Baryon Chiral Perturbation Theory in Manifestly Lorentz Invariant Form

H. Leutwyler; T. Becher

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Baryon Chiral Perturbation Theory in Manifestly Lorentz Invariant Form

T. Becher, H. Leutwyler

High Energy Physics - Phenomenology · Submitted 22 Jan 1999 · 42 references

Pith's verdict: A real methods paper: infrared regularization is a genuine scheme, the p4 form factor result is new, and the two acknowledged gaps are narrower than the stress-test suggests.

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arXiv IDhep-ph/9901384 (version 1)

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CitationH. Leutwyler, T. Becher. "Baryon Chiral Perturbation Theory in Manifestly Lorentz Invariant Form." arXiv:hep-ph/9901384 (1999). https://pith.science/paper/W5XBFFE5

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Editor's note

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This is the paper that introduced infrared regularization, and it holds up. The core move is simple and correct: split each one-loop integral into an infrared part I, whose chiral expansion carries fractional powers of p, and a regular part R, which is an ordinary Taylor series, then absorb R into the effective couplings. The decomposition is defined by extending one Feynman parameter from [0,1] to [0,∞), which is clean, Lorentz invariant, and reduces to the standard relativistic calculation everywhere except in the loop integrals themselves. The worked examples — nucleon mass to p4, wave function renormalization, and the scalar form factor to p4 — are explicit, and the form factor representation stays valid near t = 4M² where HBχPT diverges. That last point is the real physics payoff, and it is delivered, not promised. The Feynman–Hellmann check in §12.2 and the elastic-unitarity check in §12.3 are the right kind of consistency tests, and they pass. The agreement with HBχPT order by order (conclusion point 4) is the structural argument that the scheme is a legitimate regularization, and I find it convincing. On the stress-test: I think it overstates the §7.2 gap. The Ward-identity argument does not require the chiral expansion of I to converge in the physical region; it requires only that at noninteger d the two pieces have different analytic structure in p, so a linear identity with polynomial coefficients must hold separately. That is a statement about the integrals, not about a series. §9.3's concession that the expansion has holes near threshold is a separate and honestly stated limitation, and it does not undercut the invariance argument. Footnote 7 is a real omission — the general case is asserted, not shown — but it is a gap in exposition, not a circular step. The soft spots that are actually soft: the renormalization scale is fixed at μ = m by prescription, justified by the intrinsic nucleon scale, and the paper does not prove that no residual scale dependence survives in observables; and the numerical σ-term and Δσ numbers lean on Höhler's subthreshold coefficients, whose uncertainties propagate. Both are flagged. Appendix D's Δ estimates are clearly labelled as saturation, not derivation. Who should read it: anyone doing one-loop baryon χPT, and anyone who has hit the threshold breakdown of the heavy-baryon series. It deserves referees.

Referee report

Significance

This is a foundational methodological paper. If the construction holds, it supplies a regularization of baryonic chiral perturbation theory that keeps Lorentz and chiral invariance manifest while reproducing the HBχPT power counting, and it removes the threshold pathologies of the heavy-baryon expansion. The paper earns credit for several concrete strengths: the explicit representation of the renormalized infrared part of the self energy in eq. (33), which makes the convergence claim of §9.2 checkable rather than asserted; the complete renormalization of the one-loop scalar integrals in §8, including the non-trivial counter terms ν12 and ν21; the unitarity check of §12.3; the Feynman–Hellmann consistency check of §12.2; and agreement of the nucleon-mass result (34) with refs. [11,12] and of σ(2Mπ²) with ref. [19]. The M³ and M⁴ ln(M/m) coefficients in eqs. (34) and (42) are parameter-free predictions of the scheme, and the numerical comparison of Δσ with the dispersive value (40) is a falsifiable test. The paper is also candid about what it has not done, which is a virtue but, as noted below, is load-bearing in one place.

Major objections (2)

[§7.2 and footnote 7] The abstract claims that chiral invariance is kept 'explicit at all stages' (abstract:s3), and §7.2 is the passage meant to establish this. The argument given there is that dimensional regularization preserves the Ward identities at any d, that the chiral expansion of I contains only fractional powers of p while that of R contains only integer powers, and that the identities must therefore be satisfied by I and R separately, so that R may be absorbed into ΔL. Footnote 7 states plainly that 'we did not perform the corresponding analysis for the present, more general case.' As written, then, the argument is a plausibility argument rather than a proof for general graphs. The paper does supply a sound alternative in the same subsection — 'the equivalence with the standard heavy baryon approach ensures chiral symmetry' — and that is sufficient, but §7.2 currently presents the power-counting separation as the demonstration. I recommend restructuring §7.2 to lead with the equivalence argument and to present the fractional/integer-power separation as heuristic, or supplying the missing Ward identity analysis. There is also a tension with §9.3, where the authors concede that the low-energy region 'in general contains holes, where the chiral expansion breaks down' and that no suitable expansion variables are known for general integrals. The power-counting separation presupposes that the chiral expansion is a valid ordering device, which §9.3 says it is not everywhere. This does not undermine the method itself, which does not rely on the expansion of I, but it does weaken the §7.2 argument as stated.
[§12.4, eq. (40) and following] The conclusion that 'the contribution from the coupling constant ē2 is small, as it should be' rests on the comparison of 14.0 MeV + 2M⁴ē2 with the dispersive value 15.2 ± 0.4 MeV. No theoretical uncertainty is attached to the 14.0 MeV. The individual contributions quoted are 7.6, 7.8 and −1.4 MeV, and the coefficients c_i^(0) entering Δ3 are determined only to O(M) by eq. (39), while the O(M⁵) remainder is dropped. A shift in c2 or c3 within the stated O(M) accuracy would move Δ3 by an amount comparable to the 1.2 MeV inferred for 2M⁴ē2. Please provide an error estimate for the 14.0 MeV, propagating the O(M) uncertainty of the c_i^(0) and estimating the truncation error, or state explicitly that the comparison bounds ē2 only at the level of the neglected higher orders.

Minor objections (7)

[§12.5] The estimate 'σ1M² + 2ē1M⁴ = 76 MeV, subject to an uncertainty of about 8 MeV' is quoted without indicating how the 8 MeV is obtained; please state the source of this error estimate.
[Conclusion, point 13] The application of the method to πK scattering is attributed to ref. [41], which is listed as a PhD thesis 'in preparation'. Since this is an unpublished source carrying a substantive claim, either mark it as a private communication or qualify the statement.
[§13.4] The statement that the cutoff calculation 'evidently yields a much smaller value for Δσ than the one that follows, either from dispersion theory or from the evaluation of the chiral perturbation series to order p⁴' is an assertion about refs. [26,34,35] rather than a demonstration. Either show the calculation or soften the wording.
[§6.2] The uniqueness of the decomposition is asserted and the proof is said to 'closely follow' §5.2. It would help to state explicitly the analytic characterization — the cut structure on the right and left — that is claimed to single out I and R, so that a reader can see why no alternative split differing by a function analytic in the whole low-energy domain is admissible.
[§12.2 and appendix B] Eq. (36) is written with a remainder O(p⁵), while the representation of Ī21(t) in appendix B is stated to be accurate only modulo O(p). Please make explicit that eq. (36) is exact in Ī21 and that the appendix B formula is a convenient approximation whose error is covered by the stated O(p⁵) remainder.
[Fig. 6] The caption uses 'nf_{0+}' without defining n; please state in the caption that n(t) is the weight of eq. (41) and give the units of the plotted quantity.
[Conclusion, point 1, and §13.3] The acronym 'BχPT' appears where 'HBχPT' or 'chiral perturbation theory' seems to be intended; please standardize the acronym throughout.

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The paper

The paper claims

A new split of loop integrals makes baryon chiral perturbation theory valid across the low-energy region while keeping Lorentz and chiral symmetry explicit.

The reading

The paper asks how to compute low-energy quantities involving nucleons without giving up either Lorentz invariance or the power counting that makes chiral perturbation theory predictive. It shows that the standard expansion in meson momenta and quark masses fails in part of the low-energy region: for the scalar form factor $t=4M_2^2$, because relativistic kinematics generates an infinite series of internal-line insertions that the heavy-baryon method truncates. The authors propose to split each one-loop integral into an infrared part, which is retained, and a regular part, which is absorbed into effective couplings; they call the resulting scheme infrared regularization. This keeps Lorentz and chiral invariance explicit and yields a representation that remains coherent across the low-energy region. They illustrate the method with the nucleon mass and the scalar form factor to order $p^4$.

What carries the argument

The load-bearing device is the decomposition $H=I+R$ of a one-loop integral into an infrared part $I$ and a regular part $R$. In the simplest self-energy case, $H=1i d^d k(2)^d1(M^2-k^2-i)(m^2-(P-k)^2-i)$; the infrared part is defined by extending the Feynman-parameter integral for the combined denominator to infinity, $I=0 dz C^{d/2-2}$, while $R$ is the remainder. The split is designed so that $I$ carries the fractional powers of the chiral expansion parameter and $R$ is a polynomial that can be cancelled by local counterterms. This is what lets the authors keep the full relativistic loop integral's low-energy singularity structure while preserving the chiral power counting and the symmetries order by order.

Extended reading notes

Core claim

The central claim is that baryon chiral perturbation theory can be reorganized so that the infrared singular pieces of one-loop graphs are kept exactly while their regular, polynomial remainders are moved into the effective Lagrangian. For noninteger dimension the two pieces are distinguished by their chiral expansions: the infrared part contains fractional powers of the chiral parameter, the regular part an ordinary Taylor series, and the authors argue that the two separately obey the chiral Ward identities. Operationally, the split is made by extending one Feynman-parameter integration from $0<z<1$ to $0<z<1$, which sums the internal-line insertions generated by relativistic kinematics to all orders. The resulting infrared regularization reproduces heavy-baryon chiral perturbation theory wherever that expansion converges, but it also covers the threshold region where the standard expansion fails. The paper demonstrates this with a calculation of the nucleon mass and the scalar form factor to order $p^4$, including the $t=4M_2^2$ term and the difference $t=4M_2^2$.

Load-bearing premise

The load-bearing premise is that the infrared and regular parts of every one-loop integral separately satisfy the chiral Ward identities, so that dropping the regular part and absorbing it into local effective couplings does not break chiral symmetry; the authors assert this from the fractional-versus-integer power structure but note in footnote 7 that they did not carry out the general analysis.

Editorial extensions

If this is right

Calculations of $N$ scattering and nucleon form factors can be carried out in a manifestly Lorentz-invariant setting while retaining the chiral power counting that heavy-baryon methods provide.
The threshold region of the scalar form factor and of $N$ amplitudes becomes accessible without summing an infinite tower of nonrelativistic internal-line insertions by hand.
The scheme gives a systematic rule for absorbing polynomial loop contributions into effective couplings, which is the step needed to renormalize the theory consistently while preserving chiral Ward identities.
The $p^4$ calculations of the nucleon mass, wave-function renormalization and scalar form factor provide concrete templates for extending the method to other observables and to systems with other heavy degrees of freedom.

Reading between the lines

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

If the Ward-identity argument holds for general graphs, infrared regularization could become a practical default for relativistic baryon chiral perturbation theory, making heavy-baryon calculations reproducible without the nonrelativistic expansion.
The same splitting strategy should be useful wherever a heavy particle and a light Goldstone boson produce a threshold branch point close to the low-energy region, because the method keeps the branch-point structure while pushing polynomial terms into couplings.
The paper's observation that large infrared pieces cancel between the $t=4M_2^2$ term and $N$ subthreshold coefficients suggests that tests of the method should compare relations among observables, not just the size of individual chiral corrections.
A useful extension would be to implement the scheme at two loops or for a general graph and check that the renormalized amplitudes are scale independent; that would turn the present one-loop demonstration into a general regularization proof.

Original abstract

We show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region. The expansion of the scalar form factor $\sigma(t)$, for instance, breaks down in the vicinity of $t=4M_\pi^2$. In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region only results if the multiple internal line insertions generated by relativistic kinematics are summed up to all orders. We propose a method that yields a coherent representation throughout the low energy region while keeping Lorentz and chiral invariance explicit at all stages. The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order $p^4$.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,342 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.83 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region. The expansion of the scalar form factor $\sigma(t)$, for instance, breaks down in the vicinity of $t=4M_\pi^2$. In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region only results if the multiple internal line insertions generated by relativistic kinematics are summed up to all orders. We propose a method that yields a coherent representation throughout the low energy region while keeping Lorentz and chiral invariance explicit at all stages. The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order $p^4$.

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 show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region.	background 0.66	0.68	0.20	asserted 0.99
s1	The expansion of the scalar form factor $\sigma(t)$, for instance, breaks down in the vicinity of $t=4M_\pi^2$.	background 0.65	0.49	0.07	asserted 1.00
s2	In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region only results if the multiple internal line insertions generated by relativistic kinematics are summed up to all orders.	background 0.69	0.18	0.12	asserted 1.00
s3	We propose a method that yields a coherent representation throughout the low energy region while keeping Lorentz and chiral invariance explicit at all stages.	contribution 0.83	0.88	0.60	asserted 0.91
s4	The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order $p^4$.	contribution 0.69	0.94	0.09	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.98 · evidence from proof or derivation 0.95.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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.** Triangle graph. The solid, dashed and wiggly lines represent

**Figure 2.** Self energy 5.1 Singular and regular parts The integral H = H(P 2 , M2 , m2 ) converges for d < 4. We need to analyze it for nucleon momenta close to the mass shell: P = m v + r, where v is a timelike unit vector and r is a small quantity of order p. It is convenient to work with the dimensionless variables Ω = P 2 − m2 − M2 2mM , α = M m , (12) which represent quantities of order Ω = O(p 0 ) and α = O(p), respectively (recall that m is the larger one of the two masses, α ≃ 1 7 ). In the limit M → 0, the integral develops an infrared singularity, generated by small va

**Figure 3.** Internal line insertions. The double line denotes the heavy

**Figure 4.** One loop graphs contributing to the self energy of the nuc ()

**Figure 5.** The loop graphs contributing to the scalar form factor at

**Figure 6.** The t-channel I = J = 0 partial wave f 0 +(t). The normalization factor n is chosen such that ∆σ is the area under the curve (dotted: Born approximation, dash-dotted: tree graphs of L (1) N +L (2) N , full: dispersion theory, all quantities in units of Mπ). are enhanced by a chiral logarithm. The underlying physics can be sorted out by noting that the elastic unitarity condition (37) leads to the representation ∆σ = Z ∞ 4M2 π dt n(t) σ ⋆ π (t) f 0 +(t) , (41) n(t) = 3M2 π p t − 4 M2 π π t 3 2 (t − 2M2 π ) (4m2 N − t) . The one loop calculation discussed above

Figures reproduced from arXiv:hep-ph/9901384 by the authors.

References

Works cited (42)

[19]

V. Bernard, N. Kaiser and U.-G. Meissner, Phys. Lett. B389 (1 996) 144

View on Pith
[1]

J. Gasser, M. E. Sainio and A. Svarc, Nucl. Phys. B307 (1988) 77 9

View on Pith 1988
[2]

E. Jenkins and A. V. Manohar, Phys. Lett. B255 (1991) 558

View on Pith 1991
[3]

V. Bernard, N. Kaiser, J. Kambor and U.-G. Meissner, Nucl. Phys . B388 (1992) 315

View on Pith 1992
[4]

G. Ecker, Czech. J. Phys. 44 (1994) 405

View on Pith 1994
[5]

V. Bernard, N. Kaiser and U.-G. Meissner, Int. J. Mod. Phys. E4 (1995) 193

View on Pith 1995
[6]

M. Mojˇ ziˇ s, Eur. Phys. J. C2 (1998) 181

View on Pith 1998
[7]

N. Fettes, U.-G. Meissner and S. Steininger, Nucl. Phys. A640 (1 998) 199

View on Pith
[8]

H.-B. Tang, A new approach to chiral perturbation theory for matter ﬁelds, hep-ph/9607436 P. J. Ellis and H.-B. Tang, Phys. Rev. C57 (1998) 3356 A similar approach was used in J. Bijnens, H. Sonoda and M. B. Wise, Nucl. Phys. B261 (1985) 185

View on Pith Pith review arXiv 1998
[9]

S. Okubo, Prog. Theor. Phys. 12 (1954) 102, 603 A. Das, Mod. Phys. Lett. A9 (1994) 341 S. Balk, J. G. K¨ orner and D. Pirjol, Nucl. Phys. B428 (1994) 499 61

View on Pith 1954
[10]

G. Ecker and M. Mojˇ ziˇ s, Phys. Lett. B410 (1997) 266, B438 (1998) 446 (E)

View on Pith 1997
[11]

S. Steininger, U.-G. Meissner and N. Fettes, J. High Energy Phy s. 9809 (1998) 8

View on Pith 1998
[12]

J. Kambor and M. Mojˇ ziˇ s,Field redeﬁnitions and wave function renor- malization to O(p4) in HBχPT, hep-ph/9901235

View on Pith Pith review arXiv
[13]

S. Weinberg, Nucl. Phys. B363 (1991) 3, Phys. Lett. B251 (19 90) 288 D. B. Kaplan, M. J. Savage, M. B. Wise, Nucl. Phys. B534 (1998) J. V. Steele, Comparison of regularization methods for nucleon-nucleon eﬀective ﬁeld theory , nucl-th/9807022

View on Pith Pith review arXiv 1991
[14]

G. Ecker, Phys. Lett. B336 (1994) 508 G. Ecker and M. Mojˇ ziˇ s, Phys. Lett. B365 (1996) 312

View on Pith 1994
[15]

see for instance A. F. Falk, B. Grinstein and M. E. Luke, Nucl. Phys. B357 (1991) 185

View on Pith 1991
[16]

O. V. Tarasov, Nucl. Phys. B502 (1997) 455

View on Pith 1997
[17]

H. Leutwyler, Ann. Phys. (N.Y.) 235 (1994) 165

View on Pith 1994
[18]

B. Borasoy and U.-G. Meissner, Ann. Phys. (N.Y.) 254 (1997) 19 2

View on Pith 1997
[20]

J. Gasser, H. Leutwyler and M. E. Sainio, Phys. Lett. B253 (19 91) 252, 260

View on Pith
[21]

G. H¨ ohler, in Landolt-B¨ ornstein, vol. 9 b2, ed. H. Schopper ( Springer, Berlin, 1983)

View on Pith 1983
[22]

Particle data group, Eur. Phys. J. C3 (1998) 1

View on Pith 1998
[23]

J. Gasser and U.-G. Meissner, Nucl. Phys. B357 (1991) 90

View on Pith 1991
[24]

J. Bijnens, G. Colangelo and P. Talavera, J. High Energy Phys. 0 5 (1998) 014

View on Pith 1998
[25]

V. Bernard, N. Kaiser and U.-G. Meissner, Nucl. Phys. A615 (19 97) 483

View on Pith
[26]

J. Gasser and H. Leutwyler, Phys. Reports 87C (1982) 77, se ction 10 and appendix C 62

View on Pith 1982
[27]

J. Bijnens, G. Colangelo, G. Ecker, J. Gasser and M. E. Sainio, Phys. Lett. B374 (1996) 210, Nucl. Phys. B508 (1997) 263, B517 (1998) 639 (E)

View on Pith 1996
[28]

L. Girlanda, M. Knecht, B. Moussallam and J. Stern, Phys. Lett . B409 (1997) 461

View on Pith 1997
[29]

V. Bernard, N. Kaiser and U.-G. Meissner, Z. Phys. C60 (1993) 111

View on Pith 1993
[30]

E. Jenkins and A. V. Manohar, Phys. Lett. B259 (1991) 353 E. Jenkins and A. V. Manohar, in Eﬀective Theories of the Standard Model, ed. U.-G. Meissner, (World Scientiﬁc, Singapore, 1991)

View on Pith 1991
[31]

J. Kambor, in Proc. Baryons ’95 , eds. B. F. Gibson et al., (World Sci- entiﬁc, Singapore, 1996) T. R. Hemmert, B. R. Holstein and J. Kambor, Phys. Lett. B395 (19 97) 89, Phys. Rev. D55 (1997) 5598, J. Phys. G24 (1998) 1831 G. C. Gellas, T. R. Hemmert, C. N. Ktorides and G. I. Poulis, The Delta nucleon transition form-factors in chiral perturbat ion theor...

View on Pith 1997
[32]

J. Kambor, in Proc. Workshop on Chiral Dynamics: Theory and Ex- periment, Mainz, Germany (1997), eds. A. Bernstein, D. Drechsel, T. Walcher, Lecture Notes in Physics, Vol. 513, Springer-Verlag, 1 998

View on Pith 1997
[33]

E. M. Henley and W. Thirring, Elementary quantum ﬁeld theory , McGraw-Hill Book Company Inc., New York (1962)

View on Pith 1962
[34]

J. F. Donoghue and B. R. Holstein, Improving the convergence of SU(3) baryon chiral perturbation theory , hep-ph/9803312 J. F. Donoghue, B. R. Holstein and B. Borasoy, SU(3) baryon chiral perturbation theory and long distance regularization , hep-ph/9804281

View on Pith Pith review arXiv
[35]

B. Borasoy, Sigma terms in heavy baryon chiral perturbation theory re- visited, hep-ph/9807453

View on Pith Pith review arXiv
[36]

U.-G. Meissner, G. Mueller and S. Steininger, Renormalization of the chiral pion-nucleon Lagrangian beyond next-to-leading or der, hep-ph/9809446

View on Pith Pith review arXiv
[37]

P. F. A. Goudsmit, H. J. Leisi, E. Matsinos, B. L. Birbrair and A. B. Gridnev, Nucl. Phys. A575 (1994) 673 63 H. J. Leisi, Experimental results in πN scattering: QCD symmetry tests , in Proc. of the Zuoz Summer School on Hidden symmetries and Higgs phenomena, Zuoz (Engadin, Switzerland, 1998), Paul-Scherrer- Institut, CH-5232 Villigen, Switzerland E. Mats...

View on Pith Pith review arXiv 1994
[38]

V. Bernard, N. Kaiser and U.-G. Meissner, Nucl. Phys. B457 (19 95) 147

View on Pith
[39]

G. Sommer, Fortschr. Phys. 18 (1970) 577

View on Pith 1970
[40]

L. S. Brown,, W. J. Pardee and R. D. Peccei, Phys. Rev. D4 (197 1) 2801

View on Pith
[41]

A. Roessl, πK scattering near the threshold in chiral SU(2) perturbation theory, PhD Thesis, University of Bern, in preparation

View on Pith
[42]

J. Bijnens, P. Gosdzinsky and P. Talavera, Nucl. Phys. B501 (1 997) 495, Phys. Lett. B429 (1998) 111 64

View on Pith 1998

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nucl-th 2015-07 conditional novelty 6.0 of 10

Matching Roy-Steiner subthreshold parameters to chiral perturbation theory at N3LO yields pion-nucleon low-energy constants with a full covariance matrix, though chiral-truncation error dominates the budget.
Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects
hep-ph 2013-12 accept novelty 6.0 of 10

Using SU(2) chiral perturbation theory, the proton and neutron scalar couplings relevant for dark matter direct detection are expressed in terms of the pion-nucleon sigma-term alone, and the traditional isospin-violat...
Nucleon mass and sigma term from lattice QCD with two light fermion flavors
hep-lat 2012-06 conditional novelty 6.0 of 10

Simultaneously fitting two-flavor lattice nucleon masses and a directly computed sigma term to O(p^4) baryon chiral perturbation theory gives sigma = 37(8)(6) MeV and r0 = 0.501(10)(11) fm.
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.
Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea
hep-lat 2008-06 conditional novelty 6.0 of 10

Across six pion masses from about 480 down to 300 MeV the nucleon mass is fit by a straight line in the pion mass, and re-plotting four other collaborations' published nucleon masses shows the same linearity.
Chiral Corrections to the Hyperon Vector Form Factors
hep-ph 2006-03 conditional novelty 6.0 of 10

A complete O(p^4) heavy baryon chiral perturbation theory calculation shows the SU(3)-breaking corrections to hyperon f1(0) are large and the three-flavor chiral expansion for baryons, especially with decuplet states,...
The expansion by regions in pi K scattering
hep-ph 2006-03 conditional novelty 6.0 of 10

Two-loop pion-kaon threshold integrals are expanded in M_pi/M_K by the method of regions, and the resulting formulas yield a new two-loop strange quark contribution to the pion mass.
Magnetic moments of heavy baryons in the relativistic three-quark model
hep-ph 2006-02 conditional novelty 6.0 of 10

Using a relativistic three-quark model, the authors predict magnetic moments for single, double, and triple heavy baryons, reproducing heavy-quark symmetry limits and giving new values for states such as Omega_ccb and...
Pion photoproduction off nucleons in covariant chiral perturbation theory
hep-ph 2019-08 conditional novelty 5.0 of 10

Including the Delta(1232) resonance in a third-order covariant chiral perturbation theory fit reproduces near-threshold pion photoproduction data across all charge channels far better than leaving it out.
Reconciling threshold and subthreshold expansions for pion-nucleon scattering
nucl-th 2016-10 conditional novelty 5.0 of 10

Including the Δ(1232) explicitly and using covariant baryon ChPT both reduce the low-energy constants of pion-nucleon scattering to natural size and bring predicted threshold parameters closer to the Roy-Steiner values.
Roy-Steiner-equation analysis of pion-nucleon scattering
hep-ph 2015-10 accept novelty 5.0 of 10

Solving Roy-Steiner equations for pion-nucleon scattering with pionic-atom scattering lengths imposed as constraints yields a pion-nucleon sigma-term of 59.1 +/- 3.5 MeV, about 14 MeV above the long-quoted canonical value.
Dispersive analysis of the scalar form factor of the nucleon
hep-ph 2012-04 conditional novelty 5.0 of 10

A two-channel dispersive analysis gives Delta_sigma = (13.9 +/- 0.3) MeV, with explicit linear dependence on the pion-nucleon coupling and subthreshold parameters.
Nucleon structure from mixed action calculations using 2+1 flavors of asqtad sea and domain wall valence fermions
hep-lat 2010-01 conditional novelty 5.0 of 10

Lattice QCD with 2+1 flavors puts the proton axial charge about 9% below experiment, the charge radii near two thirds of measured values, and the connected quark angular momentum at Ju+d = 0.238(8), with up and down o...
$|\Delta I|=3/2$ non-leptonic hyperon decays in covariant baryon chiral perturbation theory
hep-ph 2026-08 conditional novelty 4.0 of 10

In covariant baryon chiral perturbation theory, decuplet-baryon contributions with the consistent coupling scheme, plus pion loops, most improve the fit to the |ΔI|=3/2 hyperon decay amplitudes.
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...
Towards a theory of hadron resonances
hep-ph 2022-06 accept novelty 3.0 of 10

The review consolidates lattice-QCD and effective-field-theory methods for hadron resonances and argues that Breit-Wigner parameterizations are incompatible with chiral symmetry in strongly coupled channels.
The phase diagram of nuclear and quark matter at high baryon density
hep-ph 2013-01 conditional novelty 3.0 of 10

The review argues that a third regime, quarkyonic matter, sits between confined nuclear matter and deconfined quark matter in large-Nc QCD, with pressure scaling as O(Nc).
Generalized Parton Distributions: Phenomenology, Extraction, and Hadron Imaging
hep-ph 2026-09 unverdicted novelty 2.0 of 10

A comprehensive review of GPD phenomenology covering the two inverse problems (CFF extraction and GPD reconstruction), parametrizations, lattice QCD inputs, Bayesian inference, machine learning, and the prospects at J...
Multi-particle systems on the lattice and chiral extrapolations: a brief review
hep-lat 2021-02 accept novelty 2.0 of 10

Finite-volume quantization conditions combined with unitarized chiral perturbation theory form a workable pipeline from lattice energy levels to two- and three-hadron scattering amplitudes and resonance parameters, th...
Review of the ${\mathbf \Lambda}$(1405): A curious case of a strange-ness resonance
nucl-th 2020-09 conditional novelty 2.0 of 10

The Lambda(1405) is best described by two poles, a narrow one near 1420 MeV and a broad one near 1380 MeV, and this two-pole picture survives every modern model class once kaonic-hydrogen and CLAS photoproduction data...
Heavy Hadrons in Nuclear Matter
hep-ph 2016-06 accept novelty 2.0 of 10

The review consolidates three decades of theory on charm and bottom hadrons in nuclear matter, organized by chiral symmetry and heavy quark spin symmetry, and reports where competing models agree and where they do not.
Beta Decays and Non-Standard Interactions in the LHC Era
hep-ph 2013-03 accept novelty 2.0 of 10

Precision beta-decay and light-meson measurements probe non-standard charged-current interactions at scales of 7 to 11 TeV and remain complementary to direct LHC searches.

How later papers used it

80 later papers cite it

Evidence: substantial. 80 of the citing papers share no author with it, and 21 of those carry a confident label from Pith's citation classifier.

Pith read 25 of the 128 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

10 later papers by other authors are listed below: 10 used its method or tool.

Uses its method or tool 10 of 16 papers with this label

Followed the infrared regularization method developed by Becher and Leutwyler to overcome the problem that finite baryon masses spoil the correspondence between loop and chiral expansions under conventional dimensional regularization.

Mass splittings within heavy baryon isospin multiplets in chiral perturbation theory (2008) · 1.00 · paraphrased: the licence does not allow quoting
Applied the infrared regularization scheme to allow for both a systematic expansion of loop contributions in powers of p and manifest Lorentz covariance.

Chiral extrapolation of nucleon wave function normalization constants (2011) · 0.99 · paraphrased: the licence does not allow quoting
Chose, following this paper, to absorb a certain combination instead of subtracting pole parts in the epsilon expansion, replacing the original 't Hooft parameter.

Infrared renormalization of two-loop integrals and the chiral expansion of the nucleon mass (2007) · 0.99 · paraphrased: the licence does not allow quoting
Calculated the loop diagrams in a manifestly covariant form using infrared regularization.

Hyperon decay form factors in chiral perturbation theory (2007) · 1.00 · paraphrased: the licence does not allow quoting
Utilized the infrared regularization method developed in this paper to deal with power counting violations generated by the nucleon mass in a covariant formulation of baryon chiral perturbation theory.

Isospin violation in low-energy pion-nucleon scattering revisited (2009) · 1.00 · paraphrased: the licence does not allow quoting
Evaluated the loop diagrams using the so-called infrared regularization scheme to obtain a consistent power counting.

New insights into the neutron electric dipole moment (2009) · 1.00 · paraphrased: the licence does not allow quoting
Used IR regularization, as a consequence of which its result contains higher order divergencies that have to be set to zero by hand.

Model-independent calculation of $SU(3)_f$ violation in baryon octet light-cone distribution amplitudes (2015) · 0.94 · paraphrased: the licence does not allow quoting
Considered the so-called reordering prescription that has proven useful in the case of baryon masses and magnetic moments.

Aspects of meson-baryon scattering in three- and two-flavor chiral perturbation theory (2009) · 0.88 · paraphrased: the licence does not allow quoting
Evaluated the integral using the rules of this paper and found the scalar form factor at NLO, with singularities near the pion-production threshold that exactly cancel.

New lessons from the nucleon mass, lattice QCD and heavy baryon chiral perturbation theory (2008) · 0.95 · paraphrased: the licence does not allow quoting
Considered the calculation of g_A to two loops using two covariant schemes, namely the extended-on-mass-shell approach and the method of infrared regularization.

Calculation of the axial-vector coupling constant $g_A$ to two loops in covariant chiral perturbation theory (2025) · 0.94 · paraphrased: the licence does not allow quoting

How the literature uses it

79 arXiv papers cite this in 130 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

We show that the chiral expansion of these amplitudes breaks down in certain regions of phase space and present a framework which leads to a coherent description throughout the low energy region, while keeping Lorentz and chiral invariance manifest at every stage of the calculation.

Lorentz Invariant Baryon CHPT · 0.98

Papers citing it · 73 sentences without a confident label

Uses its method or tool 16 papers

Defining α = Mm, s=P^2, Ω= s-m^2-M^2/2 M m, λ̅ = m^d-4/(4π)^2 [1d-4 - 12(ln(4π)+Γ'(1)+1)], the infrared singular part of the loop integral H(s) = 1i∫d^dk/(2π)^d 1/(M^2-k^2) [m^2-(P-k)^2], is (the expression for $-1<Ω<1$ is given in Ref. [ref] ) I(s) = I̅(s) - s-m^2+M^2/sλ̅, I̅(s) = - 116π^2 α/1+2αΩ+α^2 [ (Ω+α)(2lnα-1) + F(s)], where F(s) = √(Ω^2-1) [ ln(-√(Ω^2-1)-Ω-α) - ln(√(Ω^2-1)-Ω-α) ], Ω<-1, 2√(1-Ω^2) arccos(-Ω+α/√(1+2αΩ+α^2)), -1<Ω<1, √(Ω^2-1) [ ln(√(Ω^2-1)+Ω+α) - ln(Ω+α-√(Ω^2-1)) - 2iπ], Ω>1.

Mass splittings within heavy baryon isospin multiplets in chiral perturbation theory · Loop integrals · 0.84
To allow for both a systematic expansion of loop contributions in powers of $p$ and manifest Lorentz covariance we apply the infrared regularization (IR) scheme [ref] .

Chiral extrapolation of nucleon wave function normalization constants · Covariant baryon chiral perturbation theory · 0.99
The full one-loop result for the generalized form factors obtained by a manifestly covariant calculation in the infrared regularization scheme [ref] is presented in Appendix [ref].

First moments of nucleon generalized parton distributions in chiral perturbation theory at full one-loop order · Calculation · 0.93

Compares with it 2 papers

Putting everything together, we find [equation] These results are in reasonable agreement with [ref] , and remarkably close to the $(p^4)$ ChPT analysis of [ref] (for earlier work in ChPT on $Δ_σ$ see [ref] ) Δ_σ=14.0 MeV+2^4 e̅_2where $e̅_2$ is an $(p^4)$ low-energy constant.[In fact, $e̅_2$ contributes to the chiral expansion of $d_01^+$.] The potentially largest correction in [ref] originates from $d_01^+$, e.g. taking $d_01^+=1.27 ^-3$ from [ref] increases $Δ_σ$ by $1.6 MeV$.

Dispersive analysis of the scalar form factor of the nucleon · Scalar form factor of the nucleon · 0.80
This generates the chiral expansion of the infrared regular part $R$, which is given by [equation] and which coincides with the expansion of $R$ given in Ref. [ref] .

Infrared renormalization of two-loop integrals and the chiral expansion of the nucleon mass · Infrared regularization of one-loop integrals · 1.00

Cites it as support 2 papers

For this reason, it is of utmost importance to maintain exact relativistic kinematics wherever possible, which is by no means guaranteed in a non-relativistic heavy-mass expansion ( also Refs. [ref] ).

Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints · D(*)D(*)→ππ and B(*)B(*)→ππ P-Wave Amplitudes · 0.96
For instance, the scalar form factor of the nucleon at $t=4 M_π^2$ diverges [ref] .

Chiral effective Lagrangian for doubly charmed baryons up to $\mathcal{O}(q^4)$ · Introduction · 0.96

Cites it as background 24 papers

Among these, the infrared (IR) [ref] and extended-on-mass-shell (EOMS) [ref] schemes are the mostly studied.

Recent developments in SU(3) covariant baryon chiral perturbation theory · Introduction · 0.98
The nucleon mass was later calculated up to the complete two-loop order [ref] , detailed in Ref. [ref] , within an alternative renormalization scheme, the infrared regularization (IR) prescription [ref] .

Chiral Representation of the Nucleon Mass at Leading Two-loop Order · Introduction · 0.87
Three influential schemes have been proposed to overcome the PC problem, exemplified by the heavy baryon (HB) formalism [ref] , the infrared (IR) regularization [ref] and the extended-on-mass-shell (EOMS) renormalization scheme [ref] .

Light quark mass dependence of nucleon mass to two-loop order · Introduction · 0.92

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.

[1] [19]

V. Bernard, N. Kaiser and U.-G. Meissner, Phys. Lett. B389 (1 996) 144

View on Pith

[2] [1]

J. Gasser, M. E. Sainio and A. Svarc, Nucl. Phys. B307 (1988) 77 9

View on Pith 1988

[3] [2]

E. Jenkins and A. V. Manohar, Phys. Lett. B255 (1991) 558

View on Pith 1991

[4] [3]

V. Bernard, N. Kaiser, J. Kambor and U.-G. Meissner, Nucl. Phys . B388 (1992) 315

View on Pith 1992

[5] [4]

G. Ecker, Czech. J. Phys. 44 (1994) 405

View on Pith 1994

[6] [5]

V. Bernard, N. Kaiser and U.-G. Meissner, Int. J. Mod. Phys. E4 (1995) 193

View on Pith 1995

[7] [6]

M. Mojˇ ziˇ s, Eur. Phys. J. C2 (1998) 181

View on Pith 1998

[8] [7]

N. Fettes, U.-G. Meissner and S. Steininger, Nucl. Phys. A640 (1 998) 199

View on Pith

[9] [8]

H.-B. Tang, A new approach to chiral perturbation theory for matter ﬁelds, hep-ph/9607436 P. J. Ellis and H.-B. Tang, Phys. Rev. C57 (1998) 3356 A similar approach was used in J. Bijnens, H. Sonoda and M. B. Wise, Nucl. Phys. B261 (1985) 185

View on Pith Pith review arXiv 1998

[10] [9]

S. Okubo, Prog. Theor. Phys. 12 (1954) 102, 603 A. Das, Mod. Phys. Lett. A9 (1994) 341 S. Balk, J. G. K¨ orner and D. Pirjol, Nucl. Phys. B428 (1994) 499 61

View on Pith 1954

[11] [10]

G. Ecker and M. Mojˇ ziˇ s, Phys. Lett. B410 (1997) 266, B438 (1998) 446 (E)

View on Pith 1997

[12] [11]

S. Steininger, U.-G. Meissner and N. Fettes, J. High Energy Phy s. 9809 (1998) 8

View on Pith 1998

[13] [12]

J. Kambor and M. Mojˇ ziˇ s,Field redeﬁnitions and wave function renor- malization to O(p4) in HBχPT, hep-ph/9901235

View on Pith Pith review arXiv

[14] [13]

S. Weinberg, Nucl. Phys. B363 (1991) 3, Phys. Lett. B251 (19 90) 288 D. B. Kaplan, M. J. Savage, M. B. Wise, Nucl. Phys. B534 (1998) J. V. Steele, Comparison of regularization methods for nucleon-nucleon eﬀective ﬁeld theory , nucl-th/9807022

View on Pith Pith review arXiv 1991

[15] [14]

G. Ecker, Phys. Lett. B336 (1994) 508 G. Ecker and M. Mojˇ ziˇ s, Phys. Lett. B365 (1996) 312

View on Pith 1994

[16] [15]

see for instance A. F. Falk, B. Grinstein and M. E. Luke, Nucl. Phys. B357 (1991) 185

View on Pith 1991

[17] [16]

O. V. Tarasov, Nucl. Phys. B502 (1997) 455

View on Pith 1997

[18] [17]

H. Leutwyler, Ann. Phys. (N.Y.) 235 (1994) 165

View on Pith 1994

[19] [18]

B. Borasoy and U.-G. Meissner, Ann. Phys. (N.Y.) 254 (1997) 19 2

View on Pith 1997

[20] [20]

J. Gasser, H. Leutwyler and M. E. Sainio, Phys. Lett. B253 (19 91) 252, 260

View on Pith

[21] [21]

G. H¨ ohler, in Landolt-B¨ ornstein, vol. 9 b2, ed. H. Schopper ( Springer, Berlin, 1983)

View on Pith 1983

[22] [22]

Particle data group, Eur. Phys. J. C3 (1998) 1

View on Pith 1998

[23] [23]

J. Gasser and U.-G. Meissner, Nucl. Phys. B357 (1991) 90

View on Pith 1991

[24] [24]

J. Bijnens, G. Colangelo and P. Talavera, J. High Energy Phys. 0 5 (1998) 014

View on Pith 1998

[25] [25]

V. Bernard, N. Kaiser and U.-G. Meissner, Nucl. Phys. A615 (19 97) 483

View on Pith

[26] [26]

J. Gasser and H. Leutwyler, Phys. Reports 87C (1982) 77, se ction 10 and appendix C 62

View on Pith 1982

[27] [27]

J. Bijnens, G. Colangelo, G. Ecker, J. Gasser and M. E. Sainio, Phys. Lett. B374 (1996) 210, Nucl. Phys. B508 (1997) 263, B517 (1998) 639 (E)

View on Pith 1996

[28] [28]

L. Girlanda, M. Knecht, B. Moussallam and J. Stern, Phys. Lett . B409 (1997) 461

View on Pith 1997

[29] [29]

V. Bernard, N. Kaiser and U.-G. Meissner, Z. Phys. C60 (1993) 111

View on Pith 1993

[30] [30]

E. Jenkins and A. V. Manohar, Phys. Lett. B259 (1991) 353 E. Jenkins and A. V. Manohar, in Eﬀective Theories of the Standard Model, ed. U.-G. Meissner, (World Scientiﬁc, Singapore, 1991)

View on Pith 1991

[31] [31]

J. Kambor, in Proc. Baryons ’95 , eds. B. F. Gibson et al., (World Sci- entiﬁc, Singapore, 1996) T. R. Hemmert, B. R. Holstein and J. Kambor, Phys. Lett. B395 (19 97) 89, Phys. Rev. D55 (1997) 5598, J. Phys. G24 (1998) 1831 G. C. Gellas, T. R. Hemmert, C. N. Ktorides and G. I. Poulis, The Delta nucleon transition form-factors in chiral perturbat ion theor...

View on Pith 1997

[32] [32]

J. Kambor, in Proc. Workshop on Chiral Dynamics: Theory and Ex- periment, Mainz, Germany (1997), eds. A. Bernstein, D. Drechsel, T. Walcher, Lecture Notes in Physics, Vol. 513, Springer-Verlag, 1 998

View on Pith 1997

[33] [33]

E. M. Henley and W. Thirring, Elementary quantum ﬁeld theory , McGraw-Hill Book Company Inc., New York (1962)

View on Pith 1962

[34] [34]

J. F. Donoghue and B. R. Holstein, Improving the convergence of SU(3) baryon chiral perturbation theory , hep-ph/9803312 J. F. Donoghue, B. R. Holstein and B. Borasoy, SU(3) baryon chiral perturbation theory and long distance regularization , hep-ph/9804281

View on Pith Pith review arXiv

[35] [35]

B. Borasoy, Sigma terms in heavy baryon chiral perturbation theory re- visited, hep-ph/9807453

View on Pith Pith review arXiv

[36] [36]

U.-G. Meissner, G. Mueller and S. Steininger, Renormalization of the chiral pion-nucleon Lagrangian beyond next-to-leading or der, hep-ph/9809446

View on Pith Pith review arXiv

[37] [37]

P. F. A. Goudsmit, H. J. Leisi, E. Matsinos, B. L. Birbrair and A. B. Gridnev, Nucl. Phys. A575 (1994) 673 63 H. J. Leisi, Experimental results in πN scattering: QCD symmetry tests , in Proc. of the Zuoz Summer School on Hidden symmetries and Higgs phenomena, Zuoz (Engadin, Switzerland, 1998), Paul-Scherrer- Institut, CH-5232 Villigen, Switzerland E. Mats...

View on Pith Pith review arXiv 1994

[38] [38]

V. Bernard, N. Kaiser and U.-G. Meissner, Nucl. Phys. B457 (19 95) 147

View on Pith

[39] [39]

G. Sommer, Fortschr. Phys. 18 (1970) 577

View on Pith 1970

[40] [40]

L. S. Brown,, W. J. Pardee and R. D. Peccei, Phys. Rev. D4 (197 1) 2801

View on Pith

[41] [41]

A. Roessl, πK scattering near the threshold in chiral SU(2) perturbation theory, PhD Thesis, University of Bern, in preparation

View on Pith

[42] [42]

J. Bijnens, P. Gosdzinsky and P. Talavera, Nucl. Phys. B501 (1 997) 495, Phys. Lett. B429 (1998) 111 64

View on Pith 1998