Implications of factorization for the determination of hadronic form factors in $D_s^+ \ra φ$ transition

Details Implications of factorization for the determination of hadronic form factors in $D_s^+ \ra φ$ transition Implications of factorization for the determination of hadronic form factors in $D_s^+ \ra φ$ transition

1994-07-29

arxiv.org/abs/hep-ph/9407400v1

Phys.Lett. B339 (1994) 173-180

Physics

High Energy Physics

High Energy Physics - Phenomenology

Latex 10 pages( 4 figures), PAR/LPTHE/94-30

Scientific paper

10.1016/0370-2693(94)91151-7

Using factorization we determine the allowed domains of the ratios of form factors, $x = A_2(0)/A_1(0)$ and $y = V(0)/A_1(0)$, from the experimentally measured ratio $R_h \equiv \Gamma(D_s^+ \ra \phi \rho^+)/\Gamma(D_s^+ \ra \phi \pi^+)$ assuming three different scenarios for the $q^2$-dependence of the form factors. We find that the allowed domains overlap with those obtained by using the experimentally measured ratio $R_{s\ell} = \Gamma(D^+_s \ra \phi \ell^+ \nu_{\ell})/\Gamma(D^+_s \ra \phi \pi^+)$ provided that the phenomenological parameter $a_1$ is $1.23$. Such a comparison presents a genuine test of factorization. We calculate the longitudinal polarization fraction, $\Gamma_L/\Gamma \equiv \Gamma(D_s^+ \ra \phi_L \rho^+_L)/\Gamma(D_s^+ \ra \phi \rho^+)$, in the three scenarios for the $q^2$-dependence of the form factors and emphasize the importance of measuring $\Gamma_L/\Gamma $. Finally we discuss the $q^2$-distribution of the semileptonic decay and find that it is rather insensitive to the scenarios for the $q^2$-dependence of the form factors, and unless very accurate data can be obtained it is unlikely to discriminate between the different scenarios. Useful information on the value of $x$ might be obtained by the magnitude of the $q^2$-distribution near $q^2 = 0$. However the most precise information on $x$ and $y$ would come from the knowledge of the longitudinal and left-right transverse polarizations of the final vector mesons in hadronic and/or semileptonic decays.

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