[Paper Review] Supersymmetric Scaling Violations (I). Solving the Supersymmetric DGLAP Evolution

Claudio Corianò|arXiv (Cornell University)|Sep 19, 2000

Particle physics theoretical and experimental studies9 references4 citations

TL;DR

This paper develops a recursive x-space algorithm to solve the supersymmetric DGLAP evolution equations in N=1 SQCD, enabling accurate parton distribution evolution across regular QCD and supersymmetric thresholds. It computes all parton distributions—including gluino and squark contributions—under a broken SUSY scenario with a light gluino and decoupled squarks, providing a foundation for LHC SUSY searches and cosmic ray physics.

ABSTRACT

We analize the renormalization group equations of supersymmetric QCD with N=1 for the evolution of parton distributions. For this purpose we develope a simple recursive algorithm in x-space to include both regular regions and supersymmetric regions in the evolution in the step approximation. Supersymmetric distributions are generated within a radiative model, with vanishing initial conditions for the superpartners. Here we focus on a scenario with broken susy, characterized by a lighter gluino coupled to the standard evolution and a decoupled scalar quark. Predictions for the all the distributions are presented.

Motivation & Objective

• To extend the DGLAP evolution formalism to supersymmetric QCD (SQCD) for N=1 SUSY with broken supersymmetry.
• To develop a numerical algorithm that handles both regular QCD and supersymmetric evolution regions, including threshold crossings.
• To generate supersymmetric parton distributions starting from vanishing initial conditions for superpartners.
• To provide a quantitative tool for assessing gluino and squark effects in high-energy collider processes and cosmic ray interactions.
• To lay the groundwork for future studies on SUSY-induced scaling violations in Drell-Yan and hadron-hadron collisions at the LHC.

Proposed method

• Adapts a recursive algorithm in x-space to solve the DGLAP evolution equations in supersymmetric QCD, ensuring continuity across evolving factorization scales.
• Uses analytic discretization of convolution integrals via 'weights' to achieve high numerical accuracy, particularly in the small-x region.
• Applies a linear interpolation scheme over discrete x-intervals to approximate the integration of splitting functions and distribution functions.
• Incorporates two-loop running coupling via β₀ and β₁ coefficients, with logarithmic resummation of large logarithms in the running coupling.
• Implements a stepwise evolution scheme that dynamically includes new partonic states (e.g., gluino) when the factorization scale crosses their threshold.
• Utilizes the non-singlet and singlet evolution equations for quarks and gluons, extended to include supersymmetric states such as the gluino and squarks.

Experimental results

Research questions

• RQ1 How can the DGLAP evolution equations be consistently extended to include supersymmetric parton distributions in N=1 SQCD?
• RQ2 What is the impact of a light gluino on the evolution of parton distributions compared to standard QCD?
• RQ3 How can numerical instabilities in the small-x region be controlled during supersymmetric evolution?
• RQ4 What are the quantitative differences in parton distribution functions when supersymmetric thresholds are crossed?
• RQ5 To what extent can supersymmetric scaling violations be used to constrain the mass of the gluino or squark in future LHC data?

Key findings

• The recursive x-space algorithm successfully handles the transition between QCD and supersymmetric evolution regions, including the opening of new partonic channels at threshold.
• Supersymmetric parton distributions are generated from vanishing initial conditions for superpartners, with the gluino contributing significantly to the evolution when its mass is below the factorization scale.
• The method achieves high numerical accuracy in the small-x region by analytically discretizing the splitting function convolutions using interpolation and weight functions.
• The inclusion of supersymmetric states modifies the DGLAP evolution, particularly in the gluon and quark distribution evolution, due to new splitting functions involving the gluino.
• The model predicts distinct scaling violation patterns in the presence of a light gluino, which could be probed in precision measurements at the LHC.
• The approach is generalizable to next-to-leading order and can be extended to study SUSY effects in deep inelastic scattering and hadron-hadron collisions.