Couplings of light I=0 scalar mesons to simple operators in the complex plane

Moussallam, B.

doi:10.1140/epjc/s10052-011-1814-z

Cited by 98 publications

(157 citation statements)

References 115 publications

(225 reference statements)

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“…The dispersive method has the advantage that it provides a complete error analysis which includes, in particular, also the uncertainties associated with the presence of inelastic channels. The calculations performed in [98,99] corroborate this statement: the result for the pole position agrees with [3], within the quoted errors.…”

Section: Discussionsupporting

confidence: 80%

Regge analysis of the ππ scattering amplitude

2012

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Abstract. The theoretical predictions for the subtraction constants lead to a very accurate dispersive representation of the ππ scattering amplitude below 0.8 GeV. The extension of this representation up to the maximum energy of validity of the Roy equations (1.15 GeV) requires a more precise input at high energies. In this paper we determine the trajectories and residues of the leading Regge contributions to the ππ amplitude (Pomeron, f and ρ), using factorization, phenomenological parametrizations of the πN and N N total cross sections at high energy and a set of sum rules which connect the high and low energy properties of ππ scattering. We find that nonleading Regge terms are necessary in order to achieve a smooth transition from the partial waves to the Regge representation at or below 2 GeV. We obtain thus a Regge representation consistent both with the experimental information at high energies and the Roy equations for the partial waves with ℓ ≤ 4. The uncertainties in our result for the Regge parameters are sizable but in the solutions of the Roy equations, these only manifest themselves above KK threshold. MotivationLow energy pion physics has become a precision laboratory: the chiral symmetry properties of the Standard Model can now be compared with low energy precision experiments, using Chiral Perturbation Theory (χPT), dispersion theory and numerical simulations of QCD on a lattice. In principle, as illustrated by the prediction for the magnetic moment of the muon, physics beyond the Standard Model can show up at low energies, provided the quantity of interest can not only be measured accurately, but can also be calculated to sufficient precision. In this context, the interaction among the pions and in particular, the elastic ππ scattering amplitude play a crucial role.The Roy equations [1] provide a suitable framework for the low energy analysis of the ππ scattering amplitude, as they fully incorporate the basic properties that follow from analyticity, unitarity and crossing symmetry. They express the real parts of the partial waves as integrals over the imaginary parts that extend over all energies. The high energy behaviour of the imaginary parts thus enters the analysis, even if the Roy equations are evaluated only at low energy. More specifically, the contributions from the high energy region are contained in the so-called driving terms. Near the ππ threshold, these terms are very small. Accordingly, the results for the threshold parameters are not sensitive to the high energy contributions. The driving terms, however, grow with the energy. In [2,4], where the threshold parameters and the coupling constants of the effective chiral SU(2)×SU(2) Lagrangian relevant for ππ scattering are determined to high accuracy, the Roy equations are solved only below 0.8 GeV. On general grounds [1] these equations are valid in the region 1 s ≤ 68 M 2 π , i.e. for √ s ≤ 1.15 GeV, but in order to use them we need an accurate evaluation of the driving terms. This calls for a better understanding of the imaginary ...

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Section: Discussionsupporting

confidence: 80%

Regge analysis of the ππ scattering amplitude

2012

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“…As expected, there is good agreement throughout, apart from the fact that the IAM I = 0 phase shift avoids the rise related to the f 0 (980) and the coupling to theKK channel. We also checked that the σ properties [126] are reproduced: for the pole position we find √ s σ = (0.443 + i0.217) GeV, to be compared to √ s σ = (0.441 + i0.272) GeV [127] and similar numbers from other recent dispersive extractions [118,128]. Accordingly, the width comes out a bit too low, as does the residue at the pole g σππ .…”

Section: Jhep04(2017)161supporting

confidence: 63%

“…[122] for the analogous calculation including the mIAM correction, and can certainly be tolerated to obtain an estimate for the HLbL rescattering contribution, which, after all, only requires the amplitude on the real axis, not the analytic continuation into the complex plane where the slight discrepancy in the width would matter most. Similarly, one can check the coupling to two photons |g σγγ /g σππ | ∼ 0.014, well in line with |g σγγ /g σππ | = 0.014 and 0.015 from [55] and [118], respectively.…”

Section: Jhep04(2017)161supporting

confidence: 62%

“…However, approaches that exploit more comprehensively the analytic properties of the amplitude, see [54,55,118] for on-shell photons, can be extended towards the off-shell case with limited data input required to determine parameters, as demonstrated for the singly-virtual process in [56]. The essential features of the generalization towards the doubly-virtual case, i.e.…”

Section: Application: Two-pion Rescatteringmentioning

confidence: 99%

“…The essential features of the generalization towards the doubly-virtual case, i.e. the appearance of anomalous thresholds for time-like kinematics [57] and the modifications to tensor basis and kernel functions [28,31], have already been laid out in previous work, but the practical implementation involves a number of challenges: due to the strong coupling between the ππ/KK channels in the isospin-0 S-wave a single-channel analysis is limited to rather low energies [54,56,117,118], assumptions for the LHC and number of subtractions need to be carefully studied to reliably assess the sensitivity to the high-energy input in the dispersive integrals [55], a full analysis of the generalized Roy-Steiner equations [28,31,55] involves solving coupled S-and D-wave systems of various helicity projections, and last but not least constraints on the γ * γ * → ππ amplitudes from asymptotic behavior and the sum rules derived in section 2.4.3 need to be incorporated. A full analysis along these lines will be left for future work.…”

Section: Application: Two-pion Rescatteringmentioning

confidence: 99%

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

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

385

257

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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 .

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Correlations of C and CP violation in η → π0ℓ+ℓ− and η′ → ηℓ+ℓ−

Akdag,

Kubis,

Wirzba

2024

J. High Energ. Phys.

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Based on recent progress in the systematic analysis of C and CP violation in the light-meson sector, we calculate the C-odd transition amplitudes η → π0ℓ+ℓ− and η′ → ηℓ+ℓ−. Focusing on long-distance contributions driven by the lowest-lying hadronic intermediate states, we work out the correlations between these beyond-the-Standard-Model signals and the Dalitz-plot asymmetries in η → π0π+π− and η′ → ηπ+π−, using dispersion theory.

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Couplings of light I=0 scalar mesons to simple operators in the complex plane

Cited by 98 publications

References 115 publications

Regge analysis of the ππ scattering amplitude

Regge analysis of the ππ scattering amplitude

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

Correlations of C and CP violation in η → π0ℓ+ℓ− and η′ → ηℓ+ℓ−

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