Low-energy photon-photon collisions to two loops revisited

JINR); Juerg Gasser (Bern U.); Mikhail A. Ivanov (Dubna; Mikko E. Sainio (Helsinki U.)

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Low-energy photon-photon collisions to two loops revisited

Juerg Gasser (Bern U.), Mikhail A. Ivanov (Dubna, JINR), Mikko E. Sainio (Helsinki U.)

High Energy Physics - Phenomenology · Submitted 25 Jun 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The cross section for the reaction gamma+gamma->pi0+pi0 agrees with the earlier calculation within a fraction of a percent.

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arXiv IDhep-ph/0506265 (version 1)

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CitationJINR), Juerg Gasser (Bern U.), Mikhail A. Ivanov (Dubna, Mikko E. Sainio (Helsinki U.). "Low-energy photon-photon collisions to two loops revisited." arXiv:hep-ph/0506265 (2005). https://pith.science/paper/N5HWHRRR

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What the abstract itself states, as probabilities: claims first 0.28 · states limitation 0.33 · human participants 0.02 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.51 · compares with prior results 0.98 · mentions code or data availability 0.03.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

In view of ongoing experimental activities to determine the pion polarizabilities, we have started to recalculate the available two-loop expressions in the framework of chiral perturbation theory, because they have never been checked before. We make use of the chiral Lagrangian at order p^6 now available, and of improved techniques to evaluate the two-loop diagrams. Here, we present the result for the neutral pions. The cross section for the reaction gamma+gamma->pi0+pi0 agrees with the earlier calculation within a fraction of a percent. We present analytic results for the dipole and quadrupole polarizabilities, and compare the latter with a recent evaluation from data on gamma+gamma->pi0+pi0.

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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	In view of ongoing experimental activities to determine the pion polarizabilities, we have started to recalculate the available two-loop expressions in the framework of chiral perturbation theory, because they have never been checked before.	gap 0.54	0.77	0.06	asserted 0.99
s1	We make use of the chiral Lagrangian at order p^6 now available, and of improved techniques to evaluate the two-loop diagrams.	method 0.99	0.68	0.03	asserted 0.98
s2	Here, we present the result for the neutral pions.	contribution 0.93	0.85	0.07	asserted 0.85
s3	The cross section for the reaction gamma+gamma->pi0+pi0 agrees with the earlier calculation within a fraction of a percent.	result 1.00	0.85	0.38	asserted 1.00
s4	We present analytic results for the dipole and quadrupole polarizabilities, and compare the latter with a recent evaluation from data on gamma+gamma->pi0+pi0.	result 0.71	0.90	0.29	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.90.

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Original abstract

In view of ongoing experimental activities to determine the pion polarizabilities, we have started to recalculate the available two-loop expressions in the framework of chiral perturbation theory, because they have never been checked before. We make use of the chiral Lagrangian at order p^6 now available, and of improved techniques to evaluate the two-loop diagrams. Here, we present the result for the neutral pions. The cross section for the reaction gamma+gamma->pi0+pi0 agrees with the earlier calculation within a fraction of a percent. We present analytic results for the dipole and quadrupole polarizabilities, and compare the latter with a recent evaluation from data on gamma+gamma->pi0+pi0.

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References

Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Dispersion relation for hadronic light-by-light scattering: two-pion contributions
hep-ph 2017-02 accept novelty 7.0 of 10

A partial-wave dispersion formalism fixes the two-pion contribution to hadronic light-by-light scattering at -24(1) x 10^-11, of which the pion box alone is -15.9(2) x 10^-11.
Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
hep-ph 2017-01 accept novelty 7.0 of 10

A dispersive, data-driven evaluation gives the pion-box plus S-wave pion-rescattering contribution to hadronic light-by-light as -24(1) x 10^-11, with the pion box alone at -15.9(2) x 10^-11.
Roy-Steiner equations for gamma gamma -> pi pi
hep-ph 2011-06 conditional novelty 7.0 of 10

A new Roy-Steiner system for photon-pion scattering yields a sum rule for the isospin-two S-wave and a prediction of the sigma resonance two-photon width of 1.7 plus or minus 0.4 keV.
Unified dispersive approach to real and virtual photon-photon scattering at low energy
hep-ph 2013-05 conditional novelty 6.0 of 10

A Muskhelishvili-Omnes representation of photon-photon to pion-pair amplitudes is generalized to one virtual photon, with a finite-width resonance propagator that keeps the left-hand cut separated from the unitarity c...
Couplings of light I=0 scalar mesons to simple operators in the complex plane
hep-ph 2011-10 conditional novelty 6.0 of 10

Complex-plane residues of Roy-equation pion-pion amplitudes yield quark, gluon and two-photon couplings for the sigma(600) and f0(980) that are compatible with a conventional nonet assignment.

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MO analysis of the high statistics Belle results on $\gamma\gamma\to \pi^+\pi^-,\pi^0\pi^0$ with chiral constraints
hep-ph 2010-06 conditional novelty 6.0 of 10

A modified Muskhelishvili-Omnes dispersive representation, fitted to Belle's charged and neutral two-photon pion-pair data with chiral constraints, yields updated pion dipole and quadrupole polarizabilities and p6 chi...
The expansion by regions in pi K scattering
hep-ph 2006-03 conditional novelty 6.0 of 10

Two-loop pion-kaon threshold integrals are expanded in M_pi/M_K by the method of regions, and the resulting formulas yield a new two-loop strange quark contribution to the pion mass.
Roy-Steiner-equation analysis of pion-nucleon scattering
hep-ph 2015-10 accept novelty 5.0 of 10

Solving Roy-Steiner equations for pion-nucleon scattering with pionic-atom scattering lengths imposed as constraints yields a pion-nucleon sigma-term of 59.1 +/- 3.5 MeV, about 14 MeV above the long-quoted canonical value.
Revisiting \gamma\gamma->\pi^+\pi^- at low energies
hep-ph 2006-02 accept novelty 5.0 of 10

A two-loop chiral perturbation theory recalculation of gamma gamma to pi+ pi- confirms the previous amplitude and predicts a charged pion dipole polarizability of (5.7 ± 1.0) x 10^-4 fm^3, conflicting with the MAMI va...
Chiral Perturbation Theory Beyond One Loop
hep-ph 2006-04 conditional

A practitioner-written review of all order-p^6 ChPT calculations in the mesonic sector, summarizing the two-loop results and their experimental comparisons.

How the literature uses it

15 arXiv papers cite this in 45 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 · 28 sentences without a confident label

Uses its data or values 3 papers

Here, using the $(p^6)$ LEC determinations in [ref] , we carry out a phenomenological analysis of the $γγ→ππ$ reaction, as this matrix element depends on a transparent way on the $(p^6)$ LEC's [ref] .

Low-energy photon and pion scattering in holographic QCD · Introduction · 0.81
These subtraction constants can be identified with pion polarizabilities and were taken from $2$-loop [ref] in [ref] .

Dispersion relation for hadronic light-by-light scattering: two-pion contributions · $γ^*γ^*→ππ$ helicity partial waves from the inverse-amplitude method · 0.98
Here, some of these estimates have been extracted from $SU(2)$ analyses [ref] under the assumption that the $1/N_C$–suppressed loop corrections are neglected in the relation between the $SU(3)$ and $SU(2)$ LECs at large $N_C$.

Holography, chiral Lagrangian and form factor relations · Even-intrinsic parity LECs · 0.90

Compares with it 3 papers

The results for these quantities deduced from our fitted amplitudes are collected in table polartable and compared with the results from ChPT at NNLO as given in [ref] .

MO analysis of the high statistics Belle results on $\gamma\gamma\to \pi^+\pi^-,\pi^0\pi^0$ with chiral constraints · Results of the fit · 0.99
In particular, we quote the outcome of dispersive analyses such as the Muskhelishvili-Omnès (MO) relation in terms of the $ππ$–scattering phase-shifts [ref] and the Roy-Steiner equations [ref] , together with the result of the $χ$PT computation at $(p^6)$ [ref] .

Low-energy photon and pion scattering in holographic QCD · Polarizabilities and cross sections for $γγ→ππ$ scattering · 0.99
* We find our prediction for $(α_2-β_2)_π^0 ≃20×10^-4$fm$^5$ is only half that predicted by the ChPT plus Resonance model [ref] .

Pion Polarizabilities from $\gamma\gamma\to\pi\pi$ Analysis · Pion Polarizabilities from Dispersion Relations · 0.98

Cites it as background 8 papers

These pionic observables have been computed in Chiral perturbation theory at next to leading order [ref] and then at next-to-next to leading order [ref] .

MO analysis of the high statistics Belle results on $\gamma\gamma\to \pi^+\pi^-,\pi^0\pi^0$ with chiral constraints · Polarizabilities · 0.91
To establish connection to the notation of the crossed process [ref] , which we will refer to as the $t$-channel reaction, we briefly discuss γ(q_1,λ_1)γ(q_2,λ_2)→π^a(p_1)π^b(p_2) in terms of the Mandelstam variables =(q_1+q_2)^2, =(q_1-p_1)^2, =(q_1-p_2)^2, and the amplitudes [equation] They are related to the $s$-channel amplitudes by

Roy-Steiner equations for gamma gamma -> pi pi · Relation to $γγ→ππ$ · 0.87
The calculation of the $γγ$ amplitudes at NNLO have been performed [ref] .

Unified dispersive approach to real and virtual photon-photon scattering at low energy · Case $q^2=0$ · 0.87

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