In-medium pion weak decay constants

Abstract

In nuclear matter, the pion weak decay constant is separated into the two components $f_t,f_s$ 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 $i\int d^{4}x{e}^{ip\cdot x}<\rho |T[\bar{d}(x)i{\gamma }_{5}u(x)\bar{u}(0){\gamma }_{\mu }{\gamma }_{5}d(0)]|\rho >$. It is found that the sum rule for $f_t$ satisfies the in-medium Gell-Mann--Oakes--Renner (GOR) relation precisely while the $f_s$ sum rule does not. The $f_s$ sum rule contains the non-negligible contribution from the dimension 5 condensate $<\bar{q}i{D}_{0}i{D}_{0}q{>}_N+\frac{1}{8}<\bar{q}{g}_s\sigma \cdot \mathcal{G}q{>}_N$ 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 $f_t=105$ MeV at the nuclear saturation density. The prediction for $f_s$ depends on values of the dimension 5 condensate and on the Borel mass. However, the OPE constrains that $f_s/f_t\ge 1$, which does not agree with the prediction from the in-medium chiral perturbation theory. Depending on the value of the dimension 5 condensate, $f_s$ at the saturation density is found to be in the range $112\sim 134$ MeV at the Borel mass $M^2\sim 1$ GeV${}^2$.

19 pages including two postscript figures, substantially revised

References in corpus (1)

• QCD sum rules for the pseudoscalar decay constants - To constrain the strange quark mass

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