A New Expansion for Nucleon-Nucleon Interactions

David B. Kaplan; Mark B. Wise; Martin J. Savage

REVIEW

A New Expansion for Nucleon-Nucleon Interactions

David B. Kaplan, Martin J. Savage, Mark B. Wise

Nuclear Theory · Submitted 19 Jan 1998 · 20 references

Pith's verdict: The PDS subtraction and mu~p counting are the real contribution and they hold up; the coupled-channel half of the paper rests on an unpublished companion and should be read as a progress report, not a finished demonstration.

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arXiv IDnucl-th/9801034 (version 2)

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CitationDavid B. Kaplan, Mark B. Wise, Martin J. Savage. "A New Expansion for Nucleon-Nucleon Interactions." arXiv:nucl-th/9801034 (1998). https://pith.science/paper/ZJE4HFAE

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Editor's note

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This is the paper that made nuclear EFT look like EFT. The core is small and checkable: subtract the D=3 pole as well as the D=4 one (eq. 3), and the contact coupling runs so that at mu ~ p only C0 needs to be summed while C2, D2 and everything above stay perturbative. The beta functions in eqs. 10, 17 and 18 are exact, eq. 13 follows from the bubble chain, and the subleading 1S0 amplitudes in eq. 15 are closed-form and can be checked by hand in an afternoon. That is the part worth your time, and it is not in Weinberg [1], Lepage [11] or their own earlier paper [4]. The contrast with those is stated plainly rather than politely, which I appreciate. I'd push back on the reader's circularity score of 4. The counting is derived from the subtracted integral and the RG, not fitted; the Nijmegen comparison is a demonstration, not the argument. Scoring it as if the fits carried the claim undersells the paper. Two soft spots, and they are not the same size. The smaller one: the split of one-pion exchange into a static potential pion dressed by C0 plus perturbative radiation pions is called 'convenient' and shown explicitly only in 1S0 (eqs. 14-15, Fig. 2). Whether the same suppression survives the tensor force is exactly the question, and the paper does not answer it. The larger one: the abstract [abstract:s2] claims results for both channels, but the 3S1-3D1 order-p0 amplitude elements are deferred to ref. [19], listed as 'in preparation'. What is in the text is a three-parameter fit to the Nijmegen PWA and a plot. That is a real gap, not a citation quibble, and it is where the tensor-channel worry would have to be settled. On the empirical side the authors are honest: they say A0/A-1 exceeds 0.5 above p ~ 100 MeV, so the agreement out to 250-300 MeV sits outside the stated validity of the truncation. They flag it themselves; I would not hold it against them, but I would not quote the high-momentum curves either. Read it for the scheme and the 1S0 algebra. Treat the coupled channel as a preview. Yes to referees.

Referee report

Significance

If the counting holds, this is a foundational result: it gives nuclear EFT a systematic, analytic expansion in a regime where the scattering lengths are unnaturally large, and it explains why earlier applications of chiral perturbation theory to NN scattering stalled. The PDS scheme itself is a transferable tool, and the authors correctly note its relevance to other finely tuned theories with power-law divergences. The paper is also commendably explicit about where its own expansion is strained: it states that for p > 100 MeV the ratio A_0/A_{-1} exceeds roughly 0.5 and that the truncation is hard to justify, and it notes that C0 and D2 are individually meaningless because only the combination C0 + D2 m_π² enters at this order. The genuinely parameter-free predictions for ε1 and δ2 in the coupled channel, once δ0 is fitted, are a real falsifiable test and are presented as such.

Major objections (3)

[Abstract; §3S1-3D1 discussion and Fig. 3] The abstract states that 'we present the results for both the 1S0 and 3S1-3D1 channels', but the analytic amplitude elements A_{LL'} to order p^0 in the coupled channel are not in the manuscript; the text says only that 'in a future publication [19] analytic formulae for the elements A_{LL'} will be given to order p^0', and ref. [19] is listed as 'in preparation'. What the reader can check for the tensor channel is therefore a parameter count, a fit output, and Fig. 3. This matters because the tensor channel is precisely where the treatment of one-pion exchange is most delicate: the 1S0 demonstration that the potential-pion insertion is order p^0 (Eqs. 14-15, Fig. 2) does not by itself establish the analogous suppression in a channel with a singular tensor force and a bound state. I would ask the authors either to include the order-p^0 expressions for A_{00}, A_{02}, A_{20}, A_{22} and the explicit operator basis for the three fitted parameters, or to narrow the abstract's claim so that it does not assert presented results for a channel whose calculational details are deferred to an unpublished companion.
[Eq. (21), Fig. 3, and the paragraph beginning 'All that remains is to fit our free parameters'] The three parameters per channel are fitted to the Nijmegen partial wave analysis over p ≤ 200 MeV, and the resulting curves are then compared with the same analysis over the same range in Fig. 3. The statement that 'the agreement of the phase shift with data is excellent at quite large values of p' is therefore an in-sample statement, and the figure should say so explicitly. The one genuinely out-of-sample test in the figure is the pair (ε1, δ2), which the text correctly identifies as parameter-free once δ0 is fitted; those curves are visibly the weakest in the figure, and the manuscript's explanation (subleading order in δ0 but only leading order in ε1 and δ2) is plausible but is not backed by an error estimate. Relatedly, the fit range p ≤ 200 MeV extends beyond the range the authors themselves identify as under control ('for p > 100 MeV the magnitude of the ratio A0/A-1 is greater than ~0.5 and it is difficult to justify the approximations we have made'), and Fig. 3 is plotted out to 300 MeV. I would ask for the fit range to be reconciled with the stated range of validity, and for the text to distinguish clearly between fitted curves and parameter-free predictions.
[Conclusion, final paragraph; footnote 3] The conclusion states that the paper has 'demonstrated the failure of Weinberg's power counting for these systems'. The supporting argument is confined to footnote 3: a D2 m_π² operator is required for a subtraction-point-independent amplitude and is not suppressed relative to one-pion exchange once C0 is resummed. That is a real and interesting consistency argument in the 1S0 channel, but it is an argument, not a demonstration, and it is not extended to the coupled channel or to higher orders. Since this sentence will be read as a headline claim about an alternative scheme, I would ask that it be softened to reflect what is actually shown, or that the argument be developed in the text rather than left to a footnote.

Minor objections (6)

[Eq. (16) and the surrounding paragraph] The expansion scale Λ_NN ≈ 300 MeV is numerically close to m_π, so at the momenta of interest the expansion parameter p/Λ_NN is of order one half. The paper acknowledges this later, but the number would be more informative if this were flagged where Λ_NN is first introduced, since it sets the reader's expectation for how well the subleading calculation should do.
[Footnote 2] The footnote refers to 'some recent papers' that have criticized the applicability of dimensional regularization to NN scattering without naming them. Since refs. [7], [11] and [14] appear to be the works in question, they should be cited directly so the reader can judge the rebuttal.
[Fig. 1 and Fig. 2] The graph labels in Figs. 1 and 2 are difficult to parse in the current version (for example the vertex annotations in Fig. 1 and the 'gray blob' reference in the Fig. 2 caption). The captions are clear in prose, but the figures themselves should be redrawn so that each vertex and each diagram can be identified without consulting the text.
[Author block and affiliations] The author block contains broken words in the affiliations ('Washing ton', 'Se attle', 'US A'). These should be corrected in the typeset version.
[Eq. (15)] The decomposition of A_0 into the five pieces A_0^(I) through A_0^(V) is the technical heart of the 1S0 result, and the reader would benefit from one sentence stating which of these are μ-independent by themselves and which are not, since only A_0^(IV) is noted to carry logarithmic μ dependence.
[Discussion of the deuteron] The 3S1 channel contains the deuteron bound state, and the paper mentions deuteron properties only as future work in ref. [19]. A brief remark on whether the PDS counting is expected to accommodate the bound state pole at the same order would help the reader assess the coupled-channel claims.

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The paper

The paper claims

Nucleon-nucleon scattering can be organized into a systematic expansion once the subtraction scheme removes power-law divergences as well as logarithmic ones, with the leading contact coupling summed to all orders and everything else kept.

The reading

Nucleon-nucleon scattering has resisted the usual chiral expansion because the two-nucleon scattering lengths are enormous compared with the range of the force, which makes the contact couplings blow up and the momentum series fail to converge. The paper argues that this is a property of the subtraction scheme, not of the physics. By subtracting not only the $D=4$ poles but also the $D=3$ pole that corresponds to a linear power divergence, a procedure the authors call power divergence subtraction, the contact couplings become running couplings whose size depends on the subtraction point $mu$. Choosing $mu$ of order the external momentum $p$ makes the leading contact coupling $C_0$ scale as $1/p$, so every diagram with $C_0$ at each vertex contributes at the same order and must be summed, while all momentum-dependent operators stay perturbative. The payoff is a systematic expansion $A = A_{-1} + A_0 + A_1 + dots$ with $A_q$ of order $p^q$, computable analytically, and the authors show it tracks the Nijmegen phase shifts in the $^1S_0$ channel out to momenta of order 200 MeV with three fitted parameters.

What carries the argument

Power divergence subtraction (PDS): dimensional regularization in which counterterms remove poles at both $D=4$ and $D=3$, the latter corresponding to what a momentum cutoff would call a linear ultraviolet divergence. This is what makes the contact couplings run with the subtraction point $mu$ in a way that lets the scaling $C_{2n} sim p^{-(n+1)}$ be arranged at $mu sim p$, converting an unmanageable sum of equally large contact terms into a single resummed coupling $C_0$ plus a controlled perturbation series. The renormalization group equations $mu, d/dmu, C_0 = (M/4pi) C_0^2 mu$ and $mu, d/dmu, C_2 = (M/2pi) C_0 C_2 mu$, later modified by pion contributions, carry the argument that $mu$ dependence cancels order by order in the amplitude.

Extended reading notes

Core claim

The central claim is that a consistent power counting for nucleon-nucleon effective field theory exists once the regularization scheme is chosen to subtract power divergences, not just logarithmic ones. In the power divergence subtraction scheme the bubble integral carries a pole at $D=3$ whose residue is $M(M E)^n mu/4 pi$; subtracting it leaves $I_n^{rm PDS} = -(M E)^n (M/4 pi)(mu + i p)$, and the resummed amplitude becomes $iA = -iC(p^2,mu)/[1 + M C(p^2,mu)(mu+ip)/4pi]$. The renormalization group then fixes $C_0(mu) = (4pi/M), 1/(-mu + 1/a)$ and $C_2(mu) = (2pi/M), r_0/(-mu+1/a)^2$, so that at $mu sim p$ the coefficients scale as $C_{2n} sim p^{-(n+1)}$ and only $C_0$ needs to be treated to all orders. With pions included as a static potential pion dressed by $C_0$ plus perturbatively small radiation pions, the authors give closed-form expressions for $A_{-1}$ and $A_0$ in the $^1S_0$ channel, including the five sub-graphs of their Fig. 2, and fit $C_0(m_pi)$, $C_2(m_pi)$ and $D_2(m_pi)$ to the Nijmegen partial wave analysis. The paper states its own limit plainly: for $p > 100$ MeV the ratio $A_0/A_{-1}$ exceeds about $0.5$, so the neglected higher orders are not obviously small in the fitted region.

Load-bearing premise

That splitting one-pion exchange into a static potential pion inserted once and dressed by $C_0$, plus perturbatively small radiation-pion corrections, keeps the pion contribution at the order the counting assigns it in every channel, including the tensor-coupled one.

Editorial extensions

If this is right

Nucleon-nucleon phase shifts in the $^1S_0$ channel can be computed analytically to subleading order from three parameters, and the resulting curve follows the Nijmegen partial wave analysis out to center-of-mass momenta of roughly 200 MeV.
The same counting applies to the coupled $^3S_1$-$^3D_1$ channels, where the leading order uses a single parameter and predicts the mixing angle $\varepsilon_1$ and the $D$-wave phase shift $\delta_2$ to vanish, with no free parameters left after fitting $\delta_0$.
The subtraction scheme is offered as a general tool for finely tuned theories with power-law divergences, named in the paper as the standard model with a light Higgs and the Nambu-Jona-Lasinio model, and for any nonrelativistic theory with a large scattering length from a short-range force.
Because the method is defined in dimensional regularization, it preserves chiral symmetry, gauge symmetry and Galilean invariance, so the same machinery can be carried to other partial waves, inelastic processes, deuteron properties and few-body problems.
The paper uses its result to argue that Weinberg's power counting is not consistent for these systems, since the operator proportional to $D_2 m_pi^2$ is not subdominant to one-pion exchange once $C_0$ is summed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the counting holds, the natural next test is the deuteron: its binding momentum sits near the pion mass where the expansion parameter is least comfortable, so a deuteron calculation would probe the scheme where it is most likely to strain.
The scheme's logic is not specific to nucleons; any nonrelativistic short-range interaction with a scattering length much larger than the force range should admit the same reorganization, which suggests looking for cold-atom or halo-nucleus systems where the same scaling could be checked against precise data.
The stated breakdown at $p > 100$ MeV suggests a diagnostic use: measuring how fast $|A_0/A_{-1}|$ falls as $p$ decreases would quantify the scheme's domain of validity channel by channel, rather than asserting one momentum cutoff for all channels.
The split between potential pions and radiation pions is the step most likely to need revisiting in the tensor-coupled channel, so a useful extension would be to check whether the potential-pion insertion stays perturbative there or requires its own resummation.

Original abstract

We introduce a new and well defined power counting for the effective field theory describing nucleon-nucleon interactions. Because of the large NN scattering lengths it differs from other applications of chiral perturbation theory and is facilitated by introducing an unusual subtraction scheme and renormalization group analysis. Calculation to subleading order in the expansion can be done analytically, and we present the results for both the 1S0 and 3S1-3D1 channels.

The compiled record

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,968 input tokens.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.43 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We introduce a new and well defined power counting for the effective field theory describing nucleon-nucleon interactions. Because of the large NN scattering lengths it differs from other applications of chiral perturbation theory and is facilitated by introducing an unusual subtraction scheme and renormalization group analysis. Calculation to subleading order in the expansion can be done analytically, and we present the results for both the 1S0 and 3S1-3D1 channels.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We introduce a new and well defined power counting for the effective field theory describing nucleon-nucleon interactions.	contribution 1.00	0.94	0.46	asserted 1.00
s1	Because of the large NN scattering lengths it differs from other applications of chiral perturbation theory and is facilitated by introducing an unusual subtraction scheme and renormalization group analysis.	method 0.79	0.48	0.12	asserted 1.00
s2	Calculation to subleading order in the expansion can be done analytically, and we present the results for both the 1S0 and 3S1-3D1 channels.	result 0.63	0.95	0.18	asserted 0.91

What kind of paper the classifier reports this is: method or tool 0.72 · evidence from proof or derivation 0.99.

What was examined, and what was not

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not examined

full text
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levels run

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** The Feynman graphs contributing to A−1 and A0. Each of the resummed vertices is a factor of C0, while the vertex marked with a square is a factor of C2p 2 . Summing the graphs yield the expressions in eq. (13). where Aq is of order p q . The leading amplitude is given by the sum of loop graphs with C0 vertices, while subleading contributions correspond to perturbative insertions of the momentum dependent interactions, dressed to all orders by C0. The first two terms in the expansion of A are A−1 = −C0 h 1 + C0M 4π (µ + ip) i and A0 = −C2p 2 h 1 + C0M 4π (µ + ip) i2 , (13) which…

**Figure 2.** The five sub-graphs contributing to A0 computed in eq. (15). The gray blob is defined in

**Figure 3.** The phase shifts δ in the 1S0 channel, and δ0, ε1, and δ2 in the 3S1 − 3D1 coupled channels, plotted in degrees versus center of mass momentum p. The dot-dashed line represents the leading p −1 order calculation for δ and δ0; at this order one finds ε1 = δ2 = 0. The dashed lines are the results from the order p 0 calculation. Solid lines are results from the Nijmegen partial wave analysis of scattering data [17]. The fits involve three parameters in the 1S0 channel and three parameters in the 3S1 − 3D1 coupled channels. However, for p > 100 MeV the magnitude of the ratio A0/A−1 is…

Figures reproduced from arXiv:nucl-th/9801034 by the authors.

References

Works cited (20)

[1]

S. Weinberg, Phys. Lett. B251 (1990) 288; Nucl. Phys. B363 (1991) 3

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[11]

G.P. Lepage, nucl-th/9706029, Lectures given at 9th Jo rge Andre Swieca Summer School: Particles and Fields, Sao Paulo, Brazil, 16-28 Feb 1 997

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[4]

D.B. Kaplan, M.J. Savage and M.B. Wise, Nucl. Phys. B478 (1996) 629

View on Pith 1996
[19]

D.B. Kaplan, M.J. Savage and M.B. Wise, in preparation. 10

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[2]

C. Ordonez, U. van Kolck, Phys. Lett. B291 (1992) 459; C. Ordonez, L.Ray, U. van Kolck, Phys. Rev. Lett. 72 (1994) 1982; Phys. Rev. C53 (1996) 2086.; U. van Kolck, Phys. Rev. C49 (1994) 2932

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T.S. Park, D.P. Min, M. Rho, Phys. Rev. Lett. 74 (1995) 4153; Nucl. Phys. A596 (1996) 515

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T. Cohen, J.L. Friar, G.A. Miller and U. van Kolck, Phys. R ev. C53 (1996), 2661

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D. B. Kaplan, Nucl. Phys. B 494 (1997) 471

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T.D. Cohen, Phys. Rev. C55 (1997) 67. D.R. Phillips, T.D. Cohen, Phys. Lett. B390 (1997) 7. K.A. Scaldeferri, D.R. Phillips, C.W. Kao, T.D. Co hen, Phys. Rev. C56 (1997)

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J.L. Friar, Few Body Syst. 99 (1996) 1, nucl-th/9607020

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M.J. Savage, Phys. Rev. C55 (1997) 2185

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M. Luke and A.V. Manohar, Phys. Rev. D55 (1997) 4129

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M.B. Wise, hep-ph/9707522, Talk given at Internationa l Conference (7th Blois Work- shop) on Elastic and Diﬀractive Scattering - Recent Advance s in Hadron Physics, Seoul, Korea, 10-14 Jun 1997

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S.K. Adhikari and A. Ghosh, J. Phys. A30 (1997) 6553

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K.G. Richardson, M.C. Birse, J.A. McGovern, hep-ph/97 08435

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T.S. Park, K.Kubodera, D.P. Min, M. Rho, hep-ph/971146 3

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M.M. Nagels, T.A. Rijken, J.J. de Swart, Phys. Rev. D17 (1978) 768; V.G.J. Stoks, R.A.M. Klomp, C.P.F. Terheggen, J.J. de Swart, Phys. Rev. C49, (1994) 2950

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P. Labelle, hep-ph/9608491; B. Grinstein and I. Rothst ein, Phys.Rev. D57 (1998) 78. M. Luke and M.J. Savage, Phys. Rev. D57 (1998) 413. M. Beneke and V.A. Smirnov, hep-ph/9711391. H.W. Griesshammer, hep-ph/9712467

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Lattice QCD at a 450 MeV pion mass yields a bound deuteron (about 14 MeV) and dineutron (about 12.5 MeV) and S-wave phase shifts close to the experimental ones.
Two-Nucleon Systems in a Finite Volume: (I) Quantization Conditions
hep-lat 2013-05 accept novelty 6.0 of 10

The paper derives and tabulates finite-volume quantization conditions relating two-nucleon lattice energy eigenvalues to S-, P-, D-, and F-wave scattering parameters, including partial-wave mixing, for three boost classes.
Nucleon-Nucleon Scattering Parameters in the Limit of SU(3) Flavor Symmetry
hep-lat 2013-01 conditional novelty 6.0 of 10

At a pion mass near 800 MeV, lattice QCD yields nucleon-nucleon scattering lengths and effective ranges in the 1S0 and 3S1 channels that are within about 20% of each other, consistent with Wigner's SU(4) spin-flavor symmetry.
The Heavy Quark Spin Symmetry Partners of the X(3872)
hep-ph 2012-04 conditional novelty 6.0 of 10

Heavy quark spin symmetry forces a 2++ D*Dbar* partner of the X(3872) at about 4012 MeV, and, assuming X(3915) is a 0++ molecule, fixes a six-state molecular spectrum.
Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules
hep-ph 2012-04 conditional novelty 6.0 of 10

Tensor one-pion exchange in heavy meson molecules is perturbative below critical momenta of roughly 200 to 700 MeV, leaving a contact-range effective field theory at leading order.
Moving Multi-Channel Systems in a Finite Volume with Application to Proton-Proton Fusion
hep-lat 2012-04 conditional novelty 6.0 of 10

A finite-volume formalism connects moving, multi-channel two-hadron energy levels and weak matrix elements to infinite-volume scattering parameters and the proton-proton fusion amplitude.
Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
nucl-th 2011-07 accept novelty 6.0 of 10

A detailed chiral calculation shows that feared infrared enhancements in the pion-deuteron scattering length cancel, yielding a few-percent prediction and improved pion-nucleon scattering lengths.
Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice
nucl-th 2004-02 conditional novelty 6.0 of 10

A background vector potential with zero field strength (twisted boundary conditions) lets lattice QCD extract nucleon-nucleon phase shifts at tunable momenta on lattices as small as 5 fm.
Two Nucleons on a Lattice
hep-lat 2003-12 accept novelty 6.0 of 10

Finite-volume pionless effective field theory shows that two-nucleon scattering parameters can be extracted from lattices of order 10 to 15 fm, not the 80 to 150 fm previously assumed.
Two-Nucleon Systems from Effective Field Theory
nucl-th 1998-02 accept novelty 6.0 of 10

A new subtraction scheme (PDS) makes the effective field theory expansion for nucleon-nucleon scattering consistent, yielding analytic amplitudes to subleading order in the 1S0 and 3S1-3D1 channels.
Quantum Resources and Wigner Symmetry in Nucleon-Nucleon Scattering from Effective Field Theory
nucl-th 2026-06 unverdicted novelty 5.0 of 10

Under Wigner's SU(4) symmetry the neutron-proton scattering amplitude generates no new quantum resources while same-nucleon channels do due to identical-particle constraints.
Bootstrapping Two-Nucleon Effective Field Theories
nucl-th 2026-05 unverdicted novelty 5.0 of 10

Bootstrap consistency checks show that the NLO chiral EFT potential for the 1S0 two-nucleon wave remains valid over a significantly wider energy range than the LO version when compared to Granada phase shifts.
Auxiliary counterterms and their role in effective field theory
nucl-th 2026-03 unverdicted novelty 5.0 of 10

Auxiliary counterterms provide exact cutoff independence in EFTs but encode no new physics and aid renormalization consistency and convergence.
Short-range production of three bottom mesons
hep-ph 2025-11 unverdicted novelty 5.0 of 10

Leading-order predictions for three-body point production rates of B and B* meson systems are derived in short-range NREFT from two-body input alone.
BB interactions with static bottom quarks from Lattice QCD
hep-lat 2015-10 conditional novelty 5.0 of 10

Two B mesons made of static bottom antiquarks and physical-mass light quarks are found to bind into a tetraquark with a binding energy of about 90 MeV in the scalar isosinglet channel.
Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules
hep-ph 2012-10 conditional novelty 5.0 of 10

Fixing four contact couplings from three assumed molecular states plus the X(3872) isospin-violating decay ratio yields a predicted spectrum of charmed meson-antimeson molecules and excludes an isovector X(3872) partn...
Using effective field theory to analyse low-energy Compton scattering data from protons and light nuclei
nucl-th 2012-03 conditional novelty 5.0 of 10

New chiral-EFT fits to proton and deuteron Compton data give alpha_p = 10.7 +/- 0.3 (stat) +/- 0.2 (Baldin) +/- 0.8 (theory) and beta_p = 3.1 -/+ 0.3 +/- 0.2 +/- 0.8, in units of 10^-4 fm^3.
Heavy Quark Symmetry Predictions for Weakly Bound B-Meson Molecules
hep-ph 2011-09 accept novelty 5.0 of 10

Assuming the Zb(10610) and Zb(10650) are shallow B-meson molecules, heavy quark spin symmetry fixes relations among the binding momenta and widths of six predicted states, plus testable ratios of their pion decay rates.
On-shell renormalization in NREFT: a simplified description of resonances, bound states, and coupled channel effects
hep-ph 2026-08 conditional novelty 4.0 of 10

On-shell renormalization in NREFT reproduces Weinberg's bound-state compositeness relations, gives Z=1 for above-threshold resonances by construction, and completes the p-wave charged-channel propagator.
Observables in Schr\"odinger CFTs: How Aliens Built the Pyramids
hep-th 2026-06 unverdicted novelty 4.0 of 10

Observables in Schrödinger CFTs have zero mass and transform in staggered pyramid representations built from alien operators, generalizing exceptional symmetry conservation laws.
Coulomb Corrections to Three-Nucleon Moments
nucl-th 2026-05 unverdicted novelty 4.0 of 10

Pionless EFT calculations find unexpectedly small O(alpha) Coulomb corrections to three-nucleon magnetic moments and GT matrix elements, yielding a fitted prediction for the proton-proton fusion reduced matrix element...
Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
hep-lat 2017-06 accept novelty 4.0 of 10

The three-body force enters the leading finite-volume energy shift of a shallow three-boson bound state only through an overall normalization constant, and the shift interpolates smoothly to the Luscher particle-dimer...
Determining universal spectra from probability distributions
nucl-th 2026-06 unverdicted novelty 3.0 of 10

Exploratory refinement of universal n-body spectra predictions using probability distributions of correlation functions via lattice methods and analytic expansions.
Scrutiny of the new class of three-nucleon forces
nucl-th 2025-12 conditional novelty 3.0 of 10

After removing renormalization-scheme-dependent short-distance parts, the scrutinized three-nucleon forces yield small contributions to neutron and symmetric nuclear matter equations of state, aligning with standard c...
High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and outlook
nucl-th 2019-11 accept novelty 3.0 of 10

Semilocally regularized chiral EFT nucleon-nucleon potentials now fit low-energy scattering data at phenomenological-potential precision, but consistent regularization of three-nucleon forces remains the main obstacle...
As Scales Become Separated: Lectures on Effective Field Theory
hep-ph 2019-03 accept novelty 3.0 of 10

A pedagogical set of lecture notes that walks through matching, renormalization group running, and a scalar toy model of Soft Collinear Effective Theory, with every loop integral done explicitly in toy scalar theories.
Lattice simulations for few- and many-body systems
nucl-th 2008-04 accept novelty 3.0 of 10

Lattice effective field theory provides a common computational framework for simulating cold atoms and low-energy nuclear systems, though sign problems and coarse lattice spacings still limit precision.
The theory of electric dipole moments: the view from below
hep-ph 2026-07 unverdicted novelty 2.0 of 10

A bottom-up review organizing the theory of EDMs from quark-gluon CP violation via chiral perturbation theory and structure calculations, with emphasis on paramagnetic system sensitivity to hadronic sources.
Lattice QCD and Neutrino-Nucleus Scattering
hep-lat 2019-04 unverdicted novelty 2.0 of 10

Lattice QCD can provide several nucleon and light-nucleus inputs needed to model neutrino-nucleus scattering, with the nucleon axial form factor as the most urgent near-term target.
The Standard Model as an Effective Field Theory
hep-ph 2017-06 accept novelty 2.0 of 10

A pedagogical review arguing that LHC precision data, especially Higgs measurements, should be projected into consistent effective field theories (SMEFT or HEFT) rather than into ad hoc parameterizations.
Five lectures on effective field theory
nucl-th 2005-10 accept novelty 2.0 of 10

A pedagogical tour of effective field theory: how scaling dimensions, symmetries, and matching let you replace unknown short-distance physics with a truncated expansion of local operators, applied to weak interactions...
Fundamental Physics at the Frontier of Noisy Quantum Computation
quant-ph 2026-09

How later papers used it

207 later papers cite it

Evidence: some. 188 of the citing papers share no author with it, and 67 of those carry a confident label from Pith's citation classifier.

Pith read 5 of the 378 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 2 used its method or tool.

Uses its method or tool 2 of 58 papers with this label

Used PDS from this paper with the Z parameterization to treat couplings that reproduce the deuteron pole location and residue.

Large-$N_c$ constraints for elastic dark matter-light nucleus scattering in pionless effective field theory (2021) · 0.93 · paraphrased: the licence does not allow quoting
Solved its loop integral using the PDS scheme of this paper.

Pionless Effective Field Theory Evaluation of Nuclear Polarizability in Muonic Deuterium (2020) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

172 arXiv papers cite this in 328 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 198 sentences without a confident label

Contests it 1 paper

Unfortunately, treating pion exchange perturbatively [ref] does not work in the low triplet waves [ref] .

A renormalized approach to neutrinoless double-beta decay · Chiral EFT · contest 0.83

Builds on it 1 paper

Following the normalization and conventions of Ref. [ref] , the mixed action two-nucleon Lagrangian also involves simple modifications to the continuum two–nucleon Lagrangian [ref] and is given by [equation] where there is an implicit sum over $j= { ^1 S_0, ^3 S_1 }$.

Universality of Mixed Action Extrapolation Formulae · Mixed Action Two–Nucleon Lagrangian · 0.80

Uses its method or tool 53 papers

In this work, we give a reassessment of the finite-size and polarizability effects in $μ$D using the pionless effective field theory ($π$EFT) of nuclear forces [ref] at next-to-next-to-next-to-leading order (N3LO), including effects generated by the structure of individual nucleons.

A reassessment of nuclear effects in muonic deuterium using pionless effective field theory at N3LO · Introduction · 0.90
The calculation is carried out in the framework of pionless effective field theory (pionless EFT) [ref] as protons and neutrons are the appropriate degrees of freedom for the triton.

Neutron-neutron distribution of the triton from pionless EFT · Introduction · 0.85
The partial wave projection operators are defined through [ref] [equation] In the power-divergence subtraction scheme [ref] , which we employ in our calculations, the low-energy couplings are given by [equation] with $$ ($$) the $^1S_0$ ($^3S_1$) scattering length and $μ$ the renormalization point.

Hadronic parity violation in pionless effective field theory · Lagrangians · 0.98

Uses its data or values 2 papers

The two-baryon sector calculated with $m_π∼800 MeV$ is found to be unnatural [ref] , with a scattering length that is larger than the range of the interaction, and hence better described by the power-counting of van Kolck [ref] and KSW [ref] .

Entanglement Suppression and Emergent Symmetries of Strong Interactions · Introduction · 0.80
Using the values for the LECs given in Ref. [ref] yields [equation] These ratios exhibit strong $μ$ dependence, reflecting the well-known strong $μ$ dependence of the LECs in the power divergence subtraction (PDS) scheme [ref] used in Ref. [ref] .

The role of intermediate $\Delta\Delta$ states in nucleon-nucleon scattering in the large-$N_c$ and unitary limits, and $\Delta\Delta$ and $\Omega\Omega$ scattering · $P$ waves and other perturbative channels · 0.88

Compares with it 5 papers

Even though the LETs for the shape parameters: $v_2,v_3$ and $v_4$ perform worse compared to the ones obtained in WPC [ref] , they are significantly improved compared to KSW counting [ref] , see <ref>.

Low-energy theorems for neutron-proton scattering in $\chi$EFT using a perturbative power counting · The $^1S_0$ partial wave · 1.00
However, the power counting we obtain is equivalent to the Kaplan, Savage and Wise proposal [ref] , modulo the obvious difference that here we are dealing with heavy mesons instead of nucleons. .

Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules · The EFT Potential · 0.83
The enhancement we find here for the S- and S-to-D-wave derivative interactions is identical to the one previously calculated in the two-nucleon system when OPE is either perturbative [ref] or not present [ref] , despite the obvious differences in the methodology.

Interpretations of the new LHCb $P_c(4337)^+$ pentaquark state · Subleading order contributions to the molecular pentaquark potential · 1.00

Cites it as support 1 paper

This is justified [ref] since the scattering amplitudes that mix $^3S_1$ to $^3D_1$ and for transitions $^3D_1$ to $^3D_1$ scattering result from one pion exchange potentials.

Theoretical Developments in Lattice Gauge Theory for Applications in Double-beta Decay Processes and Quantum Simulation · Two-nucleon scattering in pionless EFT with KSW power-counting · 0.98

Cites it as background 45 papers

In the late 1990s, Kaplan et al. [ref] proposed an RG-invariant PC where pions are treated perturbatively in all partial waves.

Low-energy theorems for neutron-proton scattering in $\chi$EFT using a perturbative power counting · Introduction · 0.89
The alternative KSW theory entails an expansion of the NN scattering amplitude, instead of the nuclear potential, effected by computing a well-defined class of Feynman diagrams at each order in the expansion [ref] .

New approach to NN with perturbative pions · Weinberg and KSW · 0.91
Nonrelativistic effective field (NREFT) for hadrons was first proposed by Weinberg [ref] to describe nucleon-nucleon interactions, and was further developed in Refs. [ref] .

On-shell renormalization in NREFT: a simplified description of resonances, bound states, and coupled channel effects · Introduction · 1.00

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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