Subtractive renormalization of the chiral potentials up to next-to-next-to-leading order in higherNNpartial waves

Abstract

We develop a subtractive renormalization scheme to evaluate the P -wave NN scattering phase shifts using chiral effective theory potentials. This allows us to consider arbitrarily high cutoffs in the Lippmann-Schwinger equation (LSE). We employ NN potentials computed up to next-to-next-to-leading order (NNLO) in chiral effective theory, using both dimensional regularization and spectral-function regularization. Our results obtained from the subtracted P -wave LSE show that renormalization of the NNLO potential can be achieved by using the generalized NN scattering lengths as input-an alternative to fitting the constant that multiplies the P -wave contact interaction in the chiral effective theory NN force. However, to obtain a reasonable fit to the NN data at NNLO the generalized scattering lengths must be varied away from the values extracted from the so-called high-precision potentials. We investigate how the generalized scattering lengths extracted from NN data using various chiral potentials vary with the cutoff in the LSE. The cutoff dependence of these observables, as well as of the phase shifts at T lab ≈ 100 MeV, suggests that for a chiral potential computed with dimensional regularization the highest LSE cutoff it is sensible to adopt is approximately 1 GeV. Using spectral-function regularization to compute the two-pion-exchange potentials postpones the onset of cutoff dependence in these quantities but does not remove it.The operators of lowest chiral order that appear in the NN potential are two S-wave contact interactions, together with the one-pion-exchange potential. These operators are all O(Q 0 ) and have been regarded as forming the "leadingorder" potential. In Refs. [18,23,24] it was shown the theory is properly renormalized in the 1 S 0 , 3 S 1 -3 D 1 channels and Ref.[25] found that the same was true in some of the higher partial waves ( In contrast, Ref. [25] showed that χ ET is not properly renormalized at LO in spin-triplet channels where an attractive singular tensor force acts (e.g., 3 P 0 , 3 D 2 , 3 P 2 -3 F 2 ) (see also Ref. [27]). In Ref. [25] it was suggested that a contact term needs to be added in these channels-even though this breaks the straightforward χ PT counting for short-distance operators. This behavior in different NN partial waves can be understood as a result of the singular behavior of the χ ET NN potential, with the channels where the leading singularity of the potential as r → 0 corresponds to an attractive force needing a counter term to stabilize the phase-shift predictions as a function of the cutoff [25,28]. Partial waves where the leading singularity has a positive coefficient-and so the dominant effect at short distances is repulsion-have -independent predictions at large [29,30]. A renormalization-group analysis confirmed these findings [21]. Reference [31] questioned the usefulness of conclusions based on a leading-order analysis, as well as the necessity of considering cutoffs >1 GeV.In this article we extend the analysis of the χ ET potential in the NN P -...

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