Anomaly and Anomaly-Free Treatment of QFTs Based on Symmetry-preserving Loop Regularization

Abstract

The triangle anomaly in massless and massive QED is investigated by adopting the symmetry-preserving loop regularization method proposed recently in \cite{LR}. The method is realized in the initial dimension of theory without modifying the original lagrangian, it preserves symmetries under non-Abelian gauge and Poincare transformations in spite of the existence of two intrinsic mass scales $M_c$ and ${\mu }_s$ which actually play the roles of UV- and IR-cut off respectively. The axialvector-vector-vector (AVV) triangle diagrams in massless and massive QED are evaluated explicitly by using the loop regularization. It is shown that when the momentum $k$ of external state is soft with $k^2\ll {\mu }_s^2,m^2$ ($m$ is the mass of loop fermions) and $M_c\to \infty$, both massless and massive QED become anomaly free. The triangle anomaly is found to appear as quantum corrections in the case that $m^2,{\mu }_s^2\ll k^2$ and $M_c\to \infty$. Especially, it is justified that in the massless QED with ${\mu }_s=0$ and $M_c\to \infty$, the triangle anomaly naturally exists as quantum effects in the axial-vector current when the ambiguity caused by the trace of gamma matrices with ${\gamma }_5$ is eliminated by simply using the definition of ${\gamma }_5$. It is explicitly demonstrated how the Ward identity anomaly of currents depends on the treatment for the trace of gamma matrices, which enables us to make a clarification whether the ambiguity of triangle anomaly is caused by the regularization scheme in the perturbation calculations or by the trace of gamma matrices with ${\gamma }_5$.

74 pages, Revtex, the ambiguities of anomaly caused by the trace of gamma matrices with gamma_5 and by the regularization schemes are further clarified. Minor corrections made without changing the conclusions

Cited by in corpus (27)

• Gravitational Contributions to the Running of Gauge Couplings
• Quantum field theory of gravity with spin and scaling gauge invariance and spacetime dynamics with quantum inflation
• Note on Higgs Decay into Two Photons $H\to \gamma \gamma$
• An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting ${\gamma }_5$
• On the Radiatively Induced Lorentz and CPT Violating Chern-Simons Term
• ${\gamma }_5$ algebra ambiguities in Feynman amplitudes: momentum routing invariance and anomalies in $D=4$ and $D=2$
• Momentum Routing Invariance in Extended QED: Assuring Gauge Invariance Beyond Tree Level
• One-Loop Renormalization of Non-Abelian Gauge Theory and βFunction Based on Loop Regularization Method
• Gravidynamics, spinodynamics and electrodynamics within the framework of gravitational quantum field theory
• Quantum Gravitational Contributions to Gauge Field Theories
• Chiral Magnetic Effect and Chiral Phase Transition
• Renormalization of Supersymmetric Field Theories in Loop Regularization with String-mode Regulators
• Charmless $B_s\to PP,PV,VV$ Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects II
• On the Bose symmetry and the left- and right-chiral anomalies
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• Charmless $B\to PP,PV,VV$ Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects
• Note on triangle anomaly with improved momentum cutoff
• Strong and Electromagnetic Decays of X(1835) as a Baryonium State
• The Explicit Derivation of QED Trace Anomaly in Symmetry-Preserving Loop Regularization at One Loop Level
• Chiral Magnetic Effect and QCD Phase Transitions with Effective Models
• Quantum Structure of Field Theory and Standard Model Based on Infinity-free Loop Regularization/Renormalization
• Consistency and Advantage of Loop Regularization Method Merging with Bjorken-Drell's Analogy Between Feynman Diagrams and Electrical Circuits
• Neutral Higgs production on LHC in the two-Higgs-doublet model with spontaneous $CP$ violation
• QCD Approach to B->D πDecays and CP Violation
• Asymptotics of Certain Sums Required in Loop Regularisation
• QCD Factorization Based on Six-Quark Operator Effective Hamiltonian from Perturbative QCD and Charmless Bottom Meson Decays $B_{(s)}\to \pi \pi ,\pi K,KK$
• Do anomalies break the momentum routing invariance?