Towards $\it{ab}$-$\it{initio}$ nuclear theory calculations of $δ_\mathrm{C}$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929299387318272 |
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| author | Seng, Chien-Yeah Gorchtein, Mikhail |
| author_facet | Seng, Chien-Yeah Gorchtein, Mikhail |
| contents | We propose a new theory framework to study the isospin-symmetry breaking correction $δ_\text{C}$ in superallowed nuclear beta decays, crucial for the precise determination of $|V_{ud}|$. Based on a general assumptions of the isovector dominance in ISB interactions, we construct a set of functions $F_{T_z}$ which involve nuclear matrix elements of isovector monopole operators and the nuclear Green's function. Via the functions $F_{T_z}$, a connection of $δ_\text{C}$ to measurable electroweak nuclear radii is established, providing an experimental gauge of the theory accuracy of $δ_\text{C}$. We outline a strategy to perform ab-initio calculations of $F_{T_z}$ based on the Lanczos algorithm, and discuss its similarity with other nuclear-structure-dependent inputs in nuclear beta decays. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03800 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards $\it{ab}$-$\it{initio}$ nuclear theory calculations of $δ_\mathrm{C}$ Seng, Chien-Yeah Gorchtein, Mikhail Nuclear Theory High Energy Physics - Experiment High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Experiment We propose a new theory framework to study the isospin-symmetry breaking correction $δ_\text{C}$ in superallowed nuclear beta decays, crucial for the precise determination of $|V_{ud}|$. Based on a general assumptions of the isovector dominance in ISB interactions, we construct a set of functions $F_{T_z}$ which involve nuclear matrix elements of isovector monopole operators and the nuclear Green's function. Via the functions $F_{T_z}$, a connection of $δ_\text{C}$ to measurable electroweak nuclear radii is established, providing an experimental gauge of the theory accuracy of $δ_\text{C}$. We outline a strategy to perform ab-initio calculations of $F_{T_z}$ based on the Lanczos algorithm, and discuss its similarity with other nuclear-structure-dependent inputs in nuclear beta decays. |
| title | Towards $\it{ab}$-$\it{initio}$ nuclear theory calculations of $δ_\mathrm{C}$ |
| topic | Nuclear Theory High Energy Physics - Experiment High Energy Physics - Lattice High Energy Physics - Phenomenology Nuclear Experiment |
| url | https://arxiv.org/abs/2304.03800 |