Light-meson properties from the Bethe-Salpeter equation

Abstract

We discuss how to extract observables from an inhomogeneous vertex Bethe-Salpeter equation without resorting to the corresponding homogeneous equation. As an example we present a prediction for the $e^+e^-$ decay width of the $\rho(1450)$ or $\rho'$ meson. We also attempt to identify the momentum range contributing to a vector meson's decay constant.Comment: 3 pages, 3 figures, talk presented at the conference "Quark Confinement and the Hadron Spectrum IX", Madrid, Spain, 30th of August-3rd of September 2010; submitted to the proceeding

Spectrum of Charmonia within a Contact Interaction

“…We only have to ensure that the reduction in the strength of the kernel is appropriately compensated by increasing the ultraviolet cut-off, a natural requirement for studying heavy quarks. We find that with a modified choice of two parameters, not only the masses of the ground state mesons, i.e., pseudo-scalar (η c (1S)), vector (J/Ψ(1S)), scalar (χ c 0 (1P )), and axial vector (χ c 1 (1P )), but also their weak decay constants, are in much better agreement with the experiments [29] as well as earlier SDE calculations with QCD based refined truncations [25]. This is an encouraging first step towards a comprehensive study of heavy mesons in this approach.…”

“…The rest of the meson masses are predictions of the model. As can be seen from Table 2, the predictions for the masses of the remaining mesons are in good agreement with the results obtained from more sophisticated SDE-BSE model calculations [25,26], lattice QCD for the charm sector [27,28] as well as experimental values [29]. On the other side, Table 2 also shows that the pseudoscalar and vector decay constants, for the model parameters used, are strongly underestimated, in disagreement both with model calculations and experimental data.…”

“…For this purpose, we set out to redefine the parameters of the CI to study the masses and weak decay constants. [26] 3.065 ---RB2 [26] 3.210 ---decay constants f ηc f J/Ψ Experiment [29] 0.361 0.416 S1rp [4] 0.239 0.198 S3ccp [4] 0.326 0.330 BK [25] 0.399 0.448 Contact Interaction 0.305 0.220 Table 3. Ground state charmonia masses and decay constants obtained with the best-fit parameter set: m g = 0.8 GeV, α IR = 0.93π/20, Λ IR = 0.24 GeV, Λ UV = 2.788 GeV.…”

Charming quasi-exotic open-flavor mesons

“…However, the latter procedure does not provide a bound state's Bethe-Salpeter amplitude (BSA) and, therefore, does not allow for a sophisticated analysis of, e. g., leptonic decay constants or other observables. Another approach still involves the use of inhomogeneous versions of the appropriate BSE, which in general provides off-shell information and can be used to fit or extrapolate desired on-shell properties, including leptonic decay constants [53][54][55].…”

On a New Approach to Meson Phenomenology with the Bethe–Salpeter Equation

“…When these were finally being overcome recently, see, e. g., [20,21], the model assumptions remained anchored to the light-quark domain nonetheless. While this still gave reasonable results for pseudoscalar and vector mesons, states identified with either radial or orbital angular momentum excitations were not well described [22][23][24][25][26][27][28][29][30]. While this could be interpreted on a general footing and the conclusion could be drawn that the RL truncation is not sufficient to provide a generally satisfying meson phenomenology and that for such satisfaction to be achieved one needs to include corrections to this truncation or, simply speaking, a quark-gluon vertex more complicated than the bare one, we challenge this line of thinking and attempt a counterexample.…”