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Related papers: Four-loop results on anomalous dimensions and spli…

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We study the next-to-next-to-leading order (NNLO) evolution of flavour singlet parton densities and structure functions in massless perturbative QCD. Present information on the corresponding three-loop splitting functions is used to derive…

High Energy Physics - Phenomenology · Physics 2009-10-31 W. L. van Neerven , A. Vogt

We present the result of a calculation for the third and fourth moments of the non-singlet four-loop anomalous dimension of Wilson twist-2 operators in QCD with full color and flavour structures. We discuss also a general expressions for…

High Energy Physics - Phenomenology · Physics 2014-12-17 V. N. Velizhanin

We have determined the fourth-order $n_f$ contributions to the two splitting functions governing the evolution of all flavor differences of quark distributions of hadrons in perturbative quantum chromodynamics with $n_f$ light flavors. The…

High Energy Physics - Phenomenology · Physics 2025-05-16 B. A. Kniehl , S. Moch , V. N. Velizhanin , A. Vogt

We compute the four-loop QCD corrections to the massless quark-anti-quark-photon form factor $F_q$ in the large-$N_c$ limit. From the pole part we extract analytic expressions for the corresponding cusp and collinear anomalous dimensions.

High Energy Physics - Phenomenology · Physics 2017-04-26 Johannes Henn , Roman N. Lee , Alexander V. Smirnov , Vladimir A. Smirnov , Matthias Steinhauser

We have extended our previous computations of the even-N moments of the flavour-singlet four-loop splitting functions to N = 12 for the pure-singlet quark case and N = 10 for all other cases. These results, obtained using physical…

High Energy Physics - Phenomenology · Physics 2023-10-10 S. Moch , B. Ruijl , T. Ueda , J. Vermaseren , A. Vogt

We have computed the even-$N$ moments $N \leq 20$ of the gluon-to-quark splitting function $P_{\rm qg}$ at the fourth order of perturbative QCD via the renormalization of off-shell operator matrix elements. Our results, derived analytically…

High Energy Physics - Phenomenology · Physics 2024-04-16 G. Falcioni , F. Herzog , S. Moch , A. Vogt

We compute the four-loop $n_f$ contribution proportional to the quartic Casimir of the QCD cusp anomalous dimension as an expansion for small cusp angle $\phi$. This piece is gauge invariant, violates Casimir scaling, and first appears at…

High Energy Physics - Phenomenology · Physics 2017-10-17 Andrey Grozin , Johannes Henn , Maximilian Stahlhofen

We calculate the small angle expansion of the four-loop QCD cusp anomalous dimension. As a byproduct of our calculation, we also obtain the four-loop anomalous dimension of the heavy-quark field in HQET. The validity of the calculational…

High Energy Physics - Phenomenology · Physics 2022-11-18 Andrey G. Grozin , Roman N. Lee , Andrey F. Pikelner

We present the first complete next-to-next-to-next-to-leading-order calculation of the matching coefficients that link unpolarized flavor non-singlet parton distribution functions with lattice QCD computable correlation functions. By using…

High Energy Physics - Phenomenology · Physics 2024-10-11 Chen Cheng , Li-Hong Huang , Xiang Li , Zheng-Yang Li , Yan-Qing Ma

We obtain the quark and gluon rapidity anomalous dimension to fourth order in QCD. We calculate the N$^3$LO rapidity anomalous dimensions to higher order in the dimensional regulator and make use of the soft/rapidity anomalous dimension…

High Energy Physics - Phenomenology · Physics 2022-05-12 Claude Duhr , Bernhard Mistlberger , Gherardo Vita

We have computed the complete next-to-next-to-leading order (NNLO) contributions to the splitting functions governing the evolution of unpolarized parton densities in perturbative QCD. Our results agree with all partial results available in…

High Energy Physics - Phenomenology · Physics 2009-11-10 S. Moch , J. A. M. Vermaseren , A. Vogt

We report on the recent completion of the three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes. This brings the state-of-the-art knowledge of long-distance singularities in multi-leg QCD…

High Energy Physics - Phenomenology · Physics 2016-06-21 Einan Gardi , Øyvind Almelid , Claude Duhr

We present the details of the analytic calculation of the three-loop angle-dependent cusp anomalous dimension in QCD and its supersymmetric extensions, including the maximally supersymmetric $\mathcal{N}=4$ super Yang-Mills theory. The…

High Energy Physics - Phenomenology · Physics 2016-02-17 Andrey Grozin , Johannes M. Henn , Gregory P. Korchemsky , Peter Marquard

We summarize recent results on the evolution of unpolarized parton densities and deep-inelastic structure functions in massless perturbative QCD. Due to last year's extension of the integer-moment calculations of the three-loop splitting…

High Energy Physics - Phenomenology · Physics 2008-11-26 W. L. van Neerven , A. Vogt

Future high luminosity polarized deep--inelastic scattering experiments will improve both the knowledge of the spin sub--structure of the nucleons and contribute further to the precision determination of the strong coupling constant, as…

High Energy Physics - Phenomenology · Physics 2022-02-16 J. Blümlein , P. Marquard , C. Schneider , K. Schönwald

We have extended our previous computations, performed analytically for a general gauge group, of the even-$N$ moments $\gamma_{\rm ik}^{\,(3)}(N)$ of the four-loop flavour-singlet splitting functions $P_{\rm ik}^{\,(3)}(x)$ to $N = 22$. The…

High Energy Physics - Phenomenology · Physics 2025-12-12 G. Falcioni , F. Herzog , S. Moch , A. Pelloni , A. Vogt

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 compute the fermionic contribution to the photon-quark form factor to four-loop order in QCD in the planar limit in analytic form. From the divergent part of the latter the cusp and collinear anomalous dimensions are extracted. Results…

High Energy Physics - Phenomenology · Physics 2016-04-19 Johannes M. Henn , Alexander V. Smirnov , Vladimir A. Smirnov , Matthias Steinhauser

We consider the collinear limit of QCD amplitudes at one-loop order, and their factorization properties directly in colour space. These results apply to the multiple collinear limit of an arbitrary number of QCD partons, and are a basic…

High Energy Physics - Phenomenology · Physics 2009-11-10 German Rodrigo , Stefano Catani , Daniel de Florian , Werner Vogelsang

The perturbative three-loop result for the thermodynamic potential of QCD at finite temperature and chemical potential as obtained in the framework of dimensional reduction is compared with the exact result in the limit of large flavor…

High Energy Physics - Phenomenology · Physics 2009-11-10 A. Ipp , A. Rebhan , A. Vuorinen