We show that D → Pη′ decay amplitudes, where P = K, π, η, cannot be simply related to their D → Pη counterparts with a single η0–η8 mixing angle. We propose a novel, consistent treatment of η0–η8 mixing for application in D → Pη and D → Pη′ decays. Using this framework, we perform a global analysis of D → Pη′ decays employing SU(3)F symmetry including linear SU(3)F breaking. We find that the assumption of 30% SU(3)F breaking is in slight tension (2.5σ) with the data when compared to a fit that allows for 50% SU(3)F breaking, the latter giving a perfect description of the data. In order to allow for further scrutinization of SU(3)F-breaking effects in the future, we give branching ratio predictions for all D → Pη′ modes. Our predictions deviate from the current data in case of the branching ratios <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26223_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">B</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{B} $</EquationSource> </InlineEquation>(<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26223_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>D</mi> <mi>s</mi> <mo>+</mo> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {D}_s^{+} $</EquationSource> </InlineEquation> → K+η′) and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26223_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">B</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{B} $</EquationSource> </InlineEquation>(D+ → K+η′). Future more precise measurements of these channels are therefore highly important in order to clarify the quality of the SU(3)F expansion in nonleptonic D → Pη′ decays.

Anatomy of non-leptonic two-body decays of charmed mesons into final states with η′

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2025年5月16日

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Carolina Bolognani,
Ulrich Nierste,
Stefan Schacht,
K. Keri Vos

摘要

We show that D → Pη′ decay amplitudes, where P = K, π, η, cannot be simply related to their D → Pη counterparts with a single η₀–η₈ mixing angle. We propose a novel, consistent treatment of η₀–η₈ mixing for application in D → Pη and D → Pη′ decays. Using this framework, we perform a global analysis of D → Pη′ decays employing SU(3)_F symmetry including linear SU(3)_F breaking. We find that the assumption of 30% SU(3)_F breaking is in slight tension (2.5σ) with the data when compared to a fit that allows for 50% SU(3)_F breaking, the latter giving a perfect description of the data. In order to allow for further scrutinization of SU(3)_F-breaking effects in the future, we give branching ratio predictions for all D → Pη′ modes. Our predictions deviate from the current data in case of the branching ratios $B$ $ \mathcal{B} $ ( $D_{s}^{+}$ $ {D}_s^{+} $ → K⁺η′) and $B$ $ \mathcal{B} $ (D⁺ → K⁺η′). Future more precise measurements of these channels are therefore highly important in order to clarify the quality of the SU(3)_F expansion in nonleptonic D → Pη′ decays.