The following functional form for the matrix element suggested by ${{\mathit \pi}}{{\mathit \pi}}$ rescattering in ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}$ `` ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ '' $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ is used for this fit (CABIBBO 2004A, CABIBBO 2005 ): Matrix element = ${{\mathit M}_{{0}}}$ + ${{\mathit M}_{{1}}}$ where ${{\mathit M}_{{0}}}$ = 1 + (1/2)${\mathit g}_{0}{{\mathit u}}$ + (1/2) ${{\mathit h}^{\,'}}{{\mathit u}^{2}}$ + (1/2)${{\mathit k}_{{0}}}{{\mathit v}^{2}}$ with ${{\mathit u}}$ = (${{\mathit s}_{{3}}}\text{-}{{\mathit s}_{{0}}})/({\mathit m}_{{{\mathit \pi}^{+}}}){}^{2}$, ${{\mathit v}}$ = (${{\mathit s}_{{2}}}\text{-}{{\mathit s}_{{1}}})/({\mathit m}_{{{\mathit \pi}^{+}}}){}^{2}$ and where ${{\mathit M}_{{1}}}$ takes into account the non-analytic piece due to pi pi rescattering amplitudes ${{\mathit a}_{{0}}}$ and ${{\mathit a}_{{2}}}$; The parameters ${\mathit g}_{0}$ and ${{\mathit h}^{\,'}}$ are related to the parameters ${{\mathit g}}$ and ${{\mathit h}}$ of the matrix element squared given in the previous section by the approximations ${\mathit g}_{0}$ $\sim{}{{\mathit g}^{{PDG}}}$ and ${{\mathit h}^{\,'}}\sim{}{{\mathit h}^{{PDG}}}$ $−$ (g/2)${}^{2}$ and ${{\mathit k}_{{0}}}$ $\sim{}{{\mathit k}^{{PDG}}}$.
In addition, we also consider the effective field theory framework of COLANGELO 2006A and BISSEGGER 2009 to extract $\mathit g{}^{}_{BB}$ and ${{\mathit h}_{{BB}}^{\,'}}$.