Search

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 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., Comment: 15 pages, 4 tables

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, $M(\phi(2 ^3D_3))=2180(5)$ MeV, appears to be in agreement with the mass of the $\phi(2170)$ resonance, and its leptonic width, $\Gamma_{ee}(2 ^3D_1)=0.20\pm 0.10$ keV, has a large theoretical uncertainty, depending on the parameters of the flattened confining potential., Comment: 7 pages, no figures

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, $\beta_n$ of the radial and $\beta_l$ of the orbital RT, decrease by $\sim 30\%$ with the value of $\beta_n=1.30(5)$~GeV$^2$ being larger than $ \beta_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 $\beta_0=0.51(1)~ $GeV$^2$ is equal to the squared centroid mass of $\rho(1S)$. 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, $\beta_n=1.15(8)$~GeV$^2$, and its value coincides with the slope of the orbital RT, $\beta_l=1.08(8)$~GeV$^2$ within theoretical errors, producing the universal RT., Comment: 11 pages, two figures

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 $\theta(\psi(4040))=27.7^\circ$ and $\theta(\psi(4160))=29.5^\circ$, $Z_1\,(\psi(4040))=0.76$, and $Z_2\,(\psi(4160))=0.62$ are obtained. It gives the leptonic widths $\Gamma_{ee}(\psi(4040))=Z_1\, 1.17=0.89$~keV, $\Gamma_{ee}(\psi(4160))=Z_2\, 0.76=0.47$~keV in good agreement with experiment. For $\psi(4415)$ the leptonic width $\Gamma_{ee}(\psi(4415))=~0.55$~keV is calculated, while for the missing resonance $\psi(4510)$ we predict $M(\psi(4500))=(4515\pm 5)$~MeV and $\Gamma_{ee}(\psi(4510)) \cong 0.50$~keV., Comment: 10 pages, 6 references corrected, some new material added

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 $M^2(n)=m_0^2 + n_r \mu^2$ GeV$^2$, where the slope $\mu^2$ is very sensitive to the parameter $\gamma$, which determines the weakening of the string tension $\sigma(r)$ at large distances. For the $\rho$-trajectory the linear behaviour starts with $n_r=1$ and the values $\mu^2=1.40(2)$~GeV$^2$ for $\gamma=0.40$ and $\mu^2=1.34(1)$~GeV$^2$ for $\gamma=0.45$ are obtained. For the excited states the leptonic widths: $\Gamma_{\rm ee}(\rho(775))=7.0(3)$~keV, $\Gamma_{\rm ee}(\rho(1450))=1.7(1)$~keV, $\Gamma_{\rm ee}(\rho(1900))=1.0(1)$~keV, $\Gamma_{\rm ee}(\rho(2150))=0.7(1)$~keV, and $\Gamma_{\rm ee}(1\,{}^3D_1)=0.26(5)$~keV are calculated, if these states are considered as purely $q\bar q$ states. The width $\Gamma_{\rm ee}(\rho(1700))$ increases if $\rho(1700)$ is mixed with the $2\,{}^3S_1$ state, giving for a mixing angle $\theta=21^\circ$ almost equal widths: $\Gamma_{\rm ee}(\rho(1700))=0.75(6)$~keV and $\Gamma_{\rm ee}(1450)=1.0(1)$~keV., Comment: 12 pages

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 $\tilde{\Gamma}_1=\Gamma(2\,{}^3P_1\rightarrow J/\psi\gamma)=85.4$~keV are obtained, giving for their ratio the value $\tilde{R_{\psi\gamma}}=\frac{\tilde{\Gamma}_2}{\tilde{\Gamma}_1}=0.84$. In the CC approach three factors are shown to be equally important. First, the admixture of the $1\,{}^3P_1$ component in the normalized wave function of $X(3872)$ due to the CC effects. Its weight $c_{\rm X}(E_{\rm R})=0.200\pm 0.015$ is calculated. Secondly, the use of the multipole function $g(r)$ instead of $r$ in the overlap integrals, determining the partial widths. Thirdly, the choice of the gluon-exchange interaction for $X(3872)$, as well as for other states above threshold. If for $X(3872)$ the gluon-exchange potential is taken the same as for low-lying charmonium states, then in the CC approach $\Gamma_1= \Gamma(X(3872)\rightarrow J/\psi\gamma) \sim 3$~keV is very small, giving the large ratio $R_{\psi\gamma}=\frac{\mathcal{B}(X(3872)\rightarrow \psi(2S)\gamma)}{\mathcal{B}(X(3872)\rightarrow J/\psi\gamma)}\gg 1.0$. Arguments are presented why the gluon-exchange interaction may be suppressed for $X(3872)$ and in this case $\Gamma_1=42.7$~keV, $\Gamma_2= 70.5$~keV, and $R_{\psi\gamma}=1.65$ are predicted for the minimal value $c_{\rm X}({\rm min})=0.185$, while for the maximal value $c_{\rm X}=0.215$ we obtained $\Gamma_1=30.8$~keV, $\Gamma_2=73.2$~keV, and $R_{\psi\gamma}=2.38$, which agrees with the LHCb data., Comment: 12 pages, no figures

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., Comment: White Paper of International Light Cone Advisory Committee

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 expressed via the string tension. The vector couplings $\alpha_{\rm V}(r)$ in the static potential and $\alpha_{\rm F}(r)$ 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 $r_0\Lambda_{\bar{\rm MS}}(n_f=3)=0.77\pm 0.03$, 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 $\Lambda_{\bar{\rm MS}}(n_f=3)=(325\pm 15)$ MeV and the frozen value of $\alpha_V=0.57\pm 0.02$. 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., Comment: 21 pages, 5 figures, revtex4

We show that there are two reasons why the partial width for the transition $\Gamma_1(\Upsilon(3S)\rightarrow \gamma\chi_{b1}(1P))$ 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: $\Gamma_2(\Upsilon(3S)\rightarrow \gamma\chi_{b2}(1P))=212$ eV, $\Gamma_0(\Upsilon(3S)\rightarrow \gamma\chi_{b0}(1P))=54$ eV, which are in good agreement with the CLEO and BaBar data, and also to $\Gamma_1(\Upsilon(3S)\rightarrow \gamma\chi_{b1}(1P))=13$ eV, which satisfies the BaBar limit, $\Gamma_1(exp.) < 22$ eV., Comment: 8 pages

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 $c_1=0.153 (\theta=8.8^\circ$), which increases the transition rate $\Gamma(X(3872)\rightarrow J/\psi\gamma)$ up to 50-70 keV, making the ratio $R=\frac{\mathcal{B}(X(3872)\rightarrow \psi^{\prime}\gamma)}{\mathcal{B}(X(3872)\rightarrow J/\psi \gamma)}=0.8\pm 0.20 (th)$ significantly smaller, as compared to $R\simeq 5$ for X(3872) as a purely $2 {}^3P_1$ state., Comment: 14 pages,2 Tables

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 ($\phi\simeq -1^\circ$), which implies that the mixing angles $\theta$ between the states with S=1 and S=0 ($J=L$) are $\theta\approx 40^\circ$ for L=2 and $\approx 42^\circ$ for L=3., Comment: 22 pages, no figures, 4 tables Two references and corresponding discussion added

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, $M(B_s^*)-M(B_s)=46.7(3)$ MeV ($n_f=4$), while in bottomonium $\Delta_{HF}(b\bar b)=M(\Upsilon(9460))-M(\eta_b(1S))=63.4$ 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 $M(\Upsilon(2S))-M(\eta_b(2S))=36(2)$ MeV, $M(\Upsilon(3S))-M(\eta(3S))=28(2)$ 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., Comment: 13 pages

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 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, $M(\Upsilon(9460))- M(\eta_b)=70.0(4)$ 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 $M(\Upsilon(2S))-M(\eta_b(2S))=36(1)$ MeV, $M(\Upsilon(3S))- M(\eta(3S))=27(1)$ 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., Comment: 5 pages revtex4

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 agreement with experiment is reached only if the 4S--3D mixing (with a mixing angle $\theta=27^\circ\pm 4^\circ$) and 6S--5D mixing (with $\theta=40^\circ\pm 5^\circ$) are taken into account. The possibility to observe higher "mixed $D$-wave" resonances, $\tilde\Upsilon(n {}^3D_1)$ with $n=3,4,5$ is discussed. In particular, $\tilde\Upsilon(\approx 11120)$, 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, $\Gamma_{ee}(n{}^3 D_1) \leq 2$ eV., Comment: 13 pages, no figures

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 $\Gamma_{ee}(\Upsilon(10580))$ and $\Gamma_{ee}(\Upsilon(11020))$. 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 $\tilde\Upsilon(n^3D_1$) resonances ($n=3,4,5$), which originate from pure $D-$wave states. The value $\Gamma_{ee}(\tilde\Upsilon(3D))=0.095^{+0.028}_{-0.025}$ keV is obtained, being only $\sim 3$ times smaller than the di-electron width of $\Upsilon(10580)$, while $\Gamma_{ee}(\tilde\Upsilon(5D))\sim 135$ eV appears to be close to $\Gamma_{ee}(\Upsilon(11020))$ 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., Comment: 5 pages, no figures

The di-electron widths of $\psi(4040)$, $\psi(4160)$, and $\psi(4415)$, 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 $\theta\approx 34^\circ$ 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, $\Gamma_{ee}(Y(4360))=0.060$ keV. On the contrary, for large mixing between the $4 {}^3S_1$ and $3 {}^3D_1$ states with the mixing angle $\theta=34.8^\circ$, $\Gamma_{ee}(\psi(4415))=0.57$ keV coincides with the experimental number, while a second physical resonance, probably Y(4360), has also a rather large $\Gamma_{ee} (Y(\sim 4400))=0.61$ keV. For the higher resonance Y(4660), considered as a pure $5 {}^3S_1$ state, we predict the di-electron width $\Gamma_{ee}(Y(4660))=0.70$ keV, but it becomes significantly smaller, namely 0.31 keV, if the mixing angle between the $5 {}^3S_1$ and $4 {}^3D_1$ states $\theta=34^\circ$. The mass and di-electron width of the $6 {}^3S_1$ charmonium state are calculated., Comment: 19 pages, no figures

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 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 $\alpha \sim {1/128}$. However, such a difference appears in the strong coupling region and is related to the properties of monopoles constructed of the hypercharge field., Comment: poster presented at LATTICE 2007

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 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., Comment: LATEX

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 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., Comment: 6 pages, no figures; revtex4

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 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., Comment: 37 pages, 10 tables, RevTeX4

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 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., Comment: 9 pages, ICHEP 2006

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 $J/\psi-\eta_c(1S)$ and $\psi(2S)-\eta'_c(2S)$ 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., Comment: 13 pages, no figures

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

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 $J/\psi-\eta_c(1S)$ and $\psi(2S)-\eta'_c(2S)$ 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., Comment: 23 pages

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 $\Delta_{\rm HF} = -0.3 \pm 0.4$ 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 $(\sigma \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 $\Delta_{\rm HF} = 1.4 (2)$ MeV is obtained, which is in accord with the recent CLEO result., Comment: 9 pages revtex 4, no figures

Agreement with the measured electronic widths of the $\psi(4040)$, $\psi(4415)$, and $\Upsilon (11019)$ 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 $\Upsilon(7S)$ and $\psi(5S)$ resonances: $\Gamma_{e^+e^-}(\Upsilon (7S))=0.11$ keV and $\Gamma(\psi(5S))\approx 0.54$ keV are predicted., Comment: 11 pages revtex4

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., Comment: Proceedings of the international workshop on: Light Cone Physics: Hadrons and Beyond, Durham (UK), August 5th-9th 2003

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., Comment: The results of our previous version are not changed here, but the presentation has been reorganized to make the discussion easier to follow

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., Comment: to appear in Yad. Fiz

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 occurs in the Vector scheme, and good agreement with the experimental data is obtained for $\Lambda_V(2$-loop, $n_f=5)= 325\pm 10$ MeV which corresponds to the conventional $\Lambda_{\bar{MS}} (2-$loop, $n_f=5)= 238\pm 7$ MeV, $\alpha_s(2-$loop, $M_Z)=0.1189\pm 0.0005,$ and a large freezing value of the background coupling: $\alpha_{\rm crit} (2$-loop, $q^2=0)=\alpha_{\rm crit} (2$-loop, $r\to \infty)=0.58\pm 0.02$. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling $\alpha_{\rm static}=const$ is introduced, as in the Cornell potential, then precise agreement with $\Delta_1({\rm exp})$ and $\Delta_2({\rm exp})$ can be reached for the rather large value $\alpha_{\rm static} =0.43\pm 0.02$. We predict a value for the mass M(2D) = 10451\pm2 MeV., Comment: 17 pages, no figures, 6 tables

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 $\omega_c$ and $\omega_b$, which define the heavy quarkonia spin structure, are shown to be by $\sim 200$ MeV larger than the pole ones., Comment: 18 pages, no figures, 8 tables

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

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., Comment: 6 pages, no figures. Shortened version

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., Comment: 22 pages Latex, 7 figures, style file amssymb used

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], Comment: 25 pages, 1 figure

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 to be $\alpha'_L = 0.80$ GeV${}^{-2}$ (for $L \leq 4$) and $\alpha_L(0) = -0.34$, in good agreement with the experimental data: $\alpha'_{L {\rm exp}} = 0.81 \pm 0.01$ GeV${}^{-2}$, $\alpha_{L {\rm exp}}(0) = -0.30 \pm 0.02$. 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 $\alpha_s \leq 0.40$ on the strong coupling is required., Comment: 18 pages RevTeX, 1 figure

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., Comment: 3 pages, proceedings of the Light Cone Meeting Trento 2001, to be published in Nucl. Phys. B - Proceedings Supplements

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., Comment: 29 pages RevTeX. submitted to Phys. Rev. D

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., Comment: 22 pages RevTeX

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., Comment: 10 pages, 6 EPS figures, LaTeX2e, uses epsfig.sty

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.

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., Comment: 8 pages, 5 postscript figures

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., Comment: 7 pages

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 $\alpha_s(\mu_1) = 0.33 \pm 0.01(exp)\pm 0.02 (th)$ at the scale $\mu_1 = 1.8 \pm 0.1$ GeV, which corresponds to the QCD constant $\Lambda^{(4)}(2-loop) = 338 \pm 30$ MeV (n_f = 4) and $\alpha_s(M_Z) = 0.119 \pm 0.002. For the 2P state the value $\alpha_s(\mu_2) = 0.40 \pm 0.02(exp)\pm 0.02(th)$ at the scale $\mu_2 = 1.02 \pm 0.2$ 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 $\alpha_s(1.0) \approx 0.40$ can be obtained in the framework of the background perturbation theory, thus demonstrating the freezing of $\alpha_s$. The relativistic corrections to $\alpha_s$ are found to be about 15%., Comment: 18 pages LaTeX

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 $\alpha_s(\mu)\approx 0.36$ 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., Comment: 12 pages

We show that the extended Abelian magnetic monopoles in the Maximal Abelian projection of lattice SU(2) gluodynamics are locally correlated with the magnetic and the electric parts of the SU(2) action density. These correlations are observed in the confined and in the deconfined phases., Comment: 11 pages, LaTeX2e, 5 figures, uses epsf.sty; revision: Introduction is extended and a few references are added

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., Comment: 17 pages, revtex, 14 figures, submitted to Phys.Rev.C

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., Comment: 13 pages, revtex, epsf, 2 large figures, minor changes, accepted for publication in Phys.Rev.D

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., Comment: 4 pages, LaTeX, 2 figures, uses epsf.sty; Talk given by M.I. Polikarpov at 31st International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, September 2-6, 1997

By numerical calculations we show that the abelian monopole currents are locally correlated with the density of SU(2) lattice action. This fact is established for the maximal abelian projection. Thus, in the maximal abelian projection the monopoles are physical objects, they carry SU(2) action. Calculations on the asymmetric lattice show that the correlation between monopole currents and the density of SU(2) lattice action also exists in the deconfinement phase of gluodynamics., Comment: 3 pages, 2 figures, LaTeX using espcrc2.sty and epsfig.sty; Talk given by M.I. Polikarpov at the International Symposium on Lattice Field Theory, 22-26 July 1997, Edinburgh, Scotland