$K\to (\pi \pi {)}_{I=2}$ decays and twisted boundary conditions

Abstract

We propose a new method to evaluate the Lellouch-Lüscher factor which relates the $\Delta I=3/2$ $K\to \pi \pi$ matrix elements computed on a finite lattice to the physical (infinite-volume) decay amplitudes. The method relies on the use of partially twisted boundary conditions, which allow the s-wave $\pi \pi$ phase shift to be computed as an almost continuous function of the centre-of-mass relative momentum and hence for its derivative to be evaluated. We successfully demonstrate the feasibility of the technique in an exploratory computation.

19 pages, 7 figures

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• Vector Correlators in Lattice QCD: methods and applications
• Lattice QCD and the Timelike Pion Form Factor
• Lattice determination of the $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude $A_2$
• Lüscher's finite size method with twisted boundary conditions: an application to $J/\psi$-$\varphi$ system to search for narrow resonance
• A Lattice Study of $({\bar{D}}_1{D}^{\ast }{)}^{\pm }$ Near-threshold Scattering
• Lattice study of scattering phase shifts for $D{D}^{\ast }$ and $B{B}^{\ast }$ systems using twisted boundary conditions: Search for bound state formation