118489229
Dynamical light vector mesons in low-energy scattering of Goldstone bosons
Abstract We present a study of Goldstone boson scattering based on the flavor SU(3) chiral Lagrangian formulated with vector mesons in the tensor field representation. A coupled-channel computation is confronted with the empirical s- and p-wave phase shifts, where good agreement with the data set is obtained up to about 1.2 GeV. There are two relevant free parameters only, the chiral limit value of the pion decay constant and the coupling constant characterizing the decay of the rho meson into a pair of pions. We apply a recently suggested approach that implements constraints from micro-causality and coupled-channel unitarity. Generalized potentials are obtained from the chiral Lagrangian and are expanded in terms of suitably constructed conformal variables. The partial-wave scattering amplitudes are defined as solutions of non-linear integral equations that are solved by means of an N/D ansatz.
118417689
Photon-fusion reactions from the chiral Lagrangian with dynamical light vector mesons
We study the reactions γγ→π0π0, π+π−, $K^{0}\bar{K}^{0}$, K+K−, ηη and π0η based on a chiral Lagrangian with dynamical light vector mesons as formulated within the hadrogenesis conjecture. At present our chiral Lagrangian contains five unknown parameters that are relevant for the photon-fusion reactions. They parameterize the strength of interaction terms involving two vector meson fields. These parameters are fitted to photon-fusion data γγ→π0π0, π+π−,π0η and to the decay η→π0γγ. In order to derive gauge invariant reaction amplitudes in the resonance region constraints from maximal analyticity and exact coupled-channel unitarity are used. Our results are in good agreement with the existing experimental data from threshold up to about 0.9 GeV for the two-pion final states. The a0 meson in the π0η channel is dynamically generated and an accurate reproduction of the γγ→π0η data is achieved up to 1.2 GeV. Based on our parameter sets we predict the γγ→ $K^{0}\bar{K}^{0}$, K+K−, ηη cross sections.
119118966
The hyperfine splittings in heavy-light mesons and quarkonia
AbstractHyperfine splittings (HFS) are calculated within the Field Correlator Method, taking into account relativistic corrections. The HFS in bottomonium and the Bq (q = n, s) mesons are shown to be in full agreement with experiment if a universal coupling αHF = 0.310 is taken in perturbative spinspin potential. It gives M(B*) −M(B) = 45.7(3) MeV, M(Bs* ) − M(Bs) = 46.7(3) MeV (nf = 4), while in bottomonium ΔHF(b% MathType!MTEF!2!1!+-
% feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC
% vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz
% ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb
% L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe
% pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam
% aaeaqbaaGcbaGafmOyaiMbaebaaaa!3C30!
$$
\bar b
$$) = M(Υ(9460)) − M(ηb(1S)) = 63.4 MeV for nf = 4 and 71.1 MeV for nf = 5 are obtained; just the latter agrees with recent BaBar data. For unobserved excited states we predict M(Υ(2S))−M(ηb(2S)) = 36(2)MeV,M(Υ(3S))−M(ηb(3S)) = 28(2)MeV, and also M(Bc*) = 6334(4) MeV, M(Bc(2S)) = 6868(4) MeV, M(Bc* (2S)) = 6905(4) MeV. The mass splittings between D(23S1) − D(21S0), Ds(23S1) − Ds(21S0) are predicted to be ∼75 MeV, which are significantly smaller than in several other studies but agree with the mass splitting between recently observed D(2533) and D*(2610).
119236437
Dielectron widths of the S-, D-vector bottomonium states
AbstractThe dielectron widths of Y(nS)(n = 1, …, 7) and vector decay constants are calculated using the relativistic string Hamiltonian with a universal interaction. For Y(nS) (n = 1, 2, 3) the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For Y(10580) and Y(11020) a good agreement with experiment is reached only if the 4S-3D mixing (with a mixing angle θ = 27°± 4°) and 6S-5D mixing (with θ = 40°±5°) are taken into account. The possibility to observe higher “mixed D-wave” resonances, $$
\tilde \Upsilon 
$$(n3D1) with n = 3, 4, 5 is discussed. In particular, $$
\tilde \Upsilon 
$$(≈11120), originating from the pure 53D1 state, can acquire a rather large dielectron width, ∼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, Γee(n3D1)≤ 2 eV.
17551335
On causality, unitarity and perturbative expansions
Abstract We present a pedagogical case study how to combine micro-causality and unitarity based on a perturbative approach. The method we advocate constructs an analytic extrapolation of partial-wave scattering amplitudes that is constrained by the unitarity condition. Suitably constructed conformal mappings help to arrive at a systematic approximation of the scattering amplitude in a quantum-field theoretical context. The technique is illustrated at hand of a Yukawa interaction. The typical case of a superposition of strong short-range and weak long-range forces is investigated.
123678981
Dispersive analysis ofω/ϕ→3π,πγ*
The decays ω/Φ → 3π are considered in the dispersive framework that is based on the isobar decomposition and subenergy unitarity. The inelastic contributions are parametrized by the power series in a suitably chosen conformal variable that properly accounts for the analytic properties of the amplitude. The Dalitz plot distributions and integrated decay widths are presented. Our results indicate that the final- state interactions may be sizable. As a further application of the formalism we also compute the electromagnetic transition form factors of ω/Φ → π⁰γ*.
118596022
The Hyperfine Splittings in Bottomonium and the $B_q (q=n,s,c)$ Mesons
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(B s ) − 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(B ∗ c ) − M(Bc) = 57.5(10) MeV, which gives M(B ∗ c ) = 6334(1) MeV, M(Bc(2 1S0)) = 6865(5) MeV, and M(B c (2S 3S1)) = 6901(5) MeV.
119293722
Di-electron and two-photon widths in charmonium
AbstractThe vector and pseudoscalar decay constants are calculated in the framework of the Field Correlator Method. Di-electron widths: Γee(J/ψ) = 5.41 keV, Γee(ψ′(3686)) = 2.47 keV, Γee(ψ″(3770)) = 0.248 keV, in good agreement with experiment, are obtained with the same coupling, αs = 0.165, in the QCD radiative corrections. We show that the larger αs = 0.191 ± 0.004 is needed to reach agreement with experiment for Γγγ(χc) = 7.22 keV, Γγγ(χc(3P0)) = 3.3 keV, Γγγχc(3P2)) = 0.54 keV, and also for Γ(J/ψ → 3g) = 59.5 keV, Γ(J/ψ → γ2g) = 5.7 keV. Meanwhile, even larger αs = 0.238 gives rise to good description of Γ(ψ′ → 3g) = 52.7 keV, Γ(ψ′ → γ2g) = 3.5 keV, and provides correct ratio of the branching fractions: $$
\frac{{\mathcal{B}({J \mathord{\left/
 {\vphantom {J \psi }} \right.
 \kern-\nulldelimiterspace} \psi } \to light hadrons)}}
{{\mathcal{B}(\psi ' \to light hadrons)}} = 0.24
$$.