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Finite-volume partially-quenched two-pion amplitudes in the I=0 channel

Finite-volume partially-quenched two-pion amplitudes in the I=0 channel
Finite-volume partially-quenched two-pion amplitudes in the I=0 channel
We 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-? states. Our Letter implies that extracting ?I=1/2, K??? decay amplitudes from simulations with ms=md,u is not possible in partially quenched QCD (and is very difficult in full QCD).
0370-2693
207-217
Lin, C.J.D.
6ed1cbe7-f3d9-4eb7-bd84-62525461628f
Martinelli, G.
3949da7a-7efe-4ebd-b1f7-92f1ca150d66
Pallante, E.
beba5f56-f008-4986-8ade-36e466e10db0
Sachrajda, C.T.
0ed6568b-f52f-4314-8677-4aeeb925d6f7
Villadoro, G.
e031a98e-8777-45c1-920d-05e3bd0e9b20
Lin, C.J.D.
6ed1cbe7-f3d9-4eb7-bd84-62525461628f
Martinelli, G.
3949da7a-7efe-4ebd-b1f7-92f1ca150d66
Pallante, E.
beba5f56-f008-4986-8ade-36e466e10db0
Sachrajda, C.T.
0ed6568b-f52f-4314-8677-4aeeb925d6f7
Villadoro, G.
e031a98e-8777-45c1-920d-05e3bd0e9b20

Lin, C.J.D., Martinelli, G., Pallante, E., Sachrajda, C.T. and Villadoro, G. (2004) Finite-volume partially-quenched two-pion amplitudes in the I=0 channel. Physics Letters B, 581 (3-4), 207-217. (doi:10.1016/j.physletb.2003.12.019).

Record type: Article

Abstract

We 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-? states. Our Letter implies that extracting ?I=1/2, K??? decay amplitudes from simulations with ms=md,u is not possible in partially quenched QCD (and is very difficult in full QCD).

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More information

Submitted date: 13 August 2003
Published date: 19 February 2004
Organisations: Physics & Astronomy

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Local EPrints ID: 57425
URI: http://eprints.soton.ac.uk/id/eprint/57425
ISSN: 0370-2693
PURE UUID: 37b67372-ee6d-461c-a507-6d0525523d80

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Date deposited: 14 Aug 2008
Last modified: 15 Mar 2024 11:06

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Contributors

Author: C.J.D. Lin
Author: G. Martinelli
Author: E. Pallante
Author: C.T. Sachrajda
Author: G. Villadoro

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