Spin Correlations in Monte Carlo Simulations

TL;DR

This work demonstrates that the Collins-Knowles spin-correlation framework can be extended to include production-decay spin correlations for heavy particles in Monte Carlo event generators without sacrificing the step-by-step structure or incurring combinatorial explosion. By employing spin density and decay matrices, the method propagates correlations through decay chains and, when necessary, accounts for color-flow factors to maintain linear complexity. The approach is validated against full matrix-element calculations across SM and MSSM processes, including top quark and SUSY cascades, and shows good agreement for key observables and distributions. Implemented in HERWIG, the algorithm preserves modularity and is poised for integration with parton-shower dynamics in future C++ generators, enabling more accurate simulations of heavy-particle production and decay at current and future colliders.

Abstract

We show that the algorithm originally proposed by Collins and Knowles for spin correlations in the QCD parton shower can be used in order to include spin correlations between the production and decay of heavy particles in Monte Carlo event generators. This allows correlations to be included while maintaining the step-by-step approach of the Monte Carlo event generation process. We present examples of this approach for both the Standard and Minimal Supersymmetric Standard Models. A merger of this algorithm and that used in the parton shower is discussed in order to include all correlations in the perturbative phase of event generation. Finally we present all the results needed to implement this algorithm for the Standard and Minimal Supersymmetric Standard Models.

Figures (41)

• Figure 1: Example of a Monte Carlo event. This example shows the production of $\mathrm{t\bar{t}}$ in $\mathrm{e}^+\mathrm{e}^-$ collisions followed by the semi-leptonic decay of the top quarks. The cluster hadronization model Webber:1984if is shown where the gluons left after the parton-shower phase are non-perturbatively split into quark-antiquark pairs. The quarks and antiquarks are then paired into colour-singlet clusters using the colour flow information in the event. These clusters decay to give the observed hadrons.
• Figure 2: Feynman Diagrams for the decay ${\rm \tilde{}$q̃$}_L\rightarrow{\rm q} \tilde{}$χ̃$^0_2\rightarrow{\rm q}\ell^\pm\tilde{}$ℓ̃$^\mp_R$.
• Figure 3: Feynman diagrams for the production of $\tilde{}$χ̃$^0_2\tilde{}$χ̃$^0_1$ in $\rm{e}^+\rm{e}^-$ collisions.
• Figure 4: Feynman diagrams for the decay $\tilde{}$χ̃$^0_2\rightarrow\rm{f}\bar{\rm{f}}\tilde{}$χ̃$^0_1$. The exchange of the MSSM Higgs bosons is only important for the third generation of fermions.
• Figure 5: Angle between the lepton produced in $\rm{e}^+\rm{e}^-\rightarrow\tilde{}$χ̃$^0_2\tilde{}$χ̃$^0_1\rightarrow\ell^+\ell^-\tilde{}$χ̃$^0_1\tilde{}$χ̃$^0_1$ and the incoming electron beam in the laboratory frame for a centre-of-mass energy of 500 GeV with (a) no polarization, (b) negatively polarized electrons and positively polarized positrons and (c) positively polarized electrons and negatively polarized positrons. The solid line shows the default result from HERWIG which treats the production and decay as independent and uses a phase-space distribution for the decay products of the neutralino, the dot-dashed line also includes a matrix element for the neutralino decay, the dashed line gives the full result from the 4-body matrix element and the dotted line the result of the spin correlation algorithm.