2001/05/31 by Hungchong Kim
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph #nucl-th
paper · pdf · doi:10.1103/physrevc.65.055201
published as Phys.Rev. C65 (2002) 055201 · 19 pages including two postscript figures, substantially revised
arxiv created 2001/09/25 · openalex publication_date 2002/04/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In nuclear matter, the pion weak decay constant is separated into two components ft and 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\ensuremath∫d4x e^ip\ensuremath⋅x〈\ensuremathρ|T[d(x)i\ensuremathγ5u(x) \ifmmode u\else \=u\fi(0)\ensuremathγ_\ensuremathμ\ensuremathγ5d(0)]|\ensuremathρ〉. It is found that the sum rule for ft satisfies the in-medium Gell-Mann--Oakes--Renner relation precisely, while the fs sum rule does not. The fs sum rule contains the non-negligible contribution from the dimension 5 condensate 〈qiD0iD0q〉N+(1)/(8)〈qgs\ensuremathσ\ensuremath⋅Gq〉N in addition to the in-medium quark condensate. Using a 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 the dimension 5 condensate and on the Borel mass. However, because of the positivity condition for the dimension 5 condensate, the operator product expansion constrains that fs/ft>~1, which does not agree with the ``tree level'' 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\ensuremath∼1 GeV2.