${{\mathit K}_{{{{{\mathit \ell}}4}}}^{\pm}}$ FORM FACTORS

Based on the parametrizations of AMOROS 1999, the ${{\mathit K}_{{{{{\mathit \ell}}4}}}^{\pm}}$ form factors can be expressed as
 $\mathit F_{s}$ = $\mathit f_{s}$ + ${{\mathit f}_{{{s}}}^{\,'}}$ q${}^{2}$ + ${{\mathit f}_{{{s}}}^{''}}$ q${}^{4}$ + ${{\mathit f}_{{{e}}}^{\,'}}$ S$_{e}$ $/$ 4${{\mathit m}^{2}}_{{{\mathit \pi}}}$
 $\mathit F_{p}$ = $\mathit f_{p}$
 $\mathit G_{p}$ = $\mathit g_{p}$ + ${{\mathit g}_{{{p}}}^{\,'}}$ q${}^{2}$
 $\mathit H_{p}$ = $\mathit h_{p}$
where q${}^{2}$ = (S$_{{{\mathit \pi}}}$ $/$ 4${{\mathit m}^{2}}_{{{\mathit \pi}}}$) $−$ 1, S$_{{{\mathit \pi}}}$ is the invariant mass squared of the dipion, and S$_{e}$ is the invariant mass squared of the dilepton.

${{\mathit f}_{{{s}}}}$ FOR ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{\pm}}{{\mathit \nu}}$ DECAY

INSPIRE   JSON  (beta) PDGID:
S010FSF
VALUE EVTS DOCUMENT ID TECN CHG
$\bf{ 5.712 \pm0.032}$ OUR AVERAGE
$5.705$ $\pm0.003$ $\pm0.035$ 1.1M 1
BATLEY
2012
NA48 $\pm{}$
$5.75$ $\pm0.02$ $\pm0.08$ 400k 2
PISLAK
2003
B865 +
1  BATLEY 2012 uses data collected in $2003 - 2004$. The result is obtained from a measurement of $\Gamma ({{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}}{{\mathit \nu}})/\Gamma ({{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$) and assumed PDG 2012 value of $\Gamma ({{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}})/\Gamma $ = ($5.59$ $\pm0.04$) $ \times 10^{-2}$.
2  Radiative corrections included. Using Roy equations and not including isospin breaking, PISLAK 2003 obtains the following ${{\mathit \pi}}{{\mathit \pi}}$ scattering lengths $\mathit a{}^{0}_{0}$ = $0.228$ $\pm0.012$ $\pm0.004$ ${}^{+0.012}_{-0.016}$(theor.) and $\mathit a{}^{2}_{0}$ = $-0.0365$ $\pm0.0023$ $\pm0.0008$ ${}^{+0.0031}_{-0.0026}$(theor.).
References