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We calculate the radiative corrections to the Dalitz plot of K_{l3}^\pmdecays to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 isthe mass of the kaon. We restrict the analysis to the so-called four-bodyregion, which arises when no discrimination of real photons is made eitherkinematically or experimentally. We present our results in two ways: the firstone with the triple integration over the photon kinematical variables ready tobe performed numerically and the second one in a fully analytical form. Ourresults can be useful in experimental analyses of the Dalitz plot, byevaluating the model-independent coefficients of the quadratic products of theform factors; we provide some numbers as a case example. We find a small,albeit non-negligible, contribution from the four-body region to the radiativecorrection to the total decay rate of K_{l3}^\pm decays.

Radiative corrections to the Dalitz plot of K_{l3}^\pm decays: Contribution of the four-body region