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The decay $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$is an ideal process in which to study flavor-conserving $C$and $CP$violation beyond the Standard Model. We deduce the $C$- and $CP$-odd quark operators that contribute to $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$originating from the mass-dimension-six Standard Model effective field theory. The corresponding hadron-level operators that generate a nonvanishing $I=0$amplitude at order $p^6$in the chiral effective theory are presented for the first time, to the best of our knowledge, in addition to the leading-order operators ascribed to the $I=2$final state. By fitting the KLOE-2 and the most recent BESIII experimental data, we determine the coefficients of the lowest-order $I=0$and $I=2$amplitudes and estimate the potential new physics energy scale. We also perform an impact study of the future $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$experiments. Published by the American Physical Society2024 

The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to $Q^2\sim 4.3{\mathrm{GeV}}^2$and the nucleon up to $Q^2\sim 1{\mathrm{GeV}}^2$. The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from $\sim 250$to $\sim 540\mathrm{MeV}$, including the unitary point $\sim 340\mathrm{MeV}$. We calculate the radius of the glue trace anomaly for the pion and the nucleon from the $z$expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion’s form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit. Published by the American Physical Society2024 

Phase unwrapping is a very important step in fringe projection 3D imaging. In this paper, we propose a new neural network for accurate phase unwrapping to address the special needs in fringe projection 3D imaging. Instead of labeling the wrapped phase with integers directly, a two-step training process with the same network configuration is proposed. In the first step, the network (network I) is trained to label only four key features in the wrapped phase. In the second step, another network with same configuration (network II) is trained to label the wrapped phase segments. The advantages are that the dimension of the wrapped phase can be much larger from that of the training data, and the phase with serious Gaussian noise can be correctly unwrapped. We demonstrate the performance and key features of the neural network trained with the simulation data for the experimental data.