Search

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

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 $\tilde��_2=��(2\,{}^3P_1 \rightarrow ����)=71.8$~keV and large $\tilde��_1=��(2\,{}^3P_1\rightarrow J/����)=85.4$~keV are obtained, giving for their ratio the value $\tilde{R_{����}}=\frac{\tilde��_2}{\tilde��_1}=0.84$. 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 $��_1= ��(X(3872)\rightarrow J/����) \sim 3$~keV is very small, giving the large ratio $R_{����}=\frac{\mathcal{B}(X(3872)\rightarrow ��(2S)��)}{\mathcal{B}(X(3872)\rightarrow J/����)}\gg 1.0$. Arguments are presented why the gluon-exchange interaction may be suppressed for $X(3872)$ and in this case $��_1=42.7$~keV, $��_2= 70.5$~keV, and $R_{����}=1.65$ 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 $��_1=30.8$~keV, $��_2=73.2$~keV, and $R_{����}=2.38$, which agrees with the LHCb data., 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., 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 $��=0.18\pm 0.02$ GeV$^2$ and the QCD constants $��_{\bar{\rm MS}}(n_f)$, 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 $��_{\rm V}(r)$ in the static potential and $��_{\rm F}(r)$ 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 $r_0��_{\bar{\rm MS}}(n_f=3)=0.77\pm 0.03$, 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 $��_{\bar{\rm MS}}(n_f=3)=(325\pm 15)$ MeV and the frozen value of $��_V=0.57\pm 0.02$. 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., 21 pages, 5 figures, revtex4

We show that there are two reasons why the partial width for the transition $��_1(��(3S)\rightarrow ����_{b1}(1P))$ 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: $��_2(��(3S)\rightarrow ����_{b2}(1P))=212$ eV, $��_0(��(3S)\rightarrow ����_{b0}(1P))=54$ eV, which are in good agreement with the CLEO and BaBar data, and also to $��_1(��(3S)\rightarrow ����_{b1}(1P))=13$ eV, which satisfies the BaBar limit, $��_1(exp.) < 22$ eV., 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 $c_1=0.153 (��=8.8^\circ$), which increases the transition rate $��(X(3872)\rightarrow J/����)$ up to 50-70 keV, making the ratio $R=\frac{\mathcal{B}(X(3872)\rightarrow ��^{\prime}��)}{\mathcal{B}(X(3872)\rightarrow J/����)}=0.8\pm 0.20 (th)$ significantly smaller, as compared to $R\simeq 5$ for X(3872) as a purely $2 {}^3P_1$ state., 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

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 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

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 $J/��-��_c(1S)$ and $��(2S)-��'_c(2S)$ 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., 23 pages

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 $J/��-��_c(1S)$ and $��(2S)-��'_c(2S)$ 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., 13 pages, no figures

The precision measurement of the hyperfine splitting $��_{\rm HF} (1P, c\bar c)=M_{\rm cog} (��_{cJ}) - M(h_c) = -0.5 \pm 0.4$ 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 $��_{\rm HF} = -0.3 \pm 0.4$ 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 $(��\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 $��_{\rm HF} = 1.4 (2)$ MeV is obtained, which is in accord with the recent CLEO result., 9 pages revtex 4, no figures

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

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 $��_{\rm HF}(2S) = 57 \pm 8$ MeV, being by derivation the lower bound of this splitting. It results in $M(��_c(2S))= 3630 \pm 8$ MeV, which is smaller by two standard deviations than found in the Belle experiment \cite{ref.01}, but close to the $��_c(2S)$ mass observed by the same group in the experiment $e^+e^- \to J/����_c$ \cite{ref.06} where $M(��_c(2S)) = 3622 \pm 12$ MeV was found., 8 pages RevTex

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., 22 pages RevTeX

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., 8 pages, 5 postscript figures

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

Light-Front Field Theory (LFFT) is a good candidate to describe bound states. In LFFT covariance is non-manifest. Burkardt and Langnau claim that, even for scattering amplitudes, rotational invariance is broken. We will take a different path of obtaining rules for light-front time-ordered diagrams. Covariance depends on the choice of a regulator $\alpha$. We need to apply some regularisation scheme to render physical amplitudes finite. This is done by applying minus regularisation. In this process all ambiguities related to the regulator $\alpha$ are removed. Therefore there is equivalence between the perturbative expansions of covariant and LFFT., Comment: 3 pages latex, uses epsf, epsfig, wrapfig. To appear in the Proceedings of the 12th International Symposium on High-Energy Spin Physics Amsterdam Sept. 1996