000012215 001__ 12215 000012215 005__ 20250218124807.0 000012215 02470 $$ahttps://doi.org/10.1103/PhysRevD.97.065007$$2doi 000012215 037__ $$aTEXTUAL 000012215 037__ $$bArticle 000012215 041__ $$aeng 000012215 245__ $$aOperator mixing in the ϵ -expansion: Scheme and evanescent-operator independence 000012215 269__ $$a2018-03-12 000012215 336__ $$aArticle 000012215 520__ $$aWe consider theories with fermionic degrees of freedom that have a fixed point of Wilson-Fisher type in noninteger dimension $d = 4 - 2ϵ$. Due to the presence of evanescent operators, i.e., operators that vanish in integer dimensions, these theories contain families of infinitely many operators that can mix with each other under renormalization. We clarify the dependence of the corresponding anomalous-dimension matrix on the choice of renormalization scheme beyond leading order in ϵ-expansion. In standard choices of scheme, we find that eigenvalues at the fixed point cannot be extracted from a finite-dimensional block. We illustrate in examples a truncation approach to compute the eigenvalues. These are observable scaling dimensions, and, indeed, we find that the dependence on the choice of scheme cancels. As an application, we obtain the IR scaling dimension of four-fermion operators in QED in $d = 4 - 2ϵ$ at order $O(ϵ^2)$. 000012215 536__ $$oU.S. Department of Energy 000012215 540__ $$a<p>Published by the American Physical Society under the terms of the <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a> license.</p> 000012215 542__ $$fCC BY 000012215 690__ $$aPhysical Sciences Division 000012215 691__ $$aEnrico Fermi Institute 000012215 7001_ $$aDi Pietro, Lorenzo$$uPerimeter Institute for Theoretical Physics 000012215 7001_ $$aStamou, Emmanuel$$uUniversity of Chicago 000012215 773__ $$tPhysical Review D 000012215 8564_ $$9d2e18216-aefa-40db-b598-5b985787d130$$ePublic$$s492875$$uhttps://knowledge.uchicago.edu/record/12215/files/PhysRevD.97.065007.pdf 000012215 908__ $$aI agree 000012215 909CO $$ooai:uchicago.tind.io:12215$$pGLOBAL_SET 000012215 983__ $$aArticle