[Paper Review] Multiple Parton Interactions, inclusive and exclusive cross sections, sum rules

D. Treleani, G. Calucci|arXiv (Cornell University)|Jul 2, 2017

Quantum Chromodynamics and Particle Interactions9 references3 citations

TL;DR

This paper develops a simplified model of Multiple Parton Interactions (MPIs) in high-energy hadronic collisions, showing that inclusive cross sections correspond to factorial moments of the interaction multiplicity distribution, while exclusive cross sections—linked via sum rules—enable experimental testing of MPI dynamics. The key contribution is a formal framework linking inclusive and exclusive MPI cross sections through sum rules, allowing extraction of non-perturbative parameters like the effective cross section 𝜎_eff.

ABSTRACT

In a simplified model of Multiple Parton Interactions the inclusive cross sections, of processes with large momentum transfer exchange, acquire the statistical meaning of factorial moments of the distribution in multiplicity of interactions, while more exclusive cross sections, which can provide complementary information on the interaction dynamics, become experimentally viable. Inclusive and exclusive cross sections are linked by sum rules, which can be tested experimentally.

Motivation & Objective

• To establish a theoretical framework for Multiple Parton Interactions (MPIs) in high-energy hadronic collisions.
• To demonstrate that inclusive MPI cross sections correspond to factorial moments of the interaction multiplicity distribution.
• To introduce exclusive cross sections as complementary probes of MPI dynamics.
• To derive sum rules linking inclusive and exclusive cross sections for experimental validation.
• To enable extraction of non-perturbative parameters such as the effective cross section 𝜎_eff from inclusive and exclusive measurements.

Proposed method

• Introduces a simplified MPI model with a transverse momentum cutoff to separate hard and soft interactions.
• Treats each hard sub-interaction as perturbatively calculable and independent, assuming two-parton initial states.
• Uses unitarity diagrams and light-cone momentum analysis to derive kinematic constraints and loop integration limits.
• Applies a functional formalism to include two-body correlations in multi-parton distributions.
• Derives sum rules connecting inclusive cross sections (e.g., 𝜎_S) to exclusive cross sections (e.g., 𝜎_D, 𝜎_T) via relations like 𝜎_D = 𝜎_S − 𝜎̃_1 − 𝜎̃_2.
• Expresses exclusive cross sections in terms of the inclusive cross section and effective parameters like 𝜏 and 𝜎_eff.

Experimental results

Research questions

• RQ1 How can inclusive MPI cross sections be interpreted in terms of factorial moments of the interaction multiplicity distribution?
• RQ2 What is the role of sum rules in connecting inclusive and exclusive MPI cross sections?
• RQ3 How can exclusive cross sections be defined and measured to probe MPI dynamics beyond inclusive observables?
• RQ4 In what way do non-perturbative parameters like the effective cross section 𝜎_eff encode information about parton correlations?
• RQ5 How can proton-deuteron collisions help disentangle spatial and dynamical correlations in parton pairs?

Key findings

• Inclusive MPI cross sections are shown to be factorial moments of the multiplicity distribution, ensuring unitarity and order-by-order calculability.
• The cancellation of AGK interference terms holds for all MPI inclusive cross sections, both in uncorrelated and correlated cases.
• Exclusive cross sections for double (𝜎_D) and triple (𝜎_T) parton collisions are derived via sum rules, with explicit expressions in terms of the single scattering cross section 𝜎_S.
• The double parton scattering cross section is given by 𝜎_D = 𝜎_S² / (2𝜎_eff), and the triple parton scattering by 𝜎_T = 𝜎_S³ / (6𝜏𝜎_eff²), where 𝜏 is a dimensionless correlation parameter.
• The effective cross section 𝜎_eff can be extracted from inclusive and exclusive measurements, providing a handle on parton spatial and dynamical correlations.
• Proton-deuteron collisions offer a clean probe of parton pair correlations due to the well-known deuteron wave function, enabling separation of spatial and dynamical effects.