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Leading Logarithms in the Massive O(N) Nonlinear Sigma Model · Around

2009

Leading Logarithms in the Massive O(N) Nonlinear Sigma Model

Bijnens, Johan, Carloni, Lisa

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We review Buchler and Colangelo's result that leading divergences at any loop order can be calculated using only one-loop calculations and we provide an alternative proof.

We then use this method to calculate the leading divergences of and thus the leading logarithmic corrections to the meson mass in the massive O(N) nonlinear sigma model to five-loop order.
We also calculate the all-loop result to leading order in the large $N$ expansion by showing that only cactus diagrams contribute and by summing these via a generalized gap equation.

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Similar

J. Gasser and H. Leutwyler, Nucl. Phys. B 250
1985
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G. Colangelo, Phys. Lett. B 350
1995
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S. Weinberg, Phys. Rev. D 56
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J. Bijnens, G. Colangelo and G. Ecker, Phys. Lett. B 441
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Cited alongside, same era.

Then

J. Bijnens, G. Colangelo and G. Ecker, JHEP 9902
1999
Later among the works it cites.
J. Bijnens, G. Colangelo and G. Ecker, Annals Phys. 280
2000
Later among the works it cites.
M. Büchler and G. Colangelo, Eur. Phys. J. C 32
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J. Bijnens, Prog. Part. Nucl. Phys. 58
2007
Later among the works it cites.
M. Bissegger and A. Fuhrer, Phys. Lett. B 646
2007
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M. Bissegger and A. Fuhrer, Eur. Phys. J. C 51
2007
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N. Kivel, M. V. Polyakov and A. Vladimirov, Phys. Rev. Lett. 101
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J. Bijnens, G. Colangelo, G. Ecker, J. Gasser and M. E. Sainio, Nucl. Phys. B 508

1998

Cited alongside, same era.

N. A. Kivel, M. V. Polyakov and A. A. Vladimirov, arXiv:0904.3008 [hep-ph]

Cited in the paper.

J. A. M. Vermaseren, arXiv:math-ph/0010025

Cited in the paper.

J. Bijnens and L. Carloni, work in progress

Cited in the paper.

2008

Later among the works it cites.