Finite-Volume Partially-Quenched Two-Pion Amplitudes in the I=0 Channel

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dc.creatorLin, C. -J. D.
dc.creatorMartinelli, G.
dc.creatorPallante, E.
dc.creatorSachrajda, C. T.
dc.creatorVilladoro, G.
dc.date2003-08-13
dc.date.accessioned2026-07-07T11:08:54Z
dc.date.available2026-07-07T11:08:54Z
dc.descriptionWe present a study of the finite-volume two-pion matrix elements and correlation functions of the I=0 scalar operator, in full and partially quenched QCD, at one-loop order in chiral perturbation theory. In partially quenched QCD, when the sea and valence light quark masses are not equal, the lack of unitarity leads to the same inconsistencies as in quenched QCD and the matrix elements cannot be determined. It is possible, however, to overcome this problem by requiring the masses of the valence and sea quarks to be equal for the u and d quarks while keeping the strange quark (s) quenched (or partially quenched), but only in the kinematic region where the two-pion energy is below the two-kaon threshold. Although our results are obtained at NLO in chiral perturbation theory, they are more general and are also valid for non-leptonic kaon decays (we also study the matrix elements of (8,1) operators, such as the QCD penguin operator Q6). We point out that even in full QCD, where any problems caused by the lack of unitarity are clearly absent, there are practical difficulties in general, caused by the fact that finite-volume energy eigenstates are linear combination of two-pion, two-kaon and two-eta states. Our work implies that extracting Delta I=1/2, K-->pipi decay amplitudes from simulations with m_s=m_{d,u} is not possible in partially quenched QCD (and is very difficult in full QCD).
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/hep-lat/0308014
dc.identifierhttp://arxiv.org/abs/hep-lat/0308014
dc.identifierPhys.Lett.B581:207-217,2004
dc.identifierdoi:10.1016/j.physletb.2003.12.019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/190292
dc.subjectHigh Energy Physics - Lattice
dc.subjectHigh Energy Physics - Phenomenology
dc.titleFinite-Volume Partially-Quenched Two-Pion Amplitudes in the I=0 Channel
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