Pion decay constant

In particle physics, the pion decay constant is the square root of the coefficient in front of the kinetic term for the pion in the low-energy effective action. It is dimensionally an energy scale and it determines the strength of the chiral symmetry breaking. The values are:

${\displaystyle f_{\pi ^{\pm }}=130.41\pm 0.03\pm 0.20~{\mbox{MeV}}}$

${\displaystyle f_{\pi ^{0}}=130\pm 5~{\mbox{MeV}}}$

Beware: There are several conventions which differ by factors of ${\displaystyle \scriptstyle {\sqrt {2}}}$. The textbook by Weinberg uses the value 184 MeV. The textbook by Peskin and Schroeder uses the value 93 MeV.

According to Brown-Rho scaling, the masses of nucleons and most light mesons decrease at finite density as the ratio of the in-medium pion decay rate to the free-space pion decay constant. The pion mass is an exception to Brown-Rho scaling because the pion's mass is protected by its Goldstone boson nature.[1]