Regge analysis of the ππ scattering amplitude

Caprini, I.; Colangelo, Gilberto; Leutwyler, H.

doi:10.1140/epjc/s10052-012-1860-1

Cited by 160 publications

(292 citation statements)

References 132 publications

Supporting

Mentioning

277

Contrasting

Order By: Relevance

“…The ππ phase shift is taken from the extended Roy-equation analysis of [94], which determines δ 1 1 up to s m = (1.15 GeV) 2 in terms of its values at s m and s A = (0.8 GeV) 2 . Our representation thus involves 3 + p free parameters: the ρ-ω mixing parameter ρω , the two values of the phase shift at s m and s A , and p parameters from the conformal expansion of G inel .…”

Section: Jhep04(2017)161mentioning

confidence: 99%

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

362

257

View full text Add to dashboard Cite

In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g − 2) µ , including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ * γ * → ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, a π-box µ = −15.9(2)×10 −11 . As an application of the partial-wave formalism, we present a first calculation of ππ-rescattering effects in HLbL scattering, with γ * γ * → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f 0 (500) to HLbL scattering in (g − 2) µ . We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S-wave rescattering corrections reads a π-box µ + a ππ,π-pole LHC µ,J=0 = −24(1) × 10 −11 .

show abstract

Section: Jhep04(2017)161mentioning

confidence: 99%

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

362

257

View full text Add to dashboard Cite

show abstract

“…VII above, if we are prepared to make phenomenological inputs such as the D-wave scattering lengths and low-energy absorptive parts, the situation with respect to experimental comparisons improves dramatically [23].…”

Section: Discussionmentioning

confidence: 99%

“…which are not very far from the scale factors used in phenomenological fits [23]. We should remember that the phenomenological values may be dependent on the particular parametrization used to fit experimental cross sections.…”

Section: Phenomenological Comparisons For Pion-pion Scatteringmentioning

confidence: 95%

See 1 more Smart Citation

Froissart bound on inelastic cross section without unknown constants

Martin

Roy

2015

Phys. Rev. D

View full text Add to dashboard Cite

Assuming that axiomatic local field theory results hold for hadron scattering, André Martin and S. M. Roy recently obtained absolute bounds on the D wave below threshold for pion-pion scattering and thereby determined the scale of the logarithm in the Froissart bound on total cross sections in terms of pion mass only. Previously, Martin proved a rigorous upper bound on the inelastic cross-section σ inel which is onefourth of the corresponding upper bound on σ tot , and Wu, Martin, Roy and Singh improved the bound by adding the constraint of a given σ tot . Here we use unitarity and analyticity to determine, without any highenergy approximation, upper bounds on energy-averaged inelastic cross sections in terms of lowenergy data in the crossed channel. These are Froissart-type bounds without any unknown coefficient or unknown scale factors and can be tested experimentally. Alternatively, their asymptotic forms, together with the Martin-Roy absolute bounds on pion-pion D waves below threshold, yield absolute bounds on energy-averaged inelastic cross sections. For example, for π 0 π 0 scattering, definingπ . This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor s 1 is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic π 0 π 0 cross section has a bound of the same form with 1=s 1 replaced by 1=s 2 ¼ 2=s 1 .

show abstract

“…by matching to chiral perturbation theory near s = 0. The Omnès function is entirely given in terms of the appropriate pion-pion phase shift, which is particularly useful as we today have excellent information on pion-pion scattering at our disposal [21][22][23][24]. The pion vector form factor F V π (s) as extracted from τ − → π − π 0 ν τ decays, e.g., can be described very accurately by a representation (5) up to √ s = 1 GeV, employing a linear polynomial R(s) ≡ P 1 1 (s) = 1 + α V s-at higher energies, the nonlinear effects of higher, inelastic (ρ ′ , ρ ′′ ) resonances become important [25].…”

Section: Universality Of Final-state Interactionsmentioning

confidence: 99%

Towards a dispersive determination of the η and η′ transition form factors

Kubis¹

2018

EPJ Web Conf.

View full text Add to dashboard Cite

Abstract.We discuss status and prospects of a dispersive analysis of the η and η ′ transition form factors. Particular focus is put on the various pieces of experimental information that serve as input to such a calculation. These can help improve on the precision of an evaluation of the η and η ′ pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. Hadronic light-by-light scattering and the anomalous magnetic moment of the muonThere is a by now long-standing discrepancy between the experimental determination of the anomalous magnetic moment of the muon as measured by the BNL E821 experiment [1], and its calculation within the Standard Model [2], with both experiment and theory affected by a comparable uncertainty. With two different proposals to further improve on the accuracy of the measurement well under way [3,4], it is of utmost importance to also improve the accuracy of the theoretical Standard-Model prediction before a persistent discrepancy of potentially increased significance can be interpreted in terms of physics beyond the Standard Model. The Standard-Model uncertainty is entirely dominated by hadronic contributions. While the dominant hadronic vacuum polarization can be expressed, via a dispersion relation, in terms of measurable e + e − → hadrons total cross sections, which therefore can be further improved upon by a strong experimental effort to determine many of the exclusive channels contributing therein with yet improved precision [5], the situation for the α QED -suppressed hadronic light-by-light scattering is less straightforward, relying until recently to a much larger extent on modeling [6], with badly controlled errors.This presentation is part of an effort to analyze also the hadronic light-by-light scattering tensor using dispersion theory [7,8]. Dispersion theory makes maximal use of analyticity and unitarity, two fundamental consequences of relativistic quantum field theories that mathematically incorporate the principles of causality and probability conservation. The various (in principle infinitely many different) contributions to hadronic light-by-light scattering are organized in terms of their analytic structure, according to the cuts and poles in the different energy variables that are dictated by the above principles. This has the advantage that all contributions will be given in terms of on-shell form factors and scattering amplitudes, hence observables that can to a large extent again be related to experimentally accessible quantities [9]. An ordering principle will be to consider intermediate

show abstract

Regge analysis of the ππ scattering amplitude

Cited by 160 publications

References 132 publications

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Froissart bound on inelastic cross section without unknown constants

Towards a dispersive determination of the η and η′ transition form factors

Contact Info

Product

Resources

About