Renormalization-group improvement of effective actions beyond summation of leading logarithms |
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| Institution: | 1. Sue & Bill Gross School of Nursing, University of California, Irvine, CA;2. UT Health School of Nursing, San Antonio, TX;3. University of South Alabama, Mobile, AL;4. Department of Health Care Organization and Policy, The University of Alabama at Birmingham, Birmingham, AL;5. Corporal Michael J Crescenz VA Medical Center, Philadelphia, PA;6. Mercy Health Saint Mary''s, a member of Trinity Health, Grand Rapids, MI;7. Texas Woman''s University, Denton, TX;8. WellStar health System, Marietta, Georgia;9. American Association of Colleges of Nursing, Washington, DC;10. Kirkhoff College of Nursing, Cook-DeVos Center for Health Sciences, Grand Rapids, MI;11. Central Texas Veterans Health Care System, Temple, TX;1. Laboratory of Ecology, Department of Biological Applications and Technology, University of Ioannina, Ioannina 45110, Greece;2. European Forest Institute - Mediterranean Facility (EFIMED), Barcelona 08025, Spain;3. Department of Agri-Food Sciences and Technologies, University of Bologna, Bologna 40127, Italy;1. Department of Neurology, Longhua Hospital, Shanghai University of Traditional Chinese Medicine, 725 South Wanping Road, Shanghai, 200032, China;2. MassGeneral Institute for Neurodegenerative Disease, Department of Neurology, Massachusetts General Hospital, Harvard Medical School, 114 16th Street, Charlestown, MA, 02129, United States |
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| Abstract: | Invariance of the effective action under changes of the renormalization scale μ leads to relations between those (presumably calculated) terms independent of μ at a given order of perturbation theory and those higher-order terms dependent on logarithms of μ. This relationship leads to differential equations for a sequence of functions, the solutions of which give closed form expressions for the sum of all leading logs, next to leading logs, and subsequent subleading logarithmic contributions to the effective action. The renormalization group is thus shown to provide information about a model beyond the scale dependence of the model's couplings and masses. This procedure is illustrated using the φ63 model and Yang–Mills theory. In the latter instance, it is also shown by using a modified summation procedure that the μ dependence of the effective action resides solely in a multiplicative factor of g2(μ) (the running coupling). This approach is also shown to lead to a novel expansion for the running coupling in terms of the one-loop coupling that does not require an order-by-order redefinition of the scale factor ΛQCD. Finally, logarithmic contributions of the instanton size to the effective action of an SU(2) gauge theory are summed, allowing a determination of the asymptotic dependence on the instanton size ρ as ρ goes to infinity to all orders in the SU(2) coupling constant. |
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