Updated analysis of $D\to PP, V\!P$ and $VV$ decays: Implications for $K_S^0-K_L^0$ asymmetries and $D^0$-$\overline {D}^0$ mixing
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2024
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| _version_ | 1866914710468689920 |
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| author | Cheng, Hai-Yang Chiang, Cheng-Wei |
| author_facet | Cheng, Hai-Yang Chiang, Cheng-Wei |
| contents | An updated analysis of the two-body $D\to PP, V\!P$ and $VV$ decays within the framework of the topological diagram approach is performed. A global fit to the Cabibbo-favored (CF) modes in the $V\!P$ sector gives many solutions with similarly small local minima in $χ^2$. The solution degeneracy is lifted once we use them to predict for the singly Cabibbo-suppressed (SCS) modes. Topological amplitudes are extracted for the $η-η'$ mixing angles $ϕ=40.4^\circ$ and $43.5^\circ$. The $K_S^0-K_L^0$ asymmetries in $D\to K_{S,L}^0M$ decays denoted by $R(D,M)$ are studied. While the predicted $R(D^0,P)$ for $P=π^0, η$ and $η'$ agree with experiment, the calculated $R(D^+,π^+)$, $R(D_s^+, K^+)$, $R(D^0,ω)$ and $R(D^0,ϕ)$ deviate from the data. We conjecture that the relative phase between the topological amplitudes $(C+A)$ and $(T+C)$ should be slightly smaller than $90^\circ$ in order to explain the first two discrepancies and that additional singlet contributions due to the SU(3)-singlet nature of $ω$ and $ϕ$ are needed to account for the last two. For doubly Cabibbo-suppressed (DCS) $D\to V\!P$ decays, their topological amplitudes (double-primed) cannot be all the same as the corresponding ones in the CF modes. The assumption of $E_{V,P}''=E_{V,P}$ for the $W$-exchange amplitude leads to some inconsistencies with the experiment. Through the measured relative phases between CF and DCS channels, the relations of $E_{V,P}''$ with $E_{V,P}$ are determined. Long-distance contributions to the $D^0$-$\overline {D}^0$ mixing parameter $y$ are evaluated in the exclusive approach. In particular, we focus on $D\to PP$ and $V\!P$ decays where $y$ can be reliably estimated. We conclude that $y_{_{P\!P}}\sim (0.110\pm 0.011)\%$ and the lower bound on $y_{_{V\!P}}$ is $(0.220\pm 0.071)\%$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_06316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Updated analysis of $D\to PP, V\!P$ and $VV$ decays: Implications for $K_S^0-K_L^0$ asymmetries and $D^0$-$\overline {D}^0$ mixing Cheng, Hai-Yang Chiang, Cheng-Wei High Energy Physics - Phenomenology High Energy Physics - Experiment An updated analysis of the two-body $D\to PP, V\!P$ and $VV$ decays within the framework of the topological diagram approach is performed. A global fit to the Cabibbo-favored (CF) modes in the $V\!P$ sector gives many solutions with similarly small local minima in $χ^2$. The solution degeneracy is lifted once we use them to predict for the singly Cabibbo-suppressed (SCS) modes. Topological amplitudes are extracted for the $η-η'$ mixing angles $ϕ=40.4^\circ$ and $43.5^\circ$. The $K_S^0-K_L^0$ asymmetries in $D\to K_{S,L}^0M$ decays denoted by $R(D,M)$ are studied. While the predicted $R(D^0,P)$ for $P=π^0, η$ and $η'$ agree with experiment, the calculated $R(D^+,π^+)$, $R(D_s^+, K^+)$, $R(D^0,ω)$ and $R(D^0,ϕ)$ deviate from the data. We conjecture that the relative phase between the topological amplitudes $(C+A)$ and $(T+C)$ should be slightly smaller than $90^\circ$ in order to explain the first two discrepancies and that additional singlet contributions due to the SU(3)-singlet nature of $ω$ and $ϕ$ are needed to account for the last two. For doubly Cabibbo-suppressed (DCS) $D\to V\!P$ decays, their topological amplitudes (double-primed) cannot be all the same as the corresponding ones in the CF modes. The assumption of $E_{V,P}''=E_{V,P}$ for the $W$-exchange amplitude leads to some inconsistencies with the experiment. Through the measured relative phases between CF and DCS channels, the relations of $E_{V,P}''$ with $E_{V,P}$ are determined. Long-distance contributions to the $D^0$-$\overline {D}^0$ mixing parameter $y$ are evaluated in the exclusive approach. In particular, we focus on $D\to PP$ and $V\!P$ decays where $y$ can be reliably estimated. We conclude that $y_{_{P\!P}}\sim (0.110\pm 0.011)\%$ and the lower bound on $y_{_{V\!P}}$ is $(0.220\pm 0.071)\%$. |
| title | Updated analysis of $D\to PP, V\!P$ and $VV$ decays: Implications for $K_S^0-K_L^0$ asymmetries and $D^0$-$\overline {D}^0$ mixing |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2401.06316 |