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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.16240 |
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| _version_ | 1866913188082089984 |
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| author | Bhattacharya, Bhubanjyoti Fines-Neuschild, Mirjam Houck, Andrea Imbeault, Maxime Jean, Alexandre London, David |
| author_facet | Bhattacharya, Bhubanjyoti Fines-Neuschild, Mirjam Houck, Andrea Imbeault, Maxime Jean, Alexandre London, David |
| contents | Under flavor $SU(3)$ symmetry (SU(3)$_F$), the final-state particles in $B\to PPP$ decays ($P$ is a pseudoscalar meson) are treated as identical, and the $PPP$ must be in a fully-symmetric (FS) state, a fully-antisymmetric (FA) state, or in one of four mixed states. In this paper, we present the formalism for the FA states. We write the amplitudes for the 22 $B\to PPP$ decays that can be in an FA state in terms of both SU(3)$_F$ reduced matrix elements and diagrams. This shows the equivalence of diagrams and SU(3)$_F$. We also give 15 relations among the amplitudes in the SU(3)$_F$ limit, as well as the additional four that appear when the diagrams $E$/$A$/$PA$ are neglected. We present sets of $B \to PPP$ decays that can be used to extract $γ$ using the FA amplitudes. The value(s) of $γ$ found in this way can be compared with the value(s) found using the FS states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16240 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Charmless $B\to PPP$ Decays: the Fully-Antisymmetric Final State Bhattacharya, Bhubanjyoti Fines-Neuschild, Mirjam Houck, Andrea Imbeault, Maxime Jean, Alexandre London, David High Energy Physics - Phenomenology High Energy Physics - Experiment Under flavor $SU(3)$ symmetry (SU(3)$_F$), the final-state particles in $B\to PPP$ decays ($P$ is a pseudoscalar meson) are treated as identical, and the $PPP$ must be in a fully-symmetric (FS) state, a fully-antisymmetric (FA) state, or in one of four mixed states. In this paper, we present the formalism for the FA states. We write the amplitudes for the 22 $B\to PPP$ decays that can be in an FA state in terms of both SU(3)$_F$ reduced matrix elements and diagrams. This shows the equivalence of diagrams and SU(3)$_F$. We also give 15 relations among the amplitudes in the SU(3)$_F$ limit, as well as the additional four that appear when the diagrams $E$/$A$/$PA$ are neglected. We present sets of $B \to PPP$ decays that can be used to extract $γ$ using the FA amplitudes. The value(s) of $γ$ found in this way can be compared with the value(s) found using the FS states. |
| title | Charmless $B\to PPP$ Decays: the Fully-Antisymmetric Final State |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment |
| url | https://arxiv.org/abs/2308.16240 |