Criteria of Renormalizability in Effective Field Theories

A. M. Gasparyan; E. Epelbaum

REVIEW 4 major objections 6 minor 1 cited by

Criteria of Renormalizability in Effective Field Theories

T0 review · 4 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Chiral nuclear EFT is renormalizable only when long-range forces stay local, the cutoff sits near the hard scale, and counterterms are natural-sized.

desk verdict A solid proceedings restatement of the authors' earlier renormalizability proofs, with one genuinely new fine-tuned counterexample; useful as an entry point, not as a new proof. read the letter →

arxiv 2504.16512 v1 pith:BINRH3S6 submitted 2025-04-23 hep-ph nucl-th

A. M. Gasparyan , E. Epelbaum This is my paper · ORCID

classification hep-phnucl-th

keywords effectivefieldtheoryrenormalizabilitychiralperturbationnucleon-nucleonscatteringpowercountingcutoffregularizationseparablepotentialsexceptionalcutoffs

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Chiral effective field theory for nucleon-nucleon scattering is a nonperturbative EFT that still aims for a strict order-by-order expansion, and this paper states the precise conditions under which that expansion can be restored by renormalization at next-to-leading order. The claim is that renormalizability holds only when three criteria are met together: the long-range pion-exchange forces are local, the ultraviolet cutoff is chosen near the hard scale rather than sent to infinity, and the finite parts of the counterterms are of natural size. The paper supports each criterion by pointing to an explicit proof for the nucleon-nucleon sector and by exhibiting toy models in which violating the criterion makes renormalization fail. The payoff is a clearer map of when a finite-cutoff EFT is self-consistent and when a large-cutoff 'RG-invariant' scheme is not.

What carries the argument

The load-bearing object is the subtracted-potential bound: for a local potential whose singularities depend on momentum transfer squared, the remainder after Taylor subtraction in the smaller momentum satisfies $\Delta^{(n)} V_\alpha(p',p) \sim (p/p')^{n+1} V_\alpha(p',p)$ for $p'\gg p$. This bound is what turns divergent loop integrals into suppressed remainders after subtraction, allowing recursive subtractions to restore the expected order-by-order counting using only the short-range contact interactions already present at leading order. For nonperturbative channels, the proof is completed by the vertex function $\Upsilon(p_{\rm on})$, defined through the leading-order amplitude; the counterterm is $-T_2(0)/\Upsilon(0)^2$, so the size of $\Upsilon(0)$ controls whether the finite counterterm is natural or explodes. The three stated criteria--locality of long-range forces, $\Lambda\sim\Lambda_b$, and natural counterterm sizes--are the physical conditions that keep this machinery working.

What would settle it

Compute the renormalized NLO amplitude in the $^3P_0$ channel with a smooth regulator and scan the cutoff; if one finds a continuous family of regulators and renormalization conditions with $\Upsilon(0)$ bounded away from zero for all $\Lambda>\Lambda_b$ and a finite $\Lambda\to\infty$ limit, the claim that exceptional cutoffs block large-cutoff 'RG-invariant' schemes is refuted. A cheaper check is to test the subtraction bound of Eq. (12) directly on a realistic NLO chiral potential including its logarithmic corrections.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a set of three criteria that the paper argues are necessary for explicit renormalizability of nuclear chiral EFT at next-to-leading order. The mechanism behind them is a high-momentum bound: after subtracting a Taylor polynomial in one momentum, a local potential whose pion singularities depend only on momentum transfer squared is suppressed by powers of the ratio of the two momenta. That suppression makes the dangerous large-loop-momentum regions cancelable by finitely many counterterms of a single short-range form, applied recursively. The nonperturbative part of the argument adds one extra condition: the vertex function evaluated at zero momentum, which enters the counterterm as an inverse square, must be nonzero and of natural size, otherwise the renormalized amplitude explodes away from threshold. The paper then exhibits three counterexamples: a nonlocal separable two-pion-exchange-like interaction, the $^3P_0$ channel in a large-cutoff 'RG-invariant' scheme, and a fine-tuned short-range separable model, in which one of the criteria fails and renormalizability breaks down.

Load-bearing premise

The argument hinges on the assumption that after subtraction a local potential's high-momentum tail falls off as a clean power of the ratio of the two momenta, with no logarithmic or nonlocal pieces spoiling that falloff; if this bound fails, the recursive counterterms no longer restore the power counting.

Editorial extensions

If this is right

The standard finite-cutoff version of chiral nuclear EFT is put on a firmer footing: if the three criteria hold, an explicit renormalization recipe exists in principle, so order-by-order fitting of low-energy constants is a legitimate implicit realization of that recipe.
Large-cutoff 'RG-invariant' schemes, at least in the $^3P_0$ channel, cannot be repaired by small continuous changes of the regulator or of the renormalization conditions, because the exceptional cutoffs are infinite in number and any continuous local fix still crosses one.
Nonlocal long-range models, even when shaped like pion exchange, are not renormalizable inside a local EFT: absorbing their power-counting violations would require an infinite tower of nonlocal counterterms from leading order onward.
In nonperturbative channels, renormalizability is not guaranteed by locality and cutoff choice alone; the zero-energy vertex function must have natural size, so monitoring $\Upsilon(0)$ can reveal a hidden breakdown before it appears in observables.

Reading between the lines

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

An implication the paper leaves implicit is that any future chiral EFT with a cutoff far above the hard scale should be treated as a different effective theory, not as a scheme variation of the standard one, because the two cannot be connected by a continuous renormalized flow.
The subtraction bound offers a practical pre-screening tool: before adopting a new regulator, one can numerically test whether the high-momentum tail of the regulated potential is power-suppressed after subtraction; a violation would predict renormalization trouble before any loop calculation is done.
The exceptional-cutoff phenomenon warns that sparse cutoff scans in numerical EFT studies can miss narrow breakdown regions; monitoring the zero-energy vertex function across the cutoff would catch the explosion points.
The closed-form separable toy models could serve as testbeds for alternative renormalization prescriptions, since the exact location of the pathological parameter values is known and the failure mechanism can be studied analytically.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: if you already know Gasparyan and Epelbaum's two big papers (PRC 105 and PRC 107), this talk won't surprise you. It restates the three criteria they derived there—locality of long-range forces, cutoff at the hard scale, natural-size counterterms—and adds three toy counterexamples. The one in Sec. 6 is the only genuinely new piece: a separable, purely short-range model with a sharp regulator where a fine-tuned choice makes the vertex function vanish at zero, so the counterterm blows up and renormalization fails even though the perturbative series converges. That's a nice explicit demonstration of a nonperturbative subtlety.

What's good: the three criteria are cleanly formulated, and the paper is honest about what is proven where. The connection to BPHZ subtractions and the Fredholm extension is sketched accurately, and the Sec. 5 discussion of the 'RG-invariant' scheme makes a sharp point: exceptional cutoffs are not isolated accidents but unavoidable if you stick to continuous renormalization conditions. The counterexamples are chosen to isolate each criterion rather than mimic full QCD.

Soft spots: the stress-test is right to focus on Eq. (12), the large-momentum bound for subtracted potentials. It is load-bearing—everything downstream depends on the power suppression (p/p')^{D+1}—and in this text it is asserted as a 'direct consequence' with no derivation. For a proceedings paper that is acceptable because the proof lives in Refs. [8,9], but the paper's own caveat 'we neglect logarithmic corrections' hints the bound is not meant literally. If the real NN potential has logs that distort the power form, the subtraction counting could shift; a referee should push for either a derivation or an explicit statement of what is proven in [8,9]. The Sec. 5 continuity argument is also genuinely sketched: the closed-path reasoning is plausible, but the planar-geometry claim needs more than a sentence. And Sec. 4 leans on Ref. [23] 'in preparation,' so that example cannot be fully checked from the text.

None of this kills the paper. The central claim—that chiral EFT in the NN sector is renormalizable at NLO under the three criteria—is already established in the published references, and this version is a fair summary. For someone outside the immediate circle, it is a good map of a technical literature. For someone inside, the Sec. 6 example is worth a quick look.

My recommendation: send it to review. It deserves a serious referee—not because it is a new proof, but because it is a well-organized summary with one new instructive counterexample. The referee's main job is to check that the delegation to [8,9] is accurate and to ask for a fuller Sec. 5 argument. Minor issues, no cheap shot.

Referee Report

4 major / 6 minor

Summary. This proceedings paper formulates three criteria for renormalizability of nuclear chiral effective field theory in the NN sector at next-to-leading order: locality of the long-range interactions, cutoff of order the hard scale, and natural-size finite parts of counterterms. It sketches the derivation using subtractive renormalization with BPHZ-type subtractions, relying on the large-momentum bound in Eq. (12), and then presents three counterexamples: a nonlocal separable model that violates locality, the appearance of 'exceptional' cutoffs in an RG-invariant scheme for the 3P0 channel, and a fine-tuned separable short-range model that makes the counterterm unnatural. The paper concludes that violations of the criteria break renormalizability and support the self-consistency of the finite-cutoff Weinberg-style power counting over large-cutoff RG-invariant schemes.

Significance. If the claims are correct, the paper provides a sharp and useful set of criteria that clarify an ongoing debate in nuclear EFT, with concrete counterexamples to illustrate where renormalization fails. The main strength is its grounding in previously published rigorous derivations (Refs. [8,9]) and the formulation of falsifiable conditions: each criterion is stated precisely enough to be tested on explicit models. The counterexamples, especially the separable models, are instructive and directly demonstrate the role of the criteria. However, the paper is a proceedings contribution, and several load-bearing steps are only sketched or deferred to unpublished work, which limits the extent to which the criteria are established from this text alone.

major comments (4)

[§3.1, Eq. (12)] The large-momentum bound in Eq. (12) is the central analytic input for the recursive BPHZ subtractions that restore power counting, but it is asserted as a 'direct consequence' of locality with the caveat 'we neglect logarithmic corrections.' Since the proof is not reproduced here, the reader cannot check whether the bound is valid in the precise form needed, including whether logarithmic corrections would alter the power-counting restoration. The authors should state the exact theorem from Ref. [8] that implies Eq. (12), including the treatment of logarithms, or provide a self-contained derivation; without this, the central claim that the criteria are sufficient for renormalizability is not fully established from the manuscript itself.
[§5, no-avoidance argument] The argument that no continuous change of renormalization conditions or regulator form can avoid an exceptional cutoff is load-bearing for the claim that no continuous flow to the infinite-cutoff limit exists, but it is presented in two sentences and rests on a planar-geometry assertion about a closed continuous path without proof. The authors should either provide a rigorous statement of the assumptions (continuity, differentiability, generic position of the root) and a proof of the intersection claim, or cite a detailed derivation, since as written this step is not sufficiently justified.
[§4, model of nonlocal separable interactions] The counterexample demonstrating violation of the locality criterion is presented as a specific model whose renormalization failure is 'analyzed in detail' in Ref. [23], which is cited as 'in preparation.' Because that reference is unavailable, the reader cannot verify the generality of the conclusion that all higher-order nonlocal counterterms would be required. The authors should include enough of the derivation in the present text to make the counterexample self-contained, or refer to a published, accessible analysis.
[§3.2, nonperturbative step] The statement that 'an explicit calculation reveals that as long as the cutoff does not exceed the hard scale ... the counterterms have natural size' is essential for the third criterion, but no details or numerical evidence are provided here. Since this is a key input to the criterion of naturalness, the authors should either present the calculation or give a specific pointer to the equation/result in Ref. [9] that establishes it.

minor comments (6)

[Abstract and §1] The abstract contains the phrase 'not a priory obvious'; this should be 'not a priori obvious.'
[§4, around Eq. (20)] There is a typo 'gerneral' in the sentence 'In gerneral, they do not hold for non-local long-range interactions'; it should be 'In general.'
[§5] The phrase 'the singular nature of the unregulated one-pion-exchange potenatial' contains a typo: 'potenatial' should be 'potential.'
[§6] The phrase '(urenormalized) /u1D4472' appears to contain a typo; it should be either 'unrenormalized' or 'renormalized' consistently with the surrounding text.
[References] Several arXiv identifiers in the reference list appear corrupted by character-encoding artifacts (e.g., Ref. [3] '3811.1338', Ref. [21] '17/zero.alt35./zero.alt32524'); these should be repaired to standard arXiv numbers.
[§5] The sentence explaining why the infinite number of exceptional cutoffs blocks the Λ→∞ limit is compressed; a more explicit explanation of how the absence of a continuous solution to Eq. (21) prevents taking the limit would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central renormalizability claim is a parameter-free mathematical result imported from the authors' prior work, and the counterexamples are explicit, self-contained models rather than fitted quantities renamed as predictions.

full rationale

The paper is a proceedings-style summary of prior proofs by the same authors. The key input is the large-momentum bound Eq. (12), which is stated as 'obtained in Ref. [8]' and described as a 'direct consequence' of locality of the long-range potential. Although this bound is load-bearing, it is not a fitted parameter and is not defined in terms of the target renormalizability claim; it is a stated analytic property of local chiral potentials. The subsequent BPHZ subtraction argument and the nonperturbative Fredholm extension are cited to Refs. [8,9], which are parameter-free mathematical derivations with stated assumptions that do not include the target result, so the self-citation constitutes real evidence rather than circularity. The counterexamples in Secs. 4 and 6 are explicitly constructed separable models whose failure of renormalizability is derived from their violation of Eq. (12) or from fine-tuned parameters, not by assuming the conclusion. Section 5 discusses 'exceptional' cutoffs using prior results [9,35], again parameter-free calculations. The only unverifiable citation is Ref. [23] ('in preparation') for the analysis of separable interactions, but the specific model used here is written out in the paper, so it is not load-bearing in a circular way. No equation is shown to be equivalent to its input by construction, and no fitted quantity is presented as a prediction. Therefore the appropriate score is 0.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central proof is not self-contained in this paper; it imports the NLO renormalizability proof and the exceptional-cutoff analysis from the authors' prior papers, and introduces fine-tuned toy parameters only to demonstrate failure modes. No new particles, forces, or fields are introduced; 'exceptional cutoffs' are locations in cutoff space where the amplitude diverges, not new entities.

free parameters (3)

Regulator cutoff Λ = Λ ~ Λ_b ≈ 500-700 MeV
The central criterion requires the cutoff to be of the order of the hard scale. This is a scheme choice, not a fit to data, but it is a hand-set scale on which the renormalizability argument depends.
LO separable coupling g0 = -(2π)^3/(M_N Λ_b)
Chosen in Eq. (31) of Sec. 6 to force the pathological condition Upsilon(0)=0 in the short-range separable toy model.
Regulator shape parameter epsilon = (5+sqrt(205))/6 ≈ 3.22
Fine-tuned in Eq. (31) together with g0 to make the vertex function vanish at threshold, triggering the renormalizability counterexample.

assumptions (6)

standard math Partial-wave Lippmann-Schwinger equation with a cutoff-regulated potential defines the LO and NLO amplitudes.
Eq. (3) is the starting point of Sec. 3; assumes the standard nonrelativistic scattering equation with the Green function K.
standard math BPHZ renormalization scheme can be applied to the nonperturbative resummed amplitude.
Sec. 3.1 uses BPHZ sector analysis to handle overlapping-divergence-like loop contributions with a≠0,b≠0. This is imported as a known mathematical method.
standard math Fredholm determinant representation provides a convergent expansion for nonperturbative amplitudes.
Sec. 3.2 assumes the Fredholm method for solving the Lippmann-Schwinger equation, including that the determinant D(p_on) contains the nonperturbative dynamics.
domain assumption The long-range NN potential is local and its pion-exchange singularities depend only on momentum transfer squared.
This is the physical input behind the bounds in Eq. (12), which are called a 'direct consequence' of the structure of interactions derived within chiral EFT in Sec. 3.1.
domain assumption The vertex function Upsilon(0) is of natural size and nonzero.
Sec. 3.2 and Eq. (16) require Upsilon(0)^2 in the denominator; if Upsilon(0)=0 or is very small, the counterterm becomes unnatural and renormalizability fails, as shown in Sec. 6.
ad hoc to paper Toy separable potentials with sharp regulators are representative of the failure modes.
Eqs. (18)-(19) and (22)-(24) are constructed specifically to violate locality or naturalness; the paper does not claim they describe physical NN interactions.

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Cite this review

Pith. "Pith review of Criteria of Renormalizability in Effective Field Theories." pith.science (2026). https://pith.science/paper/BINRH3S6

@misc{pith2026250416512,
  author       = {Pith},
  title        = {Pith review of: Criteria of Renormalizability in Effective Field Theories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BINRH3S6}},
  note         = {Machine review of arXiv:2504.16512}
}

read the original abstract

Any effective field theory relies on power counting rules that allow one to perform a systematic expansion of calculated quantities in terms of some soft scales. However, a naive power counting can be violated due to the presence of various hard scales in a given scheme. A typical example of such a scale is an ultraviolet regulator. This issue is particularly challenging when the interaction is nonperturbative. The power counting is expected to be restored in the course of renormalization, that is by redefining bare low-energy constants in the effective Lagrangian. Whether this procedure eventually leads to a self-consistent framework is not a priory obvious. We discuss various criteria of renormalizability in application to nuclear chiral effective field theory and provide several instructive counterexamples.

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Forward citations

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Renormalizability and nonrenormalizability of nonlocal potentials
nucl-th 2025-09 accept novelty 6.0 of 10

Nonlocal long-range separable potentials in a two-nucleon toy model require nonlocal counterterms at NLO, and a two-pion-exchange-like nonlocal term cannot be renormalized without moving that structure into the leadin...

Reference graph

Works this paper leans on

37 extracted references · 36 canonical work pages · cited by 1 Pith paper

[23]

Jacobi, A

N. Jacobi, A. Gasparyan and E. Epelbaum , in preparation

work page
[8]

Gasparyan and E

A.M. Gasparyan and E. Epelbaum, Nucleon-nucleon interaction in chiral eﬀective ﬁeld theory with a ﬁnite cutoﬀ: Explicit perturbative renormali zation at next-to-leading order , Phys. Rev. C 105 (2022) 024001 [211/zero.alt3.153/zero.alt32]

work page 2022
[9]

Gasparyan and E

A.M. Gasparyan and E. Epelbaum, Renormalization of nuclear chiral eﬀective ﬁeld theory with nonperturbative leading-order interactions, Phys. Rev. C 107 (2023) 044002 [23/zero.alt31.13/zero.alt332]

work page 2023
[1]

Weinberg, Nuclear forces from chiral Lagrangians, Phys

S. Weinberg, Nuclear forces from chiral Lagrangians, Phys. Lett. B251 (1990) 288

work page 1990
[2]

Weinberg, Eﬀective chiral Lagrangians for nucleon - pion interaction s and nuclear forces , Nucl

S. Weinberg, Eﬀective chiral Lagrangians for nucleon - pion interaction s and nuclear forces , Nucl. Phys. B363 (1991) 3

work page 1991
[3]

Epelbaum, H.-W

E. Epelbaum, H.-W . Hammer and U.-G. Meißner, Modern Theory of Nuclear Forces , Rev.Mod.Phys. 81 (2009) 1773 [/zero.alt3811.1338]

work page arXiv 2009
[4]

Machleidt and D

R. Machleidt and D. Entem, Chiral eﬀective ﬁeld theory and nuclear forces , Phys.Rept. 503 (2011) 1 [11/zero.alt35.2919]

work page 2011
[5]

Epelbaum, H

E. Epelbaum, H. Krebs and P. Reinert, High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and outlook, Front. in Phys. 8 (2020) 98 [1911.11875]

arXiv 2020

Show all 37 references

[6]

Hammer, S

H.W . Hammer, S. König and U. van Kolck, Nuclear eﬀective ﬁeld theory: status and perspectives, Rev. Mod. Phys. 92 (2020) 025004 [19/zero.alt36.12122]

2020
[7]

Epelbaum, A.M

E. Epelbaum, A.M. Gasparyan, J. Gegelia and U.-G. Meißne r, How (not) to renormalize integral equations with singular potentials in eﬀective ﬁe ld theory, Eur. Phys. J. A54 (2018) 186 [181/zero.alt3./zero.alt32646]

2018
[10]

Landau, A.A

L.D. Landau, A.A. Abrikosov and I.M. Khalatnikov, An asymptotic expression for the photon Green function in quantum electrodynamics, Dokl. Akad. Nauk SSSR 95 (1954) 1177

1954
[11]

Stevenson, Resolution of the Renormalization Scheme Ambiguity in Pert urbative QCD, Phys

P.M. Stevenson, Resolution of the Renormalization Scheme Ambiguity in Pert urbative QCD, Phys. Lett. B 100 (1981) 61. 11 Criteria of Renormalizability in Eﬀective Field Theories A. M. Gasparyan

1981
[12]

Brodsky, G.P

S.J. Brodsky, G.P. Lepage and P.B. Mackenzie, On the Elimination of Scale Ambiguities in Perturbative Quantum Chromodynamics, Phys. Rev. D 28 (1983) 228

1983
[13]

Kaplan, M.J

D.B. Kaplan, M.J. Savage and M.B. Wise, Two nucleon systems from eﬀective ﬁeld theory , Nucl. Phys. B534 (1998) 329 [nucl-th/98/zero.alt32/zero.alt375]

1998
[14]

Lepage, How to renormalize the Schrodinger equation, in Nuclear physics

G.P. Lepage, How to renormalize the Schrodinger equation, in Nuclear physics. Proceedings, 8th Jorge Andre Swieca Summer School, Sao Jose dos Campos, Ca mpos do Jordao, Brazil, January 26-February 7, 1997 , pp. 135–180, 1997 [ nucl-th/97/zero.alt36/zero.alt329]

1997
[15]

Gegelia, About the equivalence of cutoﬀ and conventionally renormal ized eﬀective ﬁeld theories, J

J. Gegelia, About the equivalence of cutoﬀ and conventionally renormal ized eﬀective ﬁeld theories, J. Phys. G25 (1999) 1681 [nucl-th/98/zero.alt35/zero.alt3/zero.alt38]

1999
[16]

Gegelia and S

J. Gegelia and S. Scherer, Consistency of the eﬀective ﬁeld theory approach to the nucl eon nucleon interaction problem revisited, Int. J. Mod. Phys. A21 (2006) 1079 [nucl-th//zero.alt34/zero.alt33/zero.alt352]

2006
[17]

Epelbaum and U.-G

E. Epelbaum and U.-G. Meißner, On the Renormalization of the One-Pion Exchange Potential and the Consistency of Weinberg‘s Power Counting, Few Body Syst. 54 (2013) 2175 [nucl-th//zero.alt36/zero.alt39/zero.alt337]

2013
[18]

Bogoliubov and O.S

N.N. Bogoliubov and O.S. Parasiuk, On the Multiplication of the causal function in the quantum theory of ﬁelds , Acta Math. 97 (1957) 227

1957
[19]

Hepp, Proof of the Bogolyubov-Parasiuk theorem on renormalization, Commun

K. Hepp, Proof of the Bogolyubov-Parasiuk theorem on renormalization, Commun. Math. Phys. 2 (1966) 301

1966
[20]

Zimmermann, Convergence of Bogolyubov’s method of renormalization in m omentum space, Commun

W . Zimmermann, Convergence of Bogolyubov’s method of renormalization in m omentum space, Commun. Math. Phys. 15 (1969) 208

1969
[21]

Epelbaum, J

E. Epelbaum, J. Gegelia and U.-G. Meißner, Wilsonian renormalization group versus subtractive renormalization in eﬀective ﬁeld theories for nucleon–nucleon scattering , Nucl. Phys. B 925 (2017) 161 [17/zero.alt35./zero.alt32524]

2017
[22]

R. Peng, S. Lyu, S. König and B. Long, Constructing chiral eﬀective ﬁeld theory around unnatural leading-order interactions, Phys. Rev. C 105 (2022) 054002 [2112./zero.alt3/zero.alt3947]

2022
[24]

Y .-H. Song, R. Lazauskas and U. van Kolck, Triton binding energy and neutron-deuteron scattering up to next-to-leading order in chiral eﬀective ﬁ eld theory, Phys. Rev. C 96 (2017) 024002 [1612./zero.alt39/zero.alt39/zero.alt3]

2017
[25]

Epelbaum and J

E. Epelbaum and J. Gegelia, Regularization, renormalization and ’peratization’ in eﬀ ective ﬁeld theory for two nucleons , Eur. Phys. J. A41 (2009) 341 [/zero.alt39/zero.alt36.3822]

2009
[26]

Epelbaum, A.M

E. Epelbaum, A.M. Gasparyan, J. Gegelia, U.-G. Meißner and X.L. Ren, How to renormalize integral equations with singular potentials in eﬀective ﬁe ld theory, Eur. Phys. J. A 56 (2020) 152 [2/zero.alt3/zero.alt31./zero.alt37/zero.alt34/zero.alt3]. 12 Criteria of Renormalizabili...

2020
[27]

Epelbaum, J

E. Epelbaum, J. Gegelia, H.P. Huesmann, U.-G. Meißner a nd X.L. Ren, Eﬀective Field Theory for Shallow P-Wave States, Few Body Syst. 62 (2021) 51 [21/zero.alt34./zero.alt31823]

2021
[28]

Frank, D.J

W . Frank, D.J. Land and R.M. Spector, Singular potentials, Rev. Mod. Phys. 43 (1971) 36

1971
[29]

Nogga, R

A. Nogga, R. Timmermans and U. van Kolck, Renormalization of one-pion exchange and power counting, Phys.Rev. C72 (2005) 054006 [nucl-th//zero.alt35/zero.alt36/zero.alt3/zero.alt35]

2005
[30]

Pavon Valderrama and E

M. Pavon Valderrama and E. Ruiz Arriola, Renormalization of NN interaction with chiral two pion exchange potential. central phases and the deutero n, Phys.Rev. C74 (2006) 054001 [nucl-th//zero.alt35/zero.alt36/zero.alt347]

2006
[31]

Pavon Valderrama and E

M. Pavon Valderrama and E. Ruiz Arriola, Renormalization of NN interaction with chiral two pion exchange potential: Non-central phases , Phys. Rev. C74 (2006) 064004 [nucl-th//zero.alt35/zero.alt37/zero.alt375]

2006
[32]

Zeoli, R

C. Zeoli, R. Machleidt and D.R. Entem, Inﬁnite-cutoﬀ renormalization of the chiral nucleon-nucleon interaction at /u1D4413/u1D43F/u1D442, Few Body Syst. 54 (2013) 2191 [12/zero.alt38.2657]

2013
[33]

van Kolck, The Problem of Renormalization of Chiral Nuclear Forces , Front

U. van Kolck, The Problem of Renormalization of Chiral Nuclear Forces , Front. in Phys. 8 (2020) 79 [2/zero.alt3/zero.alt33./zero.alt36721]

2020
[34]

Long and C.J

B. Long and C.J. Y ang, Renormalizing chiral nuclear forces: a case study of 3P0 , Phys. Rev. C84 (2011) 057001 [11/zero.alt38./zero.alt3985]

2011
[35]

Renormalization-group-invariant eﬀective ﬁeld theory

A.M. Gasparyan and E. Epelbaum, “Renormalization-group-invariant eﬀective ﬁeld theory” for few-nucleon systems is cutoﬀ dependent , Phys. Rev. C 107 (2023) 034001 [221/zero.alt3.16225]

2023
[36]

R. Peng, B. Long and F.-R. Xu, Contact operators in renormalization of attractive singul ar potentials, 24/zero.alt37./zero.alt38342
[37]

Y ang, A further study on the renormalization group aspect of pertu rbative corrections, 241/zero.alt3./zero.alt38845

C.J. Y ang, A further study on the renormalization group aspect of pertu rbative corrections, 241/zero.alt3./zero.alt38845. 13

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [23]

Jacobi, A

N. Jacobi, A. Gasparyan and E. Epelbaum , in preparation

work page

[2] [8]

Gasparyan and E

A.M. Gasparyan and E. Epelbaum, Nucleon-nucleon interaction in chiral eﬀective ﬁeld theory with a ﬁnite cutoﬀ: Explicit perturbative renormali zation at next-to-leading order , Phys. Rev. C 105 (2022) 024001 [211/zero.alt3.153/zero.alt32]

work page 2022

[3] [9]

Gasparyan and E

A.M. Gasparyan and E. Epelbaum, Renormalization of nuclear chiral eﬀective ﬁeld theory with nonperturbative leading-order interactions, Phys. Rev. C 107 (2023) 044002 [23/zero.alt31.13/zero.alt332]

work page 2023

[4] [1]

Weinberg, Nuclear forces from chiral Lagrangians, Phys

S. Weinberg, Nuclear forces from chiral Lagrangians, Phys. Lett. B251 (1990) 288

work page 1990

[5] [2]

Weinberg, Eﬀective chiral Lagrangians for nucleon - pion interaction s and nuclear forces , Nucl

S. Weinberg, Eﬀective chiral Lagrangians for nucleon - pion interaction s and nuclear forces , Nucl. Phys. B363 (1991) 3

work page 1991

[6] [3]

Epelbaum, H.-W

E. Epelbaum, H.-W . Hammer and U.-G. Meißner, Modern Theory of Nuclear Forces , Rev.Mod.Phys. 81 (2009) 1773 [/zero.alt3811.1338]

work page arXiv 2009

[7] [4]

Machleidt and D

R. Machleidt and D. Entem, Chiral eﬀective ﬁeld theory and nuclear forces , Phys.Rept. 503 (2011) 1 [11/zero.alt35.2919]

work page 2011

[8] [5]

Epelbaum, H

E. Epelbaum, H. Krebs and P. Reinert, High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and outlook, Front. in Phys. 8 (2020) 98 [1911.11875]

arXiv 2020