From integral to derivative dispersion relations

Ávila, R. F.; Menon, M. J.

doi:10.1590/s0103-97332007000400035

Cited by 4 publications

(4 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We recall that, for classes of functions of interest in high-energy elastic scattering, DDR can be analytically extended down to 4-5 GeV [54,56] or even below and for the whole energy interval (above the physical threshold), either in the form of a double infinity series, as first deduced by Ávila and Menon [57,58], or in the form of a single series, as demonstrated by Ferreira and Sesma [59]. However it seems to us simpler here to consider the pragmatic role of the subtraction constant, since as explained above, with this constant as a free parameter the results obtained with the DDR (10) and (11) (high-energy approximation) are the same as those obtained through the IDR ( 8) and ( 9) (without the high-energy approximation).…”

Section: 32mentioning

confidence: 95%

On the rise of proton–proton cross-sections at high energies

Fagundes¹,

Menon²,

Silva³

2013

J. Phys. G: Nucl. Part. Phys.

View full text Add to dashboard Cite

The rise of total, elastic and inelastic hadronic cross sections at high energies is investigated by means of an analytical parametrization, with the exponent of the leading logarithm contribution as a free fit parameter. Using derivative dispersion relations with one subtraction, two different fits to proton-proton and antiproton-proton total cross section and ρ parameter data are developed, reproducing well the experimental information in the energy region 5 GeV-7 TeV. The parametrization for the total cross sections is then extended to fit the elastic (integrated) cross section data in the same energy region, with satisfactory results. From these empirical results we extract the energy dependence of several physical quantities: inelastic cross section, ratios elastic/total, inelastic/total cross sections, ratio total-cross-section/elasticslope, elastic slope and optical point. All data, fitted and predicted, are quite well described. We find a statistically consistent solution indicating: (1) an increase of the hadronic cross sections with the energy faster than the logsquared bound by Froissart and Martin; (2) asymptotic limits 1/3 and 2/3 for the ratios elastic/total and inelastic/total cross sections, respectively; a result in agreement with unitarity. These indications corroborate recent theoretical arguments by Azimov on the rise of the total cross section.

show abstract

Section: 32mentioning

confidence: 95%

On the rise of proton–proton cross-sections at high energies

Fagundes¹,

Menon²,

Silva³

2013

J. Phys. G: Nucl. Part. Phys.

View full text Add to dashboard Cite

show abstract

“…As discussed in the last section this corresponds to the introduction of the effective subtraction constant as a free fit parameter in data reductions. The complete practical equivalence in data reductions between the IDR without the high energy approximation and the DDR with the subtraction constant as a free fit parameter is demonstrated in [72,79,80] and in more detail in [78]. The replacement of IDR by DDR has been also discussed by Cudell, Martynov and Selyugin [81,82] and more recently (2017) by Ferreira, Kohara and Sesma [83,84].…”

Section: C2 Derivative Dispersion Relations With the Effective Subtra...mentioning

confidence: 99%

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

Fagundes

Menon

Silva

2017

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

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...

show abstract

“…Up to our knowledge, the first results for the DDR taking into account the finite lower limit (i.e. without the high-energy approximation) and the effect of the primitive at both upper and lower limits were obtained by Ávila and Menon in 2005 [165,166]. The correction term can be expressed as a double infinite series 4 .…”

Section: Derivative Dispersion Relations With the Effective Subtracti...mentioning

confidence: 99%

“…The complete practical equivalence in data reductions between the IDR without the high-energy approximation and the DDR with the subtraction constant as a free fit parameter is demonstrated by Ávila and Menon in Refs. [157,170,171] and in more detail by Ávila in Ref. [169].…”

Section: Derivative Dispersion Relations With the Effective Subtracti...mentioning

confidence: 99%

Phenomenological analyses on hadronic cross-sections at high and asymptotic energies

Silva¹

View full text Add to dashboard Cite

To end a Ph.D. is like to end a very long trip. A trip where a lot of people cross our paths. People that we are thankful and that have helped us in several manners, both in direct and indirect ways.My special thanks to Silvia Cucatti, my beloved wife, which has been by my side since I started my Master degree. I do not have the words to say how much you help me, how much life is easy and pleasant at your side and how much I'm thankful. I love you! I thank my advisor, Prof. Márcio Menon, for everything. Thank you for the friendship, for the good moments, for the opportunity to work with you. I'll never forget what I have learned with you.The family is the ground where things start to grow. I'll be eternally thankful to my parents, my sister, and relatives for all the support during my life.Good friends are those who stay with us in easy and difficult times. And I can say that I have good friends. I'm thankful to

show abstract

From integral to derivative dispersion relations

Cited by 4 publications

References 6 publications

On the rise of proton–proton cross-sections at high energies

On the rise of proton–proton cross-sections at high energies

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

Phenomenological analyses on hadronic cross-sections at high and asymptotic energies

Contact Info

Product

Resources

About