The decays K→πl⁺l⁻ beyond leading order in the chiral expansion

Abstract

We present a model-independent analysis of K + → π + ℓ + ℓ − and K S → π 0 ℓ + ℓ − decays, including K → 3π unitarity corrections and a general decomposition of the dispersive amplitude. From the existing data on K + → π + e + e − we predict the ratio R = B(K + → π + µ + µ − )/B(K + → π + e + e − ) to be larger than 0.23, in slight disagreement with the recent measurement R = 0.167 ± 0.036. Consequences for the K ± → π ± e + e − charge asymmetries and for the K L → π 0 e + e − mode are also discussed.

Implications of a new particle from the HyperCP data on Σ+→pμ+μ−

“…The decay modes K ± → π ± µ + µ − are long-distance dominated in the SM [6] and the measured spectra agree reasonably well with the predictions [7,8]. In particular, there is no apparent bump in the m µ + µ − = 214 MeV region [9].…”

“…The branching ratio is obtained to be 8.6 +6. 6 −5.4 (stat) ± 5.5(syst) × 10 −8 [1]. The central value is considerably larger than the short-distance contribution in the standard model [2].…”

Flavour anomalies

“…We have studied in this BBG contest the K ± → π ± l + l − form factor described in CHPT by a loop function, W ππ + (z) and a polynomial in z with experimentally determined coefficients a + and b + [44]. These parameterize the intermediate region between low and high energy regimes.…”

Observation of the DecayK−→π−μ+Park1, Burnstein2, Chakravorty3 et al. 2002Phys. Rev. Lett.33060View full textAdd to dashboardCite

“…The discrepancy between these two experimental results is more than three standard deviations and is not understood. In addition the value of R obtained with the E787 result and the average value of B(K + πee ) is inconsistent with the prediction and is difficult to accommodate within the standard model [2]. It is thus important to resolve the discrepancy in the B(K + πµµ ) measurements.…”

“…Since it is difficult to calculate such effects, chiral perturbation theory (ChPT) including electroweak interactions has been applied to K + πll [1]. In a recent model-independent analysis with ChPT at O(p 6 ) [2], the K + πll decay rate and the form factor characterizing the dilepton invariant-mass spectrum are calculated in terms of two parameters a + and b + . Determining these parameters from the measured branching ratio and the dilepton mass spectrum of the K + πee decay, this analysis predicts the ratio R = B(K + πµµ )/B(K + πee ) to be greater than 0.23 and an increase in the CP asymmetry between the decay rates of K + πll and K − πll compared to the leading-order estimation in the chiral expansion [3].…”