A Simple Expression for Heavy to Light Meson Semileptonic Decays Form Factors

Abstract

Like the two-photon and two-gluon decays of the $P$-wave ${\chi }_{c0,2}$ and ${\chi }_{b0,2}$ charmonium state for which the Born term produces a very simple decgays amplitude in terms of an effective Lagrangian with two-quark local operator, the Born term for the processes $c\bar{d}\to (\pi ,K)\ell \nu$ and $b\bar{d}\to (\pi ,K)\ell \nu$, could also produce the $D$ and $B$ meson semileptonic decays with the light meson $\pi ,K$ in the final state. In this approach to heavy-light meson form factors with the $\pi$, K meson treated as Goldstone boson, a simple expression is found for the decays form factors, given as~: $f_{+}(0)/(1-q^2/(m_H^2+m_{\pi }^2))$, with $H=D,B$ for $D,B\to \pi$ form factors, and $f_{+}(0)/(1-q^2/(m_H^2+m_K^2))$ for $B,D\to K$ form factor. The purpose of this paper is to show that this expression for the form factors could describe rather well the $q^2$- behaviour observed in the BaBar, Belle and BESIII measurements and lattice simulation. In particular, the $D\to K$ form factors are in good agreement with the measured values in the whole range of $q^2$ showing evidence for $SU(3)$ breaking with the presence of $m_K^2$ term in the quark propagator, but some corrections to the Born term are needed at large $q^2$ for $D,B\to \pi$ form factors.

v4, published version, Int. J. Mod. Phys. A 33 (2018) 1850160

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Cited by in corpus (1)

• Semileptonic $D_{(s)}$-meson decays in the light of recent data