424)$ MeV for $m_c =1.40 (1.35)$ GeV. For the $1P$ states we predict the spin-averaged masses: $\bar M(B_J)=5730$ MeV and $\bar M(B_{sJ})=5830$ MeV which are in good agreement with the recent data of the D0 and CDF Collaborations, at the same time owning to the string correction being by $\sim 50$ MeV smaller than in other calculations.

hep-ph↗

arXiv2006

Masses of the η_c(nS) and η_b(nS) mesons

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 $J/ψ-η_c(1S)$ and $ψ(2S)-η'_c(2S)$ splittings and appears to be small, $r_{ss} \approx 0.06$ fm. Nevertheless, even with such a small radius an essential suppression of the hyperfine splittings ($\sim 50%)$ is observed in bottomonium. For the $nS b\bar b$ states $(n=1,2,...6)$ the values we predict (in MeV) are 28, 12, 10, 6, 6, and 3, respectively. In single-channel approximation for the $3S$ and $4S$ charmonium states the splittings 16(2) MeV and 12(4) MeV are obtained.

hep-ph↗

arXiv2006

$Z_6$ symmetry, electroweak transition, and magnetic monopoles at high temperature

We consider the lattice realization of the Standard Model with an additional $Z_6$ 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 ($M_H > 90$ Gev). The phase diagram was investigated and has been found to be different from that of the usual lattice realization of the Standard Model. It has been found, that the confinement-deconfinement phase transition lines for the SU(2) and SU(3) fields coincide. The transition line between Higgs and symmetric deconfinement parts of the phase diagram and the confinement-deconfinement transition line meet in a triple point. The transition between Higgs and symmetric parts of the phase diagram corresponds to the finite temperature electroweak transition/crossover. We see for the first time evidence that Nambu monopoles are condensed at $T>T_c$ while at $T<T_c$ their condensate vanishes.

hep-lat↗

arXiv2006

Higher $η_c(nS)$ and $η_b (nS)$ mesons

The hyperfine splittings in heavy quarkonia are studied in a model-independent way using the experimental data on di-electron widths. Relativistic correlations are taken into account together with the smearing of the spin-spin interaction. The radius of smearing is fixed by the known $J/ψ-η_c(1S)$ and $ψ(2S)-η'_c(2S)$ splittings and appears to be small, $r_{ss} \cong 0.06$ fm. Nevertheless, even with such a small radius an essential suppression of the hyperfine splittings ($\sim 50%)$ is observed in bottomonium. For the $nS~ b\bar b$ states $(n=1,2,...,6)$ we predict the values (in MeV) 28, 12, 10, 6, 6, and 3, respectively. For the $3S$ and $4S$ charmonium states the splittings 16(2) MeV and 12(4) MeV are obtained.

hep-ph↗

arXiv2005

Standard Model with the additional $Z_6$ symmetry on the lattice

An additional $Z_6$ symmetry hidden in the fermion and Higgs sectors of the Standard Model has been found recently\cite{BVZ2003}. A lattice regularization of the Standard Model was constructed that possesses this symmetry. In \cite{BVZ2004} we have reported our results on the numerical simulation of the Electroweak sector of the model. In this paper we report our results on the numerical simulation of the full ($SU(3)\otimes SU(2) \otimes U(1)$) model. The phase diagram of the model has been investigated using static quark and lepton potentials. Various types of monopoles have been constructed. Their densities appear to be sensitive to the phase transition lines. Differences between the realizations of the Standard Model which do or do not possess the mentioned $Z_6$ symmetry, are discussed.

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arXiv2004

The gluonic condensate from the hyperfine splitting $M_{\rm cog}(χ_{cJ})-M(h_c)$ in charmonium

The precision measurement of the hyperfine splitting $Δ_{\rm HF} (1P, c\bar c)=M_{\rm cog} (χ_{cJ}) - M(h_c) = -0.5 \pm 0.4$ 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 $Δ_{\rm HF} = -0.3 \pm 0.4$ MeV is obtained only if the relatively small $T_g = 0.16$ fm and $G_2 = 0.065 (3)$ GeV${}^4$ are taken. These values correspond to the ``physical'' string tension $(σ\approx 0.18 $ GeV$^2$). For $T_g \ge 0.2$ fm the hyperfine splitting is positive and grows for increasing $T_g$. In particular for $T_g = 0.2$ fm and $G_2 = 0.041 (2)$ GeV${}^4$ the splitting $Δ_{\rm HF} = 1.4 (2)$ MeV is obtained, which is in accord with the recent CLEO result.

hep-ph↗

arXiv2004

Leptonic widths of high excitations in heavy quarkonia

Agreement with the measured electronic widths of the $ψ(4040)$, $ψ(4415)$, and $Υ(11019)$ resonances is shown to be reached if two effects are taken into account: a flattening of the confining potential at large distances and a total screening of the gluon-exchange interaction at $r\ga 1.2$ fm. The leptonic widths of the unobserved $Υ(7S)$ and $ψ(5S)$ resonances: $Γ_{e^+e^-}(Υ(7S))=0.11$ keV and $Γ(ψ(5S))\approx 0.54$ keV are predicted.

hep-ph↗

arXiv2004

A critique of the angular momentum sum rules and a new angular momentum sum rule

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, based upon the rotational properties of the state vectors. Surprisingly it turns out that the results are very sensitive to the type of relativistic spin state used to describe the motion of the particle i.e. whether a canonical (i.e. boost) state or a helicity state is utilized. We present results for the matrix elements of the angular momentum operators, valid in an arbitrary Lorentz frame, both for helicity states and canonical states. These results are relevant for the construction of angular momentum sum rules, relating the angular momentum of a nucleon to the spin and orbital angular momentum of its constituents. It turns out that it is necessary to distinguish carefully whether the motion of the partons is characterized via canonical or helicity spin states. Fortunately, for the simple parton model interpretation, when the proton moves along $OZ$, our results for the sum rule based upon the matrix elements of $J_z$ agree with the often used sum rule found in the literature. But for the components $J_x, J_y$ the results are different and lead to a new and very intuitive sum rule for transverse polarization.

hep-ph↗

arXiv2004

The heavy-quark pole masses in the Hamiltonian approach

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 (string) Hamiltonian gives $m_b$(2-loop)$=4.78\pm 0.05$ GeV and $m_c$(2-loop)$=1.39 \pm 0.06$ GeV which correspond to the $\bar{\rm MS}$ running mass $\bar{m}_b(\bar{m}_b)=4.19\pm 0.04$ GeV and $\bar{m}_c(\bar{m}_c)=1.10\pm 0.05$ GeV. The masses $ω_c$ and $ω_b$, which define the heavy quarkonia spin structure, are shown to be by $\sim 200$ MeV larger than the pole ones.

hep-ph↗

arXiv2004

Bound States in the LFD Yukawa Model

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.

hep-ph↗

arXiv2004

An additional symmetry in the Weinberg - Salam model

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 results on the numerical simulation of its Electroweak sector.

hep-lat↗

arXiv2004

The restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium

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 $Δ_1= Υ({\rm 1D})-χ_b({\rm 1P})$ and other splittings are very sensitive to the QCD constant $Λ_V(n_f)$ which occurs in the Vector scheme, and good agreement with the experimental data is obtained for $Λ_V(2$-loop, $n_f=5)= 325\pm 10$ MeV which corresponds to the conventional $Λ_{\bar{MS}} (2-$loop, $n_f=5)= 238\pm 7$ MeV, $α_s(2-$loop, $M_Z)=0.1189\pm 0.0005,$ and a large freezing value of the background coupling: $α_{\rm crit} (2$-loop, $q^2=0)=α_{\rm crit} (2$-loop, $r\to \infty)=0.58\pm 0.02$. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling $α_{\rm static}=const$ is introduced, as in the Cornell potential, then precise agreement with $Δ_1({\rm exp})$ and $Δ_2({\rm exp})$ can be reached for the rather large value $α_{\rm static} =0.43\pm 0.02$. We predict a value for the mass M(2D) = 10451\pm2 MeV.

hep-ph↗

arXiv2003

A hidden symmetry in the Standard Model

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.

hep-lat↗

arXiv2003

The $η_c(3654)$ and hyperfine splitting in charmonium

The hyperfine splitting for the 2S charmonium state is calculated and the predicted number is $Δ_{\rm HF}(2S) = 57 \pm 8$ MeV, being by derivation the lower bound of this splitting. It results in $M(η_c(2S))= 3630 \pm 8$ MeV, which is smaller by two standard deviations than found in the Belle experiment \cite{ref.01}, but close to the $η_c(2S)$ mass observed by the same group in the experiment $e^+e^- \to J/ψη_c$ \cite{ref.06} where $M(η_c(2S)) = 3622 \pm 12$ MeV was found.

hep-ph↗

arXiv2002

Comparison of relativistic bound-state calculations in Front-Form and Instant-Form Dynamics

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 dependence of the wave function. After calculating the bound-state spectra we characterized all states found. Similarly, we have calculated the bound-state spectrum and wave functions in the instant-form formalism. We compare the spectra found in both forms of dynamics in the ladder approximation and show that in both forms of dynamics the O(4) symmetry is broken.

hep-ph↗

arXiv2002

Evidence for the reality of singular configurations in SU(2) gauge theory

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 do not contain the simple center vortices inside the considered Wilson loop. It leads us to the conclusion that these singular field configurations play a real role in the continuum theory.

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