The Imaginary-Part Distribution of Lattice QCD Data and Signal Improvement

Understanding the statistical fluctuations of lattice observables over gauge configurations is important both theoretically and practically. It provides physical insights to tackle famous signal-to-noise problem sign problem, inspires new thoughts in developing methodologies improve signal calculations. Among many efforts, exploring connections between real imaginary parts numerical results a novel way learn about error, since originate from same sampling fields their distributions samples are principle related. Specifically, by analyzing quenched two-point functions with high statistics non-zero momentum, this work proposes possible quantitative formula connecting these two as <i>R</i>(<i>x</i>) = ∫<i>dyS</i>(<i>y</i> - <i>x</i>) [<i>I</i>(<i>y</i>)<i>K</i>(<i>U<sub>y</sub></i>)], where stands for real-part distribution, <i>I</i>(<i>x</i>) imaginary-part <i>S</i>(<i>x</i>) underlying distribution <i>K</i>(<i>U<sub>x</sub></i>) kernel function field. This theoretical assumption general validity contains field information that determines all distributions. The numerically verified calculating non-trivial correlations kernel-function-modified further assumptions on function. found most naïve guess 1 does not work, which leads no statistically significant correlation. Meanwhile, only works well, giving rise ~ 70% Then, random distortions absolute values added different strength show even small distortion, say 1%, would reduce correlation down less than 50%. essentially proves observed highly hypothesis being captures at least some mechanisms behind scenes. Employing correlation, variance can be improved around 40%. improvement practice; however, study offers an innovative strategy understand source uncertainties QCD ratios Further studies utilizing power machine learning variety more precise data will hopefully give better indication constraint form