Interference between doubly-Cabibbo-suppressed and Cabibbo-favored amplitudes in D 0 → K S ( π 0 , η , η ′ <mml:mo …
2006; American Physical Society; Volume: 74; Issue: 5 Linguagem: Inglês
10.1103/physrevd.74.057502
ISSN1550-7998
Autores Tópico(s)Black Holes and Theoretical Physics
ResumoA definite relative phase and amplitude exists between the doubly-Cabibbo-suppressed amplitude for ${D}^{0}\ensuremath{\rightarrow}{K}^{0}{M}^{0}$ and the Cabibbo-favored amplitude for ${D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{M}^{0}$, where ${M}^{0}=({\ensuremath{\pi}}^{0},\ensuremath{\eta},{\ensuremath{\eta}}^{\ensuremath{'}})$: $A({D}^{0}\ensuremath{\rightarrow}{K}^{0}{M}^{0})=\ensuremath{-}{tan}^{2}{\ensuremath{\theta}}_{C}A({D}^{0}\ensuremath{\rightarrow}{\overline{K}}^{0}{M}^{0})$. Here ${\ensuremath{\theta}}_{C}$ is the Cabibbo angle. This relation, although previously recognized (for ${M}^{0}={\ensuremath{\pi}}^{0}$) as a consequence of the U-spin subgroup of SU(3), is argued to be less sensitive to corrections involving SU(3) breaking than related U-spin relations involving charged kaons or strange $D$ mesons. A corresponding relation between ${D}^{+}\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{+}$ and ${D}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{\ensuremath{\pi}}^{+}$ is not predicted by U-spin. As a consequence, one expects the asymmetry parameters $R({D}^{0},{M}^{0})\ensuremath{\equiv}[\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{K}_{S}{M}^{0})\ensuremath{-}\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{K}_{L}{M}^{0})/[\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{K}_{S}{M}^{0})+\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{K}_{L}{M}^{0})]$ each to be equal to $2{tan}^{2}{\ensuremath{\theta}}_{C}=0.106$, in accord with a recent CLEO measurement $R({D}^{0})\ensuremath{\equiv}R({D}^{0},{\ensuremath{\pi}}^{0})=0.122\ifmmode\pm\else\textpm\fi{}0.024\ifmmode\pm\else\textpm\fi{}0.030$. No prediction for the corresponding ratio $R({D}^{+})$ is possible on the basis of U-spin.
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