arXiv subjects

B. L. G. Bakker

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

At least 19 recordsLinked to original sources

arXiv2020

The charmed mesons in the region above 3.0 GeV

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 $ψ(4660)$ and $χ_{c0}(4700)$. The following masses of the first excitations: $M(2\,{}^3P_0)=2874$~MeV, $M(2\,{}^3P_2)=2968$~MeV, $M(2\,{}^3D_1)=3175$~MeV, and $M(2\,{}^3D_3)=3187$~MeV, and second excitations: $M(3\,{}^1S_0)=3008$~MeV, $M(3\,{}^3S_1)=3062$~MeV, $M(3\,{}^3P_0)=3229$~MeV, and $M(3\,{}^3P_2) =3264$~MeV, are predicted. The other states with $L=0,1,2$ and $n_r \geq 3$ have their masses in the region $M(nL)\geq 3.3$~GeV.

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arXiv2019

Dynamics of the quark-antiquark interaction and the universality of Regge trajectories

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, $β_n$ of the radial and $β_l$ of the orbital RT, decrease by $\sim 30\%$ with the value of $β_n=1.30(5)$~GeV$^2$ being larger than $ β_l=0.95(5)$~GeV. The self-energy correction provides the linearity of RT and remains important up to very high excitations; the string correction decreases the slope of the orbital RT, while the intercept $β_0=0.51(1)~ $GeV$^2$ is equal to the squared centroid mass of $ρ(1S)$. If the universal gluon-exchanged potential without fitting parameters and screening function, as in heavy quarkonia, is taken, then the slope of the radial RT decreases, $β_n=1.15(8)$~GeV$^2$, and its value coincides with the slope of the orbital RT, $β_l=1.08(8)$~GeV$^2$ within theoretical errors, producing the universal RT.

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arXiv2019

The Regge trajectories and leptonic widths of the vector $s\bar s$ mesons

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 $ϕ(3 ^3S_1)$ state the mass $M(ϕ(3S))=2100(20)$ MeV and the leptonic width $Γ_{ee}(ϕ(3S))=0.27(2)$ keV are obtained, while the mass of the $2 ^3D_1$ state, $M(ϕ(2 ^3D_3))=2180(5)$ MeV, appears to be in agreement with the mass of the $ϕ(2170)$ resonance, and its leptonic width, $Γ_{ee}(2 ^3D_1)=0.20\pm 0.10$ keV, has a large theoretical uncertainty, depending on the parameters of the flattened confining potential.

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arXiv2017

The leptonic widths of high $ψ$-resonances in unitary coupled-channel model

The leptonic widths of high $ψ$-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 $θ(ψ(4040))=27.7^\circ$ and $θ(ψ(4160))=29.5^\circ$, $Z_1\,(ψ(4040))=0.76$, and $Z_2\,(ψ(4160))=0.62$ are obtained. It gives the leptonic widths $Γ_{ee}(ψ(4040))=Z_1\, 1.17=0.89$~keV, $Γ_{ee}(ψ(4160))=Z_2\, 0.76=0.47$~keV in good agreement with experiment. For $ψ(4415)$ the leptonic width $Γ_{ee}(ψ(4415))=~0.55$~keV is calculated, while for the missing resonance $ψ(4510)$ we predict $M(ψ(4500))=(4515\pm 5)$~MeV and $Γ_{ee}(ψ(4510)) \cong 0.50$~keV.

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arXiv2016

The radial Regge trajectories and leptonic widths of the isovector mesons

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 with $l=0,1,2$ in agreement with experiment. The flattening effect ensures the observed linear behaviour of the radial Regge trajectories $M^2(n)=m_0^2 + n_r μ^2$ GeV$^2$, where the slope $μ^2$ is very sensitive to the parameter $γ$, which determines the weakening of the string tension $σ(r)$ at large distances. For the $ρ$-trajectory the linear behaviour starts with $n_r=1$ and the values $μ^2=1.40(2)$~GeV$^2$ for $γ=0.40$ and $μ^2=1.34(1)$~GeV$^2$ for $γ=0.45$ are obtained. For the excited states the leptonic widths: $Γ_{\rm ee}(ρ(775))=7.0(3)$~keV, $Γ_{\rm ee}(ρ(1450))=1.7(1)$~keV, $Γ_{\rm ee}(ρ(1900))=1.0(1)$~keV, $Γ_{\rm ee}(ρ(2150))=0.7(1)$~keV, and $Γ_{\rm ee}(1\,{}^3D_1)=0.26(5)$~keV are calculated, if these states are considered as purely $q\bar q$ states. The width $Γ_{\rm ee}(ρ(1700))$ increases if $ρ(1700)$ is mixed with the $2\,{}^3S_1$ state, giving for a mixing angle $θ=21^\circ$ almost equal widths: $Γ_{\rm ee}(ρ(1700))=0.75(6)$~keV and $Γ_{\rm ee}(1450)=1.0(1)$~keV.

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arXiv2013

Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics

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 gluon amplitudes, which are directly testable in experiments at existing and future facilities. We present an overview of the promises and challenges of LFQCD in the context of unsolved issues in QCD that require broadened and accelerated investigation. We identify specific goals of this approach and address its quantifiable uncertainties.

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arXiv2013

The vector coupling $α_{\rm V}(r)$ and the scales $r_0,r_1$ from the bottomonium spectrum

We study the universal static potential $V_{\rm st}(r)$ and the force, which are fully determined by two fundamental parameters: the string tension $σ=0.18\pm 0.02$ GeV$^2$ and the QCD constants $Λ_{\bar{\rm MS}}(n_f)$, taken from pQCD, while the infrared (IR) regulator $M_{\rm B}$ is taken from the background perturbation theory and expressed via the string tension. The vector couplings $α_{\rm V}(r)$ in the static potential and $α_{\rm F}(r)$ in the static force, as well as the characteristic scales, $r_1(n_f=3)$ and $r_0(n_f=3)$, are calculated and compared to lattice data. The result $r_0Λ_{\bar{\rm MS}}(n_f=3)=0.77\pm 0.03$, which agrees with the lattice data, is obtained for $M_{\rm B}=(1.15\pm 0.02)$ GeV. However, better agreement with the bottomonium spectrum is reached for a smaller $Λ_{\bar{\rm MS}}(n_f=3)=(325\pm 15)$ MeV and the frozen value of $α_V=0.57\pm 0.02$. The mass splittings $\bar M(1D)-\bar M(1P)$ and $\bar M(2P)-\bar M(1P)$ are shown to be sensitive to the IR regulator used. The masses $M(1\,^3D_3)=10169(2)$ MeV and $M(1\,^3D_1)=10155(3)$ MeV are predicted.

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arXiv2012

Dominant spin-orbit effects in radiative decays {$Υ(3S\rightarrow γχ_{bJ}(1P))$}}

We show that there are two reasons why the partial width for the transition $Γ_1(Υ(3S)\rightarrow γχ_{b1}(1P))$ is suppressed. Firstly, the spin-averaged matrix element (m.e.) $\bar{I(3S|r|1P_J)}$ is small, being equal to 0.023 GeV$^{-1}$ in our relativistic calculations. Secondly, the spin-orbit splittings produce relatively large contributions, giving $I(3S|r|1P_2)=0.066$ GeV$^{-1}$, while due to large cancellation the m.e. $I(3S|r|1P_1)=-0.020$ GeV$^{-1}$ is small and negative; at the same time the magnitude of $I(3S|r|1P_0)=-0.063$ GeV$^{-1}$ is relatively large. These m.e. give rise to the partial widths: $Γ_2(Υ(3S)\rightarrow γχ_{b2}(1P))=212$ eV, $Γ_0(Υ(3S)\rightarrow γχ_{b0}(1P))=54$ eV, which are in good agreement with the CLEO and BaBar data, and also to $Γ_1(Υ(3S)\rightarrow γχ_{b1}(1P))=13$ eV, which satisfies the BaBar limit, $Γ_1(exp.) < 22$ eV.

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arXiv2012

The ratio of decay widths of X(3872) to $ ψ^{\prime}γ$ and $ J/ψγ$ as a test of the X(3872) dynamical structure

Radiative decays of X(3872) with $J^{PC}=1^{++}$ are studied in the coupled-channel approach, where the $c\bar c$ states are described by 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 $2 {}^3P_1$ charmonium state just to the $D^0D^{*0}$ threshold was already obtained for a prescribed channel coupling to the $DD^*$ decay channels. For the same value of coupling the normalized wave function (w.f.) of X(3872) acquires admixture of the $1 {}^3P_1$ component with the w.f. fraction $c_1=0.153 (θ=8.8^\circ$), which increases the transition rate $Γ(X(3872)\rightarrow J/ψγ)$ up to 50-70 keV, making the ratio $R=\frac{\mathcal{B}(X(3872)\rightarrow ψ^{\prime}γ)}{\mathcal{B}(X(3872)\rightarrow J/ψγ)}=0.8\pm 0.20 (th)$ significantly smaller, as compared to $R\simeq 5$ for X(3872) as a purely $2 {}^3P_1$ state.

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arXiv2011

Higher excitations of the $D$ and $D_s$ mesons

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 in a relativistic model. For $D_s(1\,{}^3D_3)$ and $D_s(2P_1^H)$ the calculated masses agree with the experimental values for $D_s(2860)$ and $D_s(3040)$, and the masses of $D(2\,{}^1S_0)$, $D(2\,{}^3S_1)$, $D(1\,{}^3D_3)$, and $D(1D_2)$ are in agreement with the new BaBar data. For the yet undiscovered resonances we predict the masses $M(D(2\,{}^3P_2))=2965$ MeV, $M(D(2\,{}^3P_0))=2880$ MeV, $M(D(1\,{}^3F_4))=3030$ MeV, and $M(D_s(1\,{}^3F_2))=3090$ MeV. We show that for $L=2,3$ the states with $j_q=l+1/2$ and $j_q=l-1/2$ ($J=l$) are almost completely unmixed ($ϕ\simeq -1^\circ$), which implies that the mixing angles $θ$ between the states with S=1 and S=0 ($J=L$) are $θ\approx 40^\circ$ for L=2 and $\approx 42^\circ$ for L=3.

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arXiv2010

The Hyperfine Splittings in Heavy-Light Mesons and Quarkonia

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 $α_{HF}=0.310$ is taken in perturbative spin-spin potential. It gives $M(B^*)-M(B)=45.7(3)$ MeV, $M(B_s^*)-M(B_s)=46.7(3)$ MeV ($n_f=4$), while in bottomonium $Δ_{HF}(b\bar b)=M(Υ(9460))-M(η_b(1S))=63.4$ MeV for $n_f=4$ and 71.1 MeV for $n_f=5$ are obtained; just latter agrees with recent BaBar data. For unobserved excited states we predict $M(Υ(2S))-M(η_b(2S))=36(2)$ MeV, $M(Υ(3S))-M(η(3S))=28(2)$ MeV, and also $M(B_c^*)=6334(4)$ MeV, $M(B_c(2S))=6868(4)$ MeV, $M(B_c^*(2S))=6905(4)$ MeV. The mass splittings between $D(2^3S_1)-D(2^1S_0)$, $D_s(2^3S_1)-D_s(2^1S_0)$ are predicted to be $\sim 70$ MeV, which are significantly smaller than in several other studies.

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arXiv2010

The Hyperfine Splittings in Bottomonium and the $B_q (q=n,s,c)$ Mesons

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 $α_s(μ)=0.305(2)$ 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 HFS $M(B^*)- M(B)=45.3(3)$ MeV, $M(B_s^*) - M(B_s)=46.5(3)$ MeV are obtained in full agreement with experiment both for $n_f=3$ and $n_f=4$. In bottomonium, $M(Υ(9460))- M(η_b)=70.0(4)$ MeV for $n_f=5$ agrees with the BaBar data, while a smaller HFS, equal to 64(1) MeV, is obtained for $n_f=4$. We predict HFS $M(Υ(2S))-M(η_b(2S))=36(1)$ MeV, $M(Υ(3S))- M(η(3S))=27(1)$ MeV, and $M(B_c^*) - M(B_c)= 57.5(10)$ MeV, which gives $M(B_c^*)=6334(1)$ MeV, $M(B_c(2 {}^1S_0))=6865(5)$ MeV, and $M(B_c^*(2S {}^3S_1))=6901(5)$ MeV.

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arXiv2009

On the possibility to observe higher $n^3D_1$ bottomonium states in the $e^+e^-$ processes

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, $θ\sim30^\circ$ and this effect provides the correct values of $Γ_{ee}(Υ(10580))$ and $Γ_{ee}(Υ(11020))$. On the other hand, the $S-D$ mixing gives rise to an increase by two orders of magnitude of the di-electron widths of the mixed $\tildeΥ(n^3D_1$) resonances ($n=3,4,5$), which originate from pure $D-$wave states. The value $Γ_{ee}(\tildeΥ(3D))=0.095^{+0.028}_{-0.025}$ keV is obtained, being only $\sim 3$ times smaller than the di-electron width of $Υ(10580)$, while $Γ_{ee}(\tildeΥ(5D))\sim 135$ eV appears to be close to $Γ_{ee}(Υ(11020))$ and therefore this resonance may become manifest in the $e^+e^-$ experiments. The mass differences between $M(nD)$ and $M((n+1)S) (n=4,5)$ are shown to be rather small, $50\pm 10$ MeV.

hep-ph↗

arXiv2009

Dielectron widths of the S-, D-vector bottomonium states

The dielectron widths of $Υ(nS) (n=1,...,7)$ and vector decay constants are calculated using the Relativistic String Hamiltonian with a universal interaction. For $Υ(nS) (n=1,2,3)$ the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For $Υ(10580)$ and $Υ(11020)$ a good agreement with experiment is reached only if the 4S--3D mixing (with a mixing angle $θ=27^\circ\pm 4^\circ$) and 6S--5D mixing (with $θ=40^\circ\pm 5^\circ$) are taken into account. The possibility to observe higher "mixed $D$-wave" resonances, $\tildeΥ(n {}^3D_1)$ with $n=3,4,5$ is discussed. In particular, $\tildeΥ(\approx 11120)$, originating from the pure $5 {}^3D_1$ state, can acquire a rather large dielectron width, $\sim 130$ eV, so that this resonance may become manifest in the $e^+e^-$ experiments. On the contrary, the widths of pure $D$-wave states are very small, $Γ_{ee}(n{}^3 D_1) \leq 2$ eV.

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arXiv2009

Nambu monopoles in lattice Electroweak theory

We considered the lattice electroweak theory at realistic values of $α$ and $θ_W$ 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 over the lattice in the physical region of the phase diagram. Moreover, their percolation probability is found to be an order parameter for the transition between the symmetric and the broken phases. Therefore, these monopoles indeed appear as real physical objects. However, we have found that their density on the lattice increases with increasing ultraviolet cutoff. Thus we conclude, that the conventional lattice electroweak theory is not able to predict the density of Nambu monopoles. This means that the description of Nambu monopole physics based on the lattice Weinberg - Salam model with finite ultraviolet cutoff is incomplete. We expect that the correct description may be obtained only within the lattice theory that involves the description of TeV - scale physics.

hep-lat↗

arXiv2009

The $\mathbf{S}-\mathbf{D}$ mixing and di-electron widths of higher charmonium $\mathbf{1^{--}}$ states

The di-electron 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 $θ\approx 34^\circ$ 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, considered as a pure $3 {}^3D_1$ state, would have very small di-electron width, $Γ_{ee}(Y(4360))=0.060$ keV. On the contrary, for large mixing between the $4 {}^3S_1$ and $3 {}^3D_1$ states with the mixing angle $θ=34.8^\circ$, $Γ_{ee}(ψ(4415))=0.57$ keV coincides with the experimental number, while a second physical resonance, probably Y(4360), has also a rather large $Γ_{ee} (Y(\sim 4400))=0.61$ keV. For the higher resonance Y(4660), considered as a pure $5 {}^3S_1$ state, we predict the di-electron width $Γ_{ee}(Y(4660))=0.70$ keV, but it becomes significantly smaller, namely 0.31 keV, if the mixing angle between the $5 {}^3S_1$ and $4 {}^3D_1$ states $θ=34^\circ$. The mass and di-electron width of the $6 {}^3S_1$ charmonium state are calculated.

hep-ph↗

arXiv2008

Monopoles in lattice Electroweak theory

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 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 unphysical region of large coupling constant $α> 0.1$.

hep-lat↗

arXiv2008

The running mass $m_s$ at low scalefrom the heavy-light meson decay constants

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 $η_D =f_{D_s}/f_D\approx 1.23(15)$, recently observed in the CLEO experiment, and $η_B=f_{B_s}/f_B\approx 1.20$, obtained in unquenched lattice QCD, can be reached only if the running mass $m_s$ at low scale is $m_s(\sim 0.5 $ GeV)$= 170 - 200$ MeV. Our results follow from the analytical expression for the pseudoscalar decay constant $f_{\rm P}$ based on the path-integral representation of the meson Green's function.

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