# Relation between Light Cone Distribution Amplitudes and Shape Function in B mesons - High Energy Physics - Phenomenology

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Abstract: The Bakamjian-Thomas relativistic quark model provides a Poincar\-erepresentation of bound states with a fixed number of constituents and, in theheavy quark limit, form factors of currents satisfy covariance and Isgur-Wisescaling. We compute the Light Cone Distribution Amplitudes of $B$ mesons$\phi {\pm}^B\omega$ as well as the Shape Function $S\omega$, that entersin the decay $B \to X s \gamma$, that are also covariant in this class ofmodels. The LCDA and the SF are related through the quark model wave function.The former satisfy, in the limit of vanishing constituent light quark mass, theintegral relation given by QCD in the valence sector of Fock space. Using agaussian wave function, the obtained $S\omega$ is identical to the so-calledRoman Shape Function. From the parameters for the latter that fit the $B \toX s\gamma$ spectrum we predict the behaviour of $\phi {\pm}^B\omega$. Wediscuss the important role played by the constituent light quark mass. Inparticular, although $\phi -^B0 ot= 0$ for vanishing light quark mass, anon-vanishing mass implies the unfamiliar result $\phi -^B 0 = 0$. Moreover,we incorporate the short distance behaviour of QCD to $\phi +^B \omega$,which has sizeable effects at large $\omega$. We obtain the values for theparameters $\bar{\Lambda} \cong 0.35$ GeV and $\lambda B^{-1} \cong 1.43$GeV$^{-1}$. We compare with other theoretical approaches and illustrate thegreat variety of models found in the literature for the functions $\phi {\pm}^B\omega$; hence the necessity of imposing further constraints as in thepresent paper. We briefly review also the different phenomena that aresensitive to the LCDA.

Autor: A. Le Yaouanc, L. Oliver, J.-C. Raynal

Fuente: https://arxiv.org/