Distribution amplitudes of heavy mesons and quarkonia on the light front
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Regular Article - Theoretical Physics
Distribution amplitudes of heavy mesons and quarkonia on the light front Fernando E. Serna1,2 , Roberto Correa da Silveira1, J. J. Cobos-Martínez3,4 , Bruno El-Bennich1,2,a , Eduardo Rojas5 1
LFTC, Universidade Cidade de São Paulo, Rua Galvão Bueno, 868, 01506-000 São Paulo, SP, Brazil IFT, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271, 01140-070 São Paulo, SP, Brazil 3 Departamento de Física, Universidad de Sonora, Boulevard Luis Encinas J. y Rosales, 83000 Hermosillo, Sonora, Mexico 4 Cátedra CONACyT, Departamento de Física, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Apartado Postal 14-740, 7000 Ciudad de México, Mexico 5 Departamento de Fésica, Universidad de Nariño, A.A. 1175, San Juan de Pasto, Colombia
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Received: 21 August 2020 / Accepted: 2 October 2020 © The Author(s) 2020
Abstract The ladder kernel of the Bethe–Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the Du , Ds , Bu , Bs and Bc mesons and the heavy quarkonia ηc and ηb within the same framework at a physical pion mass. The corresponding Bethe–Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory. A comparison with the first inverse moment of the heavy meson distribution amplitude in heavy quark effective theory is made.
1 Introduction The introduction of hadronic light-cone distribution amplitudes (LCDA) dates back to the seminal works on hard exclusive reactions in perturbative QCD [1–5]. These nonperturbative and scale-dependent functions can be understood as the closest relative of quantum mechanical wave functions in quantum field theory. They describe the longitudinal momentum distribution of valence quarks in a hadron in the limit of negligible transverse momentum, here given by the leading Fock-state contribution to its light-front wave function, the so-called leading-twist LCDA. In particular, the light-front formulation of a wave function allows for a probability interpretation of partons not readily accessible in an infinite-body field theory, since particle number is conserved in this frame. In other words, φ(x, μ) expresses the light-front fraction of the hadron’s momentum carried by a valence quark. a e-mail:
The simplest hadronic distribution amplitude is that of the pion and has justifiably received much attention [6– 19] due to increasing interest in, amongst others, precision calculation of two-photon transition form factor [20–29] and of weak semi-leptonic, B → π ν , and non-leptonic B → π π, B → ρπ, B → K π . . . decays. The latter can also be treated as a hard exclusive process with associated factorization theorem, which separates the decay amplitudes for a given process into hard short-distance contributions and
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