Literature, sources, and claim tracing

A literature search becomes useful when it can answer a precise question: which source establishes which part of this claim, under which assumptions, and where? This lesson develops that skill with one effective-field-theory example. The goal is not to collect citations, but to leave a trace another researcher can inspect without guessing what you read.

Helpful background. The worked calculation uses tree-level matching from effective field theory. You can still use the source-tracing method if you treat the equations below as the scientific statement being checked.

Turn a vague statement into a claim that could fail

“Heavy particles decouple” is too loose to trace. It does not say which particles, which observables, which energy range, which perturbative order, or what “decouple” permits to remain. Start by supplying six ingredients:

1. Object: the field, observable, process, theorem, or dataset at issue.
2. Regime: dimensions, scales, states, kinematics, and other quantified conditions.
3. Operation: what is integrated out, expanded, measured, fitted, or proved.
4. Result: the coefficient, bound, relation, or qualitative conclusion asserted.
5. Accuracy: approximation order and the first omitted contribution.
6. Nonclaim: the nearby stronger statement that is not being made.

Here is the bounded claim used throughout this lesson:

In four spacetime dimensions, let a light real scalar $\phi$ couple to a heavy real scalar $H$ of mass $M$ through $\mathcal L_{\mathrm{int}}=-gH\phi^2/2$. For tree-level amplitudes with all light masses and external invariants of order $E^2\ll M^2$, exchange of $H$ is reproduced by local operators built from $\phi$. Keeping only the leading local operator incurs a relative correction of order $E^2/M^2$; including the first derivative operator moves the relative remainder to order $E^4/M^4$. This expansion is not valid near the heavy-particle pole.

That claim can be wrong in identifiable ways: the coefficient might have the wrong sign, the first correction might scale differently, or the stated regime might include the pole. It says nothing about loop matching, renormalization-group evolution, nonperturbative effects, or every theory containing a heavy field.

Give every source a specific job

Different documents answer different questions. A single document may perform more than one role, but record the role for which you actually use it.

Source role	Question it should answer	What to verify
Primary result	Where did the researchers who produced the result derive, prove, or report it?	Exact hypotheses, result, date, corrections, and any separate priority claim
Derivation or method source	Where can the needed reasoning be reconstructed clearly?	Conventions, intermediate steps, approximation, and checks
Data source	Which released observations or simulations enter the claim?	Dataset version, event or sample definition, calibration, covariance, and access record
Review	How is a body of work organized, and which primary sources should be followed?	Coverage date, selection boundaries, and whether summaries preserve the original claims
Current-status source	What is the best dated account of what is presently measured, excluded, disputed, or accepted?	Evidence cutoff, update policy, live corrections, and whether the source speaks for the relevant community

A review is usually a good search seed, not a substitute for the original proof or measurement. A pedagogical derivation can be the best source for a calculation without establishing historical priority. A current-status source may change while the primary paper does not. For a purely analytic toy model, a data source may correctly be marked “not applicable”; inventing a data citation would make the trace worse.

Search backward for foundations and forward for changes

Begin with a source that states the result intelligibly, then move in both directions.

Backward search. Follow the references attached to the exact sentence, equation, or theorem. Open those sources and repeat until you reach the work that actually bears the result and the material assumptions it imports. Stop following a branch when it supplies only general background that your claim does not use.

Forward search. Search the primary source by DOI and exact title in a citation index and on the publisher page. Screen later papers for an erratum, correction, changed convention, counterexample, extension, or discussion of failed hypotheses. Citation count is not a scientific check: a later paper matters only if its content changes how the bounded claim should be stated.

Record the search date, services used, and screening terms. “No correction found” means only “none found in this declared search,” never “no correction exists.” For the running example, a backward search from Manohar’s modern treatment leads to Appelquist and Carazzone; a forward search should include terms such as nondecoupling, exception, spontaneous symmetry breaking, and scheme because these mark familiar qualifications to naive versions of the slogan.

Verify identity, version, and printed locator

Before citing a passage, check the document rather than trusting imported metadata.

• Match authors, title, venue, year, and DOI or other persistent identifier.
• Record the version you read. For a preprint, include its version number and date; for software or data, include the release or revision.
• Use the page number printed on the work, not the PDF viewer’s page index. Add a section, theorem, equation, figure, or table number whenever possible.
• Read before and after the passage until its definitions, assumptions, and exceptions are clear.
• Check the publisher page for corrections or retractions, and compare later versions when the claim is consequential.

Version discipline prevents a common locator error in this example. Manohar’s author manuscript is arXiv:1804.05863v1, submitted 16 April 2018; its printed §5.4, equation (5.20), is on preprint p. 37, and §7 is on preprint pp. 58–61. The published Oxford chapter occupies pp. 47–136. A locator such as “Manohar 2020, p. 58” therefore does not identify the preprint passage unless that page has separately been checked in the published edition. The arXiv record and Oxford chapter record establish the two identities; they do not make their pagination interchangeable.

Check the running claim directly

Take

$$\mathcal L =\frac12(\partial\phi)^2-\frac12m^2\phi^2 +\frac12(\partial H)^2-\frac12M^2H^2 -\frac g2 H\phi^2 .$$

After integrating the heavy kinetic term by parts, the terms containing $H$ are

$$\mathcal L_H =-\frac12 H(\Box+M^2)H-\frac g2H\phi^2, \qquad (\Box+M^2)H=-\frac g2\phi^2.$$

Solving the classical equation for $H$ and substituting it back gives the exact tree-level nonlocal contribution

$$\Delta\mathcal L_{\mathrm{tree}} =\frac{g^2}{8}\phi^2\frac{1}{\Box+M^2}\phi^2.$$

For derivatives of order $E\ll M$,

$$\begin{aligned} \Delta\mathcal L_{\mathrm{tree}} &=\frac{g^2}{8M^2}\phi^4 -\frac{g^2}{8M^4}\phi^2\Box(\phi^2) \\ &\quad+O\!\left(\frac{g^2E^4}{M^6}\phi^4\right). \end{aligned}$$

The same check in one momentum channel is

$$\frac{g^2}{M^2-q^2} =\frac{g^2}{M^2} \left[1+\frac{q^2}{M^2} +O\!\left(\frac{q^4}{M^4}\right)\right].$$

For identical-scalar scattering, the leading local term gives the contact vertex $i(4!)g^2/(8M^2)=i3g^2/M^2$. The full theory has $s$-, $t$-, and $u$-channel exchange, each contributing $ig^2/M^2$ at leading order. Their agreement supplies a separate algebraic check of the factor $1/8$ and the sign, with a different failure mode but the same model and tree-level assumptions.

Thus the leading contact term has the stated positive coefficient, while the derivative expansion is controlled by $q^2/M^2=O(E^2/M^2)$. It fails as $q^2$ approaches $M^2$, where no finite polynomial in momenta can reproduce the pole. Manohar develops integrating out, power counting, and the heavy-propagator expansion in §3.5, §§4.1–4.2, and §5.4, eq. (5.20), preprint pp. 17–20 and 37, PDF; his §7, preprint pp. 58–61, PDF explains decoupling and its subtraction-scheme implementation.

Appelquist and Carazzone’s original paper studies low-momentum behavior in renormalizable field theories and states a general decoupling theorem after developing model examples Appelquist and Carazzone 1975, pp. 2856–2861. That paper supplies the broader decoupling context. The algebra above is a pedagogical tree-level illustration of locality and scale expansion; it does not re-prove the full theorem or inherit its full scope.

A filled claim trace

Claim. For the specified two-scalar theory and $E^2\ll M^2$, tree-level heavy-scalar exchange is reproduced by local light-field operators, with relative corrections in powers of $E^2/M^2$.

Object and regime. Light-field amplitudes in four dimensions; $m^2$, $s$, $t$, and $u$ are all small compared with $M^2$; kinematics remain away from $q^2=M^2$ in every exchange channel.

Approximation and remainder. Tree level. The operator $g^2\phi^4/(8M^2)$ alone leaves a relative $O(E^2/M^2)$ correction. Adding $-g^2\phi^2\Box(\phi^2)/(8M^4)$ leaves a relative $O(E^4/M^4)$ correction.

Direct check. Solve the heavy-field equation and expand $(\Box+M^2)^{-1}$, as shown above. As a second algebraic check, expand $g^2/(M^2-q^2)$ and verify that the pole at $q^2=M^2$ lies on the boundary of the series.

Derivation or method source. Manohar, arXiv:1804.05863v1 (16 April 2018), especially printed §3.5, §§4.1–4.2, and §5.4, eq. (5.20), preprint pp. 17–20 and 37. The Oxford record identifies the later published chapter, pp. 47–136; no preprint page number has been relabeled as an Oxford page number.

Primary result for the broader context. Appelquist and Carazzone, Physical Review D 11 (1975), pp. 2856–2861, DOI 10.1103/PhysRevD.11.2856. It supports the general decoupling context, not this page’s particular factor of $1/8$.

Backward and forward search. The Appelquist–Carazzone paper was followed from the modern treatment’s references. On 13 August 2026, its APS “Citing Articles” path and exact DOI were checked forward with qualification terms including nondecoupling and scheme. No later source is being used to enlarge the toy claim. This finite search does not establish that no correction or exception exists.

Other source roles. Data source: not applicable to this analytic claim. Review: useful for orientation, but unnecessary as direct support. Current-status source: unnecessary because no claim about present experimental bounds or community consensus is made.

Nonclaims. No loop-level matching, running, universality, or accuracy near the heavy pole is asserted. The toy calculation is not a proof of the Appelquist–Carazzone theorem.

Handoff sentence. “I checked the tree-level coefficient by the heavy-field equation of motion and by the propagator expansion; Manohar v1 supplies the modern method locators, while Appelquist–Carazzone is cited only for the wider decoupling context.”

Copyable claim-trace template

Claim:
Object or observable:
Regime and quantifiers:
Operation performed:
Approximation order and remainder:
Conventions needed to interpret it:

Direct source role:
Authors, title, persistent identifier:
Version or release read:
Printed section/page/equation/figure/table:
What the located passage establishes:

Backward dependencies checked:
Forward search date, services, and screening terms:
Correction or qualification found:
Data source and version, if applicable:
Review role, if applicable:
Mutable current source and evidence date, if applicable:

Independent check:
Nonclaims and failure regime:
One-sentence handoff:

If a field is not applicable, say why. An explicit “not applicable—analytic claim with no data input” is more informative than an empty line.

Common source-role errors

Citing a review as the primary result. Use the review to find and interpret the original work, then cite the original at the claim it actually establishes. Keep the review when its synthesis is itself part of your claim.

Citing a method paper as a data source. A method may define an estimator while a separate release supplies the observations. Trace both when the result depends on both.

Stopping at a citation chain. “Paper A cites paper B” does not show that B supports your sentence. Open B, locate the passage, and check its scope; sometimes B points onward again.

Mixing preprint and published locators. Record the exact version read and use its printed labels. Do not combine a journal year with an unverified preprint page number.

Treating a current source as timeless. A live database or regularly updated assessment needs an access date and evidence cutoff. A theorem paper needs version and correction checks, but not a manufactured current-consensus citation.

Promoting an illustration into a theorem. A successful heavy-scalar expansion checks one model, order, and regime. It clarifies the general theorem’s mechanism without proving all of its hypotheses or conclusions.

Exercises

1. Repair an overbroad claim

Rewrite “heavy particles have no low-energy effects” so that it matches the running calculation.

Solution

A traceable version is: “In the stated two-scalar model, for tree-level light-field amplitudes with all external invariants much smaller than $M^2$, heavy-$H$ exchange is represented by local $\phi$ operators whose leading coefficient is $g^2/(8M^2)$; the first relative correction is $O(E^2/M^2)$, and the expansion fails near the $H$ pole.”

This repair names the model, observable class, perturbative order, scale hierarchy, coefficient, remainder, and failure regime. It does not say the effects vanish: they remain in Wilson coefficients suppressed by powers of $M$.

2. Assign the source roles

You have (a) the 1975 Appelquist–Carazzone paper, (b) Manohar’s 2018 lecture notes, (c) a newly released collider likelihood, and (d) a dated collaboration combination of current limits. Which role should each play in a claim about a present collider bound interpreted with an EFT?

Solution

• (a) is the primary result for the broad decoupling theorem context, if that context is needed.
• (b) is a derivation or method source for EFT construction, power counting, and matching.
• (c) is the data source; its release version, selection, nuisance model, and covariance information must be recorded.
• (d) is the current-status source for the dated combined bound.

No source can silently replace another. The theorem paper does not contain the new data, the lecture notes do not establish the present bound, and the combination may summarize the EFT method without deriving it.

3. Diagnose a locator

A note says, “Manohar 2020, p. 37 proves the expansion,” but the researcher read arXiv:1804.05863v1. What should the trace say?

Solution

It should identify the document actually read: “Manohar, arXiv:1804.05863v1 (16 April 2018), §5.4, eq. (5.20), printed p. 37.” The published chapter may be listed as a related edition, with its DOI and full pp. 47–136 range, but its internal locator must be checked separately before use.

The year “2020” belongs to the Oxford chapter, while “p. 37” belongs to the versioned preprint. Combining them creates a locator that may send the next reader to the wrong passage.

Continue with scope and conventions

You are ready to move on when another reader can state your claim, open every supporting source at the recorded passage, distinguish direct support from context, and repeat one check with a different algebraic failure mode. Next, use the same bounded claim to separate its assumptions, conventions, evidence, and qualified conclusion in Scope, conventions, and status.

References

• Appelquist, Thomas, and J. Carazzone. “Infrared Singularities and Massive Fields.” Physical Review D 11, no. 10 (1975): 2856–2861. DOI.

• Manohar, Aneesh V. “Introduction to Effective Field Theories.” In Effective Field Theory in Particle Physics and Cosmology: Lecture Notes of the Les Houches Summer School, Volume 108, edited by Sacha Davidson, Paolo Gambino, Mikko Laine, Matthias Neubert, and Christophe Salomon, 47–136. Oxford: Oxford University Press, 2020. DOI. Author manuscript, arXiv:1804.05863v1 (2018).