Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering

Abstract

We use the large N_f self consistency formalism to compute the $O(1/N_f)$ critical exponent corresponding to the renormalization of the flavour non-singlet twist two Wilson operators which arise in the operator product expansion of currents in deep inelastic processes. Expanding the $d$-dimensional expression in powers of $\epsilon$ $=$ $(4-d)/2$ the coefficients of $\epsilon$ agree with the known two loop structure of the corresponding renormalization group function and we deduce analytic expressions for all moments, $n$, at three and higher orders in perturbation theory in the $\overline{\mbox{MS}}$ scheme at $O(1/N_f)$.

13 Latex pages, 1 figure (available from author on request), LTH-322

References in corpus (4)

• The three-loop QCD $\beta$-function and anomalous dimensions
• Electron Mass Anomalous Dimension at O(1/N^2_f) in Quantum Electrodynamics
• Quark, Gluon and Ghost Anomalous Dimensions at O(1/N_f) in Quantum Chromodynamics
• Algorithm for Computing the $\BETA$-Function of Quantum Electrodynamics in the Large N_f Expansion

Cited by in corpus (95)

• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Higgs boson production at hadron colliders in NNLO QCD
• Soft-gluon resummation for Higgs boson production at hadron colliders
• NNLO global parton analysis
• The 3-loop QCD calculation of the moments of deep inelastic structure functions
• Three-Loop Results for Quark and Gluon Form Factors
• The Quark Form Factor at Higher Orders
• Two-loop QCD corrections to gluon-gluon scattering
• NNLO evolution of deep-inelastic structure functions: the singlet case
• NNLO evolution of deep-inelastic structure functions: the non-singlet case
• Mellin Moments of the {$O({\alpha }_s^3$)} Heavy Flavor Contributions to unpolarized Deep-Inelastic Scattering at $Q^2\gg m^2$ and Anomalous Dimensions
• Some higher moments of deep inelastic structure functions at next-to-next-to leading order of perturbative QCD
• The Collinear Limit of the Energy-Energy Correlator
• Anomalous dimensions of high-spin operators beyond the leading order
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Next-to-Next-to-Leading Order Evolution of Non-Singlet Fragmentation Functions
• On quartic colour factors in splitting functions and the gluon cusp anomalous dimension
• Two-loop QCD corrections to the scattering of massless distinct quarks
• Two-loop QCD corrections to massless quark-gluon scattering
• Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell-Yan process
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• Two-loop QCD corrections to massless identical quark scattering
• Two-loop QED and QCD corrections to massless fermion-boson scattering
• The Theory of Deeply Inelastic Scattering
• The O(α_s^3) Massive Operator Matrix Elements of O(n_f) for the Structure Function F_2(x,Q^2) and Transversity
• Joint Resummation for Higgs Production
• Improved Approximations for the Three-Loop Splitting Functions in QCD
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x
• On non-singlet physical evolution kernels and large-x coefficient functions in perturbative QCD
• Two-loop QCD helicity amplitudes for massless quark-massless gauge boson scattering
• Two-loop QCD helicity amplitudes for massless quark-quark scattering
• Non-Singlet Structure Functions at Three Loops: Fermionic Contributions
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• The Four Loop QCD Rapidity Anomalous Dimension
• The Logarithmic Contributions to the O(α_s^3) Asymptotic Massive Wilson Coefficients and Operator Matrix Elements in Deeply Inelastic Scattering
• The $n_f^2$ contributions to fermionic four-loop form factors
• Four-loop quark form factor with quartic fundamental colour factor
• Soft corrections to inclusive deep-inelastic scattering at four loops and beyond
• Higher Orders in A(α_s)/[1-x]_+ of Non-Singlet Partonic Splitting Functions
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Quark and gluon form factors in four-loop QCD
• Non-singlet structure functions beyond the next-to-next-to leading order
• Computation of quark mass anomalous dimension at O(1/N_f^2) in quantum chromodynamics
• The 16th Moment of the Non--Singlet Structure Functions $F_2(x,Q^2)$ and $F_L(x,Q^2)$ to $O({\alpha }_s^3)$
• Three loop anomalous dimension of the second moment of the transversity operator in the MSbar and RI' schemes
• The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion
• The interplay between Sudakov resummation, renormalons and higher twist in deep inelastic scattering
• Determination of the anomalous dimension of gluonic operators in deep inelastic scattering at O(1/N_f)
• Four loop anomalous dimension of the second moment of the non-singlet twist-2 operator in QCD
• Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N${}^3$LL
• Absence of pi^2 terms in physical anomalous dimensions in DIS: verification and resulting predictions
• Anomalous dimensions of operators in polarized deep inelastic scattering at O(1/N_f)
• Soft-gluon effective coupling and cusp anomalous dimension
• The N${}^3$LO Scheme-invariant QCD Evolution of the Non-singlet Structure Functions \boldmath $F_2^{\mathrm{NS}}(x,Q^2)$ and $g_1^{\mathrm{NS}}(x,Q^2)$
• Quark mass anomalous dimension at O(1/N_f^2) in QCD
• 3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines
• Resummation of small-x double logarithms in QCD: inclusive deep-inelastic scattering
• High energy behaviour of form factors
• Higher orders and IR renormalon phenomenology in DVCS
• Three loop renormalization of the SU(N_c) non-abelian Thirring model
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• Taming the B --> X(s) gamma spectrum by Dressed Gluon Exponentiation
• Two- and Three-Loop Data for Groomed Jet Mass
• Perturbative Part of the Non-Singlet Structure Function F_2 in the Large-N_F Limit
• Impact of the three-loop corrections on the QCD analysis of the deep-inelastic-scattering data
• The full angle-dependence of the four-loop cusp anomalous dimension in QED
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• A planar four-loop form factor and cusp anomalous dimension in QCD
• Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL
• Renormalon chains contributions to the non-singlet evolutional kernels in ${\varphi }_6^3$ and QCD
• First results for three-loop deep-inelastic structure functions in QCD
• A multiloop improvement of non-singlet QCD evolution equations
• The QCD Splitting Functions at Three Loops: Methods and Results
• Resummed inclusive cross-section in ADD model at N${}^3$LL+NNLO
• First $O({\alpha }_s^3)$ heavy flavor contributions to deeply inelastic scattering
• Anomalous dimension of gluonic operator in polarized deep inelastic scattering at O(1/N_f)
• Evolution program for parton densities with perturbative heavy flavor boundary conditions
• Heavy Flavor DIS Wilson coefficients in the asymptotic regime
• Four loop wave function renormalization in the non-abelian Thirring model
• QCD cusp anomalous dimension: current status
• Conformal constraints for anomalous dimensions of leading twist operators
• Precision QCD phenomenology of exotic spin-2 search at the LHC
• Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering
• QCD and QED renormalization group functions - a large N_f approach
• Four-loop large-n_f contributions to the non-singlet structure functions F_2 and F_L
• Structure function evolution at next-to-leading order and beyond
• Basis transformation properties of anomalous dimensions for hard exclusive processes
• Parton densities and structure functions beyond the next-to-leading order
• Fermionic corrections to quark and gluon form factors in four-loop QCD
• Deep inelastic lepton-hadron scattering as a test of perturbative QCD
• On the n -> 0 limit of gamma_gg(a) in QCD
• Four-loop anomalous dimension of flavor non-singlet quark operator of twist two and Lorentz spin N for general gauge group: transcendental part
• Fermionic contribution to the anomalous dimension of twist-2 operators in N=4 SYM theory, critical indices and integrability
• beta-functions in higher dimensional field theories