Electromagnetic meson form factor from a relativistic coupled-channels approach

Abstract

Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for spacelike momentum transfers. The elastic scattering of an electron by a confined quark-antiquark pair is treated as a relativistic two-channel problem for the qqe and qqeγ states. With the approximation that the total velocity of the qqe system is conserved at (electromagnetic) interaction vertices this simplifies to an eigenvalue problem for a Bakamjian-Thomas type mass operator. After elimination of the qqeγ channel the electromagnetic meson current and form factor can be directly read off from the one-photon-exchange optical potential. By choosing the invariant mass of the electron-meson system large enough, cluster separability violations become negligible. An equivalence with the usual front-form expression, resulting from a spectator current in the q + = 0 reference frame, is established. The generalization of this multichannel approach to electroweak form factors for an arbitrary bound few-body system is quite obvious. By an appropriate extension of the Hilbert space this approach is also able to accommodate exchange-current effects.

Semileptonic meson decays in point-form relativistic quantum mechanics: Unambiguous extraction of weak form factors

“…It was initially applied to calculate the spectrum and decay widths of vector and axial-vector mesons within the chiral constituent quark model [8,9]. Later, electromagnetic properties of spin-0 and spin-1 twobody bound states with equal-constituent masses were studied [10][11][12]. More recently, the relativistic multichannel formalism was extended to unequal-mass constituents and to weak decay form factors in the time-like momentum transfer region [14][15][16].…”

Form Factors of Few-Body Systems: Point Form Versus Front Form

“…If M is a pseudoscalar meson it can be shown that [6,7]. Since internal momenta are integrated over, the most general covariant decomposition of J µ em thus takes on the form…”

“…"On-shell" means that (2) and the explicit expression for the meson current J µ em (k ′ M ; k M ) in terms of the constituent currents and the bound-state wave functions are given in Refs. [6,7,8].…”

“…(5) goes over into the standard front-form result for a spectator current in the q + = 0 frame [6,7] with S becoming the Meloshrotation factor. The generalization to pseudoscalar mesons with unequal-mass constituents is straightforward [8].…”

“…For equal quark and antiquark masses and pure s-wave pseudoscalar mesons it is given by [6,7] with the spin-rotation factor S being the trace of a product of Wigner D functions. Primed and unprimed momenta are related by appropriate rotationless boosts,k = lims→∞ B −1…”