We report a strong tension in εK at the 4σ level between the experimental value and the theoretical value calculated directly from the standard model using lattice QCD inputs such asBK , |V cb |, |Vus|, ξ0, ξ2, ξLD, FK , and mc. The standard model with lattice QCD inputs describes only 70% of the experimental value of εK , and does not explain its remaining 30%. We also find that this tension disappears when we use the inclusive value of |V cb | (results of the heavy quark expansion based on QCD sum rules) to determine εK . This tension is highly correlated with the present discrepancy between the exclusive and inclusive values of |V cb |. In order to resolve, in part, the issue with |V cb |, it would be highly desirable to have a comprehensive re-analysis over the entire set of experimental data on theB → D * ν decays using an alternative parametrization of the form factors, such as the BGL parametrization, and a comparison with results of the CLN method.

Natural gas liquefaction is a highly energy-intensive process due to its cryogenic operation. Therefore, a major concern in designing and optimizing natural gas liquefaction processes is the enhancement of energy efficiency. A liquefaction ratio in the natural gas liquefaction process affects the specific energy consumption, which is the energy consumption per unit mass of liquefied natural gas (LNG). However, most of the previous research has not considered the liquefaction ratio of the natural gas. This study focuses on minimizing specific energy consumption of a LNG plant considering the liquefaction ratio. To analyze the effects of the liquefaction ratio, four different cases are set and the optimizations are performed. The objective function to be minimized includes the total energy consumption and specific energy consumption. The result of minimizing total energy consumption converges on the lower bound of the liquefaction ratio, but the result of minimizing specific energy consumption converges between the lower and upper bound. This shows that the total energy minimization does not always have the same meaning as the specific energy minimization when the liquefaction ratio is not fixed. Through this analysis, the relationships between the energy consumption and the liquefaction ratio are found. As the result of the optimization, the optimal compression ratio, temperature, intermediate pressure, and refrigerant flow rate are found, and the specific power was reduced by 16.40% over that of the LNG pilot plant design while yielding the natural gas liquefaction ratio of 86.9%.

We report updated results for ε K , the indirect CP violation parameter in neutral kaons, which is evaluated directly from the standard model with lattice QCD inputs. We use lattice QCD inputs to fixB K , |V cb |, ξ 0 , ξ 2 , |V us |, and m c (m c ). Since Lattice 2016, the UTfit group has updated the Wolfenstein parameters in the angle-only-fit method, and the HFLAV group has also updated |V cb |. Our results show that the evaluation of ε K with exclusive |V cb | (lattice QCD inputs) has 4.0σ tension with the experimental value, while that with inclusive |V cb | (heavy quark expansion based on OPE and QCD sum rules) shows no tension.

We present recent updates for 𝜀 𝐾 determined directly from the standard model (SM) with lattice QCD inputs such as B𝐾 , |𝑉 𝑐𝑏 |, |𝑉 𝑢𝑠 |, 𝜉 0 , 𝜉 2 , 𝜉 LD , 𝑓 𝐾 , and 𝑚 𝑐 . We find that the standard model with exclusive |𝑉 𝑐𝑏 | and other lattice QCD inputs describes only 66% of the experimental value of |𝜀 𝐾 | and does not explain its remaining 34%, which leads to a strong tension in |𝜀 𝐾 | at the 4.5𝜎 ∼ 3.7𝜎 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.

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