Masses of the \eta_c(nS) and \eta_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 $J/\psi-\eta_c(1S)$ 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 figure

The amazing synchronicity of the Global Development (the 1300s-1450s). An institutional approach to the globalization of the late Middle Ages

In a new approach to a long-ranging debate on the causes of the Late Medieval Debasement, we offer an institutional case-study of Russia and the Levant. Avoiding the complexity of the “upstream” financial/minting centres of Western Europe, we consider the effects of debasement “downstream”, in resource-exporting periphery countries. The paper shows the amazing synchronicity of the worldwide appearance of the early modern trading system, associated with capitalism or commercial society. The centre-periphery feedback loop amplified trends and pushed towards economic and institutional changes. This is illustrated via the Hanseatic-Novgorodian and Italian-Levantine trade – under growing market pressure of the exploding transaction costs, the oligopolies gradually dissolved and were replaced by the British-Dutch traders. In this case-study the late-medieval/early-modern monetary integration served as the transitional institutional base for reducing transaction costs during a dramatic global shift. Highlighting centre-periphery links, a new trading outpost of Arkhangelsk rose synchronously with Amsterdam

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

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 figure

Strong decays and dipion transitions of Upsilon(5S)

Dipion transitions of $\Upsilon (nS)$ with $n=5, n'=1,2,3$ are studied using the Field Correlator Method, applied previously to dipion transitions with $n=2,3,4$ The only two parameters of effective Lagrangian were fixed in that earlier study, and total widths $\Gamma_{\pi\pi} (5, n')$ as well as pionless decay widths $\Gamma_{BB} (5S), \Gamma_{BB^*} (5S), \Gamma_{B^*B^*}(5S)$ and $\Gamma_{KK} (5, n')$ were calculated and are in a reasonable agreement with experiment. The experimental $\pi\pi$ spectra for $(5,1)$ and (5,2) transitions are well reproduced taking into account FSI in the $\pi\pi$.Comment: 16 pages, 6 figure

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 $\alpha_{HF}=0.310$ 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 page

Strong coupling constant from bottomonium fine structure

From a fit to the experimental data on the $b\bar{b}$ fine structure, the two-loop coupling constant is extracted. For the 1P state the fitted value is $\alpha_s(\mu_1) = 0.33 \pm 0.01(exp)\pm 0.02 (th)$ 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$GeV is extracted, which is significantly larger than in the previous analysis of Fulcher (1991) and Halzen (1993), but about 30smaller than the value given by standard perturbation theory. This value$\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 LaTe