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arXiv · 1610.01305

On a realization of $\{β\}$-expansion in QCD

S. V. Mikhailov
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Abstract

We suggest a simple algebraic approach to fix the elements of the $\{ β\}$-expansion for renormalization group invariant quantities, which uses additional degrees of freedom. The approach is discussed in detail for N$^2$LO calculations in QCD with the MSSM gluino -- an additional degree of freedom. We derive the formulae of the $\{ β\}$-expansion for the nonsinglet Adler $D$-function and Bjorken polarized sum rules in the actual N$^3$LO within this quantum field theory scheme with the MSSM gluino and the scheme with the second additional degree of freedom. We discuss the properties of the $\{ β\}$-expansion for higher orders considering the N$^4$LO as an example.

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S. V. Mikhailov. 2017-03-16. On a realization of $\{β\}$-expansion in QCD. https://doi.org/10.1007/jhep04(2017)169

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