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Measurement of the proton and deuteron structure functions, F2p and F2d, and of the ratio sigma(L)/sigma(T)

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The New Muon Collaboration (NMC)

High Energy Physics - Phenomenology · Submitted 3 Oct 1996 · 24 references

Pith's verdict: A careful, honest measurement of small-x R and low-Q2 F2 that will be cited for its tables, not its QCD comparison.

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arXiv IDhep-ph/9610231 (version 2)
Pith ID56SLQY5E, Pith's permanent record of this paper and its review
CitationThe New Muon Collaboration (NMC). "Measurement of the proton and deuteron structure functions, F2p and F2d, and of the ratio sigma(L)/sigma(T)." arXiv:hep-ph/9610231 (1996). https://pith.science/paper/56SLQY5E
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The paper

The paper claims

The New Muon Collaboration extracts the ratio of longitudinal to transverse photon absorption, $R = $sigma_L/sigma_T$, in ten bins of $x$ down to $x = 0.0045$, by comparing muon scattering cross sections taken at different beam energies.

The reading

Deep inelastic muon scattering off protons and deuterons measures a structure function, $F_2$, which is straightforward to extract when the exchanged photon is transversely polarised and the scattering is at low $y$. The awkward quantity is $R = $sigma_L/sigma_T$, the ratio of longitudinal to transverse virtual-photon absorption, because it only shows up as a small difference between cross sections measured at the same $x$ and $$Q^{2}$$ but different beam energies. The collaboration adds small-angle-trigger data at 200 and 280 GeV to its full existing sample, which pushes the reach down to $x = 0.0045$ and supplies enough lever arm in $y$ to fit $R$ rather than assume it. The payoff is a table of ten $R$ values for $0.002 < x < 0.12$, each averaged over $$Q^{2}$$ within its $x$ bin, with total uncertainties between 0.07 and 0.11. If the extraction holds, the extrapolation of the older $R$ parametrisation below $x = 0.015$ is confirmed, and one of the input uncertainties in every global fit to parton distributions at small $x$ gets smaller.

What carries the argument

The load-bearing device is the $y$-dependence of the one-photon-exchange cross section. Writing the differential cross section in terms of $F_2$ and $R$, the terms multiplying $R$ are suppressed at small $y$ and grow with $y$, so a set of cross sections at the same $(x, Q^2)$ but different incident energies $E$ traces out a curve whose shape fixes $R$ once $F_2$ is known. The collaboration implements this in two stages: first, each of the six data sets (four energies, two triggers) is fitted separately with a ten-parameter cross-section form used as Monte Carlo weights, iterating until convergence; second, all six cross sections are corrected for higher-order electroweak effects and fitted simultaneously for $F_2$ and $R$, with $F_2$ described by a fifteen-parameter form. Two cross-checks are run: a per-$x$-bin fit of an average $R$ together with a flexible $F_2^d$ parametrisation, and the traditional $varepsilon$-method that fits the cross section linearly against $varepsilon$ within individual $(x, Q^2)$ bins. All three agree within their differing sensitivities.

Extended reading notes

Core claim

The paper reports a measurement of $R = $sigma_L/sigma_T$ in the range $0.002 < x < 0.12$, obtained from the full NMC data set: 1.82 million large-angle-trigger events plus 0.54 million small-angle-trigger events recorded at 200 and 280 GeV. Because the small-angle trigger accepts scattering angles of 5 to 25 mrad, it reaches smaller $x$ and smaller $y$ than the large-angle trigger, and its inclusion both extends the kinematic reach to $x = 0.0045$ and gives the several beam energies needed to separate $R$ from $F_2$ through the $y$-dependence of the one-photon cross section. The extracted values fall from $R = 0.537$ at $x = 0.0045$ to $R = 0.043$ at $x = 0.11$, with statistical errors of 0.03 to 0.07 and systematic errors of 0.07 to 0.11 that are largely correlated between bins. The authors compare these numbers with the R1990 parametrisation used in earlier $F_2$ analyses and with a next-to-leading-order QCD calculation built from the Altarelli-Martinelli relation, and find agreement with both, including at the smallest $x$ where the parametrisation was an extrapolation. They also compare with BCDMS and CDHSW at comparable $x$ and $$Q^{2}$$, and find agreement within the correlated uncertainties, with the NMC values sitting somewhat lower. The companion structure functions $F_2^p$ and $F_2^d$ are given in full tables and agree with SLAC, BCDMS, E665, H1 and ZEUS.

Load-bearing premise

The extraction fits a single averaged $R$ to proton and deuteron data together, which assumes the two nuclei have the same ratio of longitudinal to transverse absorption to within about 0.02, and it further assumes that $R$ does not vary with $Q^2$ inside each $x$ bin, an assumption the authors state their data cannot test.

Editorial extensions

If this is right

  • Prior extractions of $F_2$ at small $x$ that relied on extrapolating the R1990 parametrisation below $x = 0.015$ are validated, since the measured $R$ agrees with that extrapolation within the correlated errors.
  • Global fits to parton distributions gain a measured, rather than assumed, value of $R$ for $0.002 < x < 0.12$, which reduces one input uncertainty in the small-$x$ region.
  • The agreement with the next-to-leading-order calculation of $F_L$ via the Altarelli-Martinelli relation supports using that relation at small $Q^2$ and small $x$, where its validity had been open to question.
  • The absence of any visible difference between $R$ measured on hydrogen and on deuterium, and between NMC and the iron-based CDHSW result, is consistent with no significant nuclear dependence of $R$.
  • Tables 5 and 6 supply $F_2^p$ and $F_2^d$ values with the NMC-measured $R$ alongside values obtained with R1990, so users can see directly how much the choice of $R$ shifts $F_2$ at small $x$.

Reading between the lines

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

  • The paper's own tables make the size of the $R$-dependence visible: at $x = 0.0045$ and $Q^2 = 0.75$ GeV$^2$, switching from the measured $R = 0.537$ to R1990's $0.326$ moves $F_2^p$ from 0.2695 to 0.2516, about 7 percent. Anyone reusing old small-$x$ $F_2$ values should check which $R$ they were extracted with.
  • Because the systematic errors are 1.5 to 3 times the statistical ones and are dominated by the 2 percent relative normalisation between data sets, the obvious next step is a dedicated running with overlapping energies designed to cancel normalisation rather than to extend reach.
  • The flat-in-$Q^2$ assumption is the natural target for a follow-up: a lepton-hadron collider reaching the same $x$ at much higher $Q^2$ would test whether the $x$-dependence seen here is really, as the authors suggest, a reflection of the average $Q^2$ drifting with $x$.
  • The comparison with E665 shows mild tension in $F_2^d$ near $x = 0.01$; a joint re-extraction using a common $R$ would separate a genuine normalisation difference from an $R$-induced shift.
Original abstract

The muon-proton and muon-deuteron inclusive deep inelastic scattering cross sections were measured in the kinematic range 0.002 < x < 0.60 and 0.5 < Q2 < 75 GeV2 at incident muon energies of 90, 120, 200 and 280 GeV. These results are based on the full data set collected by the New Muon Collaboration, including the data taken with a small angle trigger. The extracted values of the structure functions F2p and F2d are in good agreement with those from other experiments. The data cover a sufficient range of y to allow the determination of the ratio of the longitudinally to transversely polarised virtual photon absorption cross sections, R= sigma(L)/sigma(T), for 0.002 < x < 0.12 . The values of R are compatible with a perturbative QCD prediction; they agree with earlier measurements and extend to smaller x.

The compiled record

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

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,472 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.47 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The muon-proton and muon-deuteron inclusive deep inelastic scattering cross sections were measured in the kinematic range 0.002 < x < 0.60 and 0.5 < Q2 < 75 GeV2 at incident muon energies of 90, 120, 200 and 280 GeV. These results are based on the full data set collected by the New Muon Collaboration, including the data taken with a small angle trigger. The extracted values of the structure functions F2p and F2d are in good agreement with those from other experiments. The data cover a sufficient range of y to allow the determination of the ratio of the longitudinally to transversely polarised virtual photon absorption cross sections, R= sigma(L)/sigma(T), for 0.002 < x < 0.12 . The values of R are compatible with a perturbative QCD prediction; they agree with earlier measurements and extend to smaller x.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The muon-proton and muon-deuteron inclusive deep inelastic scattering cross sections were measured in the kinematic range 0.002 < x < 0.60 and 0.5 < Q2 < 75 GeV2 at incident muon energies of 90, 120, 200 and 280 GeV. method 0.57 0.96 0.06 asserted 1.00
s1 These results are based on the full data set collected by the New Muon Collaboration, including the data taken with a small angle trigger. method 0.96 0.73 0.03 asserted 1.00
s2 The extracted values of the structure functions F2p and F2d are in good agreement with those from other experiments. result 0.86 0.81 0.19 asserted 0.98
s3 The data cover a sufficient range of y to allow the determination of the ratio of the longitudinally to transversely polarised virtual photon absorption cross sections, R= sigma(L)/sigma(T), for 0.002 < x < 0.12 . contribution 0.42 0.92 0.12 asserted 0.88
s4 The values of R are compatible with a perturbative QCD prediction; they agree with earlier measurements and extend to smaller x. result 0.53 0.82 0.36 asserted 0.72

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 0.88.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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. The sensitivity of the measured structure functio
Figure 2. The standard NMC method for calculating R (filled circles) compared to two alternative extractions described in the text, per x bin (open squares) or per (x, Q2 ) bin (open triangles). Only statistical errors are shown. The three extractions are compared before any iteration is performed; in particular, the results shown for the standard method are not the final ones (these are shown in figs. 10 and 11). 15
Figure 3. The structure function Fp2 (x, Q2) versus Q2 in bins of x. The six data sets correspond to four different incident energies and two triggers. The new small angle trigger data are shown as filled symbols; bins of x where no small angle data exist are not shown. The data in each x bin have been scaled by the factors indicated in brackets. The error bars represent the quadratic sum of systematic and statistical errors. The normalisation uncertainties are not included. 16
Figure 4. The structure function Fd2 (x, Q2) versus Q2 in bins of x. The six data sets correspond to four different incident energies and two triggers. The new small angle trigger data are shown as filled symbols; bins of x where no small angle data exist are not shown. The data in each x bin have been scaled by the factors indicated in brackets. The error bars represent the quadratic sum of systematic and statistical errors. The normalisation uncertainties are not included. 17
Figure 5. The structure function Fp2 (x, Q2) versus Q2 in bins of x. The corresponding values are given in table 5. The six data sets of fig. 3 have been averaged. The data in each x bin have been scaled by the factors indicated in brackets. The error bars represent the statistical errors; the total systematic uncertainties, apart from the 2.5% normalisation uncertainty, are indicated by the bands. 18
Figure 6. The structure function Fd2 (x, Q2) versus Q2 in bins of x. The corresponding values are given in table 6. The six data sets of fig. 4 have been averaged. The data in each x bin have been scaled by the factors indicated in brackets. The error bars represent the statistical errors; the total systematic uncertainties, apart from the 2.5% normalisation uncertainty, are indicated by the bands. 19
Figure 7. The present results for Fd2 (filled circles) compared to those of BCDMS [10] (open squares) and SLAC [11] (open circles). The data have been adjusted by the normalisation shifts of table 2, and the BCDMS data have been corrected by their calibration uncertainty, as in ref. [1]. At x = 0.50 the BCDMS and SLAC data have been interpolated. The data in each x bin have been scaled by the factors indicated in brackets. The error bars represent the total errors, apart from normalisation uncertainties. 20
Figure 8. The structure function F p 2 and F d 2 from the present measurement (filled circles) compared to those of the E665 experiment at Fermilab [15] (open triangles), in the range 0.004 < x < 0.04 . The NMC data have been interpolated to the E665 x bins. The data in each x bin have been offset by the amounts indicated in brackets. The error bars represent the total errors, apart from normalisation uncertainties. 21
Figure 9. The structure function F p 2 from the present measurement (filled circles) compared to those of the DESY experiments H1 [16] (top, open crosses) and ZEUS [17] (bottom, open triangles), in the range 0.004 < x < 0.20 . The NMC data have been interpolated to the H1 and ZEUS x bins. The data in each x bin have been offset by the amounts indicated in brackets. The error bars, wherever visible, represent the total errors, apart from normalisation uncertainties. 22
Figure 10. (a) The ratio R measured in this experiment, averaged for the proton and the deuteron. The outer error bars represent the quadratic sum of the statistical and systematic uncertainties; the inner bars indicate the statistical errors. The dashed line represents the R parametrisation from ref. [2] at the average Q2 of each x bin. The solid line indicates a QCD calculation described in the text. (b) The ratio R measured in this experiment (filled circles), compared to previous results at comparable x and Q2 obtained by BCDMS [10, 20] (open squares and circles) and by CDHSW [21] (open…
Figure 11. The x dependence of the ratio R in bins of Q2 as measured in this (NMC, filled circles) and previous experiments. These are mainly the SLAC hydrogen and deuterium scattering experiments [2] (open triangles) and the SLAC E140 experiments [22, 23] (filled triangles); also shown are results from CDHSW [21] (open stars) and BCDMS [10] (open squares). The error bars represent the total errors. 24

Figures reproduced from arXiv:hep-ph/9610231 by the authors.

References
How later papers used it

76 later papers cite it

Evidence: substantial. 76 of the citing papers share no author with it, and 61 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 108 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

Uses its data or values 6 of 59 papers with this label
How the literature uses it

62 arXiv papers cite this in 89 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 · 31 sentences without a confident label

Uses its data or values 47 papers
Compares with it 3 papers

Discussion

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