Precision radiative corrections to the muon polarisation in the semileptonic decay of a charged kaon
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Precision radiative corrections to the muon polarisation in the semileptonic decay of a charged kaon M. J. Sánchez-Glez1, A. Martínez1, M. Neri1, C. Juárez-León2 , J. J. Torres3 , Rubén Flores-Mendieta4,a 1 Departamento de Física, Escuela Superior de Física y Matemáticas del Instituto Politécnico Nacional,
Apartado Postal 75-702, 07738 Mexico City, Mexico
2 Departamento de Formación Básica, Escuela Superior de Cómputo del Instituto Politécnico Nacional,
Apartado Postal 75-702, 07738 Mexico City, Mexico
3 Departamento de Posgrado, Escuela Superior de Cómputo del Instituto Politécnico Nacional, Apartado
Postal 75-702, 07738 Mexico City, Mexico
4 Instituto de Física, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, Zona Centro,
78000 San Luis Potosí, S.L.P., Mexico Received: 1 June 2020 / Accepted: 16 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract An expression for the Dalitz plot of the semileptonic decay of a charged kaon, including radiative corrections to order O [(α/π)(q/M1 )], where q is the four-momentum transfer and M1 is the mass of the decaying kaon, is obtained. Contributions of both the three- and four-body regions are accounted for. Additionally, the emitted muon is considered to be polarised, so the analysis is also focused on evaluating the radiative corrections to the longitudinal, transverse, and normal polarisation components of the muon. The final formulas, with the triple integration of the bremsstrahlung photon variables ready to be performed numerically, are general enough to be used in model-independent experimental analyses whether or not the real photon is discriminated. With the known numerical values of the weak form factors and slope parameters of the process, the radiative corrections to the components of the muon polarisation are found to be very small compared to their respective uncorrected values over most of the allowed kinematical region. Similarly, the fully integrated radiative corrections to the components of the muon polarisation vector are also rather small, around 0.2%. This might suggest that radiative corrections to the muon polarisation can be + safely ignored in an actual analysis of K μ3 decays. 1 Introduction The symmetry transformation CPT is the product of the three symmetry transformations C, P, and T, which interchange particles and antiparticles, x and −x, and t and −t, respectively. As long as CPT invariance holds, both CP and T violations are accounted for by complex relative phases in the effective coupling constants. For a CP or T asymmetry to become observable, at least two amplitudes containing different coupling constants are required [1]. Kaon physics has played an important role in all the stages of the standard model (SM), including its very construction and its tests through CP violation in K L → ππ decays. Direct
a e-mail: [email protected] (corresponding author)
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