Regularization, renormalization and 'peratization' in effective field theory for two nucleons

Epelbaum, E.; Gegelia, J.

doi:10.1140/epja/i2009-10833-3

Journal Article

PreJuSER-8529

Regularization, renormalization and 'peratization' in effective field theory for two nucleons

Epelbaum, E.FZJ* ; Gegelia, J.

2009
Springer Berlin

The European physical journal / A 41, 341 - 354 (2009) [10.1140/epja/i2009-10833-3]

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Please use a persistent id in citations: http://hdl.handle.net/2128/10363 doi:10.1140/epja/i2009-10833-3

Abstract: We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, the renormalization scheme dependence of the scattering amplitude can only be eliminated up to the order the calculations are performed. We further consider an effective theory for an exactly solvable quantum mechanical model which possesses a long- and short-range interaction to simulate pionful effective field theory. We discuss the meaning of low-energy theorems in this model and demonstrate their validity in calculations with a finite cutoff Lambda as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit Lambda -> infinity yields a finite result for the scattering amplitude but violates the low-energy theorems and is, therefore, not compatible with the effective field theory framework.

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Note: We would like to thank D. Djukanovic, U.-G. Meissner, D. Phillips and M. Pavon Valderrama for useful comments on the manuscript. The work of E. E. was supported by funds provided by the Helmholtz Association to the young investigator group "Few-Nucleon Systems in Chiral Effective Field Theory" (grant VH-NG-222) and to the virtual institute "Spin and strong QCD" (VH-VI-231), by the DFG (SFB/TR 16 "Subnuclear Structure of Matter") and by the EU Hadron-Physics2 project "Study of strongly interacting matter". J. G. acknowledges the support of the Deutsche Forschungsgemeinschaft (SFB 443) and Georgian National Foundation grant GNSF/ST08/4-400.

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