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Register a new userRadiative corrections to the Dalitz plot of K_{l3}^pm decays: Contribution of the four-body region
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We calculate the radiative corrections to the Dalitz plot of K_{l3}^pm decays to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. We restrict the analysis to the so-called four-body region, which arises when no discrimination of real photons is made either kinematically or experimentally. We present our results in two ways: the first one with the triple integration over the photon kinematical variables ready to be performed numerically and the second one in a fully analytical form. Our results can be useful in experimental analyses of the Dalitz plot, by evaluating the model-independent coefficients of the quadratic products of the form factors; we provide some numbers as a case example. We find a small, albeit non-negligible, contribution from the four-body region to the radiative correction to the total decay rate of K_{l3}^pm decays.
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We calculate the model-independent radiative corrections to the Dalitz plot of K_{l3}^pm decays to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. The final results are presented, first, with the triple integration over the variables of the bremsstrahlung photon ready to be performed numerically and, second, in an analytical form. These two forms are useful to crosscheck on one another and with other calculations. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments and is not compromised to fixing the form factors at predetermined values. It is assumed that the real photons are kinematically discriminated. Otherwise, our results have a general model-independent applicability.
A model-independent expression for the Dalitz plot of semileptonic decays of neutral kaons, K_{l3}^0, including radiative corrections to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon, is presented. The model dependence of radiative corrections is kept in a general form within this approximation, which is suitable for model-independent experimental analyses. Expressions for bremsstrahlung radiative corrections are presented in two forms: one with the triple integral over the kinematical variables of the photon ready to be performed numerically and the other one in a fully analytical form. The final result is restricted to the so-called three-body region of the Dalitz plot and it is not compromised to fixing the values of the form factors at predetermined values.
The four-body contribution of the model-independent radiative corrections to the Dalitz plot of the semileptonic decays of neutral kaons are computed to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the kaon mass. The final result is presented in two forms. The first one is given in terms of the triple integration of the bremsstrahlung photon ready to be performed numerically; the second one is a fully analytical expression. This paper is organized to make it accessible and reliable in the analysis of the Dalitz plot of precision experiments involving kaons and is not compromised to fixing the form factors at predetermined values. As a byproduct, gathering together three- and four-body contributions of radiative corrections yields, through a least-squares fit to the measured kaon decay rates, the value f_+^{K^0pi^-}|V_{us}| = 0.2168(3).
We propose a new theory framework to study the electroweak radiative corrections in $K_{l3}$ decays by combining the classic current algebra approach with the modern effective field theory. Under this framework, the most important $mathcal{O}(G_Falpha)$ radiative corrections are described by a single tensor $T^{mu u}$ involving the time-ordered product between the charged weak current and the electromagnetic current, and all remaining pieces are calculable order-by-order in Chiral Perturbation Theory. We further point out a special advantage in the $K_{l3}^{0}$ channel that it suffers the least impact from the poorly-constrained low-energy constants. This finding may serve as a basis for a more precise extraction of the matrix element $V_{us}$ in the future.
The measurements of $V_{us}$ in leptonic $(K_{mu 2})$ and semileptonic $(K_{l3})$ kaon decays exhibit a $3sigma$ disagreement, which could originate either from physics beyond the Standard Model or some large unidentified Standard Model systematic effects. Clarifying this issue requires a careful examination of all existing Standard Model inputs. Making use of a newly-proposed computational framework and the most recent lattice QCD results, we perform a comprehensive re-analysis of the electroweak radiative corrections to the $K_{e3}$ decay rates that achieves an unprecedented level of precision of $10^{-4}$, which improves the current best results by almost an order of magnitude. No large systematic effects are found, which suggests that the electroweak radiative corrections should be removed from the ``list of culprits responsible for the $K_{mu 2}$--$K_{l3}$ discrepancy.
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