$K \to ππ$ Decays in a Finite Volume

Details $K \to ππ$ Decays in a Finite Volume $K \to ππ$ Decays in a Finite Volume

2001-04-11

arxiv.org/abs/hep-lat/0104006v2

Nucl.Phys.B619:467-498,2001

Physics

High Energy Physics

High Energy Physics - Lattice

36 Pages, Expanded version accepted for publication in Nuclear Physics B. More detailed explanations, same conclusions

Scientific paper

10.1016/S0550-3213(01)00495-3

We discuss finite-volume computations of two-body hadronic decays below the inelastic threshold (e.g. $K\to\pi\pi$ decays). The relation between finite-volume matrix elements and physical amplitudes, recently derived by Lellouch and L\"uscher, is extended to all elastic states under the inelastic threshold. We present a detailed comparison of our approach with that of Lellouch and L\"uscher and discuss the possible limitations of the method which could arise due to the presence of inelastic thresholds. We also examine a standard alternative method which can be used to extract the real part of the decay amplitude from correlators of the form $< 0 |T[\pi\pi{\cal H}_WK ]| 0 >$. We show that in this case there are finite-volume corrections which vanish as inverse powers of the volume, which cannot be removed by a multiplicative factor.

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