The rare decays K+π+ννˉK^+ \to \pi^+ \nu \bar \nu and KLμ+μK_L \to \mu^+ \mu^- beyond leading logarithms

Jul, 1993
44 pages
Published in:
  • Nucl.Phys.B 412 (1994) 106-142
e-Print:
Report number:
  • MPI-PH-93-44,
  • TUM-T31-44-93

Citations per year

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Abstract:
We analyze the branching ratio for the FCNC mode K +π +ννˉK~+\to\pi~+\nu\bar\nu\ in the standard model with QCD effects taken into account consistently to next-to-leading order. This involves a two-loop renormalization group analysis for the charm contribution, presented in this paper, and the calculation of O(αs)O(\alpha_s) corrections to all orders in mt/MWm_t/M_W for the top-quark case that we have described elsewhere. The inclusion of next-to-leading corrections reduces considerably the theoretical uncertainty due to the choice of the renormalization scales, inherent in any calculation to finite order in perturbation theory. For K +π +ννˉK~+\to\pi~+\nu\bar\nu\ this point has not been discussed previously. In particular, the related uncertainty in the determination of Vtd|V_{td}| from B(K +π +ννˉ)B(K~+\to\pi~+\nu\bar\nu) is reduced from 30%\sim 30\% to 7%\sim 7\% for typical values of the parameters. Simultaneously also the dependence of B(K +π +ννˉ)B(K~+\to\pi~+\nu\bar\nu) on the choice of mcm_c is considerably reduced. We also give the next-to-leading order expression for the short-distance part of KLμ +μ K_L\to\mu~+\mu~-. Impacts of our calculations on the determination of the unitarity triangle are presented.
  • K: rare decay
  • rare decay: K
  • K+: semileptonic decay
  • semileptonic decay: K+
  • K0(L): leptonic decay
  • leptonic decay: K0(L)
  • neutral current: flavor changing
  • quantum chromodynamics: perturbation theory
  • coupling constant: strong interaction
  • strong interaction: coupling constant