Abstract
Leading-twist operators have a remarkable property that their divergence vanishes in a free theory. Recently it was suggested that this property can be used for an alternative technique to calculate anomalous dimensions of leading-twist operators and allows one to gain one order in perturbation theory so that, i.e., two-loop anomalous dimensions can be calculated from one-loop Feynman diagrams, etc. In this work we study the feasibility of this program by a toy-model example of the $$\varphi ^3$$ theory in six dimensions. Our conclusion is that this approach is valid, although it does not seem to present considerable technical simplifications as compared to the standard technique. It does provide one, however, with a very nontrivial check of the calculation as the structure of the contributions is very different.
Highlights
Calculation of anomalous dimensions of composite operators belongs to the standard tasks of any quantum field theory calculation
It was suggested that this property can be used for an alternative technique to calculate anomalous dimensions of leadingtwist operators and allows one to gain one order in perturbation theory so that, i.e., two-loop anomalous dimensions can be calculated from one-loop Feynman diagrams, etc
We have calculated two-loop anomalous dimensions of the leading-twist operators in the φ3 model using the approach proposed in Refs. [10,11]
Summary
Calculation of anomalous dimensions of composite operators belongs to the standard tasks of any quantum field theory calculation. A new approach for calculating the anomalous dimensions of leading-twist operators was proposed in Refs. In the interacting theory the r.h.s. of Eq (1) is non-zero but proportional to the coupling constant This identity allows one to extract the -loop contribution to the anomalous dimension of the operator Oμ1,...μ j from − 1 loop diagrams only. The one-loop anomalous dimensions of leading-twist operators do not require calculation of loop integrals at all [11,13]. This technique proves to be more effective and flexible as we will demonstrate on the example of calculation of two-loop anomalous dimensions in the su(n) symmetric φ3 model [17]. In the appendices we explain some technical issues and details of the derivation
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