Perturbative and nonperturbative renormalization of anomalous quark triangles

Arkady Vainshtein

doi:10.1016/j.physletb.2003.07.038

Perturbative and nonperturbative renormalization of anomalous quark triangles

Arkady Vainshtein

Physics and Astronomy (Twin Cities)

Research output: Contribution to journal › Article › peer-review

104 Scopus citations

Abstract

Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler-Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We derive a new nonrenormalization theorem for the transversal part of the triangle. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively. At the nonperturbative level we use the operator product expansion and the pion dominance in the longitudinal part to determine the magnetic susceptibility of the quark condensate, X = -N_c/(4π ²F_π²).

Original language	English (US)
Pages (from-to)	187-193
Number of pages	7
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	569
Issue number	3-4
DOIs	https://doi.org/10.1016/j.physletb.2003.07.038
State	Published - Sep 11 2003

Bibliographical note

Funding Information:
The work was supported in part by DOE grant DE-FG02-94ER408.

Keywords

Anomaly
Fermion triangle
Nonrenormalization

Publisher link

10.1016/j.physletb.2003.07.038

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title = "Perturbative and nonperturbative renormalization of anomalous quark triangles",

abstract = "Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler-Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We derive a new nonrenormalization theorem for the transversal part of the triangle. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively. At the nonperturbative level we use the operator product expansion and the pion dominance in the longitudinal part to determine the magnetic susceptibility of the quark condensate, X = -Nc/(4π 2Fπ2).",

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doi = "10.1016/j.physletb.2003.07.038",

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T1 - Perturbative and nonperturbative renormalization of anomalous quark triangles

AU - Vainshtein, Arkady

N1 - Funding Information: The work was supported in part by DOE grant DE-FG02-94ER408.

PY - 2003/9/11

Y1 - 2003/9/11

N2 - Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler-Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We derive a new nonrenormalization theorem for the transversal part of the triangle. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively. At the nonperturbative level we use the operator product expansion and the pion dominance in the longitudinal part to determine the magnetic susceptibility of the quark condensate, X = -Nc/(4π 2Fπ2).

AB - Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler-Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We derive a new nonrenormalization theorem for the transversal part of the triangle. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively. At the nonperturbative level we use the operator product expansion and the pion dominance in the longitudinal part to determine the magnetic susceptibility of the quark condensate, X = -Nc/(4π 2Fπ2).

KW - Anomaly

KW - Fermion triangle

KW - Nonrenormalization

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JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

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ER -

Perturbative and nonperturbative renormalization of anomalous quark triangles

Abstract

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