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Relativistic, model-independent, three-particle quantization condition · Around

2013

Relativistic, model-independent, three-particle quantization condition

Hansen, Maxwell T., Sharpe, Stephen R.

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This is a combined write-up for two talks which were given consecutively and which described different aspects of the same topic.

We present a generalization of L\"uscher's relation between the finite-volume spectrum and S-matrix to three particles.
Specifically, we consider a scalar field theory, which has a $\mathbb{Z}_2$ symmetry that prevents even/odd coupling.
The theory is assumed to have no two-particle bound states and to have two-particle phase shifts that are bounded by $\pi/2$ in the regime of elastic scattering.

Built on

M. Lüscher, Nucl. Phys. B354
1991
Earlier work this paper cites.
K. Rummukainen and S. A. Gottlieb, Nucl.Phys. B450
1995
Earlier work this paper cites.
L. Lellouch and M. Lüscher, Commun.Math.Phys. 219, 31 (2001) , arXiv:hep-lat/0003023 [hep-lat]
Original
2001
Earlier work this paper cites.

Similar

C. Kim, C. Sachrajda, and S. R. Sharpe, Nucl.Phys. B727
2005
Cited alongside, same era.
S. R. Beane, W. Detmold, and M. J. Savage, Phys.Rev. D76
Original
2007
Cited alongside, same era.
S. Tan, Phys.Rev. A78
Original
2008
Cited alongside, same era.
M. Lüscher, Commun. Math. Phys. 104
Cited in the paper.
M. Lüscher, Commun. Math. Phys. 105
Cited in the paper.
M. T. Hansen and S. R. Sharpe, in preparation
Cited in the paper.

Then

K. Polejaeva and A. Rusetsky, Eur.Phys.J. A48
Original
2012
Later among the works it cites.
R. A. Briceno and Z. Davoudi, Phys.Rev. D87
Original
2013
Closest in time.
S. Aoki, N. Ishii, T. Doi, Y. Ikeda, and T. Inoue, Phys.Rev. D88
Original
2013
Closest in time.

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