Measurements of semileptonic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>K</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:math>decay form factors

We present new measurements of ${K}_{L}$ semileptonic form factors using data collected in 1997 by the KTeV (E832) experiment at Fermilab. The measurements are based on $1.9\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{e}^{\ensuremath{\mp}}\ensuremath{\nu}$ and $1.5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${K}_{L}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\mu}}^{\ensuremath{\mp}}\ensuremath{\nu}$ decays. For ${f}_{+}(t)$, we measure both a linear and quadratic term: ${\ensuremath{\lambda}}_{+}^{\ensuremath{'}}=(20.64\ifmmode\pm\else\textpm\fi{}1.75)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and ${\ensuremath{\lambda}}_{+}^{\ensuremath{'}\ensuremath{'}}=(3.20\ifmmode\pm\else\textpm\fi{}0.69)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. For ${f}_{0}(t)$, we find ${\ensuremath{\lambda}}_{0}=(13.72\ifmmode\pm\else\textpm\fi{}1.31)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. These form factors are consistent with ${K}^{\ifmmode\pm\else\textpm\fi{}}$ form factors, suggesting that isospin symmetry breaking effects are small. We use our measured values of the form factors to evaluate the decay phase space integrals, ${I}_{K}^{e}=0.15350\ifmmode\pm\else\textpm\fi{}0.00105$ and ${I}_{K}^{\ensuremath{\mu}}=0.10165\ifmmode\pm\else\textpm\fi{}0.00080$, where errors include uncertainties arising from the form factor parametrizations.