[Paper Review] Fundamental problems with hadronic and leptonic interactions

P. V. Landshoff|ArXiv.org|Mar 9, 2009

Particle physics theoretical and experimental studies1 references6 citations

TL;DR

This paper challenges foundational assumptions in high-energy hadronic and leptonic interactions, arguing that unitarity constraints and DGLAP evolution at small x are poorly understood, leading to a large uncertainty in LHC total cross-section predictions—ranging from 90 to 160 mb. The author critiques eikonal models and DGLAP applications, advocating for Regge fits to structure functions as more reliable, and suggests elastic scattering at large t could be unexpectedly large at LHC energies due to hard pomeron and triple-gluon exchange contributions.

ABSTRACT

Common beliefs about unitarity are not reliable, and we do not know how to apply DGLAP evolution at small x. Together with the big discrepancy between the measurements of the total cross section at the Tevatron, a consequence is that the cross section at the LHC could be anywhere between 90 and 160 mb.

Motivation & Objective

• To assess the reliability of fundamental assumptions in high-energy hadronic and leptonic scattering, particularly unitarity and DGLAP evolution.
• To identify the theoretical and practical limitations in predicting the total cross section at the LHC.
• To evaluate the validity of eikonal models and DGLAP evolution at small x in parton density extraction.
• To explore whether elastic scattering at large t could be significant at LHC energies due to hard pomeron and triple-gluon exchange mechanisms.
• To reconcile discrepancies in Tevatron measurements with theoretical expectations, especially regarding the absence of a dip in p̄p scattering.

Proposed method

• Uses the eikonal formalism to model unitarity via χ(s,b), approximating it with single-pomeron exchange, though acknowledging its inadequacy for double-pomeron exchange.
• Applies the DGLAP evolution equation in momentum space, highlighting divergences at small z due to 1/z singularities in splitting functions.
• Introduces a modified DGLAP approach by assuming parton densities scale as x^{-ε}, allowing perturbative expansion when ε > 0.
• Constructs a phenomenological amplitude model including single soft and hard pomeron exchange, two-pomeron exchange (IIP IIP), and triple-gluon (ggg) exchange in impact parameter space.
• Fits the model to pp and p̄p elastic scattering data at Tevatron energies, adjusting parameters to reproduce the dip structure and suppress unphysical divergences.
• Extrapolates the fitted amplitude to LHC energies to estimate total cross sections, comparing models with and without two-pomeron contributions.

Experimental results

Research questions

• RQ1 To what extent can unitarity be reliably applied to hadronic and leptonic scattering amplitudes, especially in the context of pomeron exchange?
• RQ2 Why is DGLAP evolution at small x mathematically and physically problematic, and how does this affect parton density extraction?
• RQ3 Can eikonal models accurately describe double-pomeron exchange, or are they fundamentally inadequate due to missing correlations in the proton wave function?
• RQ4 What explains the observed dip in pp elastic scattering at intermediate t, and why is it absent in p̄p scattering?
• RQ5 How large might elastic cross sections be at large t in pp scattering at LHC energies, and what mechanisms could drive such behavior?

Key findings

• The total cross section at the LHC is predicted to range between 90 and 160 mb due to unresolved theoretical uncertainties in unitarity and DGLAP evolution.
• Including two-pomeron exchange in the amplitude model reduces the predicted total cross section from 160 mb to 125 mb, indicating a significant theoretical uncertainty.
• The model with single soft and hard pomeron exchange plus two-pomeron and ggg exchange fits Tevatron data well, including the dip structure in pp scattering and its absence in p̄p scattering.
• Elastic scattering at large t may be unexpectedly large at LHC energies due to contributions from hard pomeron and triple-gluon exchange, which grow rapidly with energy.
• DGLAP evolution cannot be reliably applied below Q² = 5 GeV² due to divergences in splitting functions at small z, invalidating standard perturbative expansions at small x.
• Unitarity does not constrain F₂(x,Q²) for virtual photon-proton scattering, as the unitarity relation does not hold in the same way as for hadronic scattering.