Update on pion weak decay constants in nuclear matter Original Research Article

The QCD sum rule calculation of the in-medium pion decay constants using pseudoscalar–axial-vector correlation function, View the MathML source is revisited. In particular, we argue that the dimension 5 condensate, View the MathML source, which is crucial for splitting the time (ft) and space (fs) components of the decay constant, is not necessarily restricted to be positive. Its positive value is found to yield a tachyonic pion mass. Using the in-medium pion mass as an input, we fix the dimension 5 condensate to be around −0.025 GeV2∼−0.019 GeV2. The role of the N and Δ intermediate states in the correlation function is also investigated. The N intermediate state is found not to contribute to the sum rules. For the Δ intermediate state, we either treat it as a part of the continuum or propose a way to subtract explicitly from the sum rules. With (and without) explicit Δ subtraction while allowing the in-medium pion mass to vary within View the MathML source MeV, we obtain fs/fπ=0.37∼0.78 and ft/fπ=0.63∼0.79.