The evaluation of K → ππ decay amplitudes from lattice quantum chromodynamics

Goode, Elaine Jennifer (2012) The evaluation of K → ππ decay amplitudes from lattice quantum chromodynamics. University of Southampton, Faculty of Physical and Applied Sciences, Doctoral Thesis, 183pp.

Record type: Thesis (Doctoral)

Abstract

We present results for the ΔI = 3/2 K → ππ decay amplitude computed using lattice quantum chromodynamics. The calculation is performed using 2 + 1 flavours of domain wall fermion and the Iwasaki gauge action modified by the dislocation suppressing determinant ratio, on a lattice volume of 323 × 64 × 32 at lattice spacing a^-1 = 1.364 GeV. The resulting valence pion mass is m_π = 142.11 MeV, and the kaon mass is mK = 505.5 MeV. A total of 146 configurations are analysed, giving ReA₂= 1.381(46)_stat (258)_syst × 10^-8 GeV and ImA₂ = -6.54(46)_stat (120)_syst × 10^-8 GeV. The experimental results for ReA₀ and ReA₂ and ε'/ε are combined with this lattice result for ImA2 to give ImA0 /ReA0 = -1.61(28) × 10^-4.

We also present results from a second calculation where both the ΔI = 1/2 and ΔI = 3/2 K → ππ decay amplitudes are calculated. This calculation is performed using 2 + 1 flavours of domain wall fermions with the Iwasaki gauge action and a lattice size of 16³ × 32 × 16. Since the evaluation of A₀ is technically challenging, this first ever determination of A₀ is performed at threshold with a heavy pion mass of mπ ~ 420 MeV. The results are Re(A₀) = 3.80(82) × 10^-7 GeV and Im(A₀) = 2.5(2.2) × 10¹¹ GeV.