In-medium pion weak decay constants

الأصل · EN

In nuclear matter, the pion weak decay constant is separated into the two components fₜ, fₛ corresponding to the time and space components of the axial-vector current. Using QCD sum rules, we compute the two decay constants from the pseudoscalar-axial vector correlation function in the matter i ∫ d⁴x eip· x < ρ| T[d(x) i γ₅ u (x) u(0) γμγ₅ d (0)] | ρ>. It is found that the sum rule for fₜ satisfies the in-medium Gell-Mann--Oakes--Renner (GOR) relation precisely while the fₛ sum rule does not. The fₛ sum rule contains the non-negligible contribution from the dimension 5 condensate < q i D₀ iD₀ q >ₙ + 1 8 < q gₛ σ· G q >ₙ in addition to the in-medium quark condensate. Using standard set of QCD parameters and ignoring the in-medium change of the pion mass, we obtain fₜ =105 MeV at the nuclear saturation density. The prediction for fₛ depends on values of the dimension 5 condensate and on the Borel mass. However, the OPE constrains that fₛ/fₜ ≥ 1, which does not agree with the prediction from the in-medium chiral perturbation theory. Depending on the value of the dimension 5 condensate, fₛ at the saturation density is found to be in the range 112 134 MeV at the Borel mass M² 1 GeV².