Measurements of the DecayKL→e+e−μ+μ−

Abstract

The KTeV experiment at Fermilab has isolated a total of 132 events from the rare decay KL → e + e − µ + µ − , with an estimated background of 0.8 events. The branching ratio of this mode is determined to be (2.69±0.24stat ±0.12syst)×10 −9 , with a radiative cutoff of M 2 eeµµ /M 2 K > 0.95. The first measurement using this mode of the parameter α from the D'Ambrosio, Isidori, and Portolès model of the KL γ * γ * vertex yields a result of −1.59 ± 0.37, consistent with values obtained from other decay modes. Because of the limited statistics, no sensitivity is found to the DIP parameter β. The magnitude of the angular distribution asymmetry between the e + e − and µ + µ − planes, indicative of a CP −violating contribution to the decay, is found to be consistent with zero. We set a 90% C.L. upper limit of 4.12 × 10 −11 on the branching ratio of the lepton flavor-violating mode KL → e ± e ± µ ∓ µ ∓ , a factor of three improvement over the current limit from the KTeV experiment.PACS numbers: 13.20. Eb, 14.40.Aq, 12.15.Hh, 11.30.Er, 11.30.Fs The rare decay K L → e + e − µ + µ − offers the most direct means for studying the dynamics of the K L γ * γ * vertex. This information is useful for models that relate the K L → µ + µ − branching ratio to ρ, the real part of the CKM matrix element V td [1,2,3]. This decay mode can also be used to determine the presence of any CP −violating contributions to the K L γ * γ * interaction [4]. Additionally, a search for the lepton flavorviolating counterpart K L → e ± e ± µ ∓ µ ∓ provides a constraint on physics beyond the Standard Model.In the model of D'Ambrosio, Isidori, and Portolès (DIP) [5], the K L γ * γ * form factor can be written asHere, q 1 and q 2 are the momenta of the two virtual photons, and M ρ is the mass of the ρ vector meson. In this model, α and β are two arbitrary real parameters and are expected to be of order one. The determination of both α and β is possible through the decay K L → e + e − µ + µ − by examining the dilepton invariant masses and the integrated decay rate. Knowledge of the K L γ * γ * form factor is important for understanding the long distance contributions to K L → µ + µ − and extracting the value of ρ [5].Two measurements have been made of the linear DIP parameter α to date, both by the KTeV collaboration. From the mode K L → µ + µ − γ , the shape of the dimuon invariant mass distribution (M µµ ) and the measured branching ratio have been used to determine α = −1. 54 ± 0.10 [6]. A fit to the dielectron mass distribution (M ee ) from K L → e + e − e + e − determines α = −1.1 ± 0.6 [7], where the larger error results from the smaller q 2 of the dielectron distribution. No measurements have yet been made of the quadratic DIP pa-

Radiative corrections to double-Dalitz decays revisited

“…Double-Dalitz decays of pseudoscalar mesons (P →lll 0 l 0 ) have attracted attention over the years, both theoretically [1][2][3][4][5][6][7][8][9][10][11] and experimentally [12][13][14][15][16][17][18][19][20][21][22], for different reasons. On the one hand, they contain important-Direct-information about the pseudoscalar meson structure, which is encoded in their double-virtual transition form factors (TFFs).…”

Rare kaon decays and CP violation

“…Moreover, rare kaon decays are sensitive to short-distance scales (c, t, W ± , Z) and have the potential to unravel new physics (NP) beyond the SM. In particular, high-precision searches for lepton-flavour violation (LFV) beyond the 10 −10 level [Br(K L → e ± µ ∓ ) < 4.7 • 10 −12 [2], Br(K L → e ± e ± µ ∓ µ ∓ ) < 4.12 • 10 −11 [3], Br(K + → π + µ + e − ) < 1.3 • 10 −11 [4], Br(K + → π + µ − e + ) < 5.2 • 10 −10 [5] (90% CL)] are actually exploring energy scales above the 10 TeV region. In addition, the mechanism of CP violation can be accurately tested, both in the observed kaon decay modes and through still undetected processes such as K L → π 0 νν.…”

“…(3,3, 1/3). Q and L are the left-handed quark and lepton doublets, d R and R the corresponding right-handed singlets and f c ≡ Cf T indicates the charge-conjugated field of the…”

The radiative corrections to double-Dalitz decays revisited

“…Double-Dalitz decays of pseudoscalar mesons (P → ¯ ¯ ) have attracted attention over the years, both theoretically [1][2][3][4][5][6][7][8][9][10][11] and experimentally [12][13][14][15][16][17][18][19][20][21][22], for different reasons. On the one hand, they contain important-direct-information about the pseudoscalar meson structure, which is encoded in their double-virtual transition form factors (TFFs).…”

“…21 and where z = z 12,34 , w = w 12,34 , λ = λ 12,34 22. With this notation, the four-body phase space can be expressed asdΦ4 = Sλ 2 14 π 6 ds 12 ds 34 dφ λ 12 d cos θ 12 1 λ 34 d cos θ 34 3 = Sλ 2 14 π 6 ds 12 ds 34 dy 12 dy 34 dφ,…”