Chiral potentials, perturbation theory and the<sup>1</sup>S<sub>0</sub>channel of NN scattering

Shukla, Deepshikha; Phillips, Daniel R.; Mortenson, Eric T.

doi:10.1088/0954-3899/35/11/115009

Cited by 19 publications

(29 citation statements)

References 45 publications

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“…It has also been shown in Ref. [41] that these 1/M 2 pieces of v 1π have only a small impact in the 1 S 0 channel. A precise description of phase-shift data is not our goal here, so we do not consider this correction further in what follows.…”

Section: Two-pion-exchange Potentialmentioning

confidence: 68%

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: Two-pion-exchange Potentialmentioning

confidence: 68%

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

2009

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“…Taking into account the size of the cut-off radius they use, chiral TPE is almost guaranteed to be a perturbation, especially in view of the perturbative analysis of Ref. [82]. In the power counting advocated in this work, we employ a total of 21 parameters for the s-, p-and d-waves, a figure suspiciously similar to Ref.…”

Section: Discussionmentioning

confidence: 99%

Perturbative renormalizability of chiral two-pion exchange in nucleon-nucleon scattering

2011

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We study the perturbative renormalizability of chiral two-pion exchange for singlet and triplet channels within effective field theory, provided that the one-pion exchange piece of the interaction has been fully iterated. We determine the number of counterterms/subtractions needed to obtain finite results when the cutoff is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that perturbative chiral two-pion exchange reproduce the data up to a center-of-mass momentum of k ∼ 200-300 MeV in the singlet channel and k ∼ 300-400 MeV in the triplet.

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“…[7] and applied to the peripheral spin-singlet waves. More recently it has been applied to spin-triplet waves [8] and the 1 S 0 channel [9] and closely related methods have been used by other groups to study the S waves [10,11].In this note, we extend the method of Ref.[7] by applying it to the 1 P 1 channel. We first construct DWs for the leading-order one-pion-exchange (OPE) potential.…”

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Effective short-range interaction for spin-singletP-wave nucleon-nucleon scattering

2011

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Distorted-wave methods are used to remove the effects of one-and two-pion exchange up to order Q 3 from the empirical 1 P1 phase shift. The one divergence that arises can be renormalised using an order-Q 2 counterterm which is provided by the (Weinberg) power counting appropriate to the effective field theory for this channel. The residual interaction is used to estimate the scale of the underlying physics.Effective field theories (EFTs) provide important tools for constructing nuclear forces within a systematic framework. 1 They respect the symmetries of underlying theory, in this case Quantum Chromodynamics, and offer modelindependent descriptions of the dynamics at low energy scales. They rely on the existence of clear separation of scales between the low-energy physics of interest and the underlying, high-energy (or short-distance) physics. This makes it possible to use a perturbation theory where the expansion parameters are ratios of low-to high-energy scales.To construct such a theory one begins by writing down the most general Lagrangian or Hamiltonian for the relevant low-energy degrees of freedom, containing all the interaction terms allowed by the symmetries of the system. The parameters of the theory are the (initially unknown) constants multiplying these terms. There are in general an infinite number of these but they can be organised in terms of a "power counting" of low-energy scales. To any given order in this counting, only a finite number of terms are needed.Since Weinberg first suggested that these ideas could be applied to nuclear forces [4], there has been considerable debate about the appropriate power counting to use. 2 Most of these arguments have been about channels where scattering is strong and some pieces of the potential may need to be treated nonperturbatively, namely the S waves and the lower spin-triplet waves. In the higher partial waves, especially the spin-singlet ones, the scattering is weak and the picture is clearer. For these channels, Weinberg's original power counting is valid. This is based on simple dimensional analysis, counting powers of momenta and the pion mass. These low-energy scales are generically denoted by Q.Many applications of EFTs test convergence by presenting theoretical nucleon-nucleon phase shifts, calculated at leading and higher orders, alongside empirical data. At each order, short-range interactions, expanded as polynomials in energy or momenta, have to be refitted to the data. A powerful alternative is to use distorted-wave (DW) methods to remove the effects of known long-range forces from the observed phase shifts to leave residual short-range interactions. The sizes and energy-dependences of these can then be used to test the convergence of the EFT and to estimate the scales of the underlying physics. Such an approach was proposed in Ref. [7] and applied to the peripheral spin-singlet waves. More recently it has been applied to spin-triplet waves [8] and the 1 S 0 channel [9] and closely related methods have been used by other groups to study the ...

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Chiral potentials, perturbation theory and the¹S₀channel of NN scattering

Cited by 19 publications

References 45 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

Perturbative renormalizability of chiral two-pion exchange in nucleon-nucleon scattering

Effective short-range interaction for spin-singletP-wave nucleon-nucleon scattering

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Chiral potentials, perturbation theory and the1S0channel of NN scattering

Cited by 19 publications

References 45 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

Perturbative renormalizability of chiral two-pion exchange in nucleon-nucleon scattering

Effective short-range interaction for spin-singletP-wave nucleon-nucleon scattering

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Chiral potentials, perturbation theory and the¹S₀channel of NN scattering