Total cross sections

A Donnachie; P V Landshoff

REVIEW

Total cross sections

A Donnachie, P V Landshoff

High Energy Physics - Phenomenology · Submitted 2 Sep 1992 · 2 references

Pith's verdict: The paper that fixed the two-power Regge form everyone still quotes; the physics holds up, but the parameter set lives only in a figure and no chi-squared is tabulated anywhere.

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arXiv IDhep-ph/9209205 (version 1)

Pith ID7BFEKHHN, Pith's permanent record of this paper and its review

CitationA Donnachie, P V Landshoff. "Total cross sections." arXiv:hep-ph/9209205 (1992). https://pith.science/paper/7BFEKHHN

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Referee report

Significance

If the parametrisation holds, the result is a compact, theoretically motivated alternative to the multi-parameter polynomial fits used by the Particle Data Group, and it makes the strong physical statement that the rise of all total cross sections is a property of the exchanged pomeron. The paper earns credit for several things a referee should name explicitly. It makes falsifiable predictions: the 1985 prediction of about 73 mb at √s = 1800 GeV, the 160 μb at √s = 200 GeV for σ(γp), the values 24.9 mb and 25.5 mb for the Ω−/Σ− combination at 14 and 16 GeV, and the s^(2ε)/b behaviour of γp → φp. It supplies independent cross-checks of the same parameters against the real part of the forward amplitude in πp and Kp scattering and against φ photoproduction, which is more than a pure fit-and-extrapolate exercise. The constraint X(ab) = X(pbar-b) enforces the Pomeranchuk theorem, and the footnote contrasting this with the Eq. (1) fits that would have pp overtaking pbar-p near √s = 100 GeV is a genuine and well-taken criticism of the alternative parametrisation. The additive-quark ratio X(πp)/X(pp) = 0.63 versus 2/3 is a nontrivial consistency check.

Major objections (4)

[Opening paragraph, following Eq. (1)] The headline quantitative claim of the paper is that the Regge fits use 16 free parameters against 45 for fits of the type (1), while 'in the high-energy region where Regge theory is applicable (√s greater than about 5 or 10 GeV) our χ2 are much the same.' No χ2 or χ2 per degree of freedom is tabulated anywhere in the manuscript, and the comparison is therefore asserted rather than demonstrated. Since the economy argument is the stated reason for preferring Eq. (2) over Eq. (1), the manuscript should include a table giving, for each of the nine reactions, the number of data points, the fit range in √s, and χ2/dof for both the Regge fit and the corresponding Eq. (1) fit. Without this the central claim of the abstract cannot be checked by a reader.
[Paragraph following Eq. (2); comment 1] The exponents ε and η are determined once from the pp and pbar-p data and then imposed on the other seven reactions, so the conclusion of comment 9 — that all cross sections rise at the same rate, and that the rise is therefore a property of the pomeron — is partly built into the fitting procedure. The figures show that a common exponent fits acceptably, but the manuscript never reports the comparison that would license the universality claim: a fit in which ε is freed for, say, πp, Kp, or γp, together with the resulting Δχ2 and the fitted per-reaction exponent. I would ask the authors to report at least one such freeing, for the reaction with the most data other than pp/pbar-p, so that the reader can see whether the data prefer a common power or merely tolerate one.
[Comment 1 and the paragraph preceding it] The values of the coefficients X and Y are said to be 'shown in figure 1' but are never given numerically in the text. This matters beyond convenience: the ratio X(πp)/X(pp) = 0.63 quoted in comment 5, the unconstrained value X_pn = 22.15 quoted in comment 4, and the arithmetic of Eq. (4), X_s = X_pp − 3(X_πp − X_Kp) = 16.26, cannot be checked without the individual coefficients. A short table listing X and Y for each reaction, with the fit range, would make the paper self-contained and would let the reader verify Eq. (4) directly.
[Comment 1] The argument that agreement with the Tevatron measurement is 'a definite success of the parametrisation' is weakened by the accompanying statement that the CERN collider and Tevatron points 'contribute rather little to the χ2 per degree of freedom' because the pp and pbar-p samples are dominated by low-energy data. If the high-energy points carry little weight, the agreement is less informative than the text implies, and the two statements sit awkwardly together. The authors should quote the χ2 contribution of the Tevatron points explicitly, or repeat the fit with the high-energy points weighted more heavily, so that the reader can judge how much the agreement actually tests the fit.

Minor objections (8)

[Comment 3] The sentence 'our fit 98.39s0.0808 ... exceeds (π/m_π^2) log^2(s/s0) ... only when √s > 1024 GeV' appears to have lost the exponent on the energy; the intended bound is presumably √s > 10^24 GeV. Please correct and state the assumed value of s0, since the comparison with the Froissart-Martin bound depends on it.
[Comment 3] The extrapolation to √s = 40 TeV giving 120 mb lies far outside the fitted range and rests on treating ε as constant, which the authors themselves say is not exact. The caveat is present in the text, but the 120 mb number should be explicitly labelled as an extrapolation wherever it is quoted, including any summary or abstract-level statement.
[Figure 1 caption] The caption 'Data for total cross-sections with fits of type (2)' does not say which reactions appear in which panel, nor does it give the fitted parameters. Please identify the reactions panel by panel and either print the fitted X and Y on the figure or refer to the proposed table.
[Eq. (1)] The symbol P in Eq. (1) is not defined; presumably it denotes momentum. Please define it, and state explicitly which of the parameters A, B, C, D correspond to which physical effect, so that the comparison with Eq. (2) is transparent.
[Comment 6] The discussion leaves open whether the smaller X for Kp reflects a reduced pomeron coupling to strange quarks or a smaller kaon radius. This is a legitimate open question, but the authors should say what measurement would discriminate between the two, since the additive-quark check in Eq. (4) depends on which explanation is correct.
[Reference 7] The citation 'P D B Collins and F D Gault, Physics Letters B273 (1978) 330' appears to have an inconsistent volume and year; B273 corresponds to 1992, not 1978. Please check the reference.
[Reference 14] The UA8 result on pomeron structure is cited as 'to be submitted to Physics Letters B' and is used in comment 9 to support the claim that the pomeron has a real existence. Since this is unpublished, the argument in comment 9 should be phrased so that it does not rest on it alone.
[Comment 8] The prediction of about 160 μb at √s = 200 GeV for σ(γp) is a useful falsifiable statement; please state the fit range and the data set on which it is based, since the γp fit in figure 1d is the least constrained of the nine.

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The paper

The paper claims

A single two-term Regge formula is claimed to describe every measured total cross section, with one shared pair of exponents.

The reading

This paper argues that all measured hadronic total cross sections — $pp$, $pbar p$, $pi^pm p$, $K^pm p$, $pn$, and $gamma p$ — are described by one two-term Regge formula, $sigma_{rm tot} = X s^{epsilon} + Y s^{-eta}$, with the exponents $epsilon = 0.0808$ and $eta = 0.4525$ shared by every reaction. The first term is pomeron exchange and the second is exchange of the $rho,omega,f,a$ trajectory; because the pomeron carries vacuum quantum numbers, its coefficient $X$ must be the same for a reaction and its antiparticle, a constraint the polynomial fits quoted by the Particle Data Group do not respect. Nine cross sections are fitted with 16 free parameters against 45 for the polynomial form, at comparable $chi^2$ above roughly 5 to 10 GeV, so the case rests on economy plus theoretical grounding rather than on a better fit. If the claim holds, the observed rise of cross sections with energy is a property of something exchanged rather than of the hadrons themselves, which makes the rise universal and turns the pomeron into an object with measurable couplings and structure. The same fits are used to predict the Tevatron cross section, the photon-proton cross section soon to be measured at HERA, and a relation among strange-baryon cross sections.

What carries the argument

The load-bearing object is the two-power ansatz combined with a symmetry constraint: a pomeron term $X s^{epsilon}$ whose coefficient $X$ is forced to be equal for $sigma(ab)$ and $sigma(bar a b)$ because the pomeron has vacuum quantum numbers, plus a reggeon term $Y s^{-eta}$ that carries the $C=pm1$ assignments and so differs between particle and antiparticle. The exponents are explicitly effective powers rather than trajectory intercepts: $epsilon$ is slightly below $alpha(0)-1$ because the term absorbs the effect of exchanging more than one pomeron, and $eta$ is similarly shifted by combined reggeon-plus-pomeron exchange. That single shared pair of numbers is what makes the description economical, and it is also what makes it falsifiable, since every reaction must rise at the same rate. The constraint on $X$ is what separates this fit from the polynomial fits of the Review of Particle Properties, which the authors point out would have the $pp$ cross section overtaking $pbar p$ near $sqrt{s}=100$ GeV, in violation of the Pomeranchuk theorem.

Extended reading notes

Core claim

The paper's claim is that Regge theory, truncated to two effective powers, gives a complete and economical account of hadronic total cross sections. The fitted form is $sigma_{rm tot} = X s^{epsilon} + Y s^{-eta}$ with $epsilon = 0.0808$ and $eta = 0.4525$ fixed once from a simultaneous fit to $pp$ and $pbar p$ above $sqrt{s}=10$ GeV, and then reused unchanged for every other reaction, each new pair of reactions costing only three parameters: a common $X$ and a separate $Y$ for particle and antiparticle. The authors report that the ratio of $X$ for $pi p$ to $X$ for $pp$ comes out at 0.63, close to the $2/3$ of the additive-quark rule, that $X$ for $Kp$ is somewhat smaller, and that the coefficient $Y$ for $K^+p$ is poorly determined by the data. They note that the fits reproduce the Tevatron measurement, matching their own earlier prediction of about 73 mb at $sqrt{s}=1800$ GeV, and that the rising term is already present near $sqrt{s}=5$ GeV with no visible change of slope when charm and minijet production turn on. A further consequence they draw is that the additive-quark rule, applied to the combination $2sigma(Omega^- p) - sigma(Sigma^- p)$ where only pomeron exchange can contribute, predicts $16.26, s^{0.0808}$, giving 24.9 mb at $sqrt{s}=14$ GeV against a measured $25 pm 0.7$ mb.

Load-bearing premise

The two exponents are held fixed, although the paper states immediately after its main formula that both are effective powers that vary slowly with energy and that multiple pomeron exchange should make $epsilon$ decrease as energy rises, so every coefficient and every extrapolation rests on freezing a quantity the authors say is not constant.

Editorial extensions

If this is right

The rise of every total cross section with energy is attributed to a single exchanged object rather than to the individual hadrons growing, which rules out geometric 'bigger and blacker hadron' pictures as the explanation of the rise.
The ratio of pomeron couplings, about $2/3$ for $pi p$ versus $pp$ and lower still for $Kp$, becomes a quantitative handle on how the pomeron couples to light versus strange quarks and on hadron-radius corrections to the additive-quark rule.
Because only the pomeron couples to both the proton and the $gamma p to phi p$ vertex, that cross section should behave as $s^{2epsilon}/b$ with a constant slope $b$, giving a clean test of the same exponent in a different channel.
The fits extrapolate to about 160 $mu$b for $sigma(gamma p)$ at $sqrt{s}=200$ GeV, a prediction the authors expect HERA to test shortly.
The fitted rise, if extrapolated naively to $sqrt{s}=40$ TeV, gives about 120 mb, which the authors flag as likely an over-estimate of a few mb because the effective exponent should drift downward.

Reading between the lines

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

The frozen-exponent approximation is itself testable from the same data: fitting the low-energy and high-energy halves of each dataset separately would expose the drift in $epsilon$ that the authors say must exist, and the size of that drift sets the real uncertainty on every quoted coefficient $X$ and $Y$.
If the exponent is genuinely universal, then a precise measurement of any single total cross section at a new energy constrains all the others, so the strange-baryon combination $2sigma(Omega^- p) - sigma(Sigma^- p)$ becomes a cheap indirect probe of the pomeron coupling to strange quarks.
The claim that new production channels such as minijets do not change the rate of rise, while their onset is unmistakable in multiparticle data, is a strong statement about cancellations between production processes; a measured change in slope across the minijet threshold would be evidence against the single-power description.
The comparison of $rho$, the real-to-imaginary ratio, in $pi^pm p$ and $K^pm p$ turns the fit into an over-determined system, since the same coefficients $Y$ must reproduce both the cross sections and the real parts; a better measurement of $rho$ in $K^pm p$ would tighten the poorly determined $Y_{K^+p}$ more efficiently than more cross-section points.

Original abstract

Regge theory provides a very simple and economical description of all total cross sections

The compiled record

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What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.04 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.08 · 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.

Regge theory provides a very simple and economical description of all total cross sections

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	Regge theory provides a very simple and economical description of all total cross sections	background 0.83	0.08	0.61	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.55 · evidence from argument 0.92.

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not examined

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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

References

Works cited (2)

[1]

1 Particle Data Group, Physical Review D45 (1992) number 11 2 P D B Collins, Introduction to Regge theory , Cambridge University Press (1977) 3 A Donnachie and P V Landshoﬀ, Nuclear Physics B231 (1983) 18 9 4 A Donnachie and P V Landshoﬀ, Nuclear Physics B267 (1986) 69 0 5 M Block and R N Cahn, Physics Letters B188 (1987) 143 6 M Jacob and P V Landshoﬀ, M...

View on Pith 1992
[1992]

377 13 H Cheng, J K Walker and Wu, Physics Letters 44B (1973) 97 14 UA8 collaboration: P Schlein, LPTHE’91 Conference, Gene va, July 1991, (World Scien- tiﬁc, Singapore, ed. L Di Lella) and A Brandt et al, to be submi tted to Physics Letters B. 15 I R Zhitnitsky, A A Oglobin and V L Chernyak, Sov Journ Nuc Ph ys 48 (1988) 536 16 Durham data base, telnet 1...

View on Pith 1973

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How later papers used it

100 later papers cite it

Evidence: substantial. 100 of the citing papers share no author with it, and 29 of those carry a confident label from Pith's citation classifier.

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5 later papers by other authors are listed below: 3 used its method or tool and 2 used its data or values.

Uses its method or tool 3 of 10 papers with this label

Following this paper, used a two component parametrisation for the total cross sections of kaon-nucleon scattering.

Towards a complete study of central exclusive production of $K^{+}K^{-}$ pairs in proton-proton collisions within the tensor Pomeron approach (2018) · 0.96 · paraphrased: the licence does not allow quoting
Employed the soft Pomeron model proposed by this paper, incorporating its effective Regge trajectory.

Exploring Nucleon Structure and the Proton Mass Problem through Holographic QCD (2026) · 0.97 · paraphrased: the licence does not allow quoting
Parametrized the cross sections in the form given by this paper.

Constraints on the dark photon from deep inelastic scattering (2021) · 0.89 · paraphrased: the licence does not allow quoting

Uses its data or values 2 of 11 papers with this label

Using $α^'_= 0.25 GeV^-2$ [ref] and $s = (19 GeV)^2$ [ref] , we obtain central values of

Production Effects and Final-state Interactions in $\pi_1 \to 3\pi$ (2026) · Global fit · 0.89
Used alpha(0) = 1.1 corresponding to a soft effective Pomeron from this paper.

Open charm production in Double Parton Scattering processes in the forward kinematics (2016) · 0.84 · paraphrased: the licence does not allow quoting

How the literature uses it

86 arXiv papers cite this in 104 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 · 64 sentences without a confident label

Contests it 1 paper

A more updated theory using the single pomeron exchange model while describing the Tevatron data correctly is not consistent with the Unitarity constraint ( [ref] , [ref] ).

Measurement of the Proton-Air Cross Section with Telescope Array's Middle Drum Detector and Surface Array in Hybrid Mode · Proton-Proton Cross section · contest 0.71

Uses its method or tool 8 papers

By default, the `A3' tune [ref] was used, which adopts the `Donnachie–Landshoff' [ref] choice for the pomeron flux factor to describe the $ξ$ and $t$ dependences in the diffractive channels with pomeron intercept $α(0) = 1.07$.

Measurement of differential cross sections for single diffractive dissociation in $\sqrt{s} = 8$ TeV $pp$ collisions using the ATLAS ALFA spectrometer · Monte Carlo simulation · 0.84
Following Donnachie and Landshoff [ref] we use a two component parametrisation for the total cross sections of kaon-nucleon scattering

Towards a complete study of central exclusive production of $K^{+}K^{-}$ pairs in proton-proton collisions within the tensor Pomeron approach · $K^+K^-$ continuum central production · 0.96
In Pythia 8.2 by default the total cross section is modelled by the Donnachie-Landshoff (DL) parameterisation [ref] : [equation] where $ε=0.0808$, $η=0.4525$, $A$ and $B$ denote the initial state particles and $X^AB,Y^AB$ depend upon these states.

Average Event Properties from LHC to FCC-hh · Modelling of the total, elastic and diffractive cross sections · 0.89

Uses its data or values 9 papers

Adopting [ref] , the Pomeron exchange contribution grows as $s^1.08$ and the overall factor is chosen such that $Im_VV→VV=8.56 mb s(s/s_0)^0.08$ [ref] . ] [equation] for $s≫GeV^2$, where we introduced $s_0 ∼GeV^2$.

Is the Standard Model in the Swampland? Consistency Requirements from Gravitational Scattering · Introduction · 0.97
Using $α^'_= 0.25 GeV^-2$ [ref] and $s = (19 GeV)^2$ [ref] , we obtain central values of

Production Effects and Final-state Interactions in $\pi_1 \to 3\pi$ · Global fit · 0.89
The Pomeron intercept has been obtained from the fit of equation ([ref]) to the proton-proton cross-section experimental data, obtaining to $α_P(0)=1.0808$ [ref] .

Proton helicity structure function g_1^p from a holographic Pomeron · The soft Pomeron and the BFKL Pomeron · 0.98

Compares with it 7 papers

This ratio $σ_tot^πp / σ_tot^p p$ is consistent with the result obtained in Ref. [ref] and the value which can be extracted from the results presented in Ref. [ref] , although the other ratio $σ_tot^ππ / σ_tot^p p$ is obviously smaller compared to the result in Ref. [ref] .

Elastic pion-proton and pion-pion scattering via the holographic Pomeron and Reggeon exchange · Numerical results · 1.00
This value is highly consistent with the classic Donnachie-Landshoff soft Pomeron intercept ($α_0 ≈1.08$) [ref] and is significantly lower than the hard Pomeron intercept ($α_0 ≈1.2 ∼1.4$) typically extracted from HERA data at very small $x$ [ref] .

Probing Proton Structure via Physics-Guided Neural Networks in Holographic QCD · Phenomenological Pomeron Intercept · 0.97
We shall discuss various factorization results [ref] and compare some of them with the HERA data [ref] as well as with predictions of our QCD eikonal model with resummation, hereafter referred to as the BN model [ref] .

Total photoproduction cross-section at very high energy · Introduction · 0.85

Cites it as background 12 papers

Historically, hadronic exchanges have been remarkably well described by the simple-pole model of Donnachie and Landshoff [ref] , which assumes that, at high energy, the hadronic amplitude is dominated by a simple-pole pomeron: [equation] The first question is whether this simple model extends to other processes, and in particular to those measured at HERA.

The soft and the hard pomerons: elastic scattering and unitarisation · The effective trajectory · 0.99
The simplest and most successful parametrization of the total cross-section for proton-proton and proton-antiproton scattering [ref] follows from the optical theorem and describes the initial fall through the exchange of Regge trajectories, i.e. $s^α_R(0)-1$ with $α_R(0)<1$ and the rise as due to Pomeron exchange, i.e. $s^α_P(0)-1$ with $α_P(0)>1$.

QCD Contributions to the Froissart bound for the total cross-section · Introduction · 0.85
Donnachie and Landshoff first showed that experimental data of various hadron-hadron total cross sections can be well reproduced with this description [ref] .

Elastic proton-neutron and antiproton-neutron scattering in holographic QCD · Introduction · 0.86

Discussion

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[1] [1]

1 Particle Data Group, Physical Review D45 (1992) number 11 2 P D B Collins, Introduction to Regge theory , Cambridge University Press (1977) 3 A Donnachie and P V Landshoﬀ, Nuclear Physics B231 (1983) 18 9 4 A Donnachie and P V Landshoﬀ, Nuclear Physics B267 (1986) 69 0 5 M Block and R N Cahn, Physics Letters B188 (1987) 143 6 M Jacob and P V Landshoﬀ, M...

View on Pith 1992

[2] [1992]

377 13 H Cheng, J K Walker and Wu, Physics Letters 44B (1973) 97 14 UA8 collaboration: P Schlein, LPTHE’91 Conference, Gene va, July 1991, (World Scien- tiﬁc, Singapore, ed. L Di Lella) and A Brandt et al, to be submi tted to Physics Letters B. 15 I R Zhitnitsky, A A Oglobin and V L Chernyak, Sov Journ Nuc Ph ys 48 (1988) 536 16 Durham data base, telnet 1...

View on Pith 1973