Algebraic algorithm for the computation of one-loop Feynman diagrams in lattice QCD with Wilson fermions |
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| Affiliation: | 1. Dipartimento di Fisica and INFN - Sezione di Parma, Università degli Studi di Parma, I-43100 Parma, Italy;2. Dipartimento di Fisica and INFN - Sezione di Lecce, Università degli Studi di Lecce, I-73100 Lecce, Italy;3. Dipartimento di Fisica and INFN - Sezione di Pisa, Università degli Studi di Pisa, I-56100 Pisa, Italy;1. Instituto de Física, Universidade Federal Fluminense, Campus da Praia Vermelha, Av. Litorânea s/n, 24210-346, Niterói, RJ, Brazil;2. UERJ – Universidade do Estado do Rio de Janeiro, Instituto de Física, Departamento de Física Teórica, Rua São Francisco Xavier 524, 20550-013, Maracanã, Rio de Janeiro, Brazil;1. Saint Petersburg State University, 7/9 Universitetskaya Embankment, St. Petersburg, 199034, Russia;2. Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 6 Joliot-Curie, Dubna, Moscow region, 141980, Russia;3. Department of Theoretical Physics, SAS, Institute of Experimental Physics, Watsonova 47, 040 01 Košice, Slovak Republic;4. Pavol Jozef Šafárik University in Košice (UPJŠ), Šrobárova 2, 041 80 Košice, Slovak Republic;5. New Jersey Institute of Technology, 323 Dr Martin Luther King Jr Blvd, Newark, NJ 07102, USA;6. ITMO University, Kronverkskiy prospekt 49, Saint Petersburg 197101, Russia;1. Institut für Theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany;2. CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Zhong Guan Cun East Street 55, Beijing 100190, China;3. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;4. Instituto de Física Corpuscular (centro mixto CSIC-UV), Institutos de Investigación de Paterna, C/Catedrático José Beltrán 2, E-46980 Paterna, Valencia, Spain;5. Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany;6. Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia;7. Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China;8. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China;9. Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Southern Nuclear Science Computing Center, South China Normal University, Guangzhou 510006, China;1. Department of Computational Mathematics, Science and Engineering and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA;2. Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China;3. Center for High Energy Physics, Indian Institute of Science, Bangaluru 560012, India;4. Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany;5. Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA;6. Center for Computational Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan;7. Department of Theoretical Physics, The Institute of Mathematical Sciences, Chennai 600113, India |
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| Abstract: | We describe an algebraic algorithm which allows us to express every one-loop lattice integral with gluon or Wilson-fermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. Various examples are given, including the one-loop self-energies of the quarks and gluons and the renormalization constants for some dimension-three and dimension-four lattice operators. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of Lüscher and Weisz to higher-loop integrals with fermions. |
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