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arXiv · 2501.00215

2024 Update on $\varepsilon_K$ with lattice QCD inputs

Seungyeob Jwa·Jeehun Kim·Sunghee Kim·Sunkyu Lee·Weonjong Lee·Jaehoon Leem·Sungwoo Park
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Abstract

We report recent progress on $\varepsilon_K$ evaluated directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, exclusive $|V_{cb}|$, $|V_{us}|$, $|V_{ud}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and lattice QCD inputs describes only $2/3 \cong 65\%$ of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 35\%, which represents a strong tension in $|\varepsilon_K|$ at the $5.1\sigma \sim 4.1\sigma$ level between the SM theory and experiment. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained using the heavy quark expansion based on the QCD sum rule approach. We also report results for $|\varepsilon_K|$ obtained using the Brod-Gorbahn-Stamou (BGS) method for $\eta_i$ of $u-t$ unitarity, which leads to even a stronger tension of $5.7\sigma \sim 4.2\sigma$ with lattice QCD inputs.

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Seungyeob Jwa, Jeehun Kim, Sunghee Kim, Sunkyu Lee, Weonjong Lee, Jaehoon Leem, Sungwoo Park. 2024-12-31. 2024 Update on $\varepsilon_K$ with lattice QCD inputs. https://arxiv.org/abs/2501.00215

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