Mesons as bilocal fields in the harmonic approximation: A reassessment

Abstract

The spectrum and lepton decay constants of the pion, the kaon, and their radial excitations, as well as the pion decay width in two photons, are computed in a recently proposed framework that combines the bilocal approach to mesons and the potential method treated covariantly.

APPLICATION OF JAIN AND MUNCZEK'S BOUND-STATE APPROACH TO γγ-PROCESSES OF π0, ηc AND ηb

“…Its four chief virtues, however, are (i) that it satisfies the Ward-Takahashi identity (21), (ii) that it reduces to the bare vertex in the free-field limit as must be in perturbation theory, (iii) that its transformation properties under Lorentz transformations and charge conjugation are the same as for the bare vertex, and (iv) it has no kinematic singularities. It is important to note that the correct axial-anomaly result cannot be obtained [11] analytically in the chiral limit unless a quark-photon-quark (qqγ) vertex that satisfies the Ward-Takahashi identity is used (even if DχSB is employed and the pion does appear as a Goldstone boson, as comparison with [54,55] shows).…”

Quark off-shell contributions to KL → γγ in a bound-state approach

“…Of course, with another choice of V 0 and m q , one can achieve much better agreement for meson decays if one accepts meson masses which are several times too high, as shown in [6] on the example of the pion. However, as already remarked above, the problems of accounting quantitatively for the hadronic structure and decays within the bound-state approach are out of scope of this paper.…”

“…To evaluate the hadronic matrix elements of the above effective operators (2)-(6), we use the variant [8,9] of an effective meson bilocal theory [9][10][11][12] in which the related decay π 0 → γγ was computed by two of us [6], along with the pion and kaon spectrum and the decay constants 2 F π and F K . Varying the effective bilocal action yields [9][10][11][12]7] the Schwinger-Dyson equation (SDE) for the dressed quark propagator (whose self-mass Σ(q) is thereby generated dynamically), and the Bethe-Salpeter equation (BSE) for the bilocal bound-state meson-vertex function.…”

“…For leptonic weak decays (e. g. when calculating F π or F K in ref. [6]), L(x) was simply the leptonic current coupled to the V-A quark current. Here, in order to induceK 0 → γγ , L(x) includes both the ordinary flavour diagonal photonic coupling eQγ µ A µ (x) and the electroweak FC vertices contained in (2):…”

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

“…The combination of the V-shaped potential γ |y| withṼ (y) leads to a singular funnel shaped potential. We remind the reader that, although the term ''funnel potential'' (or ''funnel interaction'') was coined in meson physics with reference to the central potential V (r) = ar − b/r in three dimensions (see [51][52][53]), it has later been used, referring to different potentials, in other areas of physics (see [54][55][56]). It is noteworthy that while there is no ambiguity as to the meaning of the δ-interaction, there have been different interpretations of the meaning of the δ ′ -interaction in the literature on the subject (see [57] for a thorough critical review of the various interpretations found in the relevant literature).…”