Derivative dispersion relations above the physical threshold

Ávila, R. F.; Menon, M. J.

doi:10.1590/s0103-97332007000300006

Cited by 16 publications

(30 citation statements)

References 23 publications

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“…The use of prescriptions seem to us unjustified in the region of intermediate and low energy data, since they are asymptotic results [37]. By constrast, derivative dispersion relations allow an analytical approach and can be extended down to 4 -5 GeV [40,41] or even below (above the physical threshold) in the form of a double infinite series [42,43] or a single series [44]. However, and that is a crucial point in this work, we shall not consider simultaneus fits to total cross section data and ρ information for the six reasons that follows.…”

Section: B Data Ensemble and Critical Commentsmentioning

confidence: 99%

Total Hadronic Cross-Section Data and the Froissart–Martin Bound

2012

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The energy dependence of the total hadronic cross section at high energies is investigated with focus on the recent experimental result by the TOTEM Collaboration at 7 TeV and the Froissart-Martin bound. On the basis of a class of analytical parametrization with the exponent γ in the leading logarithm contribution as a free parameter, different variants of fits to pp andpp total cross section data above 5 GeV are developed. Two ensembles are considered, the first comprising data up to 1.8 TeV, the second also including the data collected at 7 TeV. We shown that in all fit variants applied to the first ensemble the exponent is statistically consistent with γ = 2. Applied to the second ensemble, however, the same variants yield γ's above 2, a result already obtained in two other analysis, by U. Amaldi et al. and by the UA4/2 Collaboration. As recently discussed by Ya. I. Azimov, this faster-than-squared-logarithm rise does not necessarily violate unitarity. Our results suggest that the energy dependence of the hadronic total cross section at high energies still constitute an open problem. PACS numbers: 13.85.-t Hadron-induced high-and super-high-energy interactions, 13.85.Lg Total cross sections, 11.10.Jj Asymptotic problems and properties

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Section: B Data Ensemble and Critical Commentsmentioning

confidence: 99%

Total Hadronic Cross-Section Data and the Froissart–Martin Bound

2012

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“…Equation (74) On the other hand, from the high-energy approximate result (75), for γ = 2, we obtain the triple pole contribution (68). Moreover, from (75), in the general case, σ(s) ≈ β ln γ (s), ρ(s) ≈ γπ 2 ln(s) .…”

Section: A Exact Resultsmentioning

confidence: 88%

Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness

Fagundes

Menon

Silva

2017

Int. J. Mod. Phys. A

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Forward amplitude analyses constitute an important approach in the investigation of the energy dependence of the total hadronic cross-section σ tot and the ρ parameter. The standard picture indicates for σ tot a leading log-squared dependence at the highest c.m. energies, in accordance with the Froissart-Lukaszuk-Martin bound and as predicted by the COMPETE Collaboration in 2002. Beyond this log-squared (L2) leading dependence, other amplitude analyses have considered a log-raised-to-gamma form (Lγ), with γ as a real free fit parameter. In this case, analytic connections with ρ can be obtained either through dispersion relations (derivative forms), or asymptotic uniqueness (Phragmén-Lindelöff theorems). In this work we present a detailed discussion on the similarities and mainly the differences between the Derivative Dispersion Relation (DDR) and Asymptotic Uniqueness (AU) approaches and results, with focus on the Lγ and L2 leading terms. We also develop new Regge-Gribov fits with updated dataset on σ tot and ρ from pp andpp scattering, including all available data in the region 5 GeV -8 TeV. The recent tension between the TOTEM and ATLAS results at 7 TeV and mainly 8 TeV is discussed and considered in the data reductions. Our main conclusions are the following: (1) all fit results present agreement with the experimental data analyzed and the goodness-of-fit is slightly better in case of the DDR approach; (2) by considering only the TOTEM data at the LHC region, the fits with Lγ indicate γ ∼ 2.0 ± 0.2 (AU approach) and γ ∼ 2.3 ± 0.1 (DDR approach); (3) by including the ATLAS data the fits provide γ ∼ 1.9 ± 0.1 (AU) and γ ∼ 2.2 ± 0.2 (DDR); (4) in the formal and practical contexts, the DDR approach is more adequate for the energy interval investigated than the AU approach. A pedagogical and detailed review on the analytic results for σ tot and ρ from the Regge-Gribov, DDR and AU approaches is presented. Formal and practical aspects related to forward amplitude analyses are also critically discussed. PACS: 13.85.-t, 13.85.Lg, 11.10.Jj Keywords: Hadron-induced high-and super-high-energy interactions, total cross-sections, asymptotic problems and properties Published in International Journal of Modern Physics A 32 (2017) 1750184 In 1993, the UA4/2 Collaboration extended the analysis up to 546 GeV (pp scattering) obtaining [15] γ = 2.24 +0.35 −0.31 . This result has been confirmed by Bueno and Velasco in 1996, who develop also fits to only σ tot data, obtaining [16] γ = 2.42 +0.4 −0.6 , for cutoff at 5 GeV and γ = 2.64 +0.50 −0.32 ,for cutoff at 10 GeV. After the first measurement of the total cross section from LHC7 by the TOTEM Collaboration, Fagundes, Menon and Silva (hereafter FMS) developed in 2012 an amplitude analysis with basis on the parametrization introduced by Amaldi et al. for the total cross section [28]. As in the above works, the data reductions were limited to pp andpp scattering. This analysis was then developed and extended in [29] and further updated and discussed by Menon and Silva [30,31], leadin...

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“…The differences between the derivative representations by these authors and our final results are discussed in [6], as well as other formal aspects involved.…”

Section: Extended Derivative Dispersion Relationsmentioning

confidence: 78%

From integral to derivative dispersion relations

Ávila¹,

Menon²

2007

Braz. J. Phys.

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We demonstrate that integral dispersion relations for hadron-hadron scattering amplitudes can be replaced by differential relations, without the usual high-energy approximation. We obtain analytical expressions for the corrections associated with the low energy region and exemplify the applicability of the novel relations in the context of an analytical parametrization for proton-proton and antiproton-proton total cross sections.

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Derivative dispersion relations above the physical threshold

Cited by 16 publications

References 23 publications

Total Hadronic Cross-Section Data and the Froissart–Martin Bound

Total Hadronic Cross-Section Data and the Froissart–Martin Bound

Leading components in forward elastic hadron scattering: Derivative dispersion relations and asymptotic uniqueness

From integral to derivative dispersion relations

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