Quark-hadron duality and the determination of $α_s$ from hadronic $τ$ decay: facts vs. myths
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915242158587904 |
|---|---|
| author | Boito, Diogo Golterman, Maarten Maltman, Kim Peris, Santiago |
| author_facet | Boito, Diogo Golterman, Maarten Maltman, Kim Peris, Santiago |
| contents | Non-perturbative effects have a small but non-trivial impact on the determination of the strong coupling from hadronic $τ$ decay data. Several approaches have been proposed to take these into account, the two most important of which are the ``truncated OPE'' approach and ``DV-model'' approach. Recently, Pich and Rodríguez-Sánchez have raised a number of criticisms of the latter approach, including, most notably, claims of the existence of (i) a supposed instability with respect to variations of the model for incorporating quark-hadron duality violations, and (ii) an alleged redundancy in the fitting strategy employed in the DV-model approach. In this paper, we address these criticisms one by one, showing they fail to survive more detailed scrutiny of the mathematical or numerical arguments that underpin them. We also show that, while the redundancy claim does not apply to the DV-model approach, it does, in fact, apply to the truncated OPE approach. In particular, the $α_s$ value determined in the latter turns out to derive purely from perturbation theory, with no role played by the non-perturbative condensates determined in the rest of the analysis. This leads to the conclusion that a revision of the conventional understanding of what is learned from truncated OPE analyses is necessary and that only very limited self-consistency checks are possible within this framework. These observations raise new, non-trivial issues for the truncated OPE approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quark-hadron duality and the determination of $α_s$ from hadronic $τ$ decay: facts vs. myths Boito, Diogo Golterman, Maarten Maltman, Kim Peris, Santiago High Energy Physics - Phenomenology Non-perturbative effects have a small but non-trivial impact on the determination of the strong coupling from hadronic $τ$ decay data. Several approaches have been proposed to take these into account, the two most important of which are the ``truncated OPE'' approach and ``DV-model'' approach. Recently, Pich and Rodríguez-Sánchez have raised a number of criticisms of the latter approach, including, most notably, claims of the existence of (i) a supposed instability with respect to variations of the model for incorporating quark-hadron duality violations, and (ii) an alleged redundancy in the fitting strategy employed in the DV-model approach. In this paper, we address these criticisms one by one, showing they fail to survive more detailed scrutiny of the mathematical or numerical arguments that underpin them. We also show that, while the redundancy claim does not apply to the DV-model approach, it does, in fact, apply to the truncated OPE approach. In particular, the $α_s$ value determined in the latter turns out to derive purely from perturbation theory, with no role played by the non-perturbative condensates determined in the rest of the analysis. This leads to the conclusion that a revision of the conventional understanding of what is learned from truncated OPE analyses is necessary and that only very limited self-consistency checks are possible within this framework. These observations raise new, non-trivial issues for the truncated OPE approach. |
| title | Quark-hadron duality and the determination of $α_s$ from hadronic $τ$ decay: facts vs. myths |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2402.05588 |