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 qq pair creation when the length of the string exceeds the critical value R 1 Ӎ1.4 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 ͑predecay͒ 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 of Anisovich, Anisovich, and Sarantsev.

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 ±5 MeV. For the D and D s mesons the values of f P (1S) are equal to 210(10) and 260(10) MeV, respectively, and their ratio f Ds /f D =1.24(3) agrees with recent CLEO experiment. The values f P (1S) = 182, 216, 438 MeV are obtained for the B, B s , and B c mesons with the ratio f Bs /f B =1.19(2) and f D /f B =1.14(2). The decay constants f P (2S) for the first radial excitations as well as the decay constants f V (1S) in the vector channel are also calculated. The difference of about 20% between f Ds and f D , f Bs and f B directly follows from our analytical formulas.

A striking contradiction between lattice short range static potential (n f = 0) and standard perturbative potential, observed in Ref. [18], is investigated in the framework of the background perturbation theory. With the use of the background couplingα B (r) which contains the only background parameter -mass m B , fixed by fine structure fit in bottomonium, the lattice data are nicely explained without introduction of exotic short range linear potential with large "string tension" σ * ∼ 1 GeV 2 . A significant difference betweenα B (r) and standard perturbative vector coupling α V (r) is found in the range 0.05 fm < ∼ r < ∼ 0.15 fm, while at larger distances, r > 0.3 fmα B (r) fast approaches the freezing valueα B (∞). Some problems concerning the strong coupling properties at short and long distances are discussed and solutions are suggested. IntroductionThe property of freezing of the vector coupling constantα V (r) at long distances is widely used in QCD phenomenology [1]- [6]. On the fundamental level this phenomenon has been studied in two different theoretical approaches [7]-[9]. In the case of the static potential the freezing of the vector couplingα V (r) suggests thatα V (r) is approaching a constant α fr ≡α V (r → ∞) at relatively long distances while at small r it manifests the property of asymptotic freedom. Both characteristic features of the static potential were widely used in hadron spectroscopy. However, it was realized that the asymptotic freedom behavior does not practically affect hadron spectra being important mostly for a wave function at the origin. On the contrary, the choice ofα V (r) as a constant at all distances, i.e.α V (r) ∼ =ᾱ, appears to be a reasonable approximation and gives rise to a good description of meson spectra both for heavy quarkonia [1, 10, 11] and for heavy-light mesons [12]. Also in lattice QCD this choice gives a good fit to lattice static potential at the distances above 0.2 fm. Therefore the question arises why this simple approximation,α V (r) ≈ᾱ, works so well even in the case of bottomonium where the sizes of low-lying levels are not large, the characteristic radius R ch < ∼ 0.5 fm. To answer this question one needs to clarify another problem. Namely, to find out the precise freezing value of the vector constant in momentum and coordinate spaces, and to define the distances r where the difference betweenα V (r) and α fr is becoming inessential and therefore the approximationα V (r) =ᾱ (ᾱ = α fr in general case) gives a good description of hadron spectra and other physical characteristics.

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 ≈ 34 • 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 3 D 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 3 S 1 and 3 3 D 1 states with the mixing angle θ = 34.8 • , 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 (∼ 4400)) = 0.61 keV. For the higher resonance Y (4660), considered as a pure 5 3 S 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 3 S 1 and 4 3 D 1 states θ = 34 • . The mass and di-electron width of the 6 3 S 1 charmonium state are calculated.

The bb spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange potential between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings ∆ 1 = Υ(1D) − χ b (1P) and other splittings between low-lying states 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 ± 10 MeV which corresponds to the conventional Λ MS (2−loop, n f = 5) = 238 ± 7 MeV, α s (2−loop, M Z ) = 0.1189 ± 0.0005, and to a large freezing value of the background coupling: α crit (2-loop, q 2 = 0) = α crit (2-loop, r → ∞) = 0.58 ± 0.02. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling α static = const is introduced, as in the Cornell potential, then precise agreement with ∆ 1 (exp) and ∆ 2 (exp) can be reached for the rather large Coulomb constant α static = 0.43 ± 0.02. We predict a value for the mass M (2D) = 10451 ± 2 MeV.

The masses of higher DðnLÞ and D s ðnLÞ 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 ¼ 2 (n ¼ 1) and by 65 MeV for L ¼ 3 (n ¼ 1). An additional decrease $100 MeV takes place if the current mass of the light (strange) are almost completely unmixed ( ' À1 ), which implies that the mixing angles between the states with S ¼ 1 and S ¼ 0 (J ¼ L) are % 40 for L ¼ 2 and % 42 for L ¼ 3.

The strong coupling constant αs(µ) is extracted from the fits to charmonium spectrum and fine structure splittings. The relativistic kinematics is taken into account and relativistic corrections are shown to increase the matrix elements defining spin effects up to 40%. The value of αs(µ) at low-energy scale µ = 1.0 ± 0.2 GeV was found to be αs(µ) = 0.38 ± 0.03(exp.) + 0.04(theor.) which is about 50% lower than standard perturbative two-loop approximation and is in good agreement with the freezing αs behaviour.11.10. Jj, 11.15Bt, 12.38.Lg

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