A simple algorithm for polarized parton evolution

Abstract

We present an algorithm to include the correlation between the production and decay planes of gluons in a parton-shower simulation. The technique is based on identifying the charge currents responsible for the creation and annihilation of the vector field. It is applicable in both the hard-collinear and the soft wide-angle region. As a function of the number of particles, the algorithm scales linear in computing time and memory. We demonstrate agreement with fixed-order perturbative calculations in the relevant kinematical limits, and present a new observable that can be used to probe correlations beyond current-current interactions.

Figures (8)

• Figure 1: Diagrams leading to the quark-to-quark-gluon splitting function (a), the gluon-to-quark-antiquark splitting function (b), and the gluon-to-gluon-gluon splitting function (c) at tree level. The labels indicate the particle momenta referred to in the main text.
• Figure 2: The current-current correlator $C_{i,j}^{1,2}$ for the initial quark pair (labeled $i$ and $j$) and the emitted quark pair (labeled $1$ and $2$) in a splitting sequence $ij\to ij\widetilde{12}\to ij12$ where the intermediate gluon decays to quarks. Polarization correlated evolution is compared to uncorrelated evolution. The left panel shows the result at $z=1/2$ in the second splitting. The right panel shows the complete result at $\alpha_s(m_Z)=0.01$.
• Figure 3: The current-current correlator $C_{i,j}^{1,2}$ for the initial quark pair (labeled $i$ and $j$) and the first two gluons (labeled $1$ and $2$) in a splitting sequence $ij\to ij\widetilde{12}\to ij12$. Polarization correlated evolution is compared to uncorrelated evolution, and the second splitting is restricted to a decay, described by Eq. \ref{['eq:decay_current']}. We set $\alpha_s(m_Z)=0.12$ (left) and $\alpha_s(m_Z)=0.01$ (right).
• Figure 4: The current-current correlators $C_{i,j}^{1,2}$ (left) and $C_{i,j}^{1,3}$ (right) in a splitting sequence $ij\to ij\widetilde{123}\to ij\widetilde{13}2\to ij123$. Polarization correlated evolution is compared to uncorrelated evolution, and the second splitting is restricted to scalar radiation, described by Eq. \ref{['eq:scalar_current']}, while the third is restricted to a decay, described by Eq. \ref{['eq:decay_current']}.
• Figure 5: The current-current correlators $C_{1,3}^{2,4}$ (left) and $C_{i,j}^{1,2}$ (right) in events with four branchings, where the second, third and fourth splitting are restricted to a decay described by Eq. \ref{['eq:decay_current']}, and we enforce the splitting sequence $ij\to ij\widetilde{1234}\to ij\widetilde{13}\widetilde{24}\to ij12\widetilde{34}\to ij1234$. Decay probabilities are enhanced by a factor 100 to increase statistics.