Corrections to the Forward Limit Dispersion Relations for $γZ$-Exchange Contributions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908988200714240 |
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| author | Guo, Qian-Qian Zhou, Hai-Qing |
| author_facet | Guo, Qian-Qian Zhou, Hai-Qing |
| contents | The weak charge of the proton $Q_{\textrm{w}}$ is one of the most fundamental quantities in physics. It can be determined by measuring the parity asymmetry $A_{\textrm{PV}}$ in elastic $ep$ scattering, where the $γZ$-exchange contributions are crucial. For the past fifteen years, dispersion relations (DRs) in the forward limit have been widely used as a model-independent method to estimate these contributions. In this work, we study corrections to these forward-limit DRs. We first estimate these corrections using pointlike interactions as an illustrative example. We then estimate the $γZ$-exchange contributions for the upcoming P2 experiment through both direct calculation and the forward-limit DRs, within the framework of low-energy effective interactions. The results indicate that the correction to the forward-limit DR for $\Box_{γZ}^{V}$ is around 47\% for the upcoming P2 experiment, which will significantly modify the extracted value of $Q_{\textrm{w}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_16294 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Corrections to the Forward Limit Dispersion Relations for $γZ$-Exchange Contributions Guo, Qian-Qian Zhou, Hai-Qing High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory The weak charge of the proton $Q_{\textrm{w}}$ is one of the most fundamental quantities in physics. It can be determined by measuring the parity asymmetry $A_{\textrm{PV}}$ in elastic $ep$ scattering, where the $γZ$-exchange contributions are crucial. For the past fifteen years, dispersion relations (DRs) in the forward limit have been widely used as a model-independent method to estimate these contributions. In this work, we study corrections to these forward-limit DRs. We first estimate these corrections using pointlike interactions as an illustrative example. We then estimate the $γZ$-exchange contributions for the upcoming P2 experiment through both direct calculation and the forward-limit DRs, within the framework of low-energy effective interactions. The results indicate that the correction to the forward-limit DR for $\Box_{γZ}^{V}$ is around 47\% for the upcoming P2 experiment, which will significantly modify the extracted value of $Q_{\textrm{w}}$. |
| title | Corrections to the Forward Limit Dispersion Relations for $γZ$-Exchange Contributions |
| topic | High Energy Physics - Phenomenology Nuclear Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2306.16294 |