### Abstract

Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

Original language | English |
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Article number | 065037 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 79 |

Issue number | 6 |

DOIs | |

Publication status | Published - Mar 2 2009 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*79*(6), [065037]. https://doi.org/10.1103/PhysRevD.79.065037

**Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory.** / Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 79, no. 6, 065037. https://doi.org/10.1103/PhysRevD.79.065037

}

TY - JOUR

T1 - Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory

AU - Harada, Koji

AU - Hattori, Nozomu

AU - Kubo, Hirofumi

AU - Yamamoto, Yuki

PY - 2009/3/2

Y1 - 2009/3/2

N2 - Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

AB - Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

UR - http://www.scopus.com/inward/record.url?scp=65549170290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65549170290&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.79.065037

DO - 10.1103/PhysRevD.79.065037

M3 - Article

AN - SCOPUS:65549170290

VL - 79

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 6

M1 - 065037

ER -