[Paper Review] Multiplicity Distribution of Secondary Hadrons at LHC Energy and Total Cross Sections of Hadron-Hadron Interactions

V. A. Abramovsky, N. V. Radchenko|ArXiv.org|Dec 12, 2008

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper proposes a Low Constituents Number Model (LCNM) to explain multiplicity distributions and total cross sections in proton-proton and proton-antiproton collisions at LHC energies. It distinguishes three production mechanisms—gluon string decay (Gaussian multiplicity), and two- and three-quark string decays (negative binomial multiplicity)—with gluon string contributing a constant to total cross sections and quark string contributions growing with energy. At √s = 14 TeV, the model predicts a total cross section of 101.30 ± 6.65 mb and a mean charged multiplicity of 71.57 ± 4.37.

ABSTRACT

The multiple production processes of secondary hadrons in proton-antiproton scattering are divided into three types. The first type is a shower of secondary hadrons produced from gluon string decay, the second type is a shower of secondary hadrons produced from two quark strings decay and the third is a shower produced from three quark strings decay. At the same time there are only two types for proton-proton scattering - shower from gluon string and shower from two quark strings. These showers do not correspond to pomeron showers originating from cuts of one, two, three, ... pomerons. Multiplicity distribution in gluon string is Gaussian, in two and three quark strings it is negative binomial. Gluon string weight in the multiplicity distribution is determined by the constant contribution to total cross sections, the quark strings weights - by the growing with energy contributions. The expected value of proton-proton scattering total cross section and the multiplicity distribution at energy 14 TeV are given

Motivation & Objective

• To resolve discrepancies in QCD models regarding total cross sections and multiplicity distributions at high energies.
• To address observed anomalies such as σ_tot(π±p)/σ_tot(pp) ≈ 2/3 and low Pomeranchuk trajectory slope.
• To propose a new mechanism for hadron production distinct from pomeron-based models.
• To predict total cross sections and multiplicity distributions for pp and p̄p scattering at √s = 14 TeV.
• To validate the model using experimental data from lower-energy pp and p̄p collisions.

Proposed method

• Classify hadron production into three types: gluon string decay (Gaussian multiplicity), two-quark string decay (negative binomial), and three-quark string decay (negative binomial).
• Model gluon string contribution as a constant term in total cross section, while quark string contributions grow with energy.
• Use the central limit theorem to justify Gaussian distribution for gluon string multiplicity due to large number of similar diagrams.
• Apply negative binomial distribution to quark string decays, with shape parameter k and mean multiplicity ⟨n⟩.
• Convolve multiple negative binomial distributions (e.g., two or three strings) to model combined multiplicity, preserving negative binomial form.
• Fit the model to experimental data at √s = 52.6–1800 GeV, using χ²/ndf to assess goodness of fit.

Experimental results

Research questions

• RQ1 How do multiplicity distributions in pp and p̄p scattering differ at high energies, and what mechanisms underlie these differences?
• RQ2 Can the observed total cross sections and multiplicity distributions be explained without relying on pomeron-based models?
• RQ3 What role do gluon strings and quark strings play in shaping the total cross section and multiplicity distribution?
• RQ4 How do the contributions of gluon and quark string decays scale with increasing center-of-mass energy?
• RQ5 Can the model accurately predict multiplicity and cross section at √s = 14 TeV using lower-energy data?

Key findings

• At √s = 14 TeV, the model predicts a total cross section of 101.30 ± 6.65 mb for pp scattering.
• The mean charged multiplicity at √s = 14 TeV is estimated at 71.57 ± 4.37.
• The multiplicity distribution in gluon string decay follows a Gaussian distribution due to the central limit theorem.
• Multiplicities from two- and three-quark string decays follow negative binomial distributions, with parameters scaling linearly with the number of strings.
• The model fits experimental data at √s = 52.6–1800 GeV with χ²/ndf values ranging from 4/26 to 120/115, indicating reasonable agreement.
• The model’s inelastic processes are distinct from pomeron-based mechanisms, as they arise from color exchange between valence quarks and low-number bremsstrahlung gluons.