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Finite-volume effects in moving frames

Finite-volume effects in moving frames
Finite-volume effects in moving frames
We determine the quantization condition for the energy levels of two interacting particles in a finite box in a "moving frame", i.e. one in which the total momentum of pions is non-zero. This condition is valid up to corrections which fall exponentially withe the box size, and holds only below the inelastic threshold. It is derived using field theoretic methods, using a generalization of previous summation formulae relating sums and integrals over momenta. The result agrees with that obtained earlier by Rummakainen and Gottlieb using a relativistic quantum mechanical approach. Technically, we expand the finite-volume four-point Green function in terms of the infinite-volume Bethe-Salpeter kernel, and determine the position of the poles. The final result is written in terms of the two-pion scattering phase shift. Our result can be used to facilitate the determination of the scattering phase shift, and can be used to generalize the Lellouch-Lüscher formula relating finite-volume two-particle matrix elements to those in infinite volume.
359
Proceedings of Science
Kim, Changhoan
b9765a16-6cee-4120-a1cd-ced51a33e398
Sachrajda, Chris. T.
0ed6568b-f52f-4314-8677-4aeeb925d6f7
Sharpe, Stephen.R.
7ac4193d-f2b6-40a2-a3ea-c8900d508419
Kim, Changhoan
b9765a16-6cee-4120-a1cd-ced51a33e398
Sachrajda, Chris. T.
0ed6568b-f52f-4314-8677-4aeeb925d6f7
Sharpe, Stephen.R.
7ac4193d-f2b6-40a2-a3ea-c8900d508419

Kim, Changhoan, Sachrajda, Chris. T. and Sharpe, Stephen.R. (2006) Finite-volume effects in moving frames. In Proceedings of Science (PoS) LAT2005. Proceedings of Science. p. 359 .

Record type: Conference or Workshop Item (Paper)

Abstract

We determine the quantization condition for the energy levels of two interacting particles in a finite box in a "moving frame", i.e. one in which the total momentum of pions is non-zero. This condition is valid up to corrections which fall exponentially withe the box size, and holds only below the inelastic threshold. It is derived using field theoretic methods, using a generalization of previous summation formulae relating sums and integrals over momenta. The result agrees with that obtained earlier by Rummakainen and Gottlieb using a relativistic quantum mechanical approach. Technically, we expand the finite-volume four-point Green function in terms of the infinite-volume Bethe-Salpeter kernel, and determine the position of the poles. The final result is written in terms of the two-pion scattering phase shift. Our result can be used to facilitate the determination of the scattering phase shift, and can be used to generalize the Lellouch-Lüscher formula relating finite-volume two-particle matrix elements to those in infinite volume.

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More information

Published date: July 2006
Venue - Dates: XXIIIrd International Symposium on Lattice Field Theory, Dublin, Ireland, 2005-07-24 - 2005-07-29

Identifiers

Local EPrints ID: 57353
URI: http://eprints.soton.ac.uk/id/eprint/57353
PURE UUID: b8a0de59-134a-40df-bfce-9fba788a6f4b

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Date deposited: 14 Aug 2008
Last modified: 09 Nov 2021 09:53

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Contributors

Author: Changhoan Kim
Author: Stephen.R. Sharpe

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