{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:46:28Z","timestamp":1760150788578,"version":"build-2065373602"},"reference-count":169,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,29]],"date-time":"2023-12-29T00:00:00Z","timestamp":1703808000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A review of modern methods for effective calculations of Feynman integrals containing both massless propagators and propagators with masses is given. The effectiveness of these methods in various fields of their application is demonstrated by the examples under consideration.<\/jats:p>","DOI":"10.3390\/sym16010052","type":"journal-article","created":{"date-parts":[[2023,12,29]],"date-time":"2023-12-29T11:19:21Z","timestamp":1703848761000},"page":"52","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Effective Quantum Field Theory Methods for Calculating Feynman Integrals"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1408-2735","authenticated-orcid":false,"given":"Anatoly V.","family":"Kotikov","sequence":"first","affiliation":[{"name":"Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/0370-1573(79)90014-0","article-title":"Renormalization Group and the Deep Structure of the Proton","volume":"53","author":"Peterman","year":"1979","journal-title":"Phys. Rep."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0550-3213(72)90279-9","article-title":"Regularization and Renormalization of Gauge Fields","volume":"44","author":"Veltman","year":"1972","journal-title":"Nucl. Phys. B"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/BF02895558","article-title":"Dimensional Renormalization: The Number of Dimensions as a Regularizing Parameter","volume":"12","author":"Bollini","year":"1972","journal-title":"Nuovo Cim. B"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF02756527","article-title":"Analytic renormalization via continuous space dimension","volume":"4","author":"Cicuta","year":"1972","journal-title":"Lett. Nuovo Cim."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/0550-3213(73)90376-3","article-title":"Dimensional regularization and the renormalization group","volume":"61","author":"Hooft","year":"1973","journal-title":"Nucl. Phys. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1007\/BF02774121","article-title":"Theoretical Predictions for Critical Exponents at the Lambda Point of Bose Liquids","volume":"2","author":"Peliti","year":"1971","journal-title":"Lett. Nuovo Cim."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/BF01019296","article-title":"1\/N Expansion: Calculation of the Exponents Eta Furthermore, Nu in the Order 1\/N**2 for Arbitrary Number of Dimensions","volume":"47","author":"Vasiliev","year":"1981","journal-title":"Theor. Math. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/0370-2693(83)90816-X","article-title":"The Method of Uniqueness, a New Powerful Technique for Multiloop Calculations","volume":"133","author":"Kazakov","year":"1983","journal-title":"Phys. Lett. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/BF01018044","article-title":"Calculation of Feynman Integrals by the Method of \u2018uniqueness\u2019","volume":"58","author":"Kazakov","year":"1984","journal-title":"Theor. Math. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/BF01017127","article-title":"Calculation of Many Loop Diagrams of Perturbation Theory","volume":"54","author":"Usyukina","year":"1983","journal-title":"Theor. Math. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2811","DOI":"10.1088\/0305-4470\/16\/12\/026","article-title":"Calculation of Ladder Diagrams in Arbitrary Order","volume":"16","author":"Belokurov","year":"1983","journal-title":"J. Phys. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/BF01015778","article-title":"An Algorithm for Calculating Massless Feynman Diagrams","volume":"79","author":"Belokurov","year":"1989","journal-title":"Theor. Math. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/BF01034829","article-title":"Multiloop Calculations: Method of Uniqueness and Functional Equations","volume":"62","author":"Kazakov","year":"1985","journal-title":"Theor. Math. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/0370-2693(96)00226-2","article-title":"The Gegenbauer polynomial technique: The Evaluation of a class of Feynman diagrams","volume":"375","author":"Kotikov","year":"1996","journal-title":"Phys. Lett. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1134\/S0040577918020083","article-title":"New Results for a Two-Loop Massless Propagator-Type Feynman Diagram","volume":"194","author":"Kotikov","year":"2018","journal-title":"Theor. Math. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1134\/S1063779619010039","article-title":"Multi-loop techniques for massless Feynman diagram calculations","volume":"50","author":"Kotikov","year":"2019","journal-title":"Phys. Part. Nucl."},{"key":"ref_17","unstructured":"Kotikov, A.V. (2012). Differential Equations and Feynman Integrals. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ryder, L.H. (1996). Quantum Field Theory, Cambridge University Press.","DOI":"10.1017\/CBO9780511813900"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0550-3213(81)90199-1","article-title":"Integration By Parts: The Algorithm to Calculate Beta Functions in 4 Loops","volume":"192","author":"Chetyrkin","year":"1981","journal-title":"Nucl. Phys. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1264","DOI":"10.1007\/BF01041909","article-title":"The Method of Uniqueness: Multiloop Calculations in QCD","volume":"73","author":"Kazakov","year":"1988","journal-title":"Theor. Math. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1016\/0550-3213(88)90106-X","article-title":"Total \u03b1s Correction to Deep Inelastic Scattering Cross-section Ratio R = \u03c3L\/\u03c3T in QCD","volume":"307","author":"Kazakov","year":"1988","journal-title":"Nucl. Phys. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/BF01018678","article-title":"The Calculation of Moments of Structure Function of Deep Inelastic Scattering in QCD","volume":"78","author":"Kotikov","year":"1989","journal-title":"Theor. Math. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/0370-2693(91)90413-K","article-title":"Differential equations method: New technique for massive Feynman diagrams calculation","volume":"254","author":"Kotikov","year":"1991","journal-title":"Phys. Lett. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/0370-2693(91)90834-D","article-title":"Differential equations method: The Calculation of vertex type Feynman diagrams","volume":"259","author":"Kotikov","year":"1991","journal-title":"Phys. Lett. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/0370-2693(91)90536-Y","article-title":"Differential equation method: The Calculation of N point Feynman diagrams","volume":"267","author":"Kotikov","year":"1991","journal-title":"Phys. Lett. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3133","DOI":"10.1142\/S0217732391003626","article-title":"New method of massive N point Feynman diagrams calculation","volume":"6","author":"Kotikov","year":"1991","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1007\/BF03185566","article-title":"Differential equations for Feynman graph amplitudes","volume":"110","author":"Remiddi","year":"1997","journal-title":"Nuovo Cim. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1142\/S0217732391000695","article-title":"New method of massive Feynman diagrams calculation","volume":"6","author":"Kotikov","year":"1991","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1977","DOI":"10.1142\/S0217751X92000867","article-title":"New method of massive Feynman diagrams calculation. Vertex type functions","volume":"7","author":"Kotikov","year":"1992","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/0370-2693(83)90324-6","article-title":"Five Loop Renormalization Group Calculations in the g\u03d54 in Four-dimensions Theory","volume":"132","author":"Gorishnii","year":"1983","journal-title":"Phys. Lett. B"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6479","DOI":"10.1103\/PhysRevD.54.6479","article-title":"Connection between Feynman integrals having different values of the space-time dimension","volume":"54","author":"Tarasov","year":"1996","journal-title":"Phys. Rev. D"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/S0550-3213(97)00376-3","article-title":"Generalized recurrence relations for two loop propagator integrals with arbitrary masses","volume":"502","author":"Tarasov","year":"1997","journal-title":"Nucl. Phys. B"},{"key":"ref_33","unstructured":"Lee, R.N. (2012). Presenting LiteRed: A tool for the Loop InTEgrals REDuction. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"012059","DOI":"10.1088\/1742-6596\/523\/1\/012059","article-title":"LiteRed 1.4: A powerful tool for reduction of multiloop integrals","volume":"523","author":"Lee","year":"2014","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"020","DOI":"10.1007\/JHEP04(2010)020","article-title":"Analytic Results for Massless Three-Loop Form Factors","volume":"2010","author":"Lee","year":"2010","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0550-3213(00)00329-1","article-title":"NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories","volume":"582","author":"Kotikov","year":"2000","journal-title":"Nucl. Phys. B"},{"key":"ref_37","first-page":"338","article-title":"Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories","volume":"23","author":"Lipatov","year":"1976","journal-title":"Sov. J. Nucl. Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/0370-2693(75)90524-9","article-title":"On the Pomeranchuk Singularity in Asymptotically Free Theories","volume":"60","author":"Fadin","year":"1975","journal-title":"Phys. Lett. B"},{"key":"ref_39","first-page":"443","article-title":"Multi-Reggeon Processes in the Yang-Mills Theory","volume":"44","author":"Kuraev","year":"1976","journal-title":"Sov. Phys. JETP"},{"key":"ref_40","first-page":"199","article-title":"The Pomeranchuk Singularity in Nonabelian Gauge Theories","volume":"45","author":"Kuraev","year":"1977","journal-title":"Sov. Phys. JETP"},{"key":"ref_41","first-page":"822","article-title":"The Pomeranchuk Singularity in Quantum Chromodynamics","volume":"28","author":"Balitsky","year":"1978","journal-title":"Sov. J. Nucl. Phys."},{"key":"ref_42","first-page":"355","article-title":"Calculation of meson meson interaction cross-section in quantum chromodynamics","volume":"30","author":"Balitsky","year":"1979","journal-title":"JETP Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0370-2693(98)00473-0","article-title":"BFKL pomeron in the next-to-leading approximation","volume":"429","author":"Fadin","year":"1998","journal-title":"Phys. Lett. B"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/S0370-2693(98)00551-6","article-title":"Energy scale(s) and next-to-leading BFKL equation","volume":"430","author":"Camici","year":"1998","journal-title":"Phys. Lett. B"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0550-3213(77)90328-5","article-title":"Supersymmetric Yang-Mills Theories","volume":"121","author":"Brink","year":"1977","journal-title":"Nucl. Phys. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1016\/0550-3213(77)90206-1","article-title":"Supersymmetry, Supergravity Theories and the Dual Spinor Model","volume":"122","author":"Gliozzi","year":"1977","journal-title":"Nucl. Phys. B"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0550-3213(03)00264-5","article-title":"DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory","volume":"661","author":"Kotikov","year":"2003","journal-title":"Nucl. Phys. B"},{"key":"ref_48","unstructured":"Kotikov, A.V., and Lipatov, L.N. (2001). DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory. arXiv."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/S0370-2693(03)00184-9","article-title":"Anomalous dimensions of Wilson operators in N = 4 SYM theory","volume":"557","author":"Kotikov","year":"2003","journal-title":"Phys. Lett. B"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.physletb.2004.05.078","article-title":"Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model","volume":"595","author":"Kotikov","year":"2004","journal-title":"Phys. Lett. B"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.physletb.2013.07.013","article-title":"On DIS Wilson coefficients in N = 4 super Yang\u2013Mills theory","volume":"725","author":"Bianchi","year":"2013","journal-title":"Phys. Lett. B"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.nuclphysb.2004.03.030","article-title":"The Three loop splitting functions in QCD: The Nonsinglet case","volume":"688","author":"Moch","year":"2004","journal-title":"Nucl. Phys. B"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.nuclphysb.2004.04.024","article-title":"The Three-loop splitting functions in QCD: The Singlet case","volume":"691","author":"Vogt","year":"2004","journal-title":"Nucl. Phys. B"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.nuclphysb.2005.06.020","article-title":"The Third-order QCD corrections to deep-inelastic scattering by photon exchange","volume":"724","author":"Vermaseren","year":"2005","journal-title":"Nucl. Phys. B"},{"key":"ref_55","unstructured":"Diakonov, D. (2010). Subtleties in Quantum Field Theory, PNPI."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1134\/S1063779613020196","article-title":"The property of maximal transcendentality: Calculation of anomalous dimensions in the N = 4 SYM and master integrals","volume":"44","author":"Kotikov","year":"2013","journal-title":"Phys. Part. Nucl."},{"key":"ref_57","unstructured":"Kotikov, A.V., and Onishchenko, A.I. (2019). DGLAP and BFKL equations in N = 4 SYM: From weak to strong coupling. arXiv."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1007\/s11232-013-0079-0","article-title":"The property of maximal transcendentality: Calculation of master integrals","volume":"176","author":"Kotikov","year":"2013","journal-title":"Theor. Math. Phys."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1134\/S0040577917030084","article-title":"The property of maximal transcendentality: Calculation of Feynman integrals","volume":"190","author":"Kotikov","year":"2017","journal-title":"Theor. Math. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"361","DOI":"10.3390\/particles4030031","article-title":"Some Examples of Calculation of Massless and Massive Feynman Integrals","volume":"4","author":"Kotikov","year":"2021","journal-title":"Particles"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF01551921","article-title":"The Master Two Loop Diagram with Masses","volume":"47","author":"Broadhurst","year":"1990","journal-title":"Z. Phys. C"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/S0550-3213(99)00078-4","article-title":"Analytic two loop results for selfenergy type and vertex type diagrams with one nonzero mass","volume":"547","author":"Fleischer","year":"1999","journal-title":"Nucl. Phys. B"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"394","DOI":"10.3390\/particles3020030","article-title":"About calculation of massless and massive Feynman integrals","volume":"3","author":"Kotikov","year":"2020","journal-title":"Particles"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.nuclphysb.2012.04.007","article-title":"Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM","volume":"862","author":"Eden","year":"2012","journal-title":"Nucl. Phys. B"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"454001","DOI":"10.1088\/1751-8113\/44\/45\/454001","article-title":"Scattering amplitudes: The most perfect microscopic structures in the universe","volume":"44","author":"Dixon","year":"2011","journal-title":"J. Phys. A"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"024","DOI":"10.1007\/JHEP01(2012)024","article-title":"Analytic result for the two-loop six-point NMHV amplitude in N = 4 super Yang\u2013Mills theory","volume":"2012","author":"Dixon","year":"2012","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/JHEP03(2012)101","article-title":"The three-loop form factor in N = 4 super Yang\u2013Mills","volume":"2012","author":"Gehrmann","year":"2012","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"082","DOI":"10.1007\/JHEP05(2012)082","article-title":"Analytic two-loop form factors in N = 4 SYM","volume":"2012","author":"Brandhuber","year":"2012","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"024","DOI":"10.1007\/JHEP12(2011)024","article-title":"Form factors and scattering amplitudes in N = 4 SYM in dimensional and massive regularizations","volume":"2011","author":"Henn","year":"2011","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"475401","DOI":"10.1088\/1751-8113\/46\/47\/475401","article-title":"Motivic Multiple Zeta Values and Superstring Amplitudes","volume":"46","author":"Schlotterer","year":"2013","journal-title":"J. Phys. A"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1002\/prop.201300019","article-title":"Polylogarithms, Multiple Zeta Values and Superstring Amplitudes","volume":"61","author":"Broedel","year":"2013","journal-title":"Fortsch. Phys."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.physletb.2012.08.018","article-title":"Maximally Helicity Violating Disk Amplitudes, Twistors and Transcendental Integrals","volume":"716","author":"Stieberger","year":"2012","journal-title":"Phys. Lett. B"},{"key":"ref_73","unstructured":"Eden, B. (2012). Three-loop universal structure constants in N = 4 susy Yang\u2013Mills theory. arXiv."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1007\/JHEP01(2015)116","article-title":"Local integrands for the five-point amplitude in planar N = 4 SYM up to five loops","volume":"2015","author":"Ambrosio","year":"2015","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"031","DOI":"10.1007\/JHEP03(2016)031","article-title":"Bootstrapping correlation functions in N = 4 SYM","volume":"2016","author":"Chicherin","year":"2016","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/JHEP02(2016)165","article-title":"Three-point functions in N = 4 SYM: The hexagon proposal at three loops","volume":"2016","author":"Eden","year":"2016","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/0550-3213(80)90289-8","article-title":"New Approach to Evaluation of Multiloop Feynman Integrals: The Gegenbauer Polynomial x Space Technique","volume":"174","author":"Chetyrkin","year":"1980","journal-title":"Nucl. Phys. B"},{"key":"ref_78","first-page":"731","article-title":"Critical behavior of 3-D electrodynamics","volume":"58","author":"Kotikov","year":"1993","journal-title":"JETP Lett."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"890","DOI":"10.1134\/S1063778812070058","article-title":"On the Critical Behavior of (2+1)-Dimensional QED","volume":"75","author":"Kotikov","year":"2012","journal-title":"Phys. Atom. Nucl."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"056009","DOI":"10.1103\/PhysRevD.94.056009","article-title":"Critical behavior of (2+1)-dimensional QED: 1\/Nf corrections in the Landau gauge","volume":"94","author":"Kotikov","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"114011","DOI":"10.1103\/PhysRevD.94.114011","article-title":"Critical behavior of (2+1)-dimensional QED: 1\/Nf corrections in an arbitrary nonlocal gauge","volume":"94","author":"Kotikov","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"065038","DOI":"10.1103\/PhysRevD.89.065038","article-title":"Two-loop fermion self-energy in reduced quantum electrodynamics and application to the ultrarelativistic limit of graphene","volume":"89","author":"Kotikov","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_83","first-page":"144","article-title":"Mellin\u2013Barnes transformation for two-loop master-diagrams","volume":"494","author":"Derkachev","year":"2020","journal-title":"Zap. Nauchn. Semin."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1007\/s10958-022-05998-3","article-title":"Mellin\u2013Barnes Transformation for Two-Loop Master-Diagram","volume":"264","author":"Derkachev","year":"2022","journal-title":"J. Math. Sci."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"059","DOI":"10.1007\/JHEP06(2023)059","article-title":"Ladder and zig-zag Feynman diagrams, operator formalism and conformal triangles","volume":"2023","author":"Derkachov","year":"2023","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1134\/S004057791703014X","article-title":"The method of uniqueness and the optical conductivity of graphene: New application of a powerful technique for multiloop calculations","volume":"190","author":"Teber","year":"2017","journal-title":"Theor. Math. Phys."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/0370-2693(81)90288-4","article-title":"A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions","volume":"100","author":"Tkachov","year":"1981","journal-title":"Phys. Lett. B"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF01552503","article-title":"Exploiting the 1.440 Fold Symmetry of the Master Two Loop Diagram","volume":"32","author":"Broadhurst","year":"1986","journal-title":"Z. Phys. C"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1007\/BF01018263","article-title":"On an Approach to the Calculation of Multiloop Massless Feynman Integrals","volume":"62","author":"Gorishnii","year":"1985","journal-title":"Theor. Math. Phys."},{"key":"ref_90","unstructured":"Kazakov, D.I. (2023, May 25). Analytical Methods for Multiloop Calculations: Two Lectures on The Method of Uniqueness. Available online: https:\/\/inspirehep.net\/literature\/203305."},{"key":"ref_91","unstructured":"Broadhurst, D.J. (1999). Dimensionally continued multiloop gauge theory. arXiv."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"105017","DOI":"10.1103\/PhysRevD.100.105017","article-title":"Landau-Khalatnikov-Fradkin transformation and the mystery of even \u03b6-values in Euclidean massless correlators","volume":"100","author":"Kotikov","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0370-2693(92)90139-U","article-title":"On the value of the alpha-s correction to the Callan-Gross relation","volume":"291","author":"Kazakov","year":"1992","journal-title":"Phys. Lett. B"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0370-2693(83)91439-9","article-title":"The Algorithm for Ope Coefficient Functions in the Ms Scheme","volume":"124","author":"Gorishnii","year":"1983","journal-title":"Phys. Lett. B"},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/0550-3213(87)90283-5","article-title":"Coefficient Functions of Asymptotic Operator Expansions in Minimal Subtraction Scheme","volume":"283","author":"Gorishnii","year":"1987","journal-title":"Nucl. Phys. B"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/0370-2693(83)91438-7","article-title":"On The Operator Product Expansion in the Ms Scheme","volume":"124","author":"Tkachov","year":"1983","journal-title":"Phys. Lett. B"},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/0370-2693(83)90183-1","article-title":"Infrared R*\u2014operation and operator product expansion in the minimal subtraction scheme","volume":"126","author":"Chetyrkin","year":"1983","journal-title":"Phys. Lett. B"},{"key":"ref_98","first-page":"227","article-title":"On the Multiplication of the causal function in thequantum theory of fields","volume":"97","author":"Bogoliubov","year":"1957","journal-title":"Acta Math."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/BF01773358","article-title":"Proof of the Bogolyubov-Parasiuk theorem on renormalization","volume":"2","author":"Hepp","year":"1966","journal-title":"Commun. Math. Phys."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/BF01645676","article-title":"Convergence of Bogoliubov\u2019s method of renormalization in momentumspace","volume":"15","author":"Zimmermann","year":"1969","journal-title":"Commun. Math. Phys."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/BF01018394","article-title":"Method for Computing Renormalization Group Functions in Dimen-sional Renormalization Scheme","volume":"43","author":"Vladimirov","year":"1980","journal-title":"Theor. Math. Phys."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/0370-2693(82)90358-6","article-title":"Infrared R Operation Furthermore, Ultraviolet CountertermsIn The Ms Scheme","volume":"114","author":"Chetyrkin","year":"1982","journal-title":"Phys. Lett. B"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/0370-2693(84)91291-7","article-title":"R* Operation Corrected","volume":"144","author":"Chetyrkin","year":"1984","journal-title":"Phys. Lett. B"},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1007\/BF01017902","article-title":"R* Operation in the Minimal Subtraction Scheme","volume":"63","author":"Smirnov","year":"1985","journal-title":"Theor. Math. Phys."},{"key":"ref_105","unstructured":"Chetyrkin, K.G. (2017). Combinatorics of R-, R\u22121-, and R*-operations and asymptotic expan-sions of feynman integrals in the limit of large momenta and masses. arXiv."},{"key":"ref_106","doi-asserted-by":"crossref","unstructured":"Henn, J.M., and Plefka, J.C. (2014). Scattering Amplitudes in Gauge Theories, Springer. Lecture Notes in Physics.","DOI":"10.1007\/978-3-642-54022-6"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.nuclphysb.2006.01.013","article-title":"Two-loop sunset diagrams with three massive lines","volume":"738","author":"Kniehl","year":"2006","journal-title":"Nucl. Phys. B"},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"114780","DOI":"10.1016\/j.nuclphysb.2019.114780","article-title":"Two-loop diagrams in non-relativistic QCD with elliptics","volume":"948","author":"Kniehl","year":"2019","journal-title":"Nucl. Phys. B"},{"key":"ref_109","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1016\/j.physletb.2006.04.057","article-title":"Calculating four-loop tadpoles with one non-zero mass","volume":"638","author":"Kniehl","year":"2006","journal-title":"Phys. Lett. B"},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.physletb.2012.04.071","article-title":"Counting master integrals: Integration-by-parts procedure with effective mass","volume":"712","author":"Kniehl","year":"2012","journal-title":"Phys. Lett. B"},{"key":"ref_111","unstructured":"Lewin, L. (1981). Polylogarithms and Associated Functions, North Holland."},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02724330","article-title":"Table of Integrals and Formulae for Feynman Diagram Calculations","volume":"7","author":"Devoto","year":"1984","journal-title":"Riv. Nuovo Cim."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"072","DOI":"10.1007\/JHEP09(2021)072","article-title":"Sunrise integrals with two internal masses and pseudo-threshold kinematics in terms of elliptic polylogarithms","volume":"2021","author":"Campert","year":"2021","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.nuclphysb.2007.07.018","article-title":"Two-Loop Formfactors in Theories with Mass Gap and Z-Boson Production","volume":"788","author":"Kotikov","year":"2008","journal-title":"Nucl. Phys. B"},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.nuclphysb.2003.07.004","article-title":"Master integrals with one massive propagator for the two loop electroweak form-factor","volume":"668","author":"Aglietti","year":"2003","journal-title":"Nucl. Phys. B"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1016\/j.physletb.2004.06.063","article-title":"Two loop light fermion contribution to Higgs production and decays","volume":"595","author":"Aglietti","year":"2004","journal-title":"Phys. Lett. B"},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.physletb.2004.09.001","article-title":"Master integrals for the two-loop light fermion contributions to gg \u2014> H and H \u2014> gamma gamma","volume":"600","author":"Aglietti","year":"2004","journal-title":"Phys. Lett. B"},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"021","DOI":"10.1088\/1126-6708\/2007\/01\/021","article-title":"Analytic Results for Virtual QCD Corrections to Higgs Production and Decay","volume":"2007","author":"Aglietti","year":"2007","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"211801","DOI":"10.1103\/PhysRevLett.126.211801","article-title":"Compton Scattering Total Cross Section at Next-to-Leading Order","volume":"126","author":"Lee","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"1830015","DOI":"10.1142\/S0217751X18300156","article-title":"Analytic Computing Methods for Precision Calculations in Quantum Field Theory","volume":"A33","author":"Blumlein","year":"2018","journal-title":"Int. J. Mod. Phys."},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"096025","DOI":"10.1103\/PhysRevD.103.096025","article-title":"Iterated integrals over letters induced by quadratic forms","volume":"103","author":"Ablinger","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"102301","DOI":"10.1063\/1.3629472","article-title":"Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials","volume":"52","author":"Ablinger","year":"2011","journal-title":"Math. Phys."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0370-2693(99)00892-8","article-title":"Two-loop self-energy master integrals on shell","volume":"462","author":"Fleischer","year":"1999","journal-title":"Phys. Lett. B"},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/S0370-2693(97)01195-7","article-title":"The differential equation method: Calculation of vertex-type diagrams with one non-zero mass","volume":"417","author":"Fleischer","year":"1998","journal-title":"Phys. Lett. B"},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"042001","DOI":"10.1103\/PhysRevLett.97.042001","article-title":"Strong-coupling constant with flavor thresholds at five loops in the MS-bar scheme","volume":"97","author":"Kniehl","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"114032","DOI":"10.1103\/PhysRevD.79.114032","article-title":"Heavy-quark pair production in polarized photon-photon collisions at next-to-leading order: Fully integrated total cross sections","volume":"79","author":"Kniehl","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"193401","DOI":"10.1103\/PhysRevLett.101.193401","article-title":"Orthopositronium lifetime: Analytic results in O(\u03b1) and O(\u03b13ln(\u03b1))","volume":"101","author":"Kniehl","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_128","doi-asserted-by":"crossref","first-page":"052501","DOI":"10.1103\/PhysRevA.80.052501","article-title":"Orthopositronium lifetime at O(alpha) and O(alpha3 ln(alpha)) in closed form","volume":"80","author":"Kniehl","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_129","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.nuclphysb.2008.12.022","article-title":"Analytic three-loop Solutions for N = 4 SYM Twist Operators","volume":"813","author":"Kotikov","year":"2009","journal-title":"Nucl. Phys. B"},{"key":"ref_130","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/j.nuclphysb.2009.10.030","article-title":"Analytic solution of the multiloop Baxter equation","volume":"827","author":"Beccaria","year":"2010","journal-title":"Nucl. Phys. B"},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"054","DOI":"10.1088\/1126-6708\/2005\/05\/054","article-title":"The Factorized S-matrix of CFT\/AdS","volume":"2005","author":"Staudacher","year":"2005","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.nuclphysb.2005.06.038","article-title":"Long-range psu(2,2|4) Bethe Ansatze for gauge theory and strings","volume":"727","author":"Beisert","year":"2005","journal-title":"Nucl. Phys. B"},{"key":"ref_133","doi-asserted-by":"crossref","first-page":"P10003","DOI":"10.1088\/1742-5468\/2007\/10\/P10003","article-title":"Dressing and wrapping","volume":"0710","author":"Kotikov","year":"2007","journal-title":"J. Stat. Mech."},{"key":"ref_134","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.nuclphysb.2009.02.005","article-title":"our-loop perturbative Konishi from strings and finite size effects for multiparticle states","volume":"816","author":"Bajnok","year":"2009","journal-title":"Nucl. Phys. B"},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.nuclphysb.2010.01.008","article-title":"Five-Loop Anomalous Dimension of Twist-Two Operators","volume":"831","author":"Lukowski","year":"2010","journal-title":"Nucl. Phys. B"},{"key":"ref_136","doi-asserted-by":"crossref","first-page":"084","DOI":"10.1007\/JHEP07(2015)084","article-title":"Six-loop anomalous dimension of twist-two operators in planar N = 4 SYM theory","volume":"2015","author":"Marboe","year":"2015","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"013","DOI":"10.1007\/JHEP11(2016)013","article-title":"Twist-2 at seven loops in planar N = 4 SYM theory: Full result and analytic properties","volume":"2016","author":"Marboe","year":"2016","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.nuclphysb.2007.01.020","article-title":"On the highest transcendentality in N = 4 SUSY","volume":"769","author":"Kotikov","year":"2007","journal-title":"Nucl. Phys. B"},{"key":"ref_139","doi-asserted-by":"crossref","first-page":"131603","DOI":"10.1103\/PhysRevLett.98.131603","article-title":"A Test of the AdS\/CFT correspondence using high-spin operators","volume":"98","author":"Benna","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_140","doi-asserted-by":"crossref","first-page":"091601","DOI":"10.1103\/PhysRevLett.100.091601","article-title":"Cusp anomalous dimension in maximally supersymmetric Yang\u2013Mills theory at strong coupling","volume":"100","author":"Basso","year":"2008","journal-title":"Phys. Rev. Lett."},{"key":"ref_141","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.nuclphysb.2008.07.007","article-title":"Embedding nonlinear O(6) sigma model into N = 4 super-Yang\u2013Mills theory","volume":"807","author":"Basso","year":"2009","journal-title":"Nucl. Phys. B"},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"091","DOI":"10.1007\/JHEP12(2012)091","article-title":"Conformal Regge theory","volume":"2012","author":"Costa","year":"2012","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_143","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1016\/j.nuclphysb.2013.06.018","article-title":"Pomeron in the N = 4 supersymmetric gauge model at strong couplings","volume":"874","author":"Kotikov","year":"2013","journal-title":"Nucl. Phys. B"},{"key":"ref_144","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1007\/JHEP07(2014)156","article-title":"Quantum spectral curve at work: From small spin to strong coupling in N = 4 SYM","volume":"2014","author":"Gromov","year":"2014","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_145","doi-asserted-by":"crossref","unstructured":"Alday, L.F., and Hansen, T. (2023). The AdS Virasoro-Shapiro Amplitude. arXiv.","DOI":"10.1007\/JHEP10(2023)023"},{"key":"ref_146","doi-asserted-by":"crossref","first-page":"251601","DOI":"10.1103\/PhysRevLett.110.251601","article-title":"Multiloop integrals in dimensional regularization made simple","volume":"110","author":"Henn","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"ref_147","doi-asserted-by":"crossref","first-page":"153001","DOI":"10.1088\/1751-8113\/48\/15\/153001","article-title":"Lectures on differential equations for Feynman integrals","volume":"48","author":"Henn","year":"2015","journal-title":"J. Phys. A"},{"key":"ref_148","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1016\/j.physletb.2018.04.002","article-title":"The \u03b5-form of the differential equations for Feynman integrals in the elliptic case","volume":"781","author":"Adams","year":"2018","journal-title":"Phys. Lett. B"},{"key":"ref_149","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/JHEP04(2015)108","article-title":"Reducing differential equations for multiloop master integrals","volume":"2015","author":"Lee","year":"2015","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_150","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1007\/JHEP10(2018)176","article-title":"Symmetric \u03f5- and (\u03f5+1\/2)-forms and quadratic constraints in \u201celliptic\u201d sectors","volume":"2018","author":"Lee","year":"2018","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_151","doi-asserted-by":"crossref","first-page":"084","DOI":"10.1007\/JHEP12(2019)084","article-title":"\u03f5-regular basis for non-polylogarithmic multiloop integrals and total cross section of the process e+e\u2212\u21922(QQ)","volume":"2019","author":"Lee","year":"2019","journal-title":"J. High Energy Phys. JHEP"},{"key":"ref_152","doi-asserted-by":"crossref","unstructured":"Badger, S., Henn, J., Plefka, J., and Zoia, S. (2023). Scattering Amplitudes in Quantum Field Theory. arXiv.","DOI":"10.1007\/978-3-031-46987-9"},{"key":"ref_153","doi-asserted-by":"crossref","unstructured":"Duhr, C. (2014). Mathematical aspects of scattering amplitudes. arXiv.","DOI":"10.1142\/9789814678766_0010"},{"key":"ref_154","unstructured":"Goncharov, A.B. (2001). Multiple polylogarithms and mixed Tate motives. arXiv."},{"key":"ref_155","doi-asserted-by":"crossref","first-page":"497","DOI":"10.4310\/MRL.1998.v5.n4.a7","article-title":"Multiple polylogarithms, cyclotomy and modular complexes","volume":"5","author":"Goncharov","year":"1998","journal-title":"Math. Res. Lett."},{"key":"ref_156","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1142\/S0217751X00000367","article-title":"Harmonic polylogarithms","volume":"15","author":"Remiddi","year":"2000","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_157","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.nuclphysb.2004.08.020","article-title":"Massive Feynman diagrams and inverse binomial sums","volume":"699","author":"Davydychev","year":"2004","journal-title":"Nucl. Phys. B"},{"key":"ref_158","first-page":"133","article-title":"Gluon distribution for small x","volume":"57","author":"Kotikov","year":"1994","journal-title":"Phys. At. Nucl."},{"key":"ref_159","unstructured":"Kotikov, A.V., and Velizhanin, V.N. (2005). Analytic continuation of the Mellin moments of deep inelastic structure functions. arXiv."},{"key":"ref_160","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/0550-3213(79)90448-6","article-title":"A Simple Parametrization of the Q2 Dependence of the Quark Distributions in QCD","volume":"151","author":"Parisi","year":"1979","journal-title":"Nucl. Phys. B"},{"key":"ref_161","first-page":"438","article-title":"Deep inelastic e p scattering in perturbation theory","volume":"15","author":"Gribov","year":"1972","journal-title":"Sov. J. Nucl. Phys."},{"key":"ref_162","first-page":"675","article-title":"e+e-pair annihilation and deep inelastic e p scattering in perturbation theory","volume":"15","author":"Gribov","year":"1972","journal-title":"Sov. J. Nucl. Phys."},{"key":"ref_163","first-page":"94","article-title":"The parton model and perturbation theory","volume":"20","author":"Lipatov","year":"1975","journal-title":"Sov. J. Nucl. Phys."},{"key":"ref_164","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/0550-3213(77)90384-4","article-title":"Asymptotic Freedom in Parton Language","volume":"126","author":"Altarelli","year":"1977","journal-title":"Nucl. Phys. B"},{"key":"ref_165","first-page":"641","article-title":"Calculation of the Structure Functions for Deep Inelastic Scattering and e+ e- Annihilation by Perturbation Theory in Quantum Chromodynamics","volume":"46","author":"Dokshitzer","year":"1977","journal-title":"Sov. Phys. JETP"},{"key":"ref_166","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1134\/S1063779609070041","article-title":"Functions of the nucleon structure and determination of the strong coupling constant","volume":"40","author":"Krivokhizhin","year":"2009","journal-title":"Phys. Part. Nucl."},{"key":"ref_167","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1134\/S1063779608030015","article-title":"Small x behavior of parton distributions. A Study of higher twist effects","volume":"39","author":"Illarionov","year":"2008","journal-title":"Phys. Part. Nucl."},{"key":"ref_168","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1134\/S1063779607010017","article-title":"Deep inelastic scattering: Q**2 dependence of structure functions","volume":"38","author":"Kotikov","year":"2007","journal-title":"Phys. Part. Nucl."},{"key":"ref_169","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0370-2693(82)90701-8","article-title":"Operator Product Expansion In The Minimal Subtraction Scheme","volume":"119","author":"Chetyrkin","year":"1982","journal-title":"Phys. Lett. B"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:44:27Z","timestamp":1760132667000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,29]]},"references-count":169,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["sym16010052"],"URL":"https:\/\/doi.org\/10.3390\/sym16010052","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,12,29]]}}}