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arXiv · 2301.12375

2022 Update on $\varepsilon_K$ with lattice QCD inputs

Sunghee Kim·Sunkyu Lee·Weonjong Lee·Jaehoon Leem·Sungwoo Park
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Abstract

We present recent updates for $\varepsilon_K$ determined directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and other lattice QCD inputs describes only 65% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 35%, which leads to a strong tension in $|\varepsilon_K|$ at the $5.1\sigma \sim 3.9\sigma$ 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, although this inclusive tension is small ($\approx 1.4\sigma$) but keeps increasing as time goes on.

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Sunghee Kim, Sunkyu Lee, Weonjong Lee, Jaehoon Leem, Sungwoo Park. 2023-01-29. 2022 Update on $\varepsilon_K$ with lattice QCD inputs. https://arxiv.org/abs/2301.12375

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