Precise theoretical prediction on branching fractions and polarizations of $D\to VV$ decays

We present a precise and systematic analysis of $D\to VV$ decays within the factorization-assisted topological-amplitude (FAT) approach, where $D$ denotes the set $\{D^0,D^{+},D_s^{+}\}$ and $V$ represents the vector mesons $\rho ,K^{\ast },\omega$, and $\phi$. Given the limited current experimental data, the FAT approach serves as a available phenomenological framework for predicting charmed meson decays to both vector mesons. In this framework, incorporating flavor SU(3) symmetry breaking effects, we can express nonfactorizable contributions of different modes as a minimal set of universal parameters globally fitted to experimental data. Utilizing 36 experimental data points for $D\to VV$ decays, we precisely extract 10 nonfactorizable parameters associated with the $C$ and $E$ topological diagrams with ${\chi }^2\mathrm{/}\mathrm{d}\mathrm{.}\mathrm{o}\mathrm{.}\mathrm{f}\mathrm{.}=8.43$. We find that a large strong phase in the longitude $E$ amplitude cause strong destructive interference with the $C$ longitudinal component, yielding $f_{\parallel }>f_L$, contrary to the naive factorization predictions. Additionally, for modes processing exclusively by the $E$ diagram, the amplitude hierarchy $\mathrm{\mid }S\mathrm{\mid }<\mathrm{\mid }D\mathrm{\mid }$ leads to a $D$-wave branching fraction larger than that of the $S$-wave. This explains recent observations that contradict $S$-wave dominance predictions. The predicted branching fractions and polarizations for 28 decay modes are consistent with existing experimental data. Unobserved modes, especially those with branching fractions of order ${10}^{-3}\sim {10}^{-2}$, the $D$-wave dominated modes, and modes exhibiting $f_{\parallel }>f_L$, await measurement by BESIII, STCF, Belle II and LHCb.