Measurement of Γ(Kμ3)/Γ(Ke3) ratio using stopped positive kaons


The theory of hadron interaction is quantum chromodynamics (QCD). However, at low energies perturbative methods cannot be applied since the coupling constant becomes very large. One method uses a low energy effective model, Chiral Perturbation Theory (CHPT), which is a rigorous methodology for QCD in the low-energy regions. The predictive power of ChPT can be stringently tested by the form factors of the simplest semileptonic decay Kl3[1]. For the calculation of the Kl3 form factors, a parameterization in terms of the form factors f+ and f0 which are associated with vector and scalar exchange, respectively, are convenient. The form factor f0 is related to f+ and f- through

f0(q2) = f+(q2) + [ q2/(mK2 - mπ2) ]f-(q2) .

The assumption that f+ is linear in q2 and f- is constant leads to f0 linear in q2 as
f0(q2) = f+(0)[ 1 + λ0(q2/mπ2) ] .

The λ+ and λ0 parameters can be predicted in ChPT as,

λ+ = 0.0289±0.0006
λ0 = 0.0168±0.0012 .

Assuming μ-e universality, Kμ3 and Ke3 form factors are identical, the ratio of the Kμ3 and Ke3 decay widths, Γ(Kμ3)/Γ(Ke3), can be related to the λ+ and λ0 parameters as [2],

Γ(Kμ3)/Γ(Ke3) = 0.6457 - 0.1531λ+ + 1.5646λ0 .

If the λ+ value derived from Ke3 analysis is used, the λ0 parameter can be determined.


The Kμ3 and Ke3 events were identified by measuring μ+s and e+s masses, as shown in a figure. The Γ(Kμ3)/Γ(Ke3) ratio can be written as,

Γ(Kμ3)/Γ(Ke3) = N(Kμ3) / N(Ke3) • Ω(Ke3)/Ω(Kμ3) ,

where N and Ω are the number of accepted events and the detector acceptance obtained by a Monte Carlo simulation, respectively. The Γ(Kμ3)/Γ(Ke3) value and the associated λ0 parameter with the μ-e universality assumption were determined to be [3]

Γ(Kμ3)/Γ(Ke3) = 0.671 ± 0.007(stat.) ± 0.008(syst.),
λ0 = 0.019 ±0.005(stat.) ±0.004(syst.),

which is consistent with the ChPT prediction.
Result of kl3 ratio


[1] J. Gasser and H. Leutwyler, Nucl. Phys. B250, 517 (1985).
[2] H.W. Fearing, E. Fischbach, and J. Smith, Phys. Rev. D2, 542 (1970); Phys. Rev. Lett. 24, 189 (1970).
[3] K. Horie et al., Phys. Lett. B513 (2001) 311.

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