Froissart bound on total cross section without unknown constants

Martin, A.; Roy, S. M.

doi:10.1103/physrevd.89.045015

Cited by 17 publications

(30 citation statements)

References 45 publications

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“…Recently we [1] have obtained bounds on energy averages of the total cross section without any unknown constants such as an overall constant factor or the scale factor in the logarithm. The purpose of the present work is to obtain analogous bounds on the energy-averaged inelastic cross section without any unknown constants.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of the total cross section, both these shortcomings were removed recently [1]. Bounds on energy averages of the total cross section were obtained in which the scale s 0 is determined in terms of CðtÞ.…”

Section: Introductionmentioning

confidence: 99%

“…CðtÞ can be bounded rigorously in terms of pion mass alone for π 0 π 0 scattering. Thus we obtained the absolute bound [1], σ tot ðs; ∞Þ ≤ πðm π Þ −2 ½lnðs=s 0 Þ þ ð1=2Þ ln lnðs=s 0 Þ þ 1 2 þ Oðln lnðs=s 0 ÞÞ; …”

Section: Introductionmentioning

confidence: 99%

“…We choose the same normalizations as in Martin-Roy [1]. Fðs; tÞ denotes an ab → ab scattering amplitude at c.m.…”

Section: Introductionmentioning

confidence: 99%

“…This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor s 1 is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic π 0 π 0 cross section has a bound of the same form with 1=s 1 replaced by 1=s 2 ¼ 2=s 1 .…”

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confidence: 99%

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Froissart bound on inelastic cross section without unknown constants

Martin

Roy

2015

Phys. Rev. D

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Assuming that axiomatic local field theory results hold for hadron scattering, André Martin and S. M. Roy recently obtained absolute bounds on the D wave below threshold for pion-pion scattering and thereby determined the scale of the logarithm in the Froissart bound on total cross sections in terms of pion mass only. Previously, Martin proved a rigorous upper bound on the inelastic cross-section σ inel which is onefourth of the corresponding upper bound on σ tot , and Wu, Martin, Roy and Singh improved the bound by adding the constraint of a given σ tot . Here we use unitarity and analyticity to determine, without any highenergy approximation, upper bounds on energy-averaged inelastic cross sections in terms of lowenergy data in the crossed channel. These are Froissart-type bounds without any unknown coefficient or unknown scale factors and can be tested experimentally. Alternatively, their asymptotic forms, together with the Martin-Roy absolute bounds on pion-pion D waves below threshold, yield absolute bounds on energy-averaged inelastic cross sections. For example, for π 0 π 0 scattering, definingπ . This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor s 1 is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic π 0 π 0 cross section has a bound of the same form with 1=s 1 replaced by 1=s 2 ¼ 2=s 1 .

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…We choose the same normalizations as in Martin-Roy [1]. Fðs; tÞ denotes an ab → ab scattering amplitude at c.m.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Froissart bound on inelastic cross section without unknown constants

Martin

Roy

2015

Phys. Rev. D

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Hadronic total cross sections at high energy and the QCD spectrum

Giordano

Meggiolaro

2014

J. High Energ. Phys.

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Abstract:We show how to obtain the leading energy dependence of hadronic total cross sections, in the framework of the nonperturbative approach to soft high-energy scattering based on Wilson-loop correlation functions, if certain nontrivial analyticity assumptions are satisfied. The total cross sections turn out to be of "Froissart" type, σfor s → ∞. We also discuss under which conditions the coefficient B is universal, i.e., independent of the hadrons involved in the scattering process. In the most natural scenarios for universality, B can be related to the stable spectrum of QCD, and is predicted to be B th 0.22 mb, in fair agreement with experimental results. If we consider, instead, the stable spectrum of the quenched (i.e., pure-gauge) theory, we obtain a quite larger value B (Q) th ≥ 0.42 mb, suggesting (quite surprisingly) large unquenching effects due to the sea quarks.

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Asymptotic behaviour of pion-pion total cross-sections

Greynat¹,

Rafael

Vulvert

2014

J. High Energ. Phys.

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We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the ππ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log 2 s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for π + π − , π ± π 0 and π 0 π 0 scattering within the framework of the constituent chiral quark model (CχQM) in the limit of a large number of colours N c and discuss their asymptotic behaviours. The same ππ cross sections are also discussed within the general framework of Large-N c QCD and we show that it is possible to make an Ansatz for the isospin I = 1 and I = 0 spectrum which satisfy the FroissartMartin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-N c counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the σ total π ± π 0 (s) cross section predicted by the CχQM with the high energy behaviour predicted by the Large-N c Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the pp and pp scattering total cross sections.

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Froissart bound on total cross section without unknown constants

Cited by 17 publications

References 45 publications

Froissart bound on inelastic cross section without unknown constants

Froissart bound on inelastic cross section without unknown constants

Hadronic total cross sections at high energy and the QCD spectrum

Asymptotic behaviour of pion-pion total cross-sections

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