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Register a new userHigh-precision determination of the $K_{e3}$ radiative corrections
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We report a high-precision calculation of the Standard Model electroweak radiative corrections in the $Kto pi e^+ u(gamma)$ decay as a part of the combined theory effort to understand the existing anomaly in the determinations of $V_{us}$. Our new analysis features a chiral resummation of the large infrared-singular terms in the radiative corrections and a well-under-control strong interaction uncertainty based on the most recent lattice QCD inputs. While being consistent with the current state-of-the-art results obtained from chiral perturbation theory, we reduce the existing theory uncertainty from $10^{-3}$ to $10^{-4}$. Our result suggests that the Standard Model electroweak effects cannot account for the $V_{us}$ anomaly.
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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.
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 final state interaction of pions in the decay $K^pmto pi^+pi^-e^pm u$ allows to obtain the value of the isospin and angular momentum zero pion-pion scattering length $a_0^0$. To extract this quantity from experimental data the radiative corrections (RC) have to be taken into account. Basing on the lowest order results and the factorization hypothesis, we get the expressions for RC in the leading and next-to leading logarithmical approximation. It is shown that the decay width dependence on the lepton mass $m_e$ through the parameter $sigma=frac{alpha}{2pi}br{lnfrac{M^2}{m_e^2}-1}$ has a standard form of the Drell-Yan process and is proportional to the Sommerfeld-Sakharov factor. The numerical estimations are presented.
We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlins representation based on current algebra relations permits a clear separation between the perturbatively-calculable and incalculable pieces in the $mathcal{O}(G_Falpha)$ radiative corrections. The latter are expressed as compact hadronic matrix elements that allow systematic non-perturbative analysis such as dispersion relation and lattice QCD. This brings substantial improvements to the precision of the electroweak radiative corrections in semileptonic decays of pion, kaon, free neutron and $J^P=0^+$ nuclei that are important theory inputs in precision tests of the Standard Model. Unresolved issues and future prospects are discussed.
We revisit QCD calculations of radiative heavy meson decay form factors by including the subleading power corrections from the twist-two photon distribution amplitude at next-to-leading-order in $alpha_s$ with the method of the light-cone sum rules (LCSR). The desired hard-collinear factorization formula for the vacuum-to-photon correlation function with the interpolating currents for two heavy mesons is constructed with the operator-product-expansion technique in the presence of evanescent operators. Applying the background field approach, the higher twist corrections from both the two-particle and three-particle photon distribution amplitudes are further computed in the LCSR framework at leading-order in QCD, up to the twist-four accuracy. Combining the leading power point-like photon contribution at tree level and the subleading power resolved photon corrections from the newly derived LCSR, we update theory predictions for the nonperturbative couplings describing the electromagnetic decay processes of the heavy mesons $H^{ast , pm} to H^{pm} , gamma$, $H^{ast , 0} to H^{0} , gamma$, $H_s^{ast , pm} to H_s^{pm} , gamma$ (with $H=D, , B$). Furthermore, we perform an exploratory comparisons of our sum rule computations of the heavy-meson magnetic couplings with the previous determinations based upon different QCD approaches and phenomenological models.
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