Some General Relations between the Photoproduction and Scattering of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi></mml:math>Mesons

Watson, Kenneth

doi:10.1103/physrev.95.228

Cited by 540 publications

(386 citation statements)

References 18 publications

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“…Removing this input leads to |V ub | = 4.24(40) × 10 −3 , f + (0) = 0.166 (31), so |V ub | increases by 6%, half its error, while the error itself increases by 15%. Moreover, we checked that the output percentage error in |V ub | would decrease about one-eighth as fast as the percentage error on the LCSR input decreases.…”

Section: Resultsmentioning

confidence: 99%

“…Here, we use a multiply-subtracted Omnès dispersion relation to obtain a parameterization of the form factor based only on the Mandelstam hypothesis [30] of maximum analyticity, unitarity and an application of Watson's theorem [31]. The latter theorem implies that f + has the same phase as the elastic πB → πB scattering T -matrix in the J P = 1 − , isospin-1/2 channel,…”

Section: Introductionmentioning

confidence: 99%

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Extracting|Vub|fromB→πlνdecays using a multiply-subtracted Omnès dispersion relation

Flynn

Nieves

2007

Phys. Rev. D

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We use a multiply-subtracted Omnès dispersion relation for the form factor f + in B → π semileptonic decay, allowing the direct input of experimental and theoretical information to constrain its dependence on q 2 , thereby improving the precision of the extracted value of |V ub |. Apart from these inputs we use only unitarity and analyticity properties. We obtain |V ub | = (4.02 ± 0.35) × 10 −3 , improving the agreement with the value determined from inclusive methods, and competitive in precision with them.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extracting|Vub|fromB→πlνdecays using a multiply-subtracted Omnès dispersion relation

Flynn

Nieves

2007

Phys. Rev. D

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“…The new combinations still fulfill Watson's theorem [129] Im h 0,++ (s) ± q 2 1 q 2 2 h 0,00 (s) = sin δ 0 (s)e −iδ 0 (s) h 0,++ (s) ± q 2 1 q 2 2 h 0,00 (s) θ s − 4M 2 π , (4.10) so that the dispersion relation reduces to a standard Muskhelishvili-Omnès (MO) problem [130,131], whose solution reads…”

Section: Jhep04(2017)161mentioning

confidence: 98%

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

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

371

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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“…As for the pion vector form factor, we employ the parametrization that was used by the Belle collaboration [64], which we refer to as F Belle (s). In order to satisfy the Watson theorem [65], however, we modify F Belle (s) and for the vector form factor use F π (s) = |F Belle | exp(iδ(s)), where δ is the ππ P-wave phase shift taken from [20]. We have checked that the effect of this modification on the description of the experimental data is negligible in the energy range s = [s π , s i ].…”

Section: A ω/φ → 3πmentioning

confidence: 99%