K --> pi pi decays in a finite volume

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.

Note:

36 Pages, Expanded version accepted for publication in Nuclear Physics B. More detailed explanations, same conclusions Report-no: ROMA-1395/00, SHEP 01/10

12.38.Gc
11.15.H
lattice field theory
K: hadronic decay
threshold
effect: finite size
amplitude analysis
correlation function
propagator
quantum mechanics: nonrelativistic

References(12)

Figures(0)

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