Radiative corrections in $K_{e4}$ decay

Details Radiative corrections in $K_{e4}$ decay Radiative corrections in $K_{e4}$ decay

2009-06-02

arxiv.org/abs/0906.0516v2

Eur.Phys.J.C64:47-54,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

11 pages, 5 figures, 1 table, some minor misprints are corrected

Scientific paper

10.1140/epjc/s10052-009-1125-9

The final state interaction of pions in the decay $K^\pm\to \pi^+\pi^-e^\pm\nu$ 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 $\sigma=\frac{\alpha}{2\pi}\br{\ln\frac{M^2}{m_e^2}-1}$ has a standard form of the Drell-Yan process and is proportional to the Sommerfeld-Sakharov factor. The numerical estimations are presented.

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