Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry

Dominik St\"ockinger

REVIEW

Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry

Dominik Stöckinger

High Energy Physics - Phenomenology · Submitted 14 Mar 2005 · 25 references

Pith's verdict: A careful, honest attempt to put DRED on a firm footing; the construction is checkable and the QAP transfer is justified, with the gamma-counting rules the main place where detail is thin.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 4 major objections · 6 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/0503129 (version 3)

Pith IDUNTE7UQ2, Pith's permanent record of this paper and its review

CitationDominik St\"ockinger. "Regularization by Dimensional Reduction: Consistency, Quantum Action Principle, and Supersymmetry." arXiv:hep-ph/0503129 (2005). https://pith.science/paper/UNTE7UQ2

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The thing to know: this paper does two things that had not been done. Appendix A gives an explicit construction of the quasi-4-dimensional space Q4S as a direct sum of a formally D-dimensional and a formally epsilon-dimensional infinite-dimensional space, with gamma matrices, gamma-5, and charge conjugation all written down and checked against the algebraic relations (2.3)-(2.11). That is the first actual construction of the object Avdeev-Chochia-Vladimirov only postulated. Second, it establishes the quantum action principle for DRED, which turns the question 'does DRED preserve supersymmetry' into 'does the insertion of S(Gamma_cl) vanish in this particular Green function' — a much easier question. The phi-4 Slavnov-Taylor identity check in Section 4.3 is genuinely new and the propagator and transformation identities are pushed to two loops with a clean argument. That is real value for anyone doing SUSY loop calculations, and it is the kind of tool the SPA community needed. The stress-test note is right that the QAP transfer is not a correctness gap: eq. (3.10) follows from the Dirac propagator being the exact inverse of the kinetic operator in Q4S, which needs only the anticommutation relation and p_mu p_nu g^{mu nu} = p^2, both of which hold by construction. The combinatorial part is regularization-independent. So the reader's worry here is a presentation issue, and I would say so plainly. Where the paper is genuinely thin is the gamma-counting rules (4.10): the specific thresholds (4, 2, 3 gamma matrices for topologies a, b, c) are stated as 'explicitly checked' rather than derived, and the diagrammatic arguments in 4.3 are sketched. Example (4.11) shows the method works, and the conclusions are checkable by hand, so this is a detail-level concern, not a load-bearing flaw. The gamma-5 discussion is honest and the authors flag the axial-anomaly limitation themselves; I would not count that against them. Citation pattern is fine: the self-citations to Hollik-Kraus-Stoeckinger supply conventions and prior one-loop checks, which is legitimate. Who should read it: anyone using DRED for SUSY loops, and anyone who has ever wondered whether the scheme is actually consistent. It deserves a serious referee — the construction is checkable algebra and the QAP claim is the kind of thing a referee should verify line by line, but the paper is worth that time.

Referee report

Significance

If correct, the result puts the most widely used regularization for supersymmetric loop calculations on a firm mathematical footing and supplies a general, elegant tool for testing supersymmetry preservation: the quantum action principle reduces a check of a Slavnov–Taylor identity to a question of whether a specific insertion vanishes, which is typically far simpler than evaluating the full Green functions. The explicit construction in Appendix A is a genuine strength — the algebraic relations (2.3)–(2.11) and the representations (A.3)–(A.5) are checkable, and the trace definition (A.8) is concrete. The φ4 identity (4.8) has not previously been considered in the literature, and the gamma-counting rules, if derived, would give a practical diagnostic for when DRED can be expected to preserve supersymmetry. The paper is also candid about the residual γ5 problem, which it acknowledges in the conclusions rather than obscuring.

Major objections (4)

[§3, Eq. (3.10) and the transfer from Ref. [18]] The quantum action principle is the paper's central claim, but the proof in Section 3 is a sketch that defers to the DREG proof of Breitenlohner–Maison [18] with the statement 'the same proof is also valid in DRED without changes.' The DRED-specific ingredients that this transfer requires should be made explicit rather than asserted. In particular: (i) the ε-scalar sector — the QεS components of the gauge field propagate and appear in both L0 and Lint, and it should be shown that the cancellation between the δL0 and δLint terms of Eq. (3.9) goes through with the ε-scalar kinetic terms included; (ii) the trace definition (A.8) with its lim_{N→∞} prescription — the QAP must be compatible with this trace, especially for diagrams containing γ5; (iii) the vanishing of scaleless integrals in the Q4S setting, which the paper invokes but does not verify against the two-space structure. Since the abstract claims the QAP 'is shown to hold,' a paragraph identifying which steps of [18] are regularization-independent and which need re-verification in Q4S would substantially strengthen the central claim.
[§2 and Appendix A, Eqs. (A.1) and (A.8)] The paper states that the explicit construction 'guarantees that all calculational rules are consistent and that all calculations lead to unambiguous and well-defined results.' Uniqueness of results, however, requires more than the existence of the objects: it requires that the trace (A.8) and the momentum integral (A.1) are compatible, i.e. that Tr and ∫ commute and that Tr(γ^μ γ^ν) = 4 g^{μν} holds with the same g^{μν} that appears in the propagator. This compatibility is used throughout Section 4 but is not stated or checked in Appendix A. A short demonstration — for example that the trace of a product of gamma matrices factorizes through the loop integral — would close the gap between 'the objects exist' and 'the results are unambiguous.'
[§4.2, Eq. (4.4)] The breaking terms S(Γcl) are presented as 'we obtain' without derivation, yet the whole of Section 4 rests on this list. The reader needs either an appendix with the derivation or, at minimum, a check that each term in (4.4b)–(4.4h) vanishes in four dimensions via Fierz rearrangement and that the list is complete for the stated field content. The statement Δfix = 0 in (4.4c) is particularly in need of justification: the gauge-fixing and ghost sector normally contributes to the Slavnov–Taylor identity, and the paper should show explicitly that its contribution to S(Γcl) is Fierz-reducible. If Δfix were nonzero, the conclusions of Section 4.3 could change, so this is a correctness-risk concern rather than a presentational one.
[§4.3, Eqs. (4.10)] The gamma-counting rules — that the expressions (4.10) vanish only if B contains no more than 4, 2, or 3 gamma matrices in cases (a), (b), (c) respectively — are stated as something that 'can be explicitly checked' but are not derived. Since the one- and two-loop conclusions for all three identities rest on these counts, the paper should either derive them (for example by giving the general reduction identities for γ^μ B γ^μ as a function of the number of gamma matrices in B) or provide a table of the relevant cases. In addition, the argument that after loop integration B contains at most three gamma matrices should address whether ε-scalar contributions and g̃^{μν} contractions can generate additional gamma-matrix structures beyond the external covariants /p_i; the example (4.11) illustrates the method but does not settle this question.

Minor objections (6)

[§2, Eq. (2.10a)] The two expressions for the charge-conjugated spinor, ψ^C = −iγ^0 C ψ* and ψ^C_1 = −iψ^T C, are not obviously consistent in notation; the role of γ^0 in the first and its absence in the second should be reconciled or explained.
[§4.3, Eq. (4.7)] The '2/p + ...' in Eq. (4.7) leaves the reader unable to tell what is omitted; the ellipsis should be replaced by an explicit statement of the class of omitted terms and why they do not affect the argument.
[§4.1] The review of previous checks is useful, but the citation to [20] should specify which Ward identities were checked and at which loop order, so that the reader can judge what the present paper adds beyond the earlier work.
[Appendix A, Eq. (A.4)] The hermiticity property (2.5) should be verified explicitly for the ε-sector gamma matrices γ̃^μ defined in (A.4), since the construction of the QεS sector is the novel part of the representation and its Dirac-algebra properties are used throughout.
[§2, Eq. (2.3a)] The notation g^{μν} versus g_{μν} is used somewhat loosely in Eqs. (2.3) and (2.7); a consistent convention for raised and lowered indices in Q4S would help the reader follow the contractions.
[General] There are several typographical issues, including 'v anish' in the discussion following Eq. (4.10) and inconsistent spacing in 'D ij' in Eq. (3.10); a careful proofreading pass is warranted.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Dimensional reduction, the regularization most loop calculations in supersymmetric theories rely on, is given an explicit consistent construction, and the quantum action principle is shown to hold in it.

The reading

Dimensional reduction is the regularization scheme most loop calculations in supersymmetric theories use, because the rival scheme, ordinary dimensional regularization, visibly breaks supersymmetry by giving gauge bosons and their partners different numbers of degrees of freedom. But dimensional reduction was known to be internally contradictory: combining genuinely four-dimensional gamma matrices and epsilon tensors with a $D$-dimensional metric forces the relation $0 = D(D-1)(D-2)(D-3)(D-4)$, which no non-integer $D$ satisfies. This paper's aim is to remove that contradiction by construction rather than by convention. The author builds the four-dimensional space as a direct sum of an infinite-dimensional formally $D$-dimensional space and an infinite-dimensional formally $(4-D)$-dimensional one, defines all the objects a Feynman calculation needs inside it, and then argues that the quantum action principle — the statement that a symmetry variation of a Green function equals the insertion of the variation of the Lagrangian — survives the construction. If that holds, one gains a general, all-orders bookkeeping device for asking exactly where dimensional reduction does and does not preserve supersymmetry, instead of checking identities one diagram at a time.

What carries the argument

The quasi-four-dimensional space $Q_4S$, built as the direct sum of a formally $D$-dimensional and a formally $(4-D)$-dimensional infinite-dimensional space, with metric tensors satisfying $g^{mn} = g^{mn} + g^{mn}$, $g^{mn}g_{mn} = D$, $g^{mn}g_{mn} = 4-D$, and $g^{mn}g_{mn} = 0$. It is what allows the $D$-dimensional momentum space to sit inside the four-dimensional one, so that $p p = p^2$ and the Dirac propagator $(p+m)/(p^2-m^2)$ really inverts $(p-m)$ — the property the whole consistency argument rests on. On top of it, the quantum action principle converts a statement about symmetry breaking into a statement about inserting a specific operator into 1PI Green functions, and the paper reduces the question of whether a given Slavnov-Taylor identity holds to counting how many gamma matrices can survive in the closed fermion line of the relevant diagrams.

Extended reading notes

Core claim

The paper makes two claims and then uses the second to do physics. First, dimensional reduction can be given a mathematically consistent formulation: the space in which the four-dimensional objects live is not four-dimensional but a quasi-four-dimensional space $Q_4S = Q_DS + Q_4S$, the direct sum of two infinite-dimensional spaces carrying metric tensors $g^{mn}$ and $g^{mn}$ with $g^{mn}g_{mn} = D$ and $g^{mn}g_{mn} = 4-D$. Appendix A gives explicit gamma matrices, an anticommuting $g_5$, a charge conjugation matrix, and a trace definition in this space, so that index counting fails (five Lorentz indices can all be different) while the Dirac algebra, hermiticity, and the usual charge-conjugation rearrangements still hold. The practical cost is that Fierz identities are not available. Second, in this formulation the quantum action principle holds at all orders: $i d <T f_1...f_n> = <T f_1...f_n D>$, where $D$ is the integrated variation of the Lagrangian. The proof is the one known for dimensional regularization, and it turns on two facts that the construction preserves: the free propagator is genuinely the inverse of the kinetic operator, $D_ij P_jk = i d_ik$, and scaleless integrals vanish. Applied to the Slavnov-Taylor identity of a general supersymmetric gauge theory, this yields a master equation $S(G_DRED) = i[S(G_cl)] · G_DRED$, and the author evaluates $S(G_cl)$ explicitly: it is a sum of four-fermion operators, all of which vanish in strictly four dimensions where Fierz rearrangements are allowed, and none of which vanish identically in the quasi-four-dimensional space.

Load-bearing premise

The proof that the quantum action principle holds in dimensional regularization is taken over to the new space without being re-derived step by step; that transfer needs the free propagator to remain the exact inverse of the kinetic operator inside the infinite-dimensional construction.

Editorial extensions

If this is right

Dimensional reduction can be used without the internal contradiction that made it hard to prove general statements about it; the calculational rules of Section 2 are self-consistent, with the single exception that Fierz identities may not be used.
The supersymmetry Slavnov-Taylor identity relating the scalar and fermion propagators of a chiral multiplet holds in dimensional reduction up to the two-loop level, because the closed fermion line in the relevant diagrams can carry at most three gamma matrices.
The identity governing the loop-corrected supersymmetry transformations of the scalar and fermion holds up to two loops by the same counting argument.
The Slavnov-Taylor identity that fixes the quartic scalar coupling in terms of gauge and superpotential couplings — the relation behind the tree-level Higgs mass bound — holds at one loop in dimensional reduction, a case not previously checked.
If a totally anticommuting $g_5$ is used, the breaking terms are purely four-fermion operators; if instead a strictly four-dimensional $g_5$ is used, even the simplest one-loop propagator identities fail, just as in dimensional regularization.
The counting rules indicate where violations could first appear at higher orders, so supersymmetry-restoring counterterms, if needed, would be needed only in a much narrower class of diagrams than in dimensional regularization.

Reading between the lines

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

The paper's counting criterion — how many gamma matrices can survive in the closed fermion loop after loop-momentum integration — is a practical diagnostic that could be applied diagram-by-diagram in real calculations to decide in advance whether a given Green function is safe in dimensional reduction.
Because the construction replaces four-dimensional index counting with an infinite-dimensional space, any calculation that silently relies on identities valid only for a finite number of dimensions (Fierz being the named example) becomes suspect; this suggests auditing existing dimensional-reduction results for hidden Fierz use rather than re-deriving them wholesale.
The same master-equation technique should transfer to other symmetries with equal ease, since the machinery only needs the classical action and the variation of the Lagrangian; gauge and translational Ward identities are the obvious next targets.
The explicit two-loop violation channel the author flags for the quartic-coupling identity — an exchanged vector boson supplying an extra covariant to the fermion line — is concrete enough to be checked directly, and would be the natural first place to look for a genuine breakdown.

Original abstract

It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and elegant relation between the D-dimensional Lagrangian and Ward or Slavnov-Taylor identities, and it can be used in particular to study to what extent dimensional reduction preserves supersymmetry. We give several examples of previously unchecked cases.

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, 3,525 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.20 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and elegant relation between the D-dimensional Lagrangian and Ward or Slavnov-Taylor identities, and it can be used in particular to study to what extent dimensional reduction preserves supersymmetry. We give several examples of previously unchecked cases.

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	It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way.	result 0.95	0.88	0.78	asserted 1.00
s1	In this formulation the quantum action principle is shown to hold.	result 0.99	0.91	0.14	asserted 1.00
s2	This provides an intuitive and elegant relation between the D-dimensional Lagrangian and Ward or Slavnov-Taylor identities, and it can be used in particular to study to what extent dimensional reduction preserves supersymmetry.	interpretation 0.95	0.77	0.20	asserted 0.70
s3	We give several examples of previously unchecked cases.	contribution 0.93	0.90	0.03	asserted 0.91

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

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.** Basic topologies of diagrams involving an insertion of S(Γcl), eq. (4.4). Only fermion lines are drawn; additional boson lines have to be attached in the actual diagrams. The index f of Topology (cf ) corresponds to the fermion f = ˜g, ψ appearing in the loop. In the text, the γ-string attached to the second external fermion line is denoted as A, the γ-string attached to the closed fermion loop as B. ǫ¯ ψ g˜,ψ ψ φ † φ † φ

**Figure 2.** One-loop diagram corresponding to ([S(Γcl)] · Γ DRED)φ†φ†φψǫ¯ . with the three independent external momenta of the diagram. Hence after suitable simplifications B cannot contain more than three γ-matrices, and this is not enough to lead to a non-vanishing contribution. This shows that identity (4.8) is valid in DRED at the one-loop level. By the same token, however, it is possible that (4.8) is violated at the two-loop level where e.g. the exchange of an additional vector boson can lead to more covariants within B. Secondly we turn to identity (4.6) relating the φ and ψ propagators.…

**Figure 3.** A two-loop diagram corresponding to ([S(Γcl)] · Γ DRED)φ†ψǫ¯ . Such two-loop diagrams involving a virtual vector boson are the only ones where the γ-string B can contain three γ-matrices after integration over the fermion loop momentum. ǫ¯ ǫ g˜ g˜ φ † φ Yφ c ǫ¯ ǫ g˜ ψ φ † φ Yφ c ǫ¯ ǫ ψ g˜ g˜,ψ φ † φ Yφ c

**Figure 4.** Two-loop diagrams corresponding to ([S(Γcl)] · Γ DRED)φǫǫY¯ φ . momentum, and γ µ if A and B are connected by a vector boson as in

Figures reproduced from arXiv:hep-ph/0503129 by the authors.

References

Works cited (25)

[18]

P. Breitenlohner and D. Maison, Commun. Math. Phys. 52 (1977) 11

View on Pith 1977
[1]

G. ’t Hooft and M. Veltman, Nucl. Phys. B 44 (1972) 189

View on Pith 1972
[2]

W. Siegel, Phys. Lett. B 84 (1979) 193

View on Pith 1979
[3]

W. Beenakker, R. H¨ opker and P. M. Zerwas, Phys. Lett. B 378 (1996) 159 [arXiv:hep-ph/9602378]

View on Pith Pith review arXiv 1996
[4]

W. Hollik, E. Kraus and D. St¨ ockinger, Eur. Phys. J. C 11 (1999) 365 [arXiv:hep-ph/9907393]; W. Hollik and D. St¨ ockinger,Eur. Phys. J. C 20 (2001) 105 [arXiv:hep-ph/0103009]; I. Fischer, W. Hollik, M. Roth and D. St¨ ockinger, Phys. Rev. D 69 (2004) 015004 [arXiv:hep-ph/0310191]

View on Pith Pith review arXiv 1999
[5]

P. L. White, Class. Quant. Grav. 9 (1992) 1663

View on Pith 1992
[6]

N. Maggiore, O. Piguet and S. Wolf, Nucl. Phys. B 458 (1996) 403 [Erratum-ibid. B 469 (1996) 513] [arXiv:hep-th/9507045], Nucl. Phys. B 476 (1996) 329 [arXiv:hep-th/9604002]. – 17 –

View on Pith Pith review arXiv 1996
[7]

W. Hollik, E. Kraus and D. St¨ ockinger, Eur. Phys. J. C 23 (2002) 735 [arXiv:hep-ph/0007134]; W. Hollik, E. Kraus, M. Roth, C. Rupp, K. Sibold and D. St¨ ocki nger, Nucl. Phys. B 639 (2002) 3 [arXiv:hep-ph/0204350]

View on Pith Pith review arXiv 2002
[8]

W. Siegel, Phys. Lett. B 94 (1980) 37

View on Pith 1980
[9]

S. Heinemeyer, W. Hollik and G. Weiglein, arXiv:hep-ph/ 0412214

View on Pith
[10]

P. M. Zerwas, Talk given at the ECF A ”Physics and Detectors for a Linear Collider” Workshop, Durham 1 - 4 September 2004; http://www.ippp.dur.ac.uk/ECFA04/program.html

View on Pith 2004
[11]

W. Beenakker, H. Kuijf, W. L. van Neerven and J. Smith, Phys. Rev. D 40 (1989) 54

View on Pith 1989
[12]

J. Smith and W. L. van Neerven, arXiv:hep-ph/0411357

View on Pith Pith review arXiv
[13]

I. Jack, D. R. T. Jones and A. F. Kord, Phys. Lett. B 579 , 180 (2004) [arXiv:hep-ph/0308231]

View on Pith Pith review arXiv 2004
[14]

I. Jack and D. R. T. Jones, “Regularisation of supersymm etric theories”, in Kane, G.L. (ed.): Perspectives on supersymmetry 149-167; [arXiv:hep-ph/9707278]

View on Pith Pith review arXiv
[15]

L. V. Avdeev, G. A. Chochia and A. A. Vladimirov, Phys. Lett. B 105 (1981) 272; L. V. Avdeev and A. A. Vladimirov, Nucl. Phys. B 219 (1983) 262

View on Pith 1981
[16]

K. G. Wilson, Phys. Rev. D 7 (1973) 2911

View on Pith 1973
[17]

J. Collins, “Renormalization ”, Cambridge Monographs on Mathematical Physics

View on Pith
[19]

J. H. Lowenstein, Phys. Rev. D 4 (1971) 2281, Commun. Math. Phys. 24 (1971) 1; Y. M. Lam, Phys. Rev. D 6 (1972) 2145; Phys. Rev. D 7 (1973) 2943

View on Pith 1971
[20]

D. M. Capper, D. R. T. Jones and P. van Nieuwenhuizen, Nucl. Phys. B 167 (1980) 479

View on Pith 1980
[21]

P. Breitenlohner and D. Maison, “Renormalization Of Su persymmetric Yang-Mills Theories,” in Cambridge 1985, Proceedings, Supersymmetry and Its Applicat ions, 309-327

View on Pith 1985
[22]

S. P. Martin and M. T. Vaughn, Phys. Lett. B 318 (1993) 331 [arXiv:hep-ph/9308222]; I. Jack, D. R. T. Jones and C. G. North, Nucl. Phys. B 473 (1996) 308 [arXiv:hep-ph/9603386], Phys. Lett. B 386 (1996) 138 [arXiv:hep-ph/9606323], Nucl. Phys. B 486 (1997) 479 [arXiv:hep-ph/9609325]. – 18 –

View on Pith Pith review arXiv 1993
[23]

C. Rupp, R. Scharf and K. Sibold, Nucl. Phys. B 612 (2001) 313 [arXiv:hep-th/0101165], [arXiv:hep-th/0101153]

View on Pith Pith review arXiv 2001
[24]

S. Heinemeyer, D. St¨ ockinger and G. Weiglein, Nucl. Phys. B 699 (2004) 103 [arXiv:hep-ph/0405255]. D. St¨ ockinger,Nucl. Phys. Proc. Suppl. 135 (2004) 311 [arXiv:hep-ph/0406306]

View on Pith Pith review arXiv 2004
[25]

S. A. Larin, Phys. Lett. B 303 (1993) 113 [arXiv:hep-ph/9302240]; T. L. Trueman, Z. Phys. C 69 (1996) 525 [arXiv:hep-ph/9504315]. – 19 –

View on Pith Pith review arXiv 1993

Forward citations

Cited by 12 Pith papers

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

Bare effective potential and Goldstone boson anti-resummation
hep-ph 2026-08 conditional novelty 7.0 of 10

Treating Goldstone-boson squared masses as interaction vertices instead of propagator masses eliminates spurious infrared logarithms and imaginary parts, giving a consistent three-loop tadpole-free effective potential...
Completing the scalar and fermionic Universal One-Loop Effective Action
hep-ph 2019-08 conditional novelty 7.0 of 10

A complete set of generic one-loop Wilson coefficients for scalar and fermion loops up to dimension six, excluding open covariant derivatives, is derived and validated on MSSM examples.
Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order
hep-ph 2006-03 conditional novelty 7.0 of 10

The paper presents the first complete NNLO QCD calculation of the charm quark contribution to K+ -> pi+ nu nu-bar, reducing the theoretical error in Pc(X) from 9.8% to 2.4%, with Pc(X)=0.38±0.04 and BR(K+ -> pi+ nu nu...
Chiral Symmetries in the Standard Model of Particle Physics and its Extensions
hep-ph 2026-10 conditional novelty 6.0 of 10

The thesis derives one-loop finite counterterms for SMEFT four-fermion operators in the BMHV scheme and obtains parameter-independent lower bounds on W_R and Z_R masses from LHC data.
Light Neutral Higgs-Boson Production at $e^+e^-$ Colliders in the Complex MSSM and NMSSM: A Full One-Loop Analysis
hep-ph 2025-07 conditional novelty 6.0 of 10

First full one-loop computation of e+e- -> h1 Z in the cNMSSM: corrections near -10%, nearly identical to the MSSM once the light Higgs mass is fixed.

Show 7 more citing papers

A prescription for projectors to compute helicity amplitudes in D dimensions
hep-ph 2019-04 accept novelty 6.0 of 10

A momentum-basis prescription for D-dimensional helicity-amplitude projectors that avoids Lorentz tensor decomposition and is argued to yield the same finite remainders as CDR.
Precise prediction for the Higgs-Boson Masses in the $\mu\nu$SSM
hep-ph 2017-12 conditional novelty 6.0 of 10

A complete one-loop renormalization of the mu-nu SSM neutral scalar sector shows its SM-like Higgs mass prediction agrees with the NMSSM to within a few keV, and the model can host a 96 GeV scalar matching LEP and CMS...
The Higgs Boson Masses and Mixings of the Complex MSSM in the Feynman-Diagrammatic Approach
hep-ph 2006-11 accept novelty 6.0 of 10

The complete one-loop Feynman-diagrammatic corrections to Higgs boson masses and mixings in the complex MSSM are computed with all phases and imaginary parts retained, and released in FeynHiggs 2.5.
Four-loop beta function in N=2 supersymmetric Yang-Mills theory, dimensional reduction, and treatment of $\gamma_5$
hep-th 2026-09 conditional novelty 5.0 of 10

At four loops the naive gamma-5 scheme yields a spurious beta-function term in N=2 SYM theory, while the reading-point scheme restores the exact vanishing beyond one loop.
Integrated dipoles with MadDipole in the MadGraph framework
hep-ph 2010-04 conditional novelty 5.0 of 10

The authors implement the analytic integration of dipole subtraction terms in the MadGraph/MadDipole framework, so the real-emission side of an NLO QCD calculation for an arbitrary process can be generated automatically.
To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
hep-ph 2017-05 accept novelty 3.0 of 10

The paper reviews and compares dimensional and four-dimensional regularization schemes, showing through explicit NLO calculations that they yield the same physical cross section while differing in intermediate bookkeeping.
A Supersymmetry Primer
hep-ph 1997-09 accept novelty 1.0 of 10

A self-contained pedagogical introduction to supersymmetry and the MSSM, from Lagrangian construction through soft breaking to collider phenomenology.

How later papers used it

62 later papers cite it

Evidence: some. 55 of the citing papers share no author with it, and 16 of those carry a confident label from Pith's citation classifier.

Pith read 8 of the 90 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 10 papers with this label

Chose to work in the dimensional reduction scheme of this paper, which preserves supersymmetry.

CP violation at one loop in the polarization-independent chargino production in e+e- collisions (2007) · 0.84 · paraphrased: the licence does not allow quoting
Used dimensional reduction, which preserves supersymmetry, to regularize one-loop integrals, citing this paper.

One-loop corrections to three-body leptonic chargino decays (2007) · 0.94 · paraphrased: the licence does not allow quoting

How the literature uses it

56 arXiv papers cite this in 74 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 · 56 sentences without a confident label

Contests it 1 paper

We note that there are inconsistencies in Siegel's RDR scheme which have been pointed out by several authors including Siegel himself [ref] .

${\cal N}=4$ supersymmetric Yang-Mills thermodynamics to order $\lambda^2$ · Introduction · contest 0.81

Builds on it 1 paper

Beyond the extensions shown in Table [ref], we also supplement the operators provided in Refs. [ref] by a set of operators that are needed when matching a UV model regularised using dimensional reduction (), as introduced in Refs. [ref] , to an EFT regularised using dimensional regularisation (), introduced in Ref. [ref] .

One Formula To Match Them All: The Bispinor Universal One-Loop Effective Action · Introduction · 0.88

Uses its method or tool 8 papers

These diagrams are regulated dimensionally in $D=4-2ε$ dimensions within the supersymmetry preserving four-dimensional helicity scheme [ref] so that UV and IR divergences appear as poles of the form $ε^-1$ and $ε^-2$.

Radiative corrections to stop-antistop annihilation into gluons and light quarks · Virtual corrections and renormalization · 1.00
As regularization scheme we have used constrained differential regularization [ref] , which has been shown to be equivalent to dimensional reduction [ref] at the level [ref] , thus preserving supersymmetry [ref] .

The Charged Higgs Boson Mass of the MSSM in the Feynman-Diagrammatic Approach · One-loop corrections · 0.93
The loop integrals are regularised via dimensional reduction [ref] , which ensures that SUSY is preserved, via the implementation described in Refs. [ref] .

Consistent on shell renormalisation of electroweakinos in the complex MSSM: LHC and LC predictions · NLO predictions at the LHC and the LC · 1.00

Cites it as support 3 papers

It is also a convenient choice regarding the non-breaking of supersymmetry [ref] .

$\gamma_{5}$ in FDH · FDH and DRED · 0.96
However, it has been shown [ref] that such inconsistencies become active only in the higher orders of perturbation theory, when, for example, traces over at least ten $γ$-matrices and anti-symmetrization over five indices are involved.

Precision Calculations in Supersymmetric Theories · Framework · 0.96
Thus the employed regularization scheme preserves SUSY [ref] and guarantees that the SUSY relations are kept intact, that the gauge couplings of the SM vertices and the Yukawa couplings of the corresponding SUSY vertices also coincide to order in the SUSY limit.

Chargino and Neutralino Production at e+e- Colliders in the Complex MSSM: A Full One-Loop Analysis · Ultraviolet, infrared and collinear divergences · 0.97

Cites it as background 4 papers

This quasi-$4$-dimensional space is decomposed as $Q4S=QdS⊕QϵS$, where $QdS$ is an infinite dimensional space that is formally $d$-dimensional and $QϵS$ is its complement, formally of dimension $ϵ=4-d$ [ref] .

Extending the Universal One-Loop Effective Action by Regularization Scheme Translating Operators · Epsilon scalars in dimensional reduction · 0.92
The problem has been known since a long time [ref] , yet the precision required to confront with experiments in order to assess evidence of indirect signals of new Beyond-the-Standard-Model (BSM) physics calls for the development of efficient tools in order to ensure the fulfillment of the relevant symmetries of the model and consequently the consistency of the inserted finite counter-terms.

Gauge-Invariant Quantum Fields · Introduction · 0.81
Among them are the Conventional Dimensional Regularisation (CDR, introduced in [ref]), the `t Hooft and Veltman (HV) scheme [ref] , the Four-Dimensional Helicity scheme (FDH) [ref] and Dimensional Reduction (DRED) [ref] .

Four-dimensional representation of scattering amplitudes and physical observables through the application of the Loop-Tree Duality theorem · A brief review of other regularisation methods · 0.99

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] [18]

P. Breitenlohner and D. Maison, Commun. Math. Phys. 52 (1977) 11

View on Pith 1977

[2] [1]

G. ’t Hooft and M. Veltman, Nucl. Phys. B 44 (1972) 189

View on Pith 1972

[3] [2]

W. Siegel, Phys. Lett. B 84 (1979) 193

View on Pith 1979

[4] [3]

W. Beenakker, R. H¨ opker and P. M. Zerwas, Phys. Lett. B 378 (1996) 159 [arXiv:hep-ph/9602378]

View on Pith Pith review arXiv 1996

[5] [4]

W. Hollik, E. Kraus and D. St¨ ockinger, Eur. Phys. J. C 11 (1999) 365 [arXiv:hep-ph/9907393]; W. Hollik and D. St¨ ockinger,Eur. Phys. J. C 20 (2001) 105 [arXiv:hep-ph/0103009]; I. Fischer, W. Hollik, M. Roth and D. St¨ ockinger, Phys. Rev. D 69 (2004) 015004 [arXiv:hep-ph/0310191]

View on Pith Pith review arXiv 1999

[6] [5]

P. L. White, Class. Quant. Grav. 9 (1992) 1663

View on Pith 1992

[7] [6]

N. Maggiore, O. Piguet and S. Wolf, Nucl. Phys. B 458 (1996) 403 [Erratum-ibid. B 469 (1996) 513] [arXiv:hep-th/9507045], Nucl. Phys. B 476 (1996) 329 [arXiv:hep-th/9604002]. – 17 –

View on Pith Pith review arXiv 1996

[8] [7]

W. Hollik, E. Kraus and D. St¨ ockinger, Eur. Phys. J. C 23 (2002) 735 [arXiv:hep-ph/0007134]; W. Hollik, E. Kraus, M. Roth, C. Rupp, K. Sibold and D. St¨ ocki nger, Nucl. Phys. B 639 (2002) 3 [arXiv:hep-ph/0204350]

View on Pith Pith review arXiv 2002

[9] [8]

W. Siegel, Phys. Lett. B 94 (1980) 37

View on Pith 1980

[10] [9]

S. Heinemeyer, W. Hollik and G. Weiglein, arXiv:hep-ph/ 0412214

View on Pith

[11] [10]

P. M. Zerwas, Talk given at the ECF A ”Physics and Detectors for a Linear Collider” Workshop, Durham 1 - 4 September 2004; http://www.ippp.dur.ac.uk/ECFA04/program.html

View on Pith 2004

[12] [11]

W. Beenakker, H. Kuijf, W. L. van Neerven and J. Smith, Phys. Rev. D 40 (1989) 54

View on Pith 1989

[13] [12]

J. Smith and W. L. van Neerven, arXiv:hep-ph/0411357

View on Pith Pith review arXiv

[14] [13]

I. Jack, D. R. T. Jones and A. F. Kord, Phys. Lett. B 579 , 180 (2004) [arXiv:hep-ph/0308231]

View on Pith Pith review arXiv 2004

[15] [14]

I. Jack and D. R. T. Jones, “Regularisation of supersymm etric theories”, in Kane, G.L. (ed.): Perspectives on supersymmetry 149-167; [arXiv:hep-ph/9707278]

View on Pith Pith review arXiv

[16] [15]

L. V. Avdeev, G. A. Chochia and A. A. Vladimirov, Phys. Lett. B 105 (1981) 272; L. V. Avdeev and A. A. Vladimirov, Nucl. Phys. B 219 (1983) 262

View on Pith 1981

[17] [16]

K. G. Wilson, Phys. Rev. D 7 (1973) 2911

View on Pith 1973

[18] [17]

J. Collins, “Renormalization ”, Cambridge Monographs on Mathematical Physics

View on Pith

[19] [19]

J. H. Lowenstein, Phys. Rev. D 4 (1971) 2281, Commun. Math. Phys. 24 (1971) 1; Y. M. Lam, Phys. Rev. D 6 (1972) 2145; Phys. Rev. D 7 (1973) 2943

View on Pith 1971

[20] [20]

D. M. Capper, D. R. T. Jones and P. van Nieuwenhuizen, Nucl. Phys. B 167 (1980) 479

View on Pith 1980

[21] [21]

P. Breitenlohner and D. Maison, “Renormalization Of Su persymmetric Yang-Mills Theories,” in Cambridge 1985, Proceedings, Supersymmetry and Its Applicat ions, 309-327

View on Pith 1985

[22] [22]

S. P. Martin and M. T. Vaughn, Phys. Lett. B 318 (1993) 331 [arXiv:hep-ph/9308222]; I. Jack, D. R. T. Jones and C. G. North, Nucl. Phys. B 473 (1996) 308 [arXiv:hep-ph/9603386], Phys. Lett. B 386 (1996) 138 [arXiv:hep-ph/9606323], Nucl. Phys. B 486 (1997) 479 [arXiv:hep-ph/9609325]. – 18 –

View on Pith Pith review arXiv 1993

[23] [23]

C. Rupp, R. Scharf and K. Sibold, Nucl. Phys. B 612 (2001) 313 [arXiv:hep-th/0101165], [arXiv:hep-th/0101153]

View on Pith Pith review arXiv 2001

[24] [24]

S. Heinemeyer, D. St¨ ockinger and G. Weiglein, Nucl. Phys. B 699 (2004) 103 [arXiv:hep-ph/0405255]. D. St¨ ockinger,Nucl. Phys. Proc. Suppl. 135 (2004) 311 [arXiv:hep-ph/0406306]

View on Pith Pith review arXiv 2004

[25] [25]

S. A. Larin, Phys. Lett. B 303 (1993) 113 [arXiv:hep-ph/9302240]; T. L. Trueman, Z. Phys. C 69 (1996) 525 [arXiv:hep-ph/9504315]. – 19 –

View on Pith Pith review arXiv 1993