Subtractive renormalization of one-pion-exchange and contact interactions

Timóteo, V. S.; Frederico, T.; Delfino, A.; Tomio, Lauro

doi:10.1590/s0103-97332005000500044

Cited by 4 publications

(6 citation statements)

References 6 publications

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“…Instead, we perform manipulations on the LSE to obtain an integral equation where we can directly input a (generalized) scattering length α 11 that is obtained from low-energy P -wave phase shifts. (An earlier, alternative subtractive-renormalization technique involves invoking the Born approximation and consequently is unreliable for the highly singular potentials being discussed here [36,37].) Using this method we can predict P -wave phase shifts at cutoffs up to 10 GeV and examine the cutoff dependence of these predictions.…”

Section: Introductionmentioning

confidence: 99%

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

2009

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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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Section: Introductionmentioning

confidence: 99%

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

2009

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“…In this work we apply the SRG transformation to evolve an effective NN interaction in leading-order (LO) ChEFT, derived within the framework of the subtracted kernel method (SKM) [17][18][19][20][21][22]. The SKM is a renormalization scheme in which instead of using a cutoff regularizing function, the LS equation is regularized by performing subtractions in the kernel at a given energy scale, while keeping the original NN interaction intact.…”

Section: Introductionmentioning

confidence: 99%

Similarity renormalization group evolution ofN Ninteractions within a subtractive renormalization scheme

Timóteo

Szpigel

Durães

2010

EPJ Web of Conferences

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Abstract.We apply the similarity renormalization group (SRG) approach to evolve a nucleon-nucleon (NN) interaction in leading-order (LO) chiral effective field theory (ChEFT), renormalized within the framework of the subtracted kernel method (SKM). We derive a fixed-point interaction and show the renormalization group (RG) invariance in the SKM approach. We also compare the evolution of NN potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS) equation and the evolution with the similarity cutoff through the SRG transformation.

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“…In the subtractive renormalization method conducted in momentum space [18,19,20] it has been shown numerically that…”

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confidence: 99%

“…In the subtractive renormalization method conducted in momentum space [18,19,20] it has been shown numerically that off-shell amplitudes are finite. Still, an analytic proof would be timely since there exist examples where a direct calculation of a Green functions in effective field theory does not necessarily guarantee off-shell finiteness from on shell renormalization conditions (see e.g.…”

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confidence: 99%

“…The problem on how these singularities should be handled from a renormalization point of view has been addressed in a series of works for the on-shell case where the finiteness can be established a priori [16,17]. In the subtractive renormalization method conducted in momentum space [18,19,20] it has been shown numerically that off-shell amplitudes are finite. Still, an analytic proof would be timely since there exist examples where a direct calculation of a Green functions in effective field theory does not necessarily guarantee off-shell finiteness from on shell renormalization conditions (see e.g.…”

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Renormalization of the off-shell chiral two-pion exchangeNNinteractions

Entem

Arriola

2009

Phys. Rev. C

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The renormalization, finiteness and off-shellness of short distance power like singular interactions is discussed. We show analytically that the renormalizability of the off-shell scattering amplitude relies completely on the corresponding on-shell amplitude without proliferation of new counterterms. We illustrate the result by complementary calculations both in coordinate as well as in momentum space in the simplest 1 S0 channel for chiral np interactions including Two Pion Exchange. A traditional source of theoretical uncertainty in the study of nuclear physics and nuclear reactions has been the relevance and significance of off-shellness in the NN force (For a review up to the mid seventies see e.g. [1] and references therein). As is well known, any off-shell ambiguity should cancel in the final results and off-shellness itself cannot be measured as a matter of principle. This does not necessarily mean, however, that off-shellness can generally be completely disposed of and most few-and many body calculations do involve off-shell quantities as intermediate stages. This feature relies on the fundamental fact that quantum mechanics is naturally formulated in terms of wave functions while they are not directly measurable quantities except at asymptotically large distances. A paralell statement for Quantum Field Theory applies for the fields themselves as well as the associated Green functions.Potential approaches to the NN interaction need the half off-shell extrapolated potential and the half off-shell T-matrix is used to determine the on-shell S−matrix. Moreover, a knowledge of the off-shell T-matrix is needed e.g. for nucleon-nucleon bremsstrahlung, the three nucleon problem as well as nuclear matter calculations and thus a phenomenological determination of the off-shell T-matrix has been the subject of intense research in the past [1]. A relevant issue in this regard is that the definition of off-shellness is largely conventional. Actually, the quantum mechanical trading between two body off- . Moreover, unitarity for the three body problem rests on off-shell unitarity for the two body problem, imposing constraints on the acceptable off-shellness [5,6].Within the Effective Field Theory (EFT) approach to nuclear physics based on chiral symmetry [7,8] (for comprehensive reviews see e.g. Ref. [9,10,11]) the ambiguities related to off-shellness can be rephrased in the freedom to undertake field dependent transformations and using the equations of motion. Actually, in purely contact EFT's, where the interaction is represented by a polynomial in momenta and/or energy, off-shellness can be completely ignored from the start by using local field redefinitions [4,12]. This fact does not generally hold for finite range interactions stemming from particle exchange if the exchanged momentum becomes comparable to the exchanged particle mass and where non-local and singular field redefinitions would be needed. Similarly to phenomenological potentials, Chiral potentials are not free from these ambiguities since by construct...

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Subtractive renormalization of one-pion-exchange and contact interactions

Cited by 4 publications

References 6 publications

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

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

Similarity renormalization group evolution ofN Ninteractions within a subtractive renormalization scheme

Renormalization of the off-shell chiral two-pion exchangeNNinteractions

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