Empirical Fit to Precision Inclusive Electron-Proton Cross Sections in the Resonance Region

M.E. Christy; P.B. Bosted

REVIEW

Empirical Fit to Precision Inclusive Electron-Proton Cross Sections in the Resonance Region

M.E. Christy, P.B. Bosted

High Energy Physics - Phenomenology · Submitted 21 Dec 2007 · 20 references

Pith's verdict: A solid, widely-used utility fit; the only real soft spot is that the 3% claim is stated for σT and σL when it was measured on σr.

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arXiv ID0712.3731 (version 4)

Pith IDNG5NHVRF, Pith's permanent record of this paper and its review

CitationM.E. Christy, P.B. Bosted. "Empirical Fit to Precision Inclusive Electron-Proton Cross Sections in the Resonance Region." arXiv:0712.3731 (2007). https://pith.science/paper/NG5NHVRF

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Editor's note

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This is the Christy-Bosted resonance-region fit, and it is what it says it is: a 75-parameter empirical parameterization of inclusive ep cross sections for 0 ≤ Q² < 8 GeV² and 1.1 < W < 3.1 GeV, constrained by the E94-110 Rosenbluth separations, E00-116 at high Q², E00-002 at low Q², and photoproduction at Q² = 0. It is a tool, and it should be judged as one. On that basis it holds up, and it has been used accordingly by people doing radiative corrections, spin-structure extraction, and neutrino cross-section modeling. The genuine advance over Stuart et al. and Niculescu is fitting σT and σL simultaneously rather than assuming R from DIS and fitting only the extracted σT. The threshold-dependent Breit-Wigner widths, the x′ damping factor that keeps the non-resonant piece from rising indefinitely in W, and the longitudinal amplitudes that vanish at both Q² endpoints are sensible, physically motivated forms. The authors are also candid about where the fit fails: the dip region at low Q², the longitudinal dip for 2 < Q² < 4 GeV², and the inconsistency of the second-region transverse form factors with exclusive analyses. That candor is worth something and I would not score those disclosures against them. The stress-test note lands, though. The 3% figure comes from Figure 5, a histogram of residuals in the reduced cross section σr, not in σT or σL separately. Where the ε lever arm is wide the separation is real and Figure 4 backs it up. Above Q² ≈ 4.5 the E00-116 points sit at single kinematic settings, so σL there is extrapolation along the fit form, and the authors say as much in §V. The abstract's 'fits both transverse and longitudinal cross sections' [abstract:s2] and the closing §V sentence read as if the 3% applies to the separated pieces across the whole range. It does not, and a user should know that before trusting σL at the top of the Q² range. The reporting gaps the reader flags are real but minor for the genre: no χ²/dof, no covariance matrix for Tables III and IV, code by email. The covariance matrix would genuinely help anyone propagating fit uncertainty, and I would ask for it, but its absence does not undermine the central claim. Send it out. It deserves referees, mainly to press on the σL extrapolation at high Q² and to get the parameter uncertainties into the paper.

Referee report

Significance

If the fit performs as claimed, it is a genuinely useful community tool: it supplies separated transverse and longitudinal cross sections rather than only σT extracted under an assumed R, it spans the full kinematic reach of the 6 GeV Jefferson Lab program, and it matches smoothly onto both the photoproduction point and DIS. The use of the E94-110 Rosenbluth-separated data to constrain σL independently is the substantive advance over the earlier Stuart and Niculescu fits, and the paper is appropriately candid that the resonance parameters are not to be interpreted as measured masses, widths, and transition form factors. The authors also make the FORTRAN implementation available on request, which materially raises the value of the work for radiative-correction and sum-rule practitioners. The paper is honest about its weakest link, namely that the assumed incoherent-sum ansatz and the Eq. 18 form for the Roper amplitude cannot reproduce the Q² behavior seen in exclusive analyses.

Major objections (5)

[§V, closing paragraph, and abstract:s2] The closing sentence claims the fit 'describes existing data at the 3% or better level over almost the entire range 0 ≤ Q² < 8 GeV² and 1.1 < W < 3.1 GeV' for 'the total inclusive transverse and longitudinal proton cross section,' and the abstract states that the fit 'fits both transverse and longitudinal cross sections.' The supporting evidence, Figure 5, is a histogram of residuals in the reduced cross section σr, not in σT or σL separately. Because σr = σT + εσL, a small residual in σr constrains only the combination sampled at the ε values actually measured; for E00-116 (4.5 < Q² < 7.5, 256 points, single kinematic setting per (W, Q²)) there is no ε lever arm at all, so σL in that region is an extrapolation of Eq. 19 rather than a fitted quantity. The authors acknowledge this in §V ('the fit for σL does rely to some extent on the extrapolation in Q2 of the fit form used'), but the abstract and the closing sentence do not carry that qualification. Please restate the 3% claim explicitly as a statement about σr, and state separately what is known about σT and σL in the region Q² > 4.5 GeV² where no separation exists.
[§III and §V; Tables III and IV] The paper reports no χ² per degree of freedom for the global fit or for any individual data set, and no uncertainties, covariance matrix, or correlation information for the 75 parameters in Tables III and IV. For a fit paper whose central claim is a quantitative accuracy statement, this is load-bearing: the statement in §V that 'more than half of the data points deviate from the fit by less than 3%' is a weak summary statistic for a 75-parameter fit to roughly 3500 points, and it cannot be compared with the earlier fits the abstract claims to improve upon. The parameter values themselves signal severe degeneracy — for resonance 2, aT = 6823.2 and bT = 33521.0, and for resonance 3, dL = 97.046 — and without correlations these entries are not interpretable by a user. Please add χ²/dof (overall and per data set), and either parameter uncertainties or an explicit statement that the parameters are strongly correlated and should not be varied individually.
[§IV] The data sets are stated to carry normalization uncertainties of about 2% (Hall C) and the fit is claimed to agree at the 3% level, but the manuscript does not describe how normalization uncertainties entered the minimization. Were overall normalization offsets floated for each data set, or were the data taken at face value? If the latter, a substantial part of the quoted 3% agreement is absorbed by normalization freedom that is not accounted for, and the residual distribution in Figure 5 is not a clean measure of fit quality. This should be stated explicitly in §IV or §III, together with the treatment of point-to-point systematic uncertainties.
[§IV and §V] The fit is motivated in §I by applications to radiative corrections and to the extraction of spin structure functions, yet the manuscript never states whether the fitted cross sections are Born-level or radiatively corrected, nor whether the data sets were radiatively corrected before entering the fit. Since the fit is offered as an input to radiative-correction calculations, this is a load-bearing ambiguity for the stated use case. Please state the radiative-correction status of both the fit output and the input data.
[§III D versus Table IV caption] There is an internal inconsistency in the treatment of Q0. Equation 22 and the surrounding text fix Q0² = 0.05 GeV², and Eq. 23 separately uses Q0² = 0.125 GeV², while the Table IV caption states that 'the parameters Q0 and m0 which determine the transition of σNRT to Q² = 0 were determined from the fit.' These three statements cannot all be correct. Please clarify which quantities are fixed and which are fitted, and use distinct symbols for the two different Q0 values appearing in Eqs. 22 and 23.

Minor objections (10)

[Eq. 20] The text states that Eq. 20 'is just the dipole form for ci = 2,' but the large-Q² limit is AiT(0)(1 + Q²/0.91)^ci · ai/bi, which reduces to the dipole form only when ai/bi = 1. For resonance 1, ai/bi = 3.36, so the statement as written is inaccurate; please qualify it.
[Eq. 24] The function t = log(log([Q² + m0]/0.332)/log(m0/0.332)) is introduced without motivation, and the numerical constants 0.332 and m0 = 4.2802 GeV are unexplained. A sentence on the origin of this form, and on the sensitivity of the fit to the choice, would help the reader.
[§III D] The text states that the x′ factor 'allows a good fit to the data to be obtained up to W = 3.2 GeV,' whereas the stated fit range and the abstract give W < 3.1 GeV. Please reconcile.
[Abstract] The abstract quotes 0 ≤ Q² < 8 GeV², while the resonance data extend to 7.5 GeV² and the SLAC DIS data to 9.5 GeV². Please state the range of the fit itself rather than a rounded envelope.
[Table III, resonance 7] For resonance 7 the entries aT = 0.000, bT = 0.000, cT = 1.000 are listed alongside fitted parameters without indicating whether they were fixed or determined. Since this state is an effective parametrization of the W ≈ 1.9 GeV region rather than a physical resonance, please say so in the table caption and mark fixed values explicitly.
[Table III and §III B] The text states that S11(1535) was excluded from the σL fit, yet Table III lists a longitudinal amplitude AL(0) = 0.0 for resonance 2 with dashes for dL and eL. Please state in the caption that this entry is absent from the longitudinal fit rather than fitted to zero.
[Figure 5] The residual histogram is restricted to Q² > 0, thereby excluding the photoproduction region where Figure 3 shows the largest oscillations around unity. A version broken down by Q² bin, or a companion table of residuals per data set, would make the accuracy claim auditable.
[§V and abstract:s2] The abstract claims improvement over previous fits, but no quantitative comparison to the Stuart or Niculescu fits is shown. A figure or table of residuals for one of those fits over the same data would substantiate the claim at little cost.
[§IV] The largest single data set in the fit, E00-002 with 1346 points, is preliminary and available only from a webpage, and the fit code is available only by email request. Given that the fit is intended as a community tool, please state clearly which results depend on the preliminary data and consider depositing the code and the fit tables in a permanent public location.
[General] The manuscript contains numerous typographical errors, including 'Cros s Sections' in the title, 'in elastic', 'transistion', 'descripton', 'consequentially', 'resonanance', 'addito n', 'uncertanties', 'explaination', 'existance', and 'discrepency'. A careful proofreading pass is needed.

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The paper

The paper claims

A 75-parameter fit reproduces electron-proton scattering data to about 3 percent across the proton resonance region, separating the transverse and longitudinal responses.

The reading

This paper asks a practical question: can one parameterized formula reproduce the measured cross section for an electron scattering off a proton across the whole resonance region — the energy band where the proton is kicked into short-lived excited states — accurately enough to stand in for the data themselves? The authors fit 75 parameters to a large body of measurements spanning $0.18 < Q^2 < 7.5$ GeV$^2$ and $1.1 < W < 3.1$ GeV, anchored by the recent longitudinal/transverse-separated measurements that pin down the two photon-absorption cross sections individually rather than through an assumed ratio. The result describes the data at the 3 percent level or better for the large majority of points, and joins smoothly onto photoproduction at $Q^2 = 0$ and onto deep inelastic scattering at high $Q^2$ and $W$. The motivation is downstream: radiative corrections, extractions of spin structure functions from asymmetry measurements, and low-energy neutrino-nucleon models all need a reliable stand-in for the proton cross section where data are sparse or absent.

What carries the argument

The load-bearing device is the threshold-dependent relativistic Breit-Wigner form, $BW_i = K_i K^i_{cm} / (K K_{cm}) cdot f_{tot,i} f_{f,i} f_i / [(W^2 - M_i^2)^2 + (M_i f_{tot,i})^2]$, multiplied by a squared $Q^2$-dependent transition amplitude $[A^i_{T,L}(Q^2)]^2$ and summed incoherently with a non-resonant background. The transverse amplitude is $A^i_T(Q^2) = A^i_T(0)(1 + Q^2/0.91)^{c_i}(1 + a_i Q^2)/(1 + b_i Q^2)$, which reduces to a dipole form at large $Q^2$ and approaches the measured photoproduction value linearly as $Q^2 to 0$. The longitudinal amplitude is $A^i_L(Q^2) = A^i_L(0) Q^2 (1 + d_i Q^2) e^{-e_i Q^2}$, which vanishes at $Q^2 = 0$ because current conservation demands it and at large $Q^2$ because helicity conservation in scattering off spin-1/2 fermions demands it. The full width is built from pion, eta, and two-pion partial widths with Blatt-Weisskopf damping factors, so that each resonance turns on correctly at its own threshold. The non-resonant transverse piece carries a factor $x' = (1 + (W^2 - (M_p + m_pi)^2)/(Q^2 + Q_0^2))^{-1}$ that approaches a constant at $Q^2 to 0$, vanishes at pion threshold, and suppresses the unphysical rise with $W$ that earlier fits of this type suffered above $W approx 2$ GeV.

Extended reading notes

Core claim

The paper's claim is that a single empirical fit can describe inclusive electron-proton cross sections over the full kinematic reach of the 6 GeV experimental program in the resonance region, and can do so separately for the transverse and longitudinal pieces. The cross section is written as $d^2f/(dE' dE) = f_c [f_T(W^2,Q^2) + f_e f_L(W^2,Q^2)]$, and the reduced cross section $f_r = f_T + f_e f_L$ is fit directly to the data, with $f_T$ and $f_L$ each parameterized as an incoherent sum of seven threshold-dependent Breit-Wigner resonances plus a smooth non-resonant background. The fit is anchored by the L/T-separated measurements, which supply the range in $f_e$ needed to constrain the two pieces independently, and by un-separated data at higher $Q^2$, deep inelastic data up to $W = 3.1$ GeV, and photoproduction data at $Q^2 = 0$. The authors report that nearly all fitted points deviate by less than 5 percent and more than half by less than 3 percent, and that the fit reproduces the data reasonably at both low and high $f_e$ for $Q^2 < 2$ GeV$^2$ — the evidence that both the transverse and longitudinal cross sections are well represented there.

Load-bearing premise

The fit assumes the cross section is an incoherent sum of Breit-Wigner resonances and a smooth background, with each resonance forced into a fixed $Q^2$ shape, so that where that shape is wrong the total may still fit while the individual resonance parameters cease to mean anything physical.

Editorial extensions

If this is right

Radiative corrections to electron-proton scattering in the resonance region can be computed from a single continuous parameterization rather than interpolated between sparse data.
Spin structure functions can be extracted from asymmetry measurements with the longitudinal and transverse pieces treated separately, instead of assuming a deep-inelastic ratio $R = f_L/f_T$ holds through the resonances.
Low-energy neutrino-nucleon cross section models gain a constrained vector-channel input over the range relevant to oscillation analyses.
Sum rules built on integrals over proton structure functions can be evaluated with a controlled treatment of the high-$x$ resonance contribution.
The fit provides a compact representation of world data spanning photoproduction to deep inelastic scattering, with continuous behavior at both kinematic ends.

Reading between the lines

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

The authors note that the resonance structure in $f_L$ peaks at different masses and prefers narrower widths than in $f_T$; letting the width parameters vary independently for the longitudinal piece is the obvious next iteration and would likely improve the worst-fitting region, the dip between the second and third resonance for $2 < Q^2 < 4$ GeV$^2$.
Because the fit is anchored at high $Q^2$ largely by single-setting data with no $f_e$ range, the longitudinal cross section there is effectively an extrapolation of the chosen functional form; a future Rosenbluth separation at $Q^2$ between 4.5 and 7.5 GeV$^2$ with wide angle coverage would test the part of the fit that is least constrained by measurement.
The authors' own remark that the incoherent sum may be failing in the dip region is a testable statement: coherence between resonant and non-resonant amplitudes would show up as a systematic, $f_e$-dependent residual in exactly that $W$ window, which the existing separated data could be re-analyzed to look for.
A fit of this kind is only as transportable as its resonance parameters; users who need the individual transition form factors rather than the total cross section should treat the per-resonance entries as effective bookkeeping rather than measured quantities, since the authors state the second-resonance-region transverse form factors disagree with exclusive extractions.

Original abstract

An empirical fit is described to measurements of inclusive inelastic electron-proton cross sections in the kinematic range of four-momentum transfer $0 \le Q^2<8$ GeV$^2$ and final state invariant mass $1.1<W<3.1$ GeV. The fit is constrained by the recent high precision longitudinal and transverse (L/T) separated cross section measurements from Jefferson Lab Hall C, un-separated Hall C measurements up to $Q^2$ $\approx 7.5$ ${\rm GeV}^2$, and photoproduction data at $Q^2 = 0$. Compared to previous fits, the present fit covers a wider kinematic range, fits both transverse and longitudinal cross sections, and features smooth transitions to the photoproduction data at $Q^2=0$ and DIS data at high $Q^2$ and $W$.

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, 3,246 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.53 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

An empirical fit is described to measurements of inclusive inelastic electron-proton cross sections in the kinematic range of four-momentum transfer $0 \le Q^2<8$ GeV$^2$ and final state invariant mass $1.1<W<3.1$ GeV. The fit is constrained by the recent high precision longitudinal and transverse (L/T) separated cross section measurements from Jefferson Lab Hall C, un-separated Hall C measurements up to $Q^2$ $\approx 7.5$ ${\rm GeV}^2$, and photoproduction data at $Q^2 = 0$. Compared to previous fits, the present fit covers a wider kinematic range, fits both transverse and longitudinal cross sections, and features smooth transitions to the photoproduction data at $Q^2=0$ and DIS data at high $Q^2$ and $W$.

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	An empirical fit is described to measurements of inclusive inelastic electron-proton cross sections in the kinematic range of four-momentum transfer $0 \le Q^2<8$ GeV$^2$ and final state invariant mass $1.1<W<3.1$ GeV.	contribution 0.96	0.83	0.10	asserted 0.99
s1	The fit is constrained by the recent high precision longitudinal and transverse (L/T) separated cross section measurements from Jefferson Lab Hall C, un-separated Hall C measurements up to $Q^2$ $\approx 7.5$ ${\rm GeV}^2$, and photoproduction data at $Q^2 = 0$.	method 0.99	0.26	0.05	asserted 1.00
s2	Compared to previous fits, the present fit covers a wider kinematic range, fits both transverse and longitudinal cross sections, and features smooth transitions to the photoproduction data at $Q^2=0$ and DIS data at high $Q^2$ and $W$.	contribution 0.91	0.88	0.41	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.52 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v4

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.** FIG. 1: (Color online) Comparison of the fit results (solid li

**Figure 2.** FIG. 2: (Color online) Comparison of fit (solid line) to the ph

**Figure 3.** FIG. 3: (Color online) Ratio of all fitted cross section data t

**Figure 4.** FIG. 4: (Color online) Ratio of selected cross section data t

**Figure 5.** FIG. 5: Frequency distribution for the percent differences o

Figures reproduced from arXiv:0712.3731 by the authors.

References

Works cited (20)

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M. MacCormick et al. , Phys. Rev. C 53, 41 (1996). 9 W2 [GeV2] s data / s fit FIG. 3: (Color online) Ratio of all ﬁtted cross section data t o the ﬁt results at the eight Q2 ranges indicated. The units of Q2are GeV 2. 10 W2 [GeV2] s data / s fit FIG. 4: (Color online) Ratio of selected cross section data t o the ﬁt at the seven Q2 ranges indicated ( Q2 in...

View on Pith 1996

Forward citations

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How later papers used it

66 later papers cite it

Evidence: substantial. 55 of the citing papers share no author with it, and 33 of those carry a confident label from Pith's citation classifier.

Pith read 21 of the 135 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

4 later papers by other authors are listed below: 2 used its method or tool, 2 used its data or values and 1 compared its own results with it. 1 of them appears under more than one label. 2 more papers by the same authors are listed: 1 used its method or tool and 1 used its data or values.

Uses its method or tool 3 of 14 papers with this label · 1 by the same authors

These polarized cross section differences were formed by measuring double-spin asymmetries and combining these with the Bosted-Christy unpolarized cross section model [ref] , as is described in detail in [ref] and calculated with: [equation] [equation] where $A_∥,⊥$ is the asymmetry measured by E08-027 using a longitudinally polarized or transverse polarized target respectively, and $σ_0$ is the unpolarized cross section which in this case was generated with the Bosted-Christy model.

A New Low $Q^2$ Measurement of the Proton's $g_1$ Spin Structure Function from Longitudinal & Transverse Polarized Data (2026) · Introduction · 0.92
Adapted this paper's Christy-Bosted parametrization of the nonresonant background for the transverse electromagnetic cross section.

Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element (2020) · 0.97 · paraphrased: the licence does not allow quoting

By the same authors

Used the same functional form as this paper for the fit form describing the transverse cross section for the average of a proton and a neutron.

Empirical Fit to Inelastic Electron-Deuteron and Electron-Neutron Resonance Region Transverse Cross Sections (2007) (same authors) · 0.90 · paraphrased: the licence does not allow quoting

Uses its data or values 3 of 19 papers with this label · 1 by the same authors

Took the numerical values of its fit parameters from this paper.

Electroweak axial structure functions and improved extraction of the $V_{ud}$ CKM matrix element (2020) · 0.83 · paraphrased: the licence does not allow quoting
Added a 3% error band to this paper's BC fit and used the same error estimate for all Regge pole residues.

Two-photon exchange correction to muon-proton elastic scattering at low momentum transfer (2015) · 0.92 · paraphrased: the licence does not allow quoting

By the same authors

Used the ratio of longitudinal to transverse cross sections from this paper's fit to world proton data to obtain W_2^I.

Empirical Fit to electron-nucleus scattering (2012) (same authors) · 0.95 · paraphrased: the licence does not allow quoting

Compares with it 1 of 9 papers with this label

Compared the contributions inferred from the data with this paper's background model.

Nucleon resonance contributions to unpolarised inclusive electron scattering (2019) · 0.97 · paraphrased: the licence does not allow quoting

How the literature uses it

46 arXiv papers cite this in 101 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

Builds on it 1 paper

Since the present underlying fit is to the average free nucleon, we can use the proton fit [ref] to obtain predictions for the ratio of neutron to proton transverse cross sections (or equivalently the ratio $F_1^n/F_1^p$), as illustrated in Fig.[ref]a.

Empirical Fit to Inelastic Electron-Deuteron and Electron-Neutron Resonance Region Transverse Cross Sections · Fit results · 0.88

Uses its method or tool 7 papers

For the estimates of [ref] , a simple dipole model with the dipole mass $Λ≈1$ GeV for all the transition resonance form factors was employed. * Model II: Another form of resonance and background contributions and transition form factors was used in [ref] to fit virtual photon data. * Model III: As Fig. [ref] clearly demonstrates, the background of [ref] cannot be used too far beyond the resonance region.

Dispersion corrections to parity violating electron scattering · Modeling Real and virtual photoabsorption data · 0.88
The fit form used to describe $σ^T_N$ (the transverse cross section for the average of a proton and a neutron) used the same functional form as Ref. [ref] .

Empirical Fit to Inelastic Electron-Deuteron and Electron-Neutron Resonance Region Transverse Cross Sections · Free Nucleon Fit Form · 0.90
Inelastic scattering was modeled using a Fermi-convolution method of “smearing” free proton [ref] and neutron [ref] cross sections.

Ratios of 15N/12C and 4He/12C inclusive electroproduction cross sections in the nucleon resonance region · Experiment · 0.95

Uses its data or values 14 papers

The parameters $C_i,j$ (i=0,1,2,j=1,2) are obtained from the fit of the experimental results on Q$^2$-evolution of the $F_1(W,Q^2)$ and $F_2(W,Q^2)$ inclusive structure functions from the CLAS data [ref] or by combining the CLAS data and the parameterization [ref] of the world data.

Evaluation of the inclusive electron scattering observables in the resonance region from the experimental data · Method for evaluation of the inclusive electron scattering of observables · 0.97
To obtain $W_2^I$, we use the relation: [equation] where [equation] where $R_p$ is the ratio of longitudinal to transverse cross sections from the fit to world proton data given in Ref. [ref] .

Empirical Fit to electron-nucleus scattering · Inelastic Fit function · 0.95
The evaluation of the polarizability corrections for higher $Q^2$ is similar to the evaluation in the electronic case, and depends upon the same combination described previously of EG1 data for $g_1/F_1$, Christy and NMC/E143 fits for $F_1$, and supplements from Simula et al. and E155 fits where there is no EG1 data [ref] .

Proton structure corrections to electronic and muonic hydrogen hyperfine splitting · Muonic hydrogen structure-dependent corrections · 0.93

Compares with it 9 papers

It can be seen in Fig. [ref] that there are two noticeable oscillations in the ratios at low $W$ and $Q^2$: this trend is also seen in the proton fit of Ref. [ref] .

Empirical Fit to Inelastic Electron-Deuteron and Electron-Neutron Resonance Region Transverse Cross Sections · Fit results · 0.99
We compare the contributions inferred from the data with the background model from Ref. [ref] , which can be considered as the continuation of the background from the deep inelastic scattering region into the resonance region.

Nucleon resonance contributions to unpolarised inclusive electron scattering · Results and discussion · 0.97
In the $x<0.5$ region, the extracted values are in good agreement with the existing phenomenological fit of inclusive data [ref] and with the BONuS result [ref] .

Nuclear final-state interactions in deep inelastic scattering off the lightest nuclei · Pole extrapolation of BONuS data · 1.00

Cites it as background 3 papers

Since the initial discovery by Bloom and Gilman in 1970, considerable progress has been made in the measurement of unpolarized structure functions at low to moderate $Q^2$ and $W$ and their interpretation in terms of quark-hadron duality, notably at the Thomas Jefferson National Accelerator Facility (also known as Jefferson Lab) [ref] .

Detailed Study of Quark-Hadron Duality in Spin Structure Functions of the Proton and Neutron · Theoretical background · 0.98
Starting from Ref. [ref] , a number of phenomenological analyses are available [ref] , in which the resonance production is considered as a superposition of the Breit-Wiegner poles and the photon-resonance couplings are described in terms of helicity amplitudes (for a recent review see [ref] ).

Hybrid model of proton structure functions · Introduction · 0.89
In the case of DIS the elementary lepton-nucleon cross section can be written as follows (cf. [ref] ): [equation] where $Ω$ and $E^'$ are, respectively, the solid angle and the energy of the scattered lepton in the laboratory frame, [equation] is the flux of virtual photons, $σ_T (σ_L)$ is the photoabsorption cross section for purely transverse (longitudinal) photons, and [equation] is the relative flux of longitudinal virtual photons, $y=ν/E$ is the fraction of the beam energy $E$ carried off by a virtual photon.

Slow neutron production as a probe of hadron formation in high-energy $\gamma^*A$ reactions · Hard interaction · 0.84

What it cites · 1 sentence without a confident label

Uses data or values from 1 paper

For $4.5 < Q^2 < 7.5$ the resonance data aremainly from experiment E00-116 [ref] .

Applications of quark-hadron duality in F2 structure function · The data sets · 1.00

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.

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M. MacCormick et al. , Phys. Rev. C 53, 41 (1996). 9 W2 [GeV2] s data / s fit FIG. 3: (Color online) Ratio of all ﬁtted cross section data t o the ﬁt results at the eight Q2 ranges indicated. The units of Q2are GeV 2. 10 W2 [GeV2] s data / s fit FIG. 4: (Color online) Ratio of selected cross section data t o the ﬁt at the seven Q2 ranges indicated ( Q2 in...

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