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Conventionally, one calculates a zero in a beta function by computing this function to a given loop order and solving for the zero.
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For N f N_{f} values that do not lead to an IR zero in β α \beta_{\alpha} , the pole in β α , N S V Z \beta_{\alpha,NSVZ} can be relevant, as discussed in I. I. Kogan and M. Shifman, Phys. Rev. Lett. 75
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T. A. Ryttov, R. Shrock, Phys. Rev. D 86
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R. Shrock, Phys. Rev. D 87
2013
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T. A. Ryttov and R. Shrock, Phys. Rev. D 83
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Relations between the NSVZ scheme and DR ¯ \overline{\rm DR} scheme have been discussed, e.g., in I. Jack, D. R. T. Jones, and C. G. North, Nucl. Phys. B 486
2014
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R. Shrock, Phys. Rev. D 88
2014
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T. A. Ryttov, Phys. Rev. D 89
2014
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M. P. Lombardo, K. Miura, T. Nunes da Silva, and E. Pallante, JHEP 1412, 183 (2014); arXiv:1411.1657
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T. A. Ryttov, R. Shrock, Phys. Rev. D 85
2012
Cited alongside, same era.
T. A. Ryttov, R. Shrock, Phys. Rev. D 86
2012
Cited alongside, same era.
The generalization to massive fermions is straightforward. As the scale μ \mu decreases below the fermion mass m m , one integrates this fermion out of the low-energy effective field theory that applies for μ < m \mu<m
Cited in the paper.
The Casimir invariants C R C_{R} and T R T_{R} are defined in the standard way as ∑ a ∑ j 𝒟 R ( T a ) i j 𝒟 R ( T a ) j k = C R δ i k \sum_{a}\sum_{j}{\cal D}_{R}(T_{a})_{ij}{\cal D}_{R}(T_{a})_{jk}=C_{R}\delta_{ik} and ∑ i , j 𝒟 R ( T a ) i j 𝒟 R ( T b ) j i = T R δ a b \sum_{i,j}{\cal D}_{R}(T_{a})_{ij}{\cal D}_{R}(T_{b})_{ji}=T_{R}\delta_{ab} , where R R is the representation with matrix 𝒟 R ( T a ) {\cal D}_{R}(T_{a}) , and T a T_{a} are the generators of G G , so that for SU( N c N_{c} ), C A = N c C_{A}=N_{c} for the adjoint ( A A ) and T f u n d = 1 / 2 T_{fund}=1/2 for the fundamental representation, etc. C f C_{f} denotes C R C_{R} for the fermion representation
Cited in the paper.
Here and below, when an expression such as N f , b 1 z N_{f,b1z} is given for N f N_{f} that sometimes evaluates to a non-integral real value, it is understood implicitly that one infers an appropriate integral value of N f N_{f} from it
Cited in the paper.
2014
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R. Shrock, Phys. Rev. D 89
2014
Later among the works it cites.