Analysis of the pion formfactor in the time-like region

Lang, C. B.; Stefanescu, I. Sabba

doi:10.1016/0370-2693(75)90587-0

Cited by 17 publications

(10 citation statements)

References 16 publications

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“…π , yet f (s) also vanishes on the negative real axis when s =s p , by definition. This zero simulates the left-hand cut in the N/D construction of the amplitude [32] and physically corresponds to a bound state [22]. The (s p − s)/s p factor in Ω(s) removes this singularity while preserving the normalization constraint.…”

Section: The Pion Form Factor and ρω "Mixing"mentioning

confidence: 99%

Rho-omega mixing and the pion form factor in the timelike region

Gardner

O'Connell

1998

Phys. Rev. D

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Section: The Pion Form Factor and ρω "Mixing"mentioning

confidence: 99%

Rho-omega mixing and the pion form factor in the timelike region

Gardner

O'Connell

1998

Phys. Rev. D

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“…Both approaches require the knowledge of zeros of the form factor, and are plagued, respectively, by uncertainties related to the unknown phase in the inelastic region, and the uncertainties of the modulus at low energies. Various analytic representations or expansions in terms of suitable sets of functions were also used in [54]- [58] for data analysis and the analytic extrapolation of the form factor.…”

Section: Analytic Continuationmentioning

confidence: 99%

Spacelike pion form factor from analytic continuation and the onset of perturbative QCD

2012

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The factorization theorem for exclusive processes in perturbative QCD predicts the behavior of the pion electromagnetic form factor F (t) at asymptotic spacelike momenta t(= −Q 2 ) < 0. We address the question of the onset energy using a suitable mathematical framework of analytic continuation, which uses as input the phase of the form factor below the first inelastic threshold, known with great precision through the Fermi-Watson theorem from ππ elastic scattering, and the modulus measured from threshold up to 3 GeV by the BaBar Collaboration. The method leads to almost model-independent upper and lower bounds on the spacelike form factor. Further inclusion of the value of the charge radius and the experimental value at −2.45 GeV 2 measured at JLab considerably increases the strength of the bounds in the region Q 2 10 GeV 2 , excluding the onset of the asymptotic perturbative QCD regime for Q 2 < 7 GeV 2 . We also compare the bounds with available experimental data and with several theoretical models proposed for the low and intermediate spacelike region.

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“…The issue of zeros is of relevance for the analytic representation of the form factor using phase (Omnès)-or modulus-type representations, which require the knowledge of the zeros. Such representations were extensively studied in the past [18,46,50,52,53,65], and often are based on the assumption that zeros are absent. Our results, which show that the zeros are excluded from a rather large region at low energies, give support to such representations, and confirm also theoretical expectations based on ChPT or more general physical arguments [18].…”

Section: Domain Where Zeros Are Excludedmentioning

confidence: 99%

Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region

2011

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The recently evaluated two-pion contribution to the muon g − 2 and the phase of the pion electromagnetic form factor in the elastic region, known from ππ scattering by Fermi-Watson theorem, are exploited by analytic techniques for finding correlations between the coefficients of the Taylor expansion at t = 0 and the values of the form factor at several points in the spacelike region. We do not use specific parametrizations and the results are fully independent of the unknown phase in the inelastic region. Using for instance, from recent determinations, r 2 π = (0.435 ± 0.005) fm 2 and F (−1.6 GeV 2 ) = 0.243 +0.022 −0.014 , we obtain the allowed ranges 3.75 GeV −4 c 3.98 GeV −4 and 9.91 GeV −6 d 10.46 GeV −6 for the curvature and the next Taylor coefficient, with a strong correlation between them. We also predict a large region in the complex plane where the form factor cannot have zeros.

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Analysis of the pion formfactor in the time-like region

Cited by 17 publications

References 16 publications

Rho-omega mixing and the pion form factor in the timelike region

Rho-omega mixing and the pion form factor in the timelike region

Spacelike pion form factor from analytic continuation and the onset of perturbative QCD

Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region

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