Hadronic forward scattering: Predictions for the Large Hadron Collider and cosmic rays

Abstract

The status of hadron–hadron interactions is reviewed, with emphasis on the forward and near-forward scattering regions. Using unitarity, the optical theorem is derived. Analyticity and crossing symmetry, along with integral dispersion relations, are used to connect particle–particle and antiparticle–particle total cross sections and ρ -values, e.g., σ pp , σ p ¯ p , ρ pp and ρ p ¯ p , where ρ is the ratio of the real to the imaginary portion of the forward scattering amplitude. Real analytic amplitudes are then introduced to exploit analyticity and crossing symmetry. Again, from analyticity, finite energy sum rules (FESRs) are introduced from which new analyticity constraints are derived. These new analyticity conditions exploit the many very accurate low-energy experimental cross sections, i.e., they constrain the values of the asymptotic cross sections and their derivatives at low energies just above the resonance regions, allowing us new insights into duality. A robust fitting technique—using a minimization of the Lorentzian squared followed by the “Sieve” algorithm—is introduced in order to ‘clean up’ large data samples that are contaminated by outliers, allowing us to make much better fits to hadron–hadron scattering data over very large regions of energy. Experimental evidence for factorization theorems for γ γ , γ p and nucleon–nucleon collisions is presented. The Froissart bound is discussed—what do we mean here by the saturation of the Froissart bound? Using our analyticity constraints, new methods of fitting high-energy hadronic data are introduced which result in much more precise estimates of the fit parameters, allowing accurate extrapolations to much higher energies. It's shown that the γ p , π ± p and nucleon–nucleon cross sections all go asymptotically as ln 2 s , saturating the bound, while conclusively ruling out ln s and s α ( α ∼ 0.08 ) behavior. Implications of this saturation for predictions of σ pp and ρ pp at the Large Hadron Collider (LHC) and for cosmic rays are given. We discuss present day cosmic ray measurements, what they measure and how they deduce p–air cross sections. Connections are made between very high-energy measurements of σ p – air prod —which have rather poor energy determination—and predictions of σ p – air prod obtained, using a Glauber model, from values of σ pp that are extrapolated from fits of accelerator data at very precisely known, albeit lower, energies.