Abstract
We study the light-front zero-mode contribution to the transition form factors (g, f, a ±, T i ) (i = 1, 2, 3) for the exclusive semileptonic P → V ℓν ℓ and rare P → V ℓ +ℓ− decays using a covariant fermion field theory model in (3+1) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γμ = γ μ − (2k − P V )μ/D, the six form factors (g, f, a +, T 1, T 2, T 3) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor (1/x)n of the struck quark with the power n > 0. Although the form factor a − is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex Γμ = γ μ term or from the other term just with a constant D (i.e. n = 0). We identify the zero-mode operator that is convoluted with the initial- and final-state valence wave functions to generate the zero-mode contribution to a −.
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Choi, HM., Ji, CR. Light-Front Zero-Mode Issue for the Transition Form Factors Between Pseudoscalar and Vector Mesons. Few-Body Syst 52, 409–414 (2012). https://doi.org/10.1007/s00601-011-0294-x
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DOI: https://doi.org/10.1007/s00601-011-0294-x