Unitarity bounds with subthreshold and anomalous cuts for $b$-hadron decays
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| Format: | Preprint |
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2024
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| _version_ | 1866912231155826688 |
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| author | Gopal, Abinand Gubernari, Nico |
| author_facet | Gopal, Abinand Gubernari, Nico |
| contents | We derive a generalisation of the Boyd-Grinstein-Lebed (BGL) parametrization. Most form factors (FFs) in $b$-hadron decays exhibit additional branch cuts -- namely subthreshold and anomalous branch cuts -- beyond the ``standard'' unitarity cut. These additional cuts cannot be adequately accounted for by the BGL parametrization. For instance, these cuts arise in the FFs for $B\to D^{(*)}$, $B\to K^{(*)}$, and $Λ_b\to Λ$ processes, which are particularly relevant from a phenomenological standpoint. We demonstrate how to parametrize such FFs and derive unitarity bounds in the presence of subthreshold and/or anomalous branch cuts. Our work paves the way for a wide range of new FF analyses based solely on first principles, thereby minimising systematic uncertainties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitarity bounds with subthreshold and anomalous cuts for $b$-hadron decays Gopal, Abinand Gubernari, Nico High Energy Physics - Phenomenology Mathematical Physics We derive a generalisation of the Boyd-Grinstein-Lebed (BGL) parametrization. Most form factors (FFs) in $b$-hadron decays exhibit additional branch cuts -- namely subthreshold and anomalous branch cuts -- beyond the ``standard'' unitarity cut. These additional cuts cannot be adequately accounted for by the BGL parametrization. For instance, these cuts arise in the FFs for $B\to D^{(*)}$, $B\to K^{(*)}$, and $Λ_b\to Λ$ processes, which are particularly relevant from a phenomenological standpoint. We demonstrate how to parametrize such FFs and derive unitarity bounds in the presence of subthreshold and/or anomalous branch cuts. Our work paves the way for a wide range of new FF analyses based solely on first principles, thereby minimising systematic uncertainties. |
| title | Unitarity bounds with subthreshold and anomalous cuts for $b$-hadron decays |
| topic | High Energy Physics - Phenomenology Mathematical Physics |
| url | https://arxiv.org/abs/2412.04388 |