Abstract
We consider the fidelity of the vector meson dominance (VMD) assumption as an instrument for relating the electromagnetic vector-meson production reaction e + p rightarrow e^prime + V + p to the purely hadronic process V + p rightarrow V+p. Analyses of the photon vacuum polarisation and the photon-quark vertex reveal that such a VMD Ansatz might be reasonable for light vector-mesons. However, when the vector-mesons are described by momentum-dependent bound-state amplitudes, VMD fails for heavy vector-mesons: it cannot be used reliably to estimate either a photon-to-vector-meson transition strength or the momentum dependence of those integrands that would arise in calculations of the different reaction amplitudes. Consequently, for processes involving heavy mesons, the veracity of both cross-section estimates and conclusions based on the VMD assumption should be reviewed, e.g., those relating to hidden-charm pentaquark production and the origin of the proton mass.
Highlights
The interaction of a heavy vector-meson, J/ψ or Υ, with a proton target offers prospects for access to a quantum chromodynamics (QCD) van der Waals interaction, generated by multiple gluon exchange [1, 2], and the QCD trace anomaly [3,4]
The interaction of a heavy vector-meson, J/ψ or Υ, with a proton target offers prospects for access to a QCD van der Waals interaction, generated by multiple gluon exchange [1, 2], and the QCD trace anomaly [3,4]. The former is of interest because it may relate to, inter alia, the observation of hiddencharm pentaquark states [5]; whereas the latter has received attention owing to its connection with emergent hadron mass (EHM), the phenomenon that is seemingly responsible for roughly 99% of the visible mass in the Universe [6,7,8,9,10,11,12]
We reiterate some points. (i) The interaction is consistent with that found in studies of QCD’s gauge sector. It expresses the result, enabled by strong non-Abelian gaugesector dynamics, that the gluon propagator is a bounded, smooth function of spacelike momenta, whose maximum value on this domain is at s = 0 [39,51,52], and capitalises on the property that the dressed gluon-quark vertex does not possess any structure which can qualitatively alter these features [68]. (ii) Equation (33) preserves the one-loop renormalisation group behaviour of QCD; e.g., the quark massfunctions produced are independent of the renormalisation point. (iii) On s (2mt )2, Eq (33) defines a two-parameter Ansatz, the details of which determine whether such corollaries of EHM as confinement and dynamical chiral symmetry breaking (DCSB) are realised in solutions of the bound-state equations [12,47]
Summary
The interaction of a heavy vector-meson, J/ψ or Υ, with a proton target offers prospects for access to a QCD van der Waals interaction, generated by multiple gluon exchange [1, 2], and the QCD trace anomaly [3,4]. From the proton ( p), in reactions like e+ p → e +V + p [13]; and the same method is proposed for use at planned higherenergy facilities [14,15] In this connection, it is typically assumed that single-pole vector meson dominance (VMD). As commonly used, it assumes: (i) that a photon, which is, at best, real, but is generally spacelike, so that Q2 ≥ 0, transmutes into an on-shell vector-meson, with timelike momentum. Where αem = e2/(4π ) is the fine structure constant of quantum electrodynamics (QED) and e2V is a squared sum of quark charges weighted by the meson’s flavour wave function, as referred to the positron charge: 2(eρ , eω2 , eφ , e2J/ψ , eΥ2 ) These values assume isospin symmetry and ideal mixing for vector-mesons, e.g., the φ-meson is a sssystem. A dimensionless coupling for vector-mesons is commonly used:
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