Unitarity Bounds of the Scattering Amplitude and the Diffraction Peak

MacDowell, S. W.; Martin, A.

doi:10.1103/physrev.135.b960

Cited by 91 publications

(20 citation statements)

References 6 publications

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“…However, the limited statistics does not allow one to draw a definite conclusion, particularly when one realizes, as discussed in Section 2. 1.3, that at these energies the p-p dip may be partially filled by a higher value of p. (66) showed that the shape of the fo rward elastic peak must satisfy the fo llowing bound, based on unitarity (disregarding terms of order l/s) :…”

Section: 3 Cornille-martin Theoremmentioning

confidence: 98%

Elastic Scattering and Total Cross Section At Very High Energies

Castaldi¹,

Sanguinetti²

1985

Annu. Rev. Nucl. Part. Sci.

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Section: 3 Cornille-martin Theoremmentioning

confidence: 98%

Elastic Scattering and Total Cross Section At Very High Energies

Castaldi¹,

Sanguinetti²

1985

Annu. Rev. Nucl. Part. Sci.

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“…For the TOTEM experiment, the value for B(s) at LHC7 corresponds to the measurement in the interval 0.02 < |t| < 0.33 GeV −2 [283]. There are general considerations which relate the asymptotic behaviour of B(s) to that of the total cross section, in particular one can derive the asymptotic relation, so called MacDowell and Martin bound [284], discussed recently in [285], given as…”

Section: About the Slope Parametermentioning

confidence: 99%

Introduction to the physics of the total cross section at LHC

Pancheri

Srivastava

2017

Eur. Phys. J. C

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This review describes the development of the physics of hadronic cross sections up to recent LHC results and cosmic ray experiments. We present here a comprehensive review -written with a historical perspective -about total cross sections from medium to the highest energies explored experimentally and studied through a variety of methods and theoretical models for over 60 years. We begin by recalling the analytic properties of the elastic amplitude and the theorems about the asymptotic behavior of the total cross section. A discussion of how proton-proton cross sections are extracted from cosmic rays at higher than accelerator energies and help the study of these asymptotic limits, is presented. This is followed by a description of the advent of particle colliders, through which high energies and unmatched experimental precisions have been attained. Thus the measured hadronic elastic and total cross sections have become crucial instruments to probe the so called soft part of QCD physics, where quarks and gluons are confined, and have led to test and refine Regge behavior and a number of diffractive models. As the c.m. energy increases, the total cross section also probes the transition into hard scattering describable with perturbative QCD, the so-called mini-jet region. Further tests are provided by cross section measurements of γ p, γ * p and γ * γ * for models based on vector meson dominance, scaling limits of virtual photons at high Q 2 and the BFKL formalism. Models interpolating from virtual to real photons are also tested.

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“…This is legitimate only if the energy is not too high. As pointed out in [76,77], unitarity imposes a bound on the shape of the diffraction peak. The parametrization in (21) violates this bound at very high energies, for the following reason.…”

Section: Regge Representation Of the ππ Amplitudementioning

confidence: 99%

Regge analysis of the ππ scattering amplitude

2012

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Abstract. The theoretical predictions for the subtraction constants lead to a very accurate dispersive representation of the ππ scattering amplitude below 0.8 GeV. The extension of this representation up to the maximum energy of validity of the Roy equations (1.15 GeV) requires a more precise input at high energies. In this paper we determine the trajectories and residues of the leading Regge contributions to the ππ amplitude (Pomeron, f and ρ), using factorization, phenomenological parametrizations of the πN and N N total cross sections at high energy and a set of sum rules which connect the high and low energy properties of ππ scattering. We find that nonleading Regge terms are necessary in order to achieve a smooth transition from the partial waves to the Regge representation at or below 2 GeV. We obtain thus a Regge representation consistent both with the experimental information at high energies and the Roy equations for the partial waves with ℓ ≤ 4. The uncertainties in our result for the Regge parameters are sizable but in the solutions of the Roy equations, these only manifest themselves above KK threshold. MotivationLow energy pion physics has become a precision laboratory: the chiral symmetry properties of the Standard Model can now be compared with low energy precision experiments, using Chiral Perturbation Theory (χPT), dispersion theory and numerical simulations of QCD on a lattice. In principle, as illustrated by the prediction for the magnetic moment of the muon, physics beyond the Standard Model can show up at low energies, provided the quantity of interest can not only be measured accurately, but can also be calculated to sufficient precision. In this context, the interaction among the pions and in particular, the elastic ππ scattering amplitude play a crucial role.The Roy equations [1] provide a suitable framework for the low energy analysis of the ππ scattering amplitude, as they fully incorporate the basic properties that follow from analyticity, unitarity and crossing symmetry. They express the real parts of the partial waves as integrals over the imaginary parts that extend over all energies. The high energy behaviour of the imaginary parts thus enters the analysis, even if the Roy equations are evaluated only at low energy. More specifically, the contributions from the high energy region are contained in the so-called driving terms. Near the ππ threshold, these terms are very small. Accordingly, the results for the threshold parameters are not sensitive to the high energy contributions. The driving terms, however, grow with the energy. In [2,4], where the threshold parameters and the coupling constants of the effective chiral SU(2)×SU(2) Lagrangian relevant for ππ scattering are determined to high accuracy, the Roy equations are solved only below 0.8 GeV. On general grounds [1] these equations are valid in the region 1 s ≤ 68 M 2 π , i.e. for √ s ≤ 1.15 GeV, but in order to use them we need an accurate evaluation of the driving terms. This calls for a better understanding of the imaginary ...

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Unitarity Bounds of the Scattering Amplitude and the Diffraction Peak

Cited by 91 publications

References 6 publications

Elastic Scattering and Total Cross Section At Very High Energies

Elastic Scattering and Total Cross Section At Very High Energies

Introduction to the physics of the total cross section at LHC

Regge analysis of the ππ scattering amplitude

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