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Motivated by the experimental measurement of the decay rate, $\Gamma$, and the longitudinal polarization, $P_L$, in the Cabibbo favored decay $D_s^+\to factorization approximation invoking several form factors models. We were able to obtain agreement with experiment for both $\Gamma$ and $P_L$ by using experimentally measured values of the form factors $A_1^{D_s\phi}(0)$, $A_2^{D_s\phi}(0)$ and $V^{D_s\phi}(0)$ in the semi-leptonic decay $D_s^+\to final state interaction ($fsi$) by working with the partial waves amplitudes $S$, $P$ and $D$. Numerical calculation shows that the decay amplitude is dominated by $S$ wave, and that the polarization is sensitive to the interference between $S$ and $D$ waves. The range of the phase difference is large

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>→</mml:mo><mml:mi>φ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>decay

Ds+→φρ+decay