From a fit to the experimental data on the bbˉ fine structure, the
two-loop coupling constant is extracted. For the 1P state the fitted value is
αs​(μ1​)=0.33±0.01(exp)±0.02(th) at the scale μ1​=1.8±0.1 GeV, which corresponds to the QCD constant Λ(4)(2−loop)=338±30 MeV (n_f = 4) and αs​(MZ​)=0.119±0.002.Forthe2Pstatethevalue\alpha_s(\mu_2) = 0.40 \pm 0.02(exp)\pm 0.02(th)atthescale\mu_2 = 1.02 \pm 0.2GeVisextracted,whichissignificantlylargerthaninthepreviousanalysisofFulcher(1991)andHalzen(1993),butabout30smallerthanthevaluegivenbystandardperturbationtheory.Thisvalue\alpha_s(1.0) \approx 0.40canbeobtainedintheframeworkofthebackgroundperturbationtheory,thusdemonstratingthefreezingof\alpha_s.Therelativisticcorrectionsto\alpha_s$ are found to be about 15%.Comment: 18 pages LaTe
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 Zi​ of the ccˉ component are derived. Since these factors
depend on energy (mass), different values of mixing angles
θ(ψ(4040))=27.7∘ and θ(ψ(4160))=29.5∘,
Z1​(ψ(4040))=0.76, and Z2​(ψ(4160))=0.62 are obtained. It gives
the leptonic widths Γee​(ψ(4040))=Z1​1.17=0.89~keV,
Γee​(ψ(4160))=Z2​0.76=0.47~keV in good agreement with
experiment. For ψ(4415) the leptonic width
Γee​(ψ(4415))= 0.55~keV is calculated, while for the missing
resonance ψ(4510) we predict M(ψ(4500))=(4515±5)~MeV and
Γee​(ψ(4510))≅0.50~keV.Comment: 10 pages, 6 references corrected, some new material adde
The masses of higher D(nL) and Ds​(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 ∼100 MeV takes place if the current mass
of the light (strange) quark is used in a relativistic model. For
Ds​(13D3​) and Ds​(2P1H​) the calculated masses agree with the
experimental values for Ds​(2860) and Ds​(3040), and the masses of
D(21S0​), D(23S1​), D(13D3​), and D(1D2​) are in
agreement with the new BaBar data. For the yet undiscovered resonances we
predict the masses M(D(23P2​))=2965 MeV, M(D(23P0​))=2880 MeV,
M(D(13F4​))=3030 MeV, and M(Ds​(13F2​))=3090 MeV. We show that
for L=2,3 the states with jq​=l+1/2 and jq​=l−1/2 (J=l) are almost
completely unmixed (ϕ≃−1∘), which implies that the mixing
angles θ between the states with S=1 and S=0 (J=L) are θ≈40∘ for L=2 and ≈42∘ for L=3.Comment: 22 pages, no figures, 4 tables Two references and corresponding
discussion adde
Radiative decays of X(3872) are studied in single-channel approximation
(SCA) and in the coupled-channel (CC) approach, where the decay channels DDˉ∗ are described with the string breaking mechanism. In SCA the transition
rate Γ~2​=Γ(23P1​→ψγ)=71.8~keV and
large Γ~1​=Γ(23P1​→J/ψγ)=85.4~keV
are obtained, giving for their ratio the value
Rψγ​~​=Γ~1​Γ~2​​=0.84. In the
CC approach three factors are shown to be equally important. First, the
admixture of the 13P1​ component in the normalized wave function of
X(3872) due to the CC effects. Its weight cX​(ER​)=0.200±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
Γ1​=Γ(X(3872)→J/ψγ)∼3~keV is very small,
giving the large ratio Rψγ​=B(X(3872)→J/ψγ)B(X(3872)→ψ(2S)γ)​≫1.0.
Arguments are presented why the gluon-exchange interaction may be suppressed
for X(3872) and in this case Γ1​=42.7~keV, Γ2​=70.5~keV, and
Rψγ​=1.65 are predicted for the minimal value cX​(min)=0.185, while for the maximal value cX​=0.215 we obtained
Γ1​=30.8~keV, Γ2​=73.2~keV, and Rψγ​=2.38, which
agrees with the LHCb data.Comment: 12 pages, no figure
The time evolution of a many-fermion system can be described by a Green's
function corresponding to an effective potential, which takes
anti-symmetrization of the wave function into account, called the
Pauli-potential. We show that this idea can be combined with the Green's
Function Monte Carlo method to accurately simulate a system of many
non-relativistic fermions. The method is illustrated by the example of systems
of several (2-9) fermions in a square well.Comment: 12 pages, LaTeX, 4 figure
A universal description of the hyperfine splittings (HFS) in bottomonium and
the Bq​(q=n,s,c) mesons is obtained with a universal strong coupling
constant αs​(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 nf​. The HFS M(B∗)−M(B)=45.3(3) MeV, M(Bs∗​)−M(Bs​)=46.5(3) MeV are obtained in full
agreement with experiment both for nf​=3 and nf​=4. In bottomonium,
M(Υ(9460))−M(ηb​)=70.0(4) MeV for nf​=5 agrees with the BaBar
data, while a smaller HFS, equal to 64(1) MeV, is obtained for nf​=4. We
predict HFS M(Υ(2S))−M(ηb​(2S))=36(1) MeV, M(Υ(3S))−M(η(3S))=27(1) MeV, and M(Bc∗​)−M(Bc​)=57.5(10) MeV, which gives
M(Bc∗​)=6334(1) MeV, M(Bc​(21S0​))=6865(5) MeV, and M(Bc∗​(2S3S1​))=6901(5) MeV.Comment: 5 pages revtex
We show that there are two reasons why the partial width for the transition
Γ1​(Υ(3S)→γχb1​(1P)) is suppressed. Firstly,
the spin-averaged matrix element (m.e.) I(3S∣r∣1PJ​)ˉ​ 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∣1P2​)=0.066 GeV−1, while due to large cancellation the m.e.
I(3S∣r∣1P1​)=−0.020 GeV−1 is small and negative; at the same time the
magnitude of I(3S∣r∣1P0​)=−0.063 GeV−1 is relatively large. These m.e.
give rise to the partial widths: Γ2​(Υ(3S)→γχb2​(1P))=212 eV, Γ0​(Υ(3S)→γχb0​(1P))=54 eV, which are in good agreement with the CLEO and
BaBar data, and also to Γ1​(Υ(3S)→γχb1​(1P))=13 eV, which satisfies the BaBar limit, Γ1​(exp.)<22 eV.Comment: 8 page
The masses of excited charmed mesons are shown to decrease by ∼(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
χc0​(4700). The following masses of the first excitations:
M(23P0​)=2874~MeV, M(23P2​)=2968~MeV, M(23D1​)=3175~MeV,
and M(23D3​)=3187~MeV, and second excitations: M(31S0​)=3008~MeV,
M(33S1​)=3062~MeV, M(33P0​)=3229~MeV, and M(33P2​)=3264~MeV, are predicted. The other states with L=0,1,2 and nr​≥3
have their masses in the region M(nL)≥3.3~GeV.Comment: 15 pages, 4 table
We considered the lattice electroweak theory at realistic values of α
and θW​ 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: LATE