An exploratory calculation of $K_{\rm L}\toμ^+μ^-$ decay from Lattice QCD at physical pion mass
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918187194384384 |
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| author | Boyle, Peter Chao, En-Hung Christ, Norman Hu, Ceran Jin, Luchang Zhao, Yidi |
| author_facet | Boyle, Peter Chao, En-Hung Christ, Norman Hu, Ceran Jin, Luchang Zhao, Yidi |
| contents | We compute the complex, long-distance two-photon-exchange amplitude which contributes to the rare $K_{\rm L}\rightarrowμ^+μ^-$ decay from lattice QCD. We use a $24^3\times 64$ physical-pion-mass gauge field ensemble at an inverse lattice spacing of $1.023$ GeV and a QED${}_\infty$-based formalism. Our implementation strategies for all five non-SU$(3)$-flavor-suppressed diagram topologies are given in detail. We achieve a 25% statistical precision on the dispersive part of this long-distance amplitude. This calculation is carried out with 2+1 quark flavors and therefore requires the addition of counter terms to compensate for the absence of the Glashow-Iliopoulos-Maiani mechanism. These counter terms are not included in the current calculation and will be the subject of a second paper. The precision of our results is limited by the reconstruction of the physical contribution of the $η$ intermediate state, for which various strategies are tested and compared. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04346 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An exploratory calculation of $K_{\rm L}\toμ^+μ^-$ decay from Lattice QCD at physical pion mass Boyle, Peter Chao, En-Hung Christ, Norman Hu, Ceran Jin, Luchang Zhao, Yidi High Energy Physics - Lattice We compute the complex, long-distance two-photon-exchange amplitude which contributes to the rare $K_{\rm L}\rightarrowμ^+μ^-$ decay from lattice QCD. We use a $24^3\times 64$ physical-pion-mass gauge field ensemble at an inverse lattice spacing of $1.023$ GeV and a QED${}_\infty$-based formalism. Our implementation strategies for all five non-SU$(3)$-flavor-suppressed diagram topologies are given in detail. We achieve a 25% statistical precision on the dispersive part of this long-distance amplitude. This calculation is carried out with 2+1 quark flavors and therefore requires the addition of counter terms to compensate for the absence of the Glashow-Iliopoulos-Maiani mechanism. These counter terms are not included in the current calculation and will be the subject of a second paper. The precision of our results is limited by the reconstruction of the physical contribution of the $η$ intermediate state, for which various strategies are tested and compared. |
| title | An exploratory calculation of $K_{\rm L}\toμ^+μ^-$ decay from Lattice QCD at physical pion mass |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2509.04346 |