Erratum: Renormalization ofNNscattering: Contact potential [Phys. Rev.C71, 034001 (2005)]

A Padé-Aided Analysis of Nonperturbative NN Scattering in 1 S 0 Channel

“…So a natural discrimination arises between 'endogenous' and 'exogenous' counter terms (or equivalent operations) that are introduced before and after the summation respectively [18,19]. The compact form of T -matrix fails the 'exogenous' counter terms [18,19]. In other words, the renormalization through 'endogenous' counter terms is the only sensible procedure in nonperturbative regime.…”

“…That is why various forms of finite cutoff prevail in literature. In whatever approaches, the compact form of T -matrix persists and makes nonperturbative prescription dependence strikingly different from the perturbative cases [19,22]: Physical boundary conditions must be imposed as a nontrivial procedure.…”

“…In other words, the renormalization through 'endogenous' counter terms is the only sensible procedure in nonperturbative regime. Since the Schrödinger equation approach [11] is intrinsically nonperturbative, any successful subtraction in the Schrödinger equation approach serves as a concrete instance for 'endogenous' renormalization in action [18,19]. In practice, 'endogenous' subtraction is a formidable task in the T -matrix formalism: To complete the subtraction AND summation to ALL orders!…”

“…Then one must specify the order for implementing the following two incommutable procedures: subtraction versus nonperturbative summation. So a natural discrimination arises between 'endogenous' and 'exogenous' counter terms (or equivalent operations) that are introduced before and after the summation respectively [18,19]. The compact form of T -matrix fails the 'exogenous' counter terms [18,19].…”

“…[18], with which the obstacle for renormalization being identified as the compact form of the T -matrix. In a concrete example [19], it was shown that the T -matrix could only be renormalized through 'endogenous' counter terms, which result in nontrivial prescription dependence. Such prescription dependence must be removed or fixed by imposing appropriate physical boundary conditions, for instance, through certain procedure of data fitting, as is frequently done in literature.…”