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${{\mathit K}_{{{{\mathit \ell}}4}}^{\pm}}$ 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   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 $ = $0.0559$ $\pm0.0004$. 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:

BATLEY 2012 PL B715 105 New Measurement of the ${{\mathit K}^{\pm}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{\pm}}{{\mathit \nu}}$ (${{\mathit K}_{{e4}}}$) Decay Branching Ratio and Hadronic Form Factors PISLAK 2003 PR D67 072004 High Statistics Measurement of ${{\mathit K}_{{e4}}}$ Decay Properties Also PR D81 119903E Erratum PISLAK 2003 : High Statistics Measurement of ${{\mathit K}_{{{e4}}}}$ Decay Properties

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