$ΔI = 3/2$ and $ΔI = 1/2$ channels of $K\toππ$ decay at the physical point with periodic boundary conditions
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| Main Authors: | , , , , , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913374490591232 |
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| author | Blum, Thomas Boyle, Peter A. Hoying, Daniel Izubuchi, Taku Jin, Luchang Jung, Chulwoo Kelly, Christopher Lehner, Christoph Soni, Amarjit Tomii, Masaaki |
| author_facet | Blum, Thomas Boyle, Peter A. Hoying, Daniel Izubuchi, Taku Jin, Luchang Jung, Chulwoo Kelly, Christopher Lehner, Christoph Soni, Amarjit Tomii, Masaaki |
| contents | We present a lattice calculation of the $K\toππ$ matrix elements and amplitudes with both the $ΔI = 3/2$ and 1/2 channels and $\varepsilon'$, the measure of direct $CP$ violation. We use periodic boundary conditions (PBC), where the correct kinematics of $K\toππ$ can be achieved via an excited two-pion final state. To overcome the difficulty associated with the extraction of excited states, our previous work \cite{Bai:2015nea,RBC:2020kdj} successfully employed G-parity boundary conditions, where pions are forced to have non-zero momentum enabling the $I=0$ two-pion ground state to express the on-shell kinematics of the $K\toππ$ decay. Here instead we overcome the problem using the variational method which allows us to resolve the two-pion spectrum and matrix elements up to the relevant energy where the decay amplitude is on-shell.
In this paper we report an exploratory calculation of $K\toππ$ decay amplitudes and $\varepsilon'$ using PBC on a coarser lattice size of $24^3\times64$ with inverse lattice spacing $a^{-1}=1.023$ GeV and the physical pion and kaon masses. The results are promising enough to motivate us to continue our measurements on finer lattice ensembles in order to improve the precision in the near future. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_06781 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $ΔI = 3/2$ and $ΔI = 1/2$ channels of $K\toππ$ decay at the physical point with periodic boundary conditions Blum, Thomas Boyle, Peter A. Hoying, Daniel Izubuchi, Taku Jin, Luchang Jung, Chulwoo Kelly, Christopher Lehner, Christoph Soni, Amarjit Tomii, Masaaki High Energy Physics - Lattice High Energy Physics - Phenomenology We present a lattice calculation of the $K\toππ$ matrix elements and amplitudes with both the $ΔI = 3/2$ and 1/2 channels and $\varepsilon'$, the measure of direct $CP$ violation. We use periodic boundary conditions (PBC), where the correct kinematics of $K\toππ$ can be achieved via an excited two-pion final state. To overcome the difficulty associated with the extraction of excited states, our previous work \cite{Bai:2015nea,RBC:2020kdj} successfully employed G-parity boundary conditions, where pions are forced to have non-zero momentum enabling the $I=0$ two-pion ground state to express the on-shell kinematics of the $K\toππ$ decay. Here instead we overcome the problem using the variational method which allows us to resolve the two-pion spectrum and matrix elements up to the relevant energy where the decay amplitude is on-shell. In this paper we report an exploratory calculation of $K\toππ$ decay amplitudes and $\varepsilon'$ using PBC on a coarser lattice size of $24^3\times64$ with inverse lattice spacing $a^{-1}=1.023$ GeV and the physical pion and kaon masses. The results are promising enough to motivate us to continue our measurements on finer lattice ensembles in order to improve the precision in the near future. |
| title | $ΔI = 3/2$ and $ΔI = 1/2$ channels of $K\toππ$ decay at the physical point with periodic boundary conditions |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2306.06781 |