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

Abstract

We present a precise and systematic analysis of $D \to V V$ 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 $\rho, K^*, \omega$, 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 $\chi^2/\mathrm{d.o.f.}=8.43$. 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 $|S|<|D|$ 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 $10^{-3}\sim10^{-2}$, the $D$-wave dominated modes, and modes exhibiting $f_\parallel >f_L $, await measurement by BESIII, STCF, Belle II and LHCb.