Axial-vector current and dimensional regularization

1979 ◽  
Vol 20 (12) ◽  
pp. 3378-3389 ◽  
Author(s):  
Steven Gottlieb ◽  
J. T. Donohue
Keyword(s):  
Axial Vector ◽  
Dimensional Regularization ◽  
Vector Current ◽  
Axial Vector Current

scholarly journals Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Taushif Ahmed ◽  
Long Chen ◽  
Michał Czakon
Keyword(s):  
Axial Vector ◽  
Dimensional Regularization ◽  
Renormalization Constant ◽  
Vector Current ◽  
Axial Vector Current ◽  
Loop Order ◽  
Axial Anomaly ◽  
Anomalous Dimensions ◽  
Anomaly Equation ◽  
The Matrix

Abstract The renormalization constant ZJ of the flavor-singlet axial-vector current with a non-anticommuting γ5 in dimensional regularization is determined to order $$ {\alpha}_s^3 $$ α s 3 in QCD with massless quarks. The result is obtained by computing the matrix elements of the operators appearing in the axial-anomaly equation $$ {\left[{\partial}_{\mu }{J}_5^{\mu}\right]}_R=\frac{\alpha_s}{4\pi }{n}_f{\mathrm{T}}_F{\left[F\tilde{F}\right]}_R $$ ∂ μ J 5 μ R = α s 4 π n f T F F F ˜ R between the vacuum and a state of two (off-shell) gluons to 4-loop order. Furthermore, through this computation, the equality between the $$ \overline{\mathrm{MS}} $$ MS ¯ renormalization constant $$ {Z}_{F\tilde{F}} $$ Z F F ˜ associated with the operator $$ {\left[F\tilde{F}\right]}_R $$ F F ˜ R and that of αs is verified explicitly to hold true at 4-loop order. This equality automatically ensures a relation between the respective anomalous dimensions, $$ {\gamma}_J=\frac{\alpha_s}{4\pi }{n}_f{\mathrm{T}}_F{\gamma}_{FJ} $$ γ J = α s 4 π n f T F γ FJ , at order $$ {\alpha}_s^4 $$ α s 4 given the validity of the axial-anomaly equation which was used to determine the non-$$ \overline{\mathrm{MS}} $$ MS ¯ piece of ZJ for the particular γ5 prescription in use.

On the conserved axial-vector current in β-decay

1964 ◽  
Vol 31 (4) ◽  
pp. 874-878 ◽  
Author(s):  
V. S. Mathur ◽  
Ravinder Nath ◽  
R. P. Saxena
Keyword(s):  
Axial Vector ◽  
Vector Current ◽  
Axial Vector Current ◽  
Β Decay
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