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Both for quark flavor asymmetry and valence, we consider the anomalous dimension of the non-singlet twist-two quark operator of arbitrary Lorentz spin N at four loops in SU(nc) color gauge theory and present its term proportional to zeta(3)…

High Energy Physics - Phenomenology · Physics 2026-05-12 B. A. Kniehl , V. N. Velizhanin

We compute the non-planar contribution to the universal anomalous dimension of twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin eighteen. Exploiting the results of this and our previous…

High Energy Physics - Theory · Physics 2021-06-30 B. A. Kniehl , V. N. Velizhanin

We use conformal symmetry to calculate the NNLO anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin $N \le 8$ from a set of gauge-invariant two-point correlation functions. Combining this result…

High Energy Physics - Phenomenology · Physics 2025-10-20 V. M. Braun , K. G. Chetyrkin , A. N. Manashov

For ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives in the general $\xi$-gauge we calculate the three-loop anomalous dimension of the matter superfields defined in terms of the bare coupling constant and demonstrate…

High Energy Physics - Theory · Physics 2022-05-04 Ilya Shirokov , Konstantin Stepanyantz

In lattice Hamiltonian systems with a quartic coupling $\gamma$, a critical value $\gamma^*$ may exist such that, when $\gamma=\gamma^*$, the leading irrelevant operator decouples from the Hamiltonian and the leading nonscaling contribution…

Statistical Mechanics · Physics 2009-11-07 Massimo Campostrini , Pietro Parruccini , Paolo Rossi

We perform a comprehensive perturbative study of the operator spectrum in multi-scalar theories with hypercubic global symmetry. This includes working out symmetry representations and their corresponding tensor structures. These structures…

High Energy Physics - Theory · Physics 2024-03-22 Alexander Bednyakov , Johan Henriksson , Stefanos R. Kousvos

We show that naive dimensional analysis (NDA) is equivalent to the result that L-loop scattering amplitudes have perturbative order N=L+Delta, with a shift Delta that depends on the NDA-weight of operator insertions. The NDA weight of an…

High Energy Physics - Phenomenology · Physics 2015-06-17 Elizabeth E. Jenkins , Aneesh V. Manohar , Michael Trott

We correct the computation of one Feynman diagram in the three-loop beta functions for the long-range quartic multi-scalar model, originally presented in (2020 J. Phys. A: Math. Theor. 53 445008) [arXiv:2007.04603]. The correction requires…

High Energy Physics - Theory · Physics 2025-04-03 Dario Benedetti , Razvan Gurau , Sabine Harribey

Two-loop $\beta$-function and anomalous dimension are calculated for N=1 supersymmetric quantum electrodynamics, regularized by higher derivatives in the minimal subtraction scheme. The result for two-loop contribution to the…

High Energy Physics - Theory · Physics 2007-05-23 A. Soloshenko , K. Stepanyantz

At the end of 2016, we computed the five-loop (N$^4$LO) contributions to the beta function in perturbative Quantum Chromodynamics (QCD), its generalization to non-Abelian gauge theories with a simple compact Lie group, and for Quantum…

High Energy Physics - Phenomenology · Physics 2025-10-31 F. Herzog , B. Ruijl , T. Ueda , J. Vermaseren , A. Vogt

We predict that the four-loop contribution \beta_3 to the QCD \beta function in the MS-bar prescription is given by \beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the…

High Energy Physics - Phenomenology · Physics 2016-09-06 John Ellis , Marek Karliner , Mark. A. Samuel

This paper presents numerical values for auxiliary integrals and coefficients of the beta function in the three-loop approximation for a four-dimensional model with a quartic interaction, using a special type of regularization function. The…

High Energy Physics - Theory · Physics 2026-03-24 A. V. Ivanov , V. A. Nikiforov

The critical behaviour of the O(n)-symmetric model with two n-vector fields is studied within the field-theoretical renormalization group approach in a D=4-2 epsilon expansion. Depending on the coupling constants the beta-functions, fixed…

Statistical Mechanics · Physics 2009-02-09 Yuri M. Pis'mak , Alexej Weber , Franz J. Wegner

We present the result of a full direct component calculation for the planar four-loop anomalous dimension of the Konishi operator in N =4 Supersymmetric Yang-Mills theory. Our result confirms the results obtained from superfield…

High Energy Physics - Theory · Physics 2009-12-10 V. N. Velizhanin

We revisit the question of how to calculate correlations of the curvature perturbation, $\zeta$, using the $\delta N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice…

Cosmology and Nongalactic Astrophysics · Physics 2018-08-28 Shailee V. Imrith , David J. Mulryne , Arttu Rajantie

Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the $\beta$-function and the anomalous dimensions of the ${O}(n)$-symmetric $\phi^4$-theory in $D=4-\ep$ dimensions we present the…

High Energy Physics - Theory · Physics 2009-10-28 H. Kleinert , J. Neu , V. Schulte-Frohlinde , K. G. Chetyrkin , S. A. Larin

Two-loop contributions to the electromagnetic form factors are calculated in the kinematic regime close to the fermion-antifermion threshold. The results are presented in an expansion in the velocity $\beta$ of the fermions in the c.m.…

High Energy Physics - Phenomenology · Physics 2014-11-17 A. H. Hoang

We consider twist $J$ operators with spin $S$ in the $sl(2)$ sector of $\mathcal N=4$ SYM. The small spin expansion of their anomalous dimension defines the so-called slope functions. Much is known about the linear term, but the study of…

High Energy Physics - Theory · Physics 2015-06-19 Matteo Beccaria , Guido Macorini

We compute the four-loop beta functions of short and long-range multi scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a $U(N)^3$ symmetry and study the renormalization group at…

High Energy Physics - Theory · Physics 2022-10-10 Sabine Harribey

We recalculate the contributions of individual six loop graphs to the $\beta$-function for a three dimensional scalar theory with an arbitrary sextic scalar potential. Previously this was calculated by Hager who specialised to a theory with…

High Energy Physics - Theory · Physics 2026-05-20 Ian Jack , Hugh Osborn