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Evaluation of the forward Compton scattering off protons: I. Spin-independent amplitude
Nuclear Theory · Submitted 31 Aug 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): $\alpha_{E1}+\beta_{M1}=14.0(2)\times 10^{-4}\,\mathrm{fm}^3$.
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The abstract, sentence by sentence
We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections. We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section, and evaluate the various spin-independent sum rules using these fits. For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): $\alpha_{E1}+\beta_{M1}=14.0(2)\times 10^{-4}\,\mathrm{fm}^3$. An analogous sum rule involving the quadrupole polarizabilities of the proton is evaluated too. The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). We remark on sum rules for the elastic component of polarizabilities.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections. | method 0.66 | 0.91 | 0.07 | asserted 1.00 |
| s1 | We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section, and evaluate the various spin-independent sum rules using these fits. | method 0.68 | 0.96 | 0.08 | asserted 1.00 |
| s2 | For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): $\alpha_{E1}+\beta_{M1}=14.0(2)\times 10^{-4}\,\mathrm{fm}^3$. | result 1.00 | 0.96 | 0.43 | asserted 1.00 |
| s3 | An analogous sum rule involving the quadrupole polarizabilities of the proton is evaluated too. | contribution 0.95 | 0.91 | 0.04 | asserted 0.98 |
| s4 | The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. | contribution 0.75 | 0.95 | 0.18 | asserted 1.00 |
| s5 | The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). | contribution 0.61 | 0.72 | 0.07 | asserted 0.98 |
| s6 | We remark on sum rules for the elastic component of polarizabilities. | interpretation 0.54 | 0.53 | 0.04 | unclear 0.89 |
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The paper
Original abstract
We evaluate the forward Compton scattering off the proton, based on Kramers-Kronig kind of relations which express the Compton amplitudes in terms of integrals of total photoabsorption cross sections. We obtain two distinct fits to the world data on the unpolarized total photoabsorption cross section, and evaluate the various spin-independent sum rules using these fits. For the sum of proton electric and magnetic dipole polarizabilities, governed by the Baldin sum rule, we obtain the following average (between the two fits): $\alpha_{E1}+\beta_{M1}=14.0(2)\times 10^{-4}\,\mathrm{fm}^3$. An analogous sum rule involving the quadrupole polarizabilities of the proton is evaluated too. The spin-independent forward amplitude of proton Compton scattering is evaluated in a broad energy range. The results are compared with previous evaluations and the only experimental data point for this amplitude (at 2.2 GeV). We remark on sum rules for the elastic component of polarizabilities.
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References
How the literature uses it
10 arXiv papers cite this in 18 sentences
Papers citing it · 9 sentences without a confident label
Uses its data or values 5 papers
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Based on the empirical evaluation of these sum rules, we use [ref] :
Partial-wave analysis of proton Compton scattering data below the pion-production threshold · Linear relations: Sum rules · 0.98
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In particular, we used the empirical amplitudes from the fit I of Refs. [ref] , that are tabulated from $E_γ=50$ MeV and correspond to $α_E1+β_M1=14.29 ±0.27$ and $γ_0 = -0.929 ±0.105$.
Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method · Available extractions of RCS scalar dipole static polarizabilities · 0.97
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The Baldin sum rule expresses the sum of dipole polarizabilities in terms of an integral of the total photoabsorption cross section $_T$: _E1+β_M1=1/2 π^2 ∫_ν_0^∞ ν σ_T (ν)/ν^2.BaldinSumRule Empirical evaluations [ref] , based on experimental cross sections of total photoabsorption on the nucleon, yield the most accurate information on proton and neutron dipole polarizabilities we presently have:
Nucleon Polarizabilities and Compton Scattering as a Playground for Chiral Perturbation Theory · Introduction · 0.89
Compares with it 3 papers
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In Fig. [ref] {lower panel}, we show our B$χ$PT predictions compared to the MAID model predictions [ref] , the HB limit of the $πN$-loop contribution [ref] , and empirical evaluations of the fourth-order Baldin sum rule [ref] for proton and neutron, respectively.
Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: the subtraction function and moments of unpolarized structure functions · $M^(4)_1(Q^2)$ — the generalized fourth-order Baldin sum rule · 1.00
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In Fig. [ref], we also show the differential cross section at forward angle $θ_lab=0^o$ from our analysis (red band) in comparison with the results obtained with the empirical forward RCS amplitudes of Refs. [ref] (blue band).
Proton scalar dipole polarizabilities from real Compton scattering data, using fixed-t subtracted dispersion relations and the bootstrap method · Available extractions of RCS scalar dipole static polarizabilities · 1.00
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It is fully consistent with a more recent determination of $+=14.0±0.2$ [ref] .
Elastic Compton Scattering from 3He and the Role of the Delta · Introduction · 0.97
Cites it as background 1 paper
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The Baldin sumrule has been instrumental for the data-driven evaluations of the nucleon polarizabilities, and since long [ref] provides the most stringent empirical constraint on the sum of proton polarizabilties, see [ref] for the state of the art.
The QED of Bernab\'eu-Tarrach sumrule for electric polarizability and its implication for the Lamb shift · Introduction · 0.80
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