π → lνγ form factors at two-loop

Bijnens, Johan; Talavera, P.

doi:10.1016/s0550-3213(97)00069-2

Cited by 105 publications

(130 citation statements)

References 33 publications

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“…. 2.9 for the same range of cutoffs as in section 4.3 indeed comes out very close to the phenomenological valuel 6 −l 5 = 3.0(0.3) [137,149,150]. As discussed in section 4.3, only the charged-pion polarizability is reproduced in this way, indicating that higher contributions to the LHC are required in the case of the neutral pion.…”

Section: Jhep04(2017)161supporting

confidence: 79%

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

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

362

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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Section: Jhep04(2017)161supporting

confidence: 79%

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

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

362

257

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“…[4], provided that the same set of LECs is used. With updated LECs at order p 4 [6,7], we find for the dipole polarizabilities the value (α 1 − β 1 ) π ± = (5.7 ± 1.0) × 10 −4 fm 3 .…”

Section: Introductionmentioning

confidence: 88%

Revisiting at low energies

2006

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We complete the recalculation of the available two-loop expressions for the reaction γγ → ππ in the framework of chiral perturbation theory. Here, we present the results for charged pions. The cross section and the values of the dipole polarizabilities agree very well with the earlier calculation, provided the same set of low-energy constants (LECs) is used. With updated values for the LECs at order p 4 , we find for the dipole polarizabilities (α 1 − β 1 ) π ± = (5.7 ± 1.0) × 10 −4 fm 3 , which is in conflict with the experimental result recently reported by the MAMI Collaboration.

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“…These were later checked by [10,17] where also ππ scattering was evaluated to O(p 6 ). The vector and scalar form factors of the pion were evaluated in [18] and the form factors of radiative pion decay in [19].…”

Section: Applicationsmentioning

confidence: 99%

Renormalization of Chiral Perturbation Theory to Order p6

2000

Self Cite

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The renormalization of chiral perturbation theory is carried out to next-tonext-to-leading order in the meson sector. We calculate the divergent part of the generating functional of Green functions of quark currents to O(p 6 ) for chiral SU (n), involving one-and two-loop diagrams. The renormalization group equations for the renormalized low-energy constants of O(p 6 ) are derived. We compare our results with previous two-loop calculations in chiral perturbation theory.

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π → lνγ form factors at two-loop

Abstract: Within Chiral Perturbation Theory (CHPT) we compute the form factors A, V and γ = A/V in the π → lνγ decay to O(p 6 ). A and γ obtain corrections of order 25%.

Cited by 105 publications

References 33 publications

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

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

Revisiting at low energies

Renormalization of Chiral Perturbation Theory to Order p6

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