https://www.selleckchem.com/products/Estrone.html Our work paves a new avenue toward the study of qPCA applications in theory and experiment.We address the ground-state properties of the long-standing and much-studied three-dimensional quantum spin liquid candidate, the S=1/2 pyrochlore Heisenberg antiferromagnet. By using SU(2) density-matrix renormalization group (DMRG), we are able to access cluster sizes of up to 128 spins. Our most striking finding is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments. We also determine the ground-state energy, E_0/N_sites=-0.490(6)J, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. These findings suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.We consider the three-loop scattering amplitudes for the production of a pair of photons in quark-antiquark annihilation in QCD. We use suitably defined projectors to efficiently calculate all helicity amplitudes. We obtain relatively compact analytic results that we write in terms of harmonic polylogarithms or, alternatively, multiple polylogarithms of up to depth three. This is the first calculation of a three-loop four-point scattering amplitude in full QCD.We perform the global analysis of polarized semi-inclusive deep inelastic scattering (SIDIS), pion-induced polarized Drell-Yan (DY) process, and W^±/Z boson production data and extract the Sivers function for u, d, s and for sea quarks. We use the framework of transverse momentum dependent factorization at next-to-next-to-next-to leading order (N^3LO) accuracy. The Qiu-Sterman function is determined in a model independent way from the extracted Sivers function. We also evaluate the significance of the predicted sign change of the Sivers function in DY process with respect