One-loop Effective Lagrangian for a Standard Model with a Heavy Charged Scalar Singlet

Arcadi Santamaria; Mikhail Bilenky

REVIEW

One-loop Effective Lagrangian for a Standard Model with a Heavy Charged Scalar Singlet

Mikhail Bilenky, Arcadi Santamaria

High Energy Physics - Phenomenology · Submitted 18 Oct 1993 · 82 references

Pith's verdict: A careful, auditable one-loop matching calculation for a toy singlet model; the methodology section is the part worth keeping, the phenomenology is thin.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 13, 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 · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9310302 (version 1)

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

CitationArcadi Santamaria, Mikhail Bilenky. "One-loop Effective Lagrangian for a Standard Model with a Heavy Charged Scalar Singlet." arXiv:hep-ph/9310302 (1993). https://pith.science/paper/MXMEBLPF

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

This one is worth your time mainly for the machinery, not the model. Bilenky and Santamaria take the Cheng-Li/Zee charged singlet, integrate it out at one loop, and write down a complete dimension-six effective Lagrangian with explicit coefficients (eq. 4.21) and explicit matching conditions (eqs. 5.1–5.5). The ingredients are borrowed — Ball's determinant expansion, 't Hooft's technique — but the assembly is theirs, and it is done with unusual care for the period. Appendix A gives the full Seeley-DeWitt coefficients, appendix B lists the off-shell amplitudes for self-energy, penguin, seagull and box diagrams, and appendix C does Z → e_a e_b in both theories. You can check the arithmetic, which is not something you can say about most papers in this genre. The section 5 point — that the effective theory alone fixes only the anomalous-dimension matrix, and the boundary conditions need either experiment or the full theory — is stated more cleanly here than in a lot of the surrounding literature, and it is still the right way to say it. The Z → e_a e_b comparison against the full amplitude in the small-w limit is a genuine internal check, not a hand-wave. On the stress-test note: it holds up, but it is a small gap, not a load-bearing one. The zero-momentum three-gauge-boson check does not probe the Abelian σ^{μν}B_{μν} dipole, so the μ → eγ coefficient rests on the explicit B-field calculation in (B.2) plus agreement with refs. [65–67]. That is a legitimate external cross-check, and the flagship Z result does not depend on it. Soft spots, in order of weight: eq. (5.5) is admittedly incomplete, with box contributions to the four-lepton matching left uncomputed — the authors say so; the phenomenology claim of abstract:s6 rests on one figure with flavour couplings set to 1 and no estimate of neglected 1/m⁴ terms; and footnote 6 asserts an error in Buchmüller-Wyler without showing the comparison, which is a minor irritation rather than a problem. Who should read it: anyone building a one-loop matching in a simple model, or wanting a worked example of why cut-off-based bounds on effective operators go wrong. Yes, send it out — the construction deserves referee time even though the model itself is a toy.

Referee report

Significance

This is a careful and unusually explicit worked example of one-loop matching in an effective field theory, written at a time when the renormalization of effective Lagrangians and the correct use of cutoffs were actively contested. Its lasting value is pedagogical and methodological: App. A gives the Seeley-DeWitt-type expansion with explicit coefficients (Eq. (A.27)), App. B lists off-shell amplitudes for all relevant topologies, and Sec. 5 states plainly that the effective theory alone yields only the anomalous-dimension matrix, with boundary conditions requiring either experiment or the full theory. The explicit full-versus-effective comparison for Z -> e_a e_b (Eqs. (C.2), (C.4), Fig. 7) is a genuine falsifiable check of the matching, and the operator-mixing discussion of Eqs. (5.9)-(5.16) anticipates later treatments. The paper is also honest about what it does not do, which is a strength.

Major objections (4)

[Sec. 4.2 and Sec. 7, Eq. (7.1)] The internal validation of the Abelian dipole operator is incomplete. The three-gauge-boson check described at the end of Sec. 4.2 is performed at zero external momentum with constant fields; for a constant Abelian B field F_{mu nu} = 0, so the sigma^{mu nu} B_{mu nu} term of Eq. (4.13) is not tested by that check, whereas the non-Abelian term is. The Z -> e_a e_b comparison of App. C tests the penguin combination of Eq. (4.12) (equivalently Eq. (6.27)), not the dipole operators of Eqs. (6.30)-(6.32). Consequently the photon dipole controlling mu -> e gamma in Eq. (7.1) rests on the explicit computation in Eq. (B.2) plus the external agreement with refs. [65-67], not on an internal full-versus-effective match. The external cross-check is legitimate and the B-field amplitude is computed explicitly, so this is a validation gap rather than an error; but the authors should say so explicitly in Sec. 7, and if feasible add a constant-background-field or nonzero-momentum check of the Abelian dipole coefficient.
[Sec. 5, Eq. (5.5) and Eqs. (5.7)-(5.12)] The matching of the four-lepton coupling is explicitly incomplete: Eq. (5.5) states that box-diagram contributions to the barred coupling f_ab have not been computed. This feeds directly into the mixing analysis, where Eq. (5.7) takes c_1(mu) = (f^dagger f)_12(mu)/m^2 with no one-loop correction and Eq. (5.12) sets the boundary condition c_1(m) = (f^dagger f)_12(m)/m^2. The authors acknowledge the omission, so the question is not whether it exists but whether its numerical impact on c_1(mu) and on the bounds discussed in Sec. 5 is under control. A short estimate of the neglected box contribution, or an argument that it is higher order in the relevant couplings, would close the gap.
[Sec. 4.4, Eqs. (4.19)-(4.21)] The paper notes that Fierz transformations used in Sec. 4 are valid only in four dimensions, and that starting from the alternative form of Eq. (4.19) would give different finite parts of the counterterms under dimensional regularization, while asserting that the two formulations are 'completely equivalent.' That equivalence is exactly the kind of scheme-dependence the paper criticizes elsewhere in the literature, so it deserves an explicit demonstration rather than an assertion. Showing, for instance, that the physical Z -> e_a e_b amplitude of Eq. (C.2) is unchanged if one starts from Eq. (4.19) would settle the point and strengthen the methodological message of Sec. 5.
[Sec. 6] The claim that using the equations of motion before or after spontaneous symmetry breaking gives the same physics is one of the paper's pedagogical points, but it is supported by a single explicit example: the penguin contribution, compared between Eq. (6.36) and Eqs. (6.26)-(6.27). One additional demonstration, for example for the four-fermion operator of Eq. (6.33) or for the dipole operators of Eqs. (6.30)-(6.32), would make the claim convincing rather than illustrative.

Minor objections (7)

[Eq. (4.6)] Please verify the matrix structure of the coupling redefinition. Redefining both lepton legs of the four-fermion operator of Eq. (3.11) generates the sum (f^dagger f f) + (f f^dagger f), and for antisymmetric f these two matrices are not obviously equal; the equation as written keeps only 2(f f^dagger f). A one-line clarification of the index structure would help.
[Eq. (3.14)] The constant 3/2 in the vacuum-energy term (m^4/2)(3/2 + Delta_epsilon) is quoted without derivation; a reference to the corresponding term in Eq. (A.27) or a brief remark would make the expression easier to check.
[Fig. 7 and its caption] The caption states that the couplings F_tau e are taken equal to 1, while the text of Sec. 7 refers to (f^dagger f)_ab = 1. Please make the normalization consistent between caption and text, and state explicitly which combination of couplings is being set to unity.
[Eq. (7.2)] The denominator 1 + (1 - 4 s_hat_W^2)^2 should be identified explicitly as the tree-level Standard Model Z -> e^+ e^- rate used for normalization, so that the branching-ratio definition is unambiguous.
[Sec. 2] The statement that total lepton number can be assigned as 1 to leptons and 2 to h, and that this forbids lepton-number-violating couplings, would benefit from one sentence making explicit which renormalizable couplings are forbidden by that assignment.
[Notation, Secs. 4-6] The paper uses barred couplings (bar g', bar f), hatted couplings (g-hat', s-hat_W), and the quantity Delta_epsilon with several constant offsets. A short table collecting these definitions at first use in Sec. 4 would reduce the burden on the reader.
[Sec. 6, Eq. (6.25)] The text states that Eq. (6.25) gives extra contributions to flavour-conserving neutral-current processes but does not indicate their expected size; a one-line estimate relative to the Standard Model would help the reader judge whether they are phenomenologically relevant.

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

The paper

The paper claims

The paper works out, end to end, how to replace a heavy charged scalar with a local effective Lagrangian and checks that the replacement reproduces the full theory at one loop.

The reading

The authors take the Standard Model, add a singly charged scalar singlet $h$ that couples only to the lepton doublet through an antisymmetric matrix $f$ in flavour space, and then ask what the theory looks like at energies far below the scalar's mass $m$. They integrate $h$ out at one loop and expand the result in $1/m^2$, keeping operators up to dimension six, so that all the heavy particle's effects are packaged in a local Lagrangian built from light fields alone. The point is not the model itself but the procedure: how to obtain such a Lagrangian, how to renormalize it, how to match its couplings to the full theory, and how to tell which of its operators can be bounded by experiment and which cannot. The reward is a concrete, fully calculable example in which every step of the effective-Lagrangian programme can be checked against an honest renormalizable calculation, including a side-by-side comparison of the flavour-changing decay $Z$ into two different charged leptons.

What carries the argument

Two devices carry the argument. The first is the functional determinant: writing the one-loop effective action as $S_{eff} = S_{SM} + S_h[h_0] + i,mathrm{Tr},log(O)$ with fluctuation operator $O = -D^2 - m^2 - beta phi^dagger phi$, and expanding $mathrm{Tr},log$ in $1/m^2$ using the constant-field trick of appendix A, which trades a general gauge configuration for a constant matrix $N_mu$ with $U = -N^2$ and then inverts the map back to the general case. This yields eq. (A.27), a compact basis of gauge-invariant traces that would be tedious to obtain diagram by diagram. The second device is propagator splitting, $1/(k^2 - m^2) = -1/m^2 + k^2/(m^2(k^2 - m^2))$: the first piece is exactly what the effective four-fermion vertex gives, and the second piece is exactly the counterterm the effective Lagrangian must supply. That identity is what makes matching systematic rather than a guess, and it is why the divergent parts of the higher-dimension operators are fixed by the effective theory's own loops while their finite parts can only come from the full theory.

Extended reading notes

Core claim

The paper's central claim is that the Lagrangian of eq. (4.20) — the Standard Model, plus the tree-level four-lepton operator $(1/m^2)(~ell f ell)(ell f^dagger ~ell)$ of eq. (3.11), plus the one-loop determinant contribution of eq. (3.15), plus the matching terms of eq. (4.21) — reproduces the full renormalizable theory for light external particles, at one loop and through order $1/m^2$. The construction is done in two complementary halves. Functional methods give, in closed gauge-invariant form, all operators generated by diagrams with only the heavy scalar in internal lines: the determinant of the fluctuation operator $-D^2 - m^2 - beta phi^dagger phi$ is expanded in $1/m^2$, yielding dimension-four pieces that are absorbed into redefinitions of the Standard Model mass, quartic coupling and $U(1)_Y$ coupling, and dimension-six pieces that survive. The remaining operators come from matching: the authors compute self-energies, penguin vertices, seagull diagrams and boxes in the full theory, subtract the corresponding effective-theory diagrams, and read off the local counterterms that make the two agree at low momentum. The payoff is a check on a real process: the full-theory amplitude for $Z to e_a e_b$ in eq. (C.4) and the effective-theory amplitude in eq. (C.2) coincide as $m gg M_Z$, and figure 7 shows the two branching ratios converging once the scalar is heavier than the $Z$.

Load-bearing premise

The operator basis is reconstructed from a small set of Green functions, and in one case — the term proportional to $p!!!/ p^2$ — the promotion of a derivative to a covariant derivative is ambiguous between three inequivalent forms, resolved only by computing extra diagrams with external gauge bosons and checking a three-gauge-boson amplitude at zero external momentum.

Editorial extensions

If this is right

Any process mediated by the heavy scalar at energies below its mass can be computed entirely within the effective theory, with the scalar's unknown mass and couplings entering only through the matching conditions of eqs. (5.1)–(5.5).
The effective couplings obey a renormalization-group equation controlled by an anomalous-dimension matrix; in the two-operator example of eqs. (5.9)–(5.10), the mixing of the four-lepton operator into the penguin operator is computable, but its boundary value is not.
Without knowledge of the full theory, a one-loop effective-Lagrangian calculation can relate an operator's coefficient at one scale to its value at another, but cannot predict its size; only experiment or a more complete theory supplies the missing boundary conditions.
After spontaneous symmetry breaking the model predicts lepton-flavour-violating processes — $Z to e_a e_b$, $mu to e gamma$, $mu^- to e^- e^- e^+$, $tau^- to e^+ mu^- e^-$ — with rates set by the antisymmetric coupling matrix $f$ and falling as $1/m^2$.
The naturalness problem reappears, in dimensional regularization, purely as a fine-tuning in the matching condition for the Higgs mass parameter, eq. (5.2), rather than as a quadratic divergence.

Reading between the lines

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

The paper is a template as much as a result: the same two-step recipe — determinant for heavy-only loops, propagator splitting for heavy-light loops — applies to any extension in which a complete gauge multiplet is integrated out, which is why the authors can claim gauge invariance of the effective theory without arguing for it separately.
The observation that a bound on one operator implies a bound on another only when the underlying theory is known is a caution against reading a single-operator analysis as a measurement of new-physics scale; in this model the ratio $c_2(m)/c_1(m) = 10 g'^2/(9(4pi)^2)$ is a fixed prediction, so a future precision measurement of both coefficients would over-determine the model and could exclude it.
The comparison in figure 7 suggests a practical diagnostic for any such effective theory: the size of the discrepancy between full and effective amplitudes at $m$ near $M_Z$ indicates where the $1/m^2$ expansion stops being trustworthy, and could be used to set the mass reach of a given experiment rather than assuming it.
Because the scalar couples only through an antisymmetric matrix, the leading flavour-violating effects are necessarily off-diagonal, so the same coefficient that drives $Z to tau e$ also drives $mu to e gamma$; the two are not independent handles on the new physics.

Original abstract

We study several problems related to the construction and the use of effective Lagrangians by considering an extension of the standard model that includes a heavy scalar singlet coupled to the leptonic doublet. Starting from the full renormalizable model, we build an effective field theory by integrating out the heavy scalar. A local effective Lagrangian (up to operators of dimension six) is obtained by expanding the one-loop effective action in inverse powers of the heavy mass. This is done by matching some Green functions calculated with both the full and the effective theories. Using this simple example we study the renormalization of effective Lagrangians in general and discuss how they can be used to bound new physics. We also discuss the effective Lagrangian after spontaneous symmetry breaking, and the use of the standard model classical equations of motion to rewrite it in different forms. The final effective Lagrangian in the physical basis is well suited to the study of the phenomenology of the model, which we comment on briefly. Finally, as an example of the use of our effective field theory, we consider the leptonic flavour-changing decay of the $Z$ boson in the effective theory and compare the results obtained with the full model calculation.

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, 6,292 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.14 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.69 · 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 study several problems related to the construction and the use of effective Lagrangians by considering an extension of the standard model that includes a heavy scalar singlet coupled to the leptonic doublet. Starting from the full renormalizable model, we build an effective field theory by integrating out the heavy scalar. A local effective Lagrangian (up to operators of dimension six) is obtained by expanding the one-loop effective action in inverse powers of the heavy mass. This is done by matching some Green functions calculated with both the full and the effective theories. Using this simple example we study the renormalization of effective Lagrangians in general and discuss how they can be used to bound new physics. We also discuss the effective Lagrangian after spontaneous symmetry breaking, and the use of the standard model classical equations of motion to rewrite it in different forms. The final effective Lagrangian in the physical basis is well suited to the study of the phenomenology of the model, which we comment on briefly. Finally, as an example of the use of our effective field theory, we consider the leptonic flavour-changing decay of the $Z$ boson in the effective theory and compare the results obtained with the full model calculation.

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 study several problems related to the construction and the use of effective Lagrangians by considering an extension of the standard model that includes a heavy scalar singlet coupled to the leptonic doublet.	contribution 0.98	0.93	0.07	asserted 0.95
s1	Starting from the full renormalizable model, we build an effective field theory by integrating out the heavy scalar.	method 0.98	0.95	0.05	asserted 1.00
s2	A local effective Lagrangian (up to operators of dimension six) is obtained by expanding the one-loop effective action in inverse powers of the heavy mass.	method 0.88	0.94	0.15	asserted 1.00
s3	This is done by matching some Green functions calculated with both the full and the effective theories.	method 1.00	0.90	0.03	asserted 1.00
s4	Using this simple example we study the renormalization of effective Lagrangians in general and discuss how they can be used to bound new physics.	contribution 0.98	0.91	0.13	asserted 0.99
s5	We also discuss the effective Lagrangian after spontaneous symmetry breaking, and the use of the standard model classical equations of motion to rewrite it in different forms.	contribution 0.75	0.86	0.05	asserted 0.86
s6	The final effective Lagrangian in the physical basis is well suited to the study of the phenomenology of the model, which we comment on briefly.	interpretation 0.52	0.85	0.16	asserted 0.99
s7	Finally, as an example of the use of our effective field theory, we consider the leptonic flavour-changing decay of the $Z$ boson in the effective theory and compare the results obtained with the full model calculation.	contribution 0.83	0.94	0.13	asserted 0.96

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 1.00.

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.** Diagram a) is the tree-level diagram contributing to the effective Lagrangian. The solid lines represent lepton doublets and the thick dashed line represents the heavy scalar. Diagram b) represents the four-lepton interaction in the effective theory. The symbol ⊗ means a scalar current insertion

**Figure 5.** fig. 5.c, we get the amplitude (B.5), which can be obtained fro

Showing 2 of the paper's 5 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/9310302 by the authors.

References

Works cited (82)

[1]

S. Weinberg, Phys. Rev. Lett. 18 (1967) 188

View on Pith 1967
[2]

S. Weinberg, Phys. Rev. 166 (1968) 1568

View on Pith 1968
[3]

S. Coleman, J. Wess and B. Zumino, Phys. Rev. 177 (1969) 2239

View on Pith 1969
[4]

W. Zimmermann, in Lectures on elementary particles and q uantum ﬁeld theory, ed. S. Deser, M. Grisaru and H. Pendleton (MIT, Cambridge, 1970)

View on Pith 1970
[5]

S. Weinberg, Physica 96A (1979) 327

View on Pith 1979
[6]

Y. Kazama and Y.P. Yao, Phys. Rev. Lett. 43 (1979) 1562

View on Pith 1979
[7]

S. Weinberg, Phys. Lett. 91B (1980) 51

View on Pith 1980
[8]

B. Ovrut and H.J. Schnitzer, Phys. Rev. D21 (1980) 3369

View on Pith 1980
[9]

Y. Kazama and Y.P. Yao, Phys. Rev. D25 (1982) 1605

View on Pith 1982
[10]

J. Gasser and H. Leutwyler, Annals of Physics 158 (1984) 142

View on Pith 1984
[11]

J. Gasser and H. Leutwyler, Nucl. Phys. B250 (1985) 517

View on Pith 1985
[12]

H. Georgi, Nucl. Phys. B361 (1991) 339

View on Pith 1991
[13]

H. Euler and B. Kockel, Naturw. 23 (1935) 246

View on Pith 1935
[14]

H. Euler, Ann. der Phys. 26 (1936) 398

View on Pith 1936
[15]

W. Heisenberg and H. Euler, Z. Phys. 98 (1936) 714

View on Pith 1936
[16]

E. Fermi, Ric. Scient. 4 (1934) 491

View on Pith 1934
[17]

E. Fermi, Nuovo Cim. 11 (1934) 1

View on Pith 1934
[18]

E. Fermi, Z. Phys. 88 (1934) 161

View on Pith 1934
[19]

H. Georgi, Weak Interactions and Modern Particle Theor y, (Benjamin/Cummings, Menlo Park, 1984)

View on Pith 1984
[20]

N. Isgur and M.B. Wise, Phys. Lett. B232 (1989) 113

View on Pith 1989
[21]

N. Isgur and M.B. Wise, Phys. Lett. B237 (1990) 527

View on Pith 1990
[22]

K.G. Wilson, Phys. Rev. B4 (1971) 3174

View on Pith 1971
[23]

K.G. Wilson and J.G. Kogut, Phys. Rep. 12 (1974) 75

View on Pith 1974
[24]

J. Polchinski, Nucl. Phys. B231 (1984) 269

View on Pith 1984
[25]

J. Polchinski, Eﬀective ﬁeld theory and the Fermi surfa ce, NSF-ITP-92-132, Lectures at TASI92, Boulder, 1992

View on Pith 1992
[26]

S. Weinberg, Conference Summary, UTTG-25-92, Talk pre sented at the XXVI Inter- national Conference on High Energy Physics, Dallas, Texas, August, 1992 35

View on Pith 1992
[27]

T. Appelquist and J. Carazzone, Phys. Rev. D11 (1975) 2856

View on Pith 1975
[28]

T. Appelquist and C. Bernard, Phys. Rev. D22 (1980) 200

View on Pith 1980
[29]

A.C. Longhitano, Phys. Rev. D22 (1980) 1166

View on Pith 1980
[30]

A.C. Longhitano, Nucl. Phys. B188 (1981) 118

View on Pith 1981
[31]

O. Cheyette, Nucl. Phys. B297 (1988) 183

View on Pith 1988
[32]

A. Dobado, D. Espriu and M.J. Herrero, Phys. Lett. B255 (1991) 405

View on Pith 1991
[33]

D. Espriu and M.J. Herrero, Nucl. Phys. B373 (1992) 117

View on Pith 1992
[34]

M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity , Proceedings of the Stony Brook Workshop, Stony Brook, New York, 1979, ed. P. van Nieuwenhuizen and D. Freedman (North-Holland, Amsterdam, 1980)

View on Pith 1979
[35]

T. Yanagida, in Proceedings of the Workshop on Uniﬁed Th eories and Baryon Number in the Universe, Tsukuba, Japan, 1979, ed. A. Sawada and A. Su gamoto (KEK Report No. 79-18, Tsukuba, 1979)

View on Pith 1979
[36]

R. Cowsik and J. McClelland, Phys. Rev. Lett. 29 (1972) 669

View on Pith 1972
[37]

S. Weinberg, Phys. Rev. Lett. 43 (1979) 1566

View on Pith 1979
[38]

F. Wilczek and A. Zee, Phys. Rev. Lett. 43 (1979) 1571

View on Pith 1979
[39]

H.A. Weldon and A. Zee, Nucl. Phys. B173 (1980) 269

View on Pith 1980
[40]

W. Buchm¨ uller and D. Wyler, Nucl. Phys. B268 (1986) 621

View on Pith 1986
[41]

B. Grinstein and M.B. Wise, Phys. Lett. B265 (1991) 326

View on Pith 1991
[42]

C.J.C. Burges and H.J. Schnitzer, Nucl. Phys. B228 (1983) 464

View on Pith 1983
[43]

C.N. Leung, S.T. Love and S. Rao, Z. Phys. C31 (1986) 433

View on Pith 1986
[44]

M. Bilenky, J.L. Kneur, F.M. Renard and D. Schildknecht , Trilinear couplings among the electroweak vector bosons and their determination at LE P2, BI-TP 92/44 (To appear in Nucl. Phys.), 1992

View on Pith 1992
[45]

G.J. Gounaris and F.M. Renard, Z. Phys. C59 (1993) 133

View on Pith 1993
[46]

A. DeR´ ujula, M.B. Gavela, P. Hernandez and E. Mass´ o, Nucl. Phys. B384 (1992) 3

View on Pith 1992
[47]

P. Hernandez and F.J. Vegas, Phys. Lett. B307 (1993) 116

View on Pith 1993
[48]

K. Hagiwara, S. Ishihara, R. Szalapski and D. Zeppenfel d, Phys. Lett. B283 (1992) 353

View on Pith 1992
[49]

K. Hagiwara, S. Ishihara, R. Szalpski and D. Zeppenfeld , Low energy eﬀects of new interactions in the electroweak boson sector, MAD/PH/737, 1993

View on Pith 1993
[50]

K.J.F. Gaemers and G.J. Gounaris, Z. Phys. C1 (1979) 259

View on Pith 1979
[51]

K. Hagiwara, R.D. Peccei, D. Zeppenfeld and K. Hikasa, N ucl. Phys. B282 (1987) 253 36

View on Pith 1987
[52]

C.P. Burgess and D. London, Uses and abuses of eﬀective L agrangians, MCGILL-92-05 (Revised version, June 1993), 1992

View on Pith 1993
[53]

C.P. Burgess and D. London, Phys. Rev. Lett. 69 (1992) 3428

View on Pith 1992
[54]

C. Arzt, M.B. Einhorn and J. Wudka, Eﬀective Lagrangian approach to precision measurements: The anomalous magnetic moment of the muon, NS F-ITP-92-122, 1992

View on Pith 1992
[55]

M.B. Einhorn, Beyond the standard model with eﬀective L agrangians, SLAC-PUB-12, 1993

View on Pith 1993
[56]

J. Wudka, Eﬀective Lagrangians and triple boson coupli ngs, UCRHEP-108, 1993

View on Pith 1993
[57]

T.P. Cheng and L.F. Li, Phys. Rev. D22 (1980) 2860

View on Pith 1980
[58]

A. Zee, Phys. Lett. 93B (1980) 389

View on Pith 1980
[59]

E. D’Hoker and E. Farhi, Nucl. Phys. B248 (1984) 59

View on Pith 1984
[60]

E. D’Hoker and E. Farhi, Nucl. Phys. B248 (1984) 77

View on Pith 1984
[61]

H. Steger, E. Flores and Y.P. Yao, Phys. Rev. Lett. 59 (1987) 385

View on Pith 1987
[62]

G.L. Lin, H. Steger and Y.P. Yao, Phys. Rev. D44 (1991) 2139

View on Pith 1991
[63]

G.L. Lin, H. Steger and Y.P. Yao, Heavy top quark eﬀects i n vertices with light external fermions, UM-TH-93-05, 1993

View on Pith 1993
[64]

F. Feruglio, A. Masiero and L. Maiani, Nucl. Phys. B387 (1992) 523

View on Pith 1992
[65]

S.T. Petcov, Phys. Lett. 115B (1982) 401

View on Pith 1982
[66]

G.K. Leontaris, K. Tamvakis and J.D. Vergados, Phys. Le tt. 162B (1985) 153

View on Pith 1985
[67]

S. Bertolini and A. Santamaria, Nucl. Phys. B310 (1988) 714

View on Pith 1988
[68]

H. Arason, P. Ramond and B.P. Wright, Phys. Rev. D43 (1991) 2337

View on Pith 1991
[69]

S. Bertolini and A. Santamaria, Nucl. Phys. B357 (1991) 222

View on Pith 1991
[70]

E. Witten, Nucl. Phys. B104 (1976) 445

View on Pith 1976
[71]

E. Witten, Nucl. Phys. B122 (1977) 109

View on Pith 1977
[72]

L. Hall, Nucl. Phys. B178 (1981) 75

View on Pith 1981
[73]

H.D. Politzer, Nucl. Phys. B172 (1980) 349

View on Pith 1980
[74]

C. Arzt, Reduced eﬀective Lagrangians, UM-TH-92-28, 1 992

View on Pith
[75]

I.J.R. Aitchison and C.M. Fraser, Phys. Rev. D31 (1985) 2605

View on Pith 1985
[76]

L.H. Chan, Phys. Rev. Lett. 54 (1985) 1222

View on Pith 1985
[77]

J.A. Zuk, Phys. Rev. D32 (1985) 2653

View on Pith 1985
[78]

J.A. Zuk, Phys. Rev. D33 (1986) 3645 37

View on Pith 1986
[79]

L.H. Chan, Phys. Rev. Lett. 57 (1986) 1199

View on Pith 1986
[80]

M.K. Gaillard, Nucl. Phys. B268 (1986) 669

View on Pith 1986
[81]

R.D. Ball, Phys. Rep. 182 (1989) 1

View on Pith 1989
[82]

G. ’t Hooft, Nucl. Phys. B62 (1973) 444 38 Figure captions Figure 1: Diagram a) is the tree-level diagram contributing to the eﬀe ctive Lagrangian. The solid lines represent lepton doublets and the thick dash ed line represents the heavy scalar. Diagram b) represents the four-lepton interaction in the eﬀective theory. The symbol ⊗ means a scalar current i...

View on Pith Pith review arXiv 1973

Forward citations

Cited by 18 Pith papers

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

Matchmakereft: automated tree-level and one-loop matching
hep-ph 2021-12 accept novelty 7.0 of 10

The authors release matchmakereft, an automated tool that computes tree-level and one-loop matching of arbitrary UV models onto arbitrary effective theories, and demonstrate it with the complete one-loop matching of a...
One-loop matching in the SMEFT extended with a sterile neutrino
hep-ph 2020-01 conditional novelty 6.0 of 10

A complete diagrammatic one-loop matching of a renormalisable sterile-neutrino model onto the neutrino-extended Standard Model effective field theory, with new off-shell operator bases and a low-energy matching.
Covariant diagrams for one-loop matching
hep-ph 2016-10 accept novelty 6.0 of 10

A diagrammatic bookkeeping scheme turns one-loop functional matching into a table-driven recipe, reproducing the Universal One-Loop Effective Action and four published model results with less work.
Higgs lepton flavour violation: UV completions and connection to neutrino masses
hep-ph 2016-05 accept novelty 6.0 of 10

Only extensions with an extra Higgs doublet can give BR(h to tau mu) near 1 percent; vector-like leptons, derivative-operator realizations, and one-loop neutrino-mass models are all forced below experimental reach by ...
The Universal One-Loop Effective Action
hep-ph 2015-12 conditional novelty 6.0 of 10

A single closed expression gives the one-loop effective action for all operators up to dimension six, with the loop integrals pre-evaluated into universal coefficients, valid for heavy multiplets with non-degenerate masses.

Show 13 more citing papers

Loop bounds on non-standard neutrino interactions
hep-ph 2009-02 accept novelty 6.0 of 10

The O(10^-4) loop-induced bound on the neutrino non-standard coupling epsilon_e_mu is model-dependent and is lost; only O(10^-1) model-independent bounds remain.
Non-Standard Neutrino Interactions with Matter from Physics Beyond the Standard Model
hep-ph 2008-07 accept novelty 6.0 of 10

In the studied classes of new physics, non-standard neutrino interactions with matter are bounded to be at most O(10^-2), and they always come with non-standard interactions at the neutrino source or detector.
Complete One-loop Matching of the Type-I Seesaw Model onto the Standard Model Effective Field Theory
hep-ph 2021-07 conditional novelty 5.0 of 10

A complete one-loop matching of the type-I seesaw model onto SMEFT yields 31 dimension-six operators in the Warsaw basis with explicit Wilson coefficients, plus threshold corrections to Standard Model couplings and to...
Integrating out heavy fields in the path integral using the background-field method: general formalism
hep-ph 2021-02 accept novelty 5.0 of 10

A background-field path-integral method integrates out a heavy Higgs boson and shows that the choice of renormalization scheme can create or remove apparent non-decoupling effects at one loop.
Field redefinitions in effective theories at higher orders
hep-ph 2018-11 accept novelty 5.0 of 10

Perturbative field redefinitions in effective theories generate higher-order terms that the equations-of-motion shortcut misses, and they do not commute with matching to a UV theory at the quantum level.
Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients
hep-ph 2017-06 conditional novelty 5.0 of 10

The authors extend the Universal One-Loop Effective Action to heavy-light loops, tabulating universal coefficients that let physicists read off dimension-six Wilson coefficients without recomputing loop integrals.
Full parameter scan of the Zee model: exploring Higgs lepton flavor violation
hep-ph 2017-01 conditional novelty 5.0 of 10

A full scan of the Zee model finds that normal neutrino ordering fits well, inverted ordering is disfavored and needs first-octant theta23, and h to tau mu can reach about 10^-2 while future lepton-flavor searches can...
Mixed Heavy-Light Matching in the Universal One-Loop Effective Action
hep-ph 2016-04 conditional novelty 5.0 of 10

A subtraction procedure extends the Universal One-Loop Effective Action to mixed heavy-light loops, demonstrated on a heavy electroweak triplet scalar where it reproduces known dimension-6 Wilson coefficients.
Right-handed neutrino magnetic moments
hep-ph 2009-04 conditional novelty 5.0 of 10

A dimension-5 magnetic-moment operator for right-handed neutrinos is identified and its consequences for Z decays, collider production, stellar cooling, and CP violation are computed.
Present and Future Bounds on Non-Standard Neutrino Interactions
hep-ph 2003-02 conditional novelty 5.0 of 10

Current and projected experimental bounds on non-standard neutrino interactions are catalogued, showing that near-detector measurements at a neutrino factory would be more sensitive than far-detector oscillations for ...
Flavour physics of leptons and dipole moments
hep-ph 2008-01 accept novelty 3.0 of 10

The report synthesizes current bounds and future prospects for charged-lepton flavor violation and electric dipole moments as probes of TeV-scale physics.
Status of non-standard neutrino interactions
hep-ph 2012-09 accept novelty 2.0 of 10

A status review of non-standard neutrino interactions that collects the theoretical models, the experimental and phenomenological bounds, and the projected sensitivities of future experiments.
Light Sterile Neutrinos: A White Paper
hep-ph 2012-04 accept novelty 2.0 of 10

Three neutrino anomalies are each consistent with an eV-scale sterile neutrino but sit in 2-3 sigma tension with disappearance data, so the paper argues for a dedicated new short-baseline program rather than a discove...

How the literature uses it

32 arXiv papers cite this in 42 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 · 23 sentences without a confident label

Uses its method or tool 3 papers

A convenient normalization of this expansion fixes the $c_k$ coefficients as [equation] As already commented, the $O_k$ are combinations of traces of dimension–2$k$ operators, so that, in general, they should have the form [equation] For the first values of $k$ ($=1,2,3$), we shall employ the following sets as bases: [equation] The method proposed in Ref. [ref] relies on the fact that Eqs.([ref]), ([ref]) and ([ref]) are valid for any field configuration.

Gauge invariance, quantization and integration of heavy modes in a gauge Kaluza-Klein theory · Extra–dimensional physics versus fundamental description · 0.94
We now use a slightly adapted form of a trick explained in the Appendix of [ref] : We evaluate expression ([ref]) in the special configuration $∂_μX̂_ν= ∂_μŶ=0$, allowing us to drop all derivatives.

Two-Higgs Doublet Model Matched to Nonlinear Effective Theory · One-loop matching of $h^n X_μνX^μν$ to all orders in $n$ · 0.98
We carry out the integration [For a detailed example of the integration procedure in the case of a singly-charged scalar see [ref] . ] by using the equations of motion for $E$ and expanding in powers of $1 / m_E$.

Exotic properties of neutrinos using effective Lagrangians and specific models · Lepton Flavour Violating processes · 0.88

Compares with it 3 papers

The one-loop matching of the SM extended by $δ$ was performed in [ref] : we agree with their results at leading-log order and with their one-loop finite dipole WCs.

Effective comparison of neutrino-mass models · Matching to the SMEFT · 1.00
We have found some minor differences that we are discussing with the authors. * Charged scalar electroweak singlet, as computed in [ref] .

Matchmakereft: automated tree-level and one-loop matching · Cross-checks · 0.93
During this procedure, we do not need to perform the nontrivial restoration of amplitudes' gauge structures, like those in Ref. [ref] , and less 1PI diagrams are involved.

Renormalization Group Equations for the SMEFT Operators up to Dimension Seven · The Green's basis for dim-7 operators · 0.87

Cites it as background 10 papers

This is due to the so called non-decoupling effects (see e.g., [ref] ), induced by loop corrections, that survive in the large mass limit of the BSM particles living in the theory assumed to be valid at high energies.

Decoupling Limits in Effective Field Theories via Higher Dimensional Operators · Introduction · 0.85
This indeed is the opposite of conventional analyses where one starts with a UV theory, identifies certain degrees of freedom as heavy and after suitably integrating out obtains a subset of the effective Lagrangian, i.e., higher mass dimension operator basis, of a low energy theory [ref] .

EFT Diagrammatica: UV Roots of the CP-conserving SMEFT · Unfolding effective operators into Lorentz invariant vertices · 0.90
There are only few available examples of complete or partial one-loop matching for the SM extended with a charged scalar singlet [ref] , a real scalar singlet [ref] , a real scalar triplet [ref] , a vector-like quark singlet [ref] , a light sterile neutrino and heavy fermions and a scalar singlet [ref] , and two scalar leptoquarks [ref] by either diagrammatic calculations or functional approaches [ref] .

Radiative Decays of Charged Leptons in the Seesaw Effective Field Theory with One-loop Matching · Introduction · 0.88

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] [1]

S. Weinberg, Phys. Rev. Lett. 18 (1967) 188

View on Pith 1967

[2] [2]

S. Weinberg, Phys. Rev. 166 (1968) 1568

View on Pith 1968

[3] [3]

S. Coleman, J. Wess and B. Zumino, Phys. Rev. 177 (1969) 2239

View on Pith 1969

[4] [4]

W. Zimmermann, in Lectures on elementary particles and q uantum ﬁeld theory, ed. S. Deser, M. Grisaru and H. Pendleton (MIT, Cambridge, 1970)

View on Pith 1970

[5] [5]

S. Weinberg, Physica 96A (1979) 327

View on Pith 1979

[6] [6]

Y. Kazama and Y.P. Yao, Phys. Rev. Lett. 43 (1979) 1562

View on Pith 1979

[7] [7]

S. Weinberg, Phys. Lett. 91B (1980) 51

View on Pith 1980

[8] [8]

B. Ovrut and H.J. Schnitzer, Phys. Rev. D21 (1980) 3369

View on Pith 1980

[9] [9]

Y. Kazama and Y.P. Yao, Phys. Rev. D25 (1982) 1605

View on Pith 1982

[10] [10]

J. Gasser and H. Leutwyler, Annals of Physics 158 (1984) 142

View on Pith 1984

[11] [11]

J. Gasser and H. Leutwyler, Nucl. Phys. B250 (1985) 517

View on Pith 1985

[12] [12]

H. Georgi, Nucl. Phys. B361 (1991) 339

View on Pith 1991

[13] [13]

H. Euler and B. Kockel, Naturw. 23 (1935) 246

View on Pith 1935

[14] [14]

H. Euler, Ann. der Phys. 26 (1936) 398

View on Pith 1936

[15] [15]

W. Heisenberg and H. Euler, Z. Phys. 98 (1936) 714

View on Pith 1936

[16] [16]

E. Fermi, Ric. Scient. 4 (1934) 491

View on Pith 1934

[17] [17]

E. Fermi, Nuovo Cim. 11 (1934) 1

View on Pith 1934

[18] [18]

E. Fermi, Z. Phys. 88 (1934) 161

View on Pith 1934

[19] [19]

H. Georgi, Weak Interactions and Modern Particle Theor y, (Benjamin/Cummings, Menlo Park, 1984)

View on Pith 1984

[20] [20]

N. Isgur and M.B. Wise, Phys. Lett. B232 (1989) 113

View on Pith 1989

[21] [21]

N. Isgur and M.B. Wise, Phys. Lett. B237 (1990) 527

View on Pith 1990

[22] [22]

K.G. Wilson, Phys. Rev. B4 (1971) 3174

View on Pith 1971

[23] [23]

K.G. Wilson and J.G. Kogut, Phys. Rep. 12 (1974) 75

View on Pith 1974

[24] [24]

J. Polchinski, Nucl. Phys. B231 (1984) 269

View on Pith 1984

[25] [25]

J. Polchinski, Eﬀective ﬁeld theory and the Fermi surfa ce, NSF-ITP-92-132, Lectures at TASI92, Boulder, 1992

View on Pith 1992

[26] [26]

S. Weinberg, Conference Summary, UTTG-25-92, Talk pre sented at the XXVI Inter- national Conference on High Energy Physics, Dallas, Texas, August, 1992 35

View on Pith 1992

[27] [27]

T. Appelquist and J. Carazzone, Phys. Rev. D11 (1975) 2856

View on Pith 1975

[28] [28]

T. Appelquist and C. Bernard, Phys. Rev. D22 (1980) 200

View on Pith 1980

[29] [29]

A.C. Longhitano, Phys. Rev. D22 (1980) 1166

View on Pith 1980

[30] [30]

A.C. Longhitano, Nucl. Phys. B188 (1981) 118

View on Pith 1981

[31] [31]

O. Cheyette, Nucl. Phys. B297 (1988) 183

View on Pith 1988

[32] [32]

A. Dobado, D. Espriu and M.J. Herrero, Phys. Lett. B255 (1991) 405

View on Pith 1991

[33] [33]

D. Espriu and M.J. Herrero, Nucl. Phys. B373 (1992) 117

View on Pith 1992

[34] [34]

M. Gell-Mann, P. Ramond and R. Slansky, in Supergravity , Proceedings of the Stony Brook Workshop, Stony Brook, New York, 1979, ed. P. van Nieuwenhuizen and D. Freedman (North-Holland, Amsterdam, 1980)

View on Pith 1979

[35] [35]

T. Yanagida, in Proceedings of the Workshop on Uniﬁed Th eories and Baryon Number in the Universe, Tsukuba, Japan, 1979, ed. A. Sawada and A. Su gamoto (KEK Report No. 79-18, Tsukuba, 1979)

View on Pith 1979

[36] [36]

R. Cowsik and J. McClelland, Phys. Rev. Lett. 29 (1972) 669

View on Pith 1972

[37] [37]

S. Weinberg, Phys. Rev. Lett. 43 (1979) 1566

View on Pith 1979

[38] [38]

F. Wilczek and A. Zee, Phys. Rev. Lett. 43 (1979) 1571

View on Pith 1979

[39] [39]

H.A. Weldon and A. Zee, Nucl. Phys. B173 (1980) 269

View on Pith 1980

[40] [40]

W. Buchm¨ uller and D. Wyler, Nucl. Phys. B268 (1986) 621

View on Pith 1986

[41] [41]

B. Grinstein and M.B. Wise, Phys. Lett. B265 (1991) 326

View on Pith 1991

[42] [42]

C.J.C. Burges and H.J. Schnitzer, Nucl. Phys. B228 (1983) 464

View on Pith 1983

[43] [43]

C.N. Leung, S.T. Love and S. Rao, Z. Phys. C31 (1986) 433

View on Pith 1986

[44] [44]

M. Bilenky, J.L. Kneur, F.M. Renard and D. Schildknecht , Trilinear couplings among the electroweak vector bosons and their determination at LE P2, BI-TP 92/44 (To appear in Nucl. Phys.), 1992

View on Pith 1992

[45] [45]

G.J. Gounaris and F.M. Renard, Z. Phys. C59 (1993) 133

View on Pith 1993

[46] [46]

A. DeR´ ujula, M.B. Gavela, P. Hernandez and E. Mass´ o, Nucl. Phys. B384 (1992) 3

View on Pith 1992

[47] [47]

P. Hernandez and F.J. Vegas, Phys. Lett. B307 (1993) 116

View on Pith 1993

[48] [48]

K. Hagiwara, S. Ishihara, R. Szalapski and D. Zeppenfel d, Phys. Lett. B283 (1992) 353

View on Pith 1992

[49] [49]

K. Hagiwara, S. Ishihara, R. Szalpski and D. Zeppenfeld , Low energy eﬀects of new interactions in the electroweak boson sector, MAD/PH/737, 1993

View on Pith 1993

[50] [50]

K.J.F. Gaemers and G.J. Gounaris, Z. Phys. C1 (1979) 259

View on Pith 1979

[51] [51]

K. Hagiwara, R.D. Peccei, D. Zeppenfeld and K. Hikasa, N ucl. Phys. B282 (1987) 253 36

View on Pith 1987

[52] [52]

C.P. Burgess and D. London, Uses and abuses of eﬀective L agrangians, MCGILL-92-05 (Revised version, June 1993), 1992

View on Pith 1993

[53] [53]

C.P. Burgess and D. London, Phys. Rev. Lett. 69 (1992) 3428

View on Pith 1992

[54] [54]

C. Arzt, M.B. Einhorn and J. Wudka, Eﬀective Lagrangian approach to precision measurements: The anomalous magnetic moment of the muon, NS F-ITP-92-122, 1992

View on Pith 1992

[55] [55]

M.B. Einhorn, Beyond the standard model with eﬀective L agrangians, SLAC-PUB-12, 1993

View on Pith 1993

[56] [56]

J. Wudka, Eﬀective Lagrangians and triple boson coupli ngs, UCRHEP-108, 1993

View on Pith 1993

[57] [57]

T.P. Cheng and L.F. Li, Phys. Rev. D22 (1980) 2860

View on Pith 1980

[58] [58]

A. Zee, Phys. Lett. 93B (1980) 389

View on Pith 1980

[59] [59]

E. D’Hoker and E. Farhi, Nucl. Phys. B248 (1984) 59

View on Pith 1984

[60] [60]

E. D’Hoker and E. Farhi, Nucl. Phys. B248 (1984) 77

View on Pith 1984

[61] [61]

H. Steger, E. Flores and Y.P. Yao, Phys. Rev. Lett. 59 (1987) 385

View on Pith 1987

[62] [62]

G.L. Lin, H. Steger and Y.P. Yao, Phys. Rev. D44 (1991) 2139

View on Pith 1991

[63] [63]

G.L. Lin, H. Steger and Y.P. Yao, Heavy top quark eﬀects i n vertices with light external fermions, UM-TH-93-05, 1993

View on Pith 1993

[64] [64]

F. Feruglio, A. Masiero and L. Maiani, Nucl. Phys. B387 (1992) 523

View on Pith 1992

[65] [65]

S.T. Petcov, Phys. Lett. 115B (1982) 401

View on Pith 1982

[66] [66]

G.K. Leontaris, K. Tamvakis and J.D. Vergados, Phys. Le tt. 162B (1985) 153

View on Pith 1985

[67] [67]

S. Bertolini and A. Santamaria, Nucl. Phys. B310 (1988) 714

View on Pith 1988

[68] [68]

H. Arason, P. Ramond and B.P. Wright, Phys. Rev. D43 (1991) 2337

View on Pith 1991

[69] [69]

S. Bertolini and A. Santamaria, Nucl. Phys. B357 (1991) 222

View on Pith 1991

[70] [70]

E. Witten, Nucl. Phys. B104 (1976) 445

View on Pith 1976

[71] [71]

E. Witten, Nucl. Phys. B122 (1977) 109

View on Pith 1977

[72] [72]

L. Hall, Nucl. Phys. B178 (1981) 75

View on Pith 1981

[73] [73]

H.D. Politzer, Nucl. Phys. B172 (1980) 349

View on Pith 1980

[74] [74]

C. Arzt, Reduced eﬀective Lagrangians, UM-TH-92-28, 1 992

View on Pith

[75] [75]

I.J.R. Aitchison and C.M. Fraser, Phys. Rev. D31 (1985) 2605

View on Pith 1985

[76] [76]

L.H. Chan, Phys. Rev. Lett. 54 (1985) 1222

View on Pith 1985

[77] [77]

J.A. Zuk, Phys. Rev. D32 (1985) 2653

View on Pith 1985

[78] [78]

J.A. Zuk, Phys. Rev. D33 (1986) 3645 37

View on Pith 1986

[79] [79]

L.H. Chan, Phys. Rev. Lett. 57 (1986) 1199

View on Pith 1986

[80] [80]

M.K. Gaillard, Nucl. Phys. B268 (1986) 669

View on Pith 1986

[81] [81]

R.D. Ball, Phys. Rep. 182 (1989) 1

View on Pith 1989

[82] [82]

G. ’t Hooft, Nucl. Phys. B62 (1973) 444 38 Figure captions Figure 1: Diagram a) is the tree-level diagram contributing to the eﬀe ctive Lagrangian. The solid lines represent lepton doublets and the thick dash ed line represents the heavy scalar. Diagram b) represents the four-lepton interaction in the eﬀective theory. The symbol ⊗ means a scalar current i...

View on Pith Pith review arXiv 1973