Direct CP violation and the ΔI = 1/2 rule in K → ππ decay in the Standard Model

We discuss the RBC & UKQCD collaborations’ recent [1] lattice calculation of ϵ′, the measure of direct CP-violation in kaon decays. This result significantly improves on our previous 2015 calculation, with nearly 4× the statistics and more reliable systematic error estimates. We discuss how our results demonstrate the Standard Model origin of the ΔI = 1/2 rule, and present our plans for future calculations.

A finite box as a tool to distinguish free quarks from confinement at high temperatures

Above the pseudocritical temperature $$T_c$$ T c of chiral symmetry restoration a chiral spin symmetry (a symmetry of the color charge and of electric confinement) emerges in QCD. This implies that QCD is in a confining mode and there are no free quarks. At the same time correlators of operators constrained by a conserved current behave as if quarks were free. This explains observed fluctuations of conserved charges and the absence of the rho-like structures seen via dileptons. An independent evidence that one is in a confining mode is very welcome. Here we suggest a new tool how to distinguish free quarks from a confining mode. If we put the system into a finite box, then if the quarks are free one necessarily obtains a remarkable diffractive pattern in the propagator of a conserved current. This pattern is clearly seen in a lattice calculation in a finite box and it vanishes in the infinite volume limit as well as in the continuum. In contrast, the full QCD calculations in a finite box show the absence of the diffractive pattern implying that the quarks are confined.

Nucleon gluon distribution function from 2 + 1 + 1-flavor lattice QCD

The parton distribution functions (PDFs) provide process-independent information about the quarks and gluons inside hadrons. Although the gluon PDF can be obtained from a global fit to experimental data, it is not constrained well in the large-[Formula: see text] region. Theoretical gluon-PDF studies are much fewer than those of the quark PDFs. In this work, we present the first lattice-QCD results that access the [Formula: see text]-dependence of the gluon unpolarized PDF of the nucleon. The lattice calculation is carried out with nucleon momenta up to 2.16 GeV, lattice spacing [Formula: see text] fm, and with valence pion masses of 310 and 690 MeV. We use reduced Ioffe-time distributions to cancel the renormalization and implement a one-loop perturbative pseudo-PDF gluon matching. We neglect mixing of the gluon operator with the quark singlet sector. Our matrix-element results in coordinate space are consistent with those obtained from the global PDF fits of CT18 NNLO and NNPDF3.1 NNLO. Our fitted gluon PDFs at both pion masses are consistent with global fits in the [Formula: see text] region.

SMALL MODULAR PWR DESIGN FOR TRU RECYCLING WITH McCARD-MASTER TWO-STEP PROCEDURE

In our previous study, a small modular PWR core was designed for TRU (Transuranics) recycling with multi-recycling scheme with a typical two-step procedure using DeCART2D/MASTER code system in which the lattice analysis for producing homogenized group constant was performed by DeCART2D while whole core analysis was conducted by MASTER code. However, the neutron spectrum hardening of the LWR core loaded with TRU requires validating the multi-group cross section library and resonance self-shielding treatment method in lattice calculation. In this study, a new procedure using McCARD/MASTER was used to analyze the SMR core, in which the lattice calculation was performed by a Monte Carlo code called McCARD with a continuous energy library to generate homogenized two-group assembly cross sections. The SMR core analysis was performed to show neutronic characteristics and TRU mass flow in the SMR core with TRU multi-recycling. The result shows that the analyses on the neutronic characteristics and TRU mass flow using the McCARD/MASTER code system showed good agreement with the previous ones using the DeCART2D/MASTER code system. The neutronic characteristics of each cycle of the core satisfied the typical limit of a commercial PWR core and the SMR core consumes effectively TRU with net TRU consumption rates of 8.46~14.33 %.