Deep inelastic scattering in improved lattice QCD (I). The first moment of structure functions |
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| Affiliation: | 1. Division of Cardiovascular Medicine, University of California San Diego, La Jolla, CA, USA;2. Division of Cardiology, Mitsui Memorial Hospital, Tokyo, Japan;3. Division of Cardiovascular Medicine, San Diego Veterans Affairs Medical Center, San Diego, CA, USA;4. Department of Cardiology, University Medical Centre Groningen, University of Groningen, Groningen, the Netherlands;5. Department of Cardiology, University Hospital Basel, University of Basel, Basel, Switzerland;6. Department of Cardiology, Athens University Hospital Attikon, University of Athens, Athens, Greece;7. Department of Emergency Medicine, Henry Ford Hospital System, Detroit, MI, USA;8. Division of Emergency Medicine and Acute Care Surgical Services, VCU Medical Center, Virginia Commonwealth University, Richmond, VA, USA;9. Division of Cardiology, VCU Medical Center, Virginia Commonwealth University, Richmond, VA, USA;10. Department of Emergency Medicine, University of Kansas Medical Center, Kansas City, KS, USA;11. Department of Nephrology and Rheumatology, University Medical Centre Göttingen, University of Göttingen, Göttingen, Germany;12. Department of Emergency Medicine, New York Methodist Hospital, New York, NY, USA;13. Department of Emergency Medicine, University of California San Diego, La Jolla, CA, USA;14. Division of Cardiology, Danylo Halytsky Lviv National Medical University, Lviv, Ukraine;15. Department of Cardiology, School of Medicine, University College Dublin, Dublin, Ireland;p. Department of Cardiology, St Vincent''s University Hospital, Dublin, Ireland;q. Department of Cardiology, Mater Misericordiae University Hospital, Dublin, Ireland;r. Department of Cardiology, Valencia University Hospital, INCLIVA, Valencia, Spain;s. Centro de Investigación Biomédica en Red (CIBER) in Cardiovascular Diseases, Madrid, Spain;t. Department of Cardiology, Mediterranea Cardiocentro, Naples, Italy;u. Department of Cardiology and Cardiovascular Medicine, Fondazione Gabriele Monasterio, Pisa, Italy;v. Department of Medicine, School of Medicine, University College Dublin, Dublin, Ireland |
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| Abstract: | We present the complete 1-loop perturbative computation of the renormalization constants and mixing coefficients of the operators that measure the first moment of deep inelastic scattering structure functions, employing the nearest neighbor improved lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order a (a being the lattice spacing) have been proven to be absent from [p]Because of the complexity of the calculations, we have checked the analytical expression of all Feynman diagrams using Schoonschip. To this end we have developed a suitable code designed to automatically carry out all the necessary lattice algebraic manipulations, starting from the elementary building blocks of each diagram. [p]We have found discrepancies with some of the published numbers, but we are in agreement with the known results on the energy-momentum tensor. |
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