Does vacuum saturation work for the higher-dimensional vacuum condensates in the QCD sum rules?

In the QCD sum rules for the tetraquark (molecular) states, the higher-dimensional vacuum condensates play an important role in extracting the tetraquark masses. We carry out the operator product expansion up to the vacuum condensates of dimension-10 and observe that the vacuum condensates of dimensions 6, 8 and 10 have the same expressions but opposite signs for the [Formula: see text]-type and [Formula: see text]-type four-quark currents, which make their influences distinguishable, and they are excellent channels to examine the vacuum saturation approximation. We introduce a parameter [Formula: see text] to parametrize the derivation from the vacuum saturation or factorization approximation, and choose two sets of parameters to examine the influences on the predicted tetraquark masses, which can be confronted to the experimental data in the future. In all the channels, smaller value of the [Formula: see text] leads to better convergent behavior in the operator product expansion, which favors the vacuum saturation approximation.

The numerical investigation of magnetic properties of single domain MnP:GaP nanoparticles

The magnetic properties of MnP:GaP nanoparticles are calculated using a statistical mechanical approach and effect of various factors on magnetization of nanoparticles is studied. The calculation is based on solution of localized partition function and evolution of magnetic moment affected by thermal fluctuation and external field is included by solving master equation. Instead of constant magnetic saturation approximation, a temperature dependent magnetic moment saturation is included to improve calculation efficiency for larger nanoparticles. In the present work, the field-cooled and zero-field-cooled (FC/ZFC) magnetization of randomly oriented anisotropy and log-normal volume distributed nanoparticles are calculated.