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Isospin breaking in \(K \rightarrow \pi\pi\) decays

  • theoretical physics
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Abstract.

We perform a complete analysis of isospin breaking in \(K \to 2 \pi\) amplitudes in chiral perturbation theory, including both strong isospin violation (\(m_u \neq m_d\)) and electromagnetic corrections to next-to-leading order in the low-energy expansion. The unknown chiral couplings are estimated at leading order in the 1/N c expansion. We study the impact of isospin breaking on CP conserving amplitudes and rescattering phases. In particular, we extract the effective couplings g 8 and g 27 from a fit to \(K \rightarrow \pi\pi\) branching ratios, finding small deviations from the isospin-limit case. The ratio \({\rm Re} A_0 /{\rm Re} A_2\) measuring the \( \Delta I = 1/2\) enhancement is found to decrease from \(22.2 \pm 0.1\) in the isospin limit to \(20.3 \pm 0.5\) in the presence of isospin breaking. We also analyze the effect of isospin violation on the CP violation parameter \(\epsilon^\prime\), finding a destructive interference between three different sources of isospin violation. Within the uncertainties of large-N c estimates for the low-energy constants, the isospin violating correction for \(\epsilon^\prime\) is below 15%.

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Authors and Affiliations

  1. Departament de Física Teórica, IFIC, Universitat de Valéncia - CSIC, Apt. Correus 22085, 46071, Valéncia, Spain

    V. Cirigliano & A. Pich

  2. Department of Physics, California Institute of Technology, 91125, Pasadena, California, USA

    V. Cirigliano

  3. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090, Wien, Austria

    G. Ecker & H. Neufeld

Authors
  1. V. Cirigliano
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  2. G. Ecker
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  3. H. Neufeld
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  4. A. Pich
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Additional information

Received: 21 November 2003, Published online: 4 February 2004

Work supported in part by IHP-RTN, Contract No. HPRN-CT2002-00311 (EURIDICE) and by Acciones Integradas, Project No. 19/2003 (Austria), HU2002-0044 (MCYT, Spain)

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Cirigliano, V., Ecker, G., Neufeld, H. et al. Isospin breaking in \(K \rightarrow \pi\pi\) decays. Eur. Phys. J. C 33, 369–396 (2004). https://doi.org/10.1140/epjc/s2003-01579-3

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