A dispersive estimate of the $a_0(980)$ contribution to $(g-2)_μ$
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| Format: | Preprint |
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2024
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| author | Deineka, Oleksandra Danilkin, Igor Vanderhaeghen, Marc |
| author_facet | Deineka, Oleksandra Danilkin, Igor Vanderhaeghen, Marc |
| contents | A dispersive implementation of the $a_0(980)$ resonance to $(g-2)_μ$ requires the knowledge of the double-virtual $S$-wave $γ^*γ^*\toπη/ K K(I=1)$ amplitudes. To obtain these amplitudes, we used a modified coupled-channel Muskhelishvili-Omnes formalism, with input from the left-hand cuts and the hadronic Omnes matrix. The latter was derived using a data-driven N/D method, where the hadronic left-hand cuts were approximated via a conformal expansion. Due to the absence of direct hadronic data in the $πη$ channel, the expansion coefficients were fitted to various experimental data sets on two-photon fusion processes with $πη$ and $K K$ final states. The resulting dispersive estimate for the $a_0(980)$ contribution to $(g-2)_μ$ is $a_μ^{HLbL}[a_0(980)]_{resc.}=-0.43(1)(2)\times 10^{-11}$, which presents an order of magnitude improvement in precision over the narrow resonance approximation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_12894 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A dispersive estimate of the $a_0(980)$ contribution to $(g-2)_μ$ Deineka, Oleksandra Danilkin, Igor Vanderhaeghen, Marc High Energy Physics - Phenomenology A dispersive implementation of the $a_0(980)$ resonance to $(g-2)_μ$ requires the knowledge of the double-virtual $S$-wave $γ^*γ^*\toπη/ K K(I=1)$ amplitudes. To obtain these amplitudes, we used a modified coupled-channel Muskhelishvili-Omnes formalism, with input from the left-hand cuts and the hadronic Omnes matrix. The latter was derived using a data-driven N/D method, where the hadronic left-hand cuts were approximated via a conformal expansion. Due to the absence of direct hadronic data in the $πη$ channel, the expansion coefficients were fitted to various experimental data sets on two-photon fusion processes with $πη$ and $K K$ final states. The resulting dispersive estimate for the $a_0(980)$ contribution to $(g-2)_μ$ is $a_μ^{HLbL}[a_0(980)]_{resc.}=-0.43(1)(2)\times 10^{-11}$, which presents an order of magnitude improvement in precision over the narrow resonance approximation. |
| title | A dispersive estimate of the $a_0(980)$ contribution to $(g-2)_μ$ |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2410.12894 |