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Register a new userParton showers with more exact color evolution
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Parton shower event generators typically approximate evolution of QCD color so that only contributions that are leading in the limit of an infinite number of colors are retained. Our parton shower generator, Deductor, has used an LC+ approximation that is better, but still quite limited. In this paper, we introduce a new scheme for color in which the approximations can be systematically improved. That is, one can choose the theoretical accuracy level, but the accuracy level that is practical is limited by the computer resources available.
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We have previously described a mathematical formulation for a parton shower based on the approximation of strongly ordered virtualities of successive parton splittings. Quantum interference, including interference among different color and spin states, was included. A practical numerical implementation strategy was left unspecified. In a subsequent paper, we showed that if we add the further approximations of taking only the leading color limit and averaging over spins, we obtain a shower evolution that can be implemented as a Markov process. In this paper, we outline a strategy for including the correlations induced by parton spins.
We have previously described a mathematical formulation for a parton shower based on the approximation of strongly ordered virtualities of successive parton splittings. Quantum interference, including interference among different color and spin states, is included. In this paper, we add the further approximations of taking only the leading color limit and averaging over spins, as is common in parton shower Monte Carlo event generators. Soft gluon interference effects remain with this approximation. We find that the leading color, spin averaged shower in our formalism is similar to that in other shower formulations. We discuss some of the differences.
Parton shower Monte Carlo event generators in which the shower evolves from hard splittings to soft splittings generally use the leading color approximation, which is the leading term in an expansion in powers of $1/N_c^2$, where $N_c = 3$ is the number of colors. We introduce a more general approximation, the LC+ approximation, that includes some of the color suppressed contributions. There is a cost: each generated event comes with a weight. There is a benefit: at each splitting the leading soft$times$collinear singularity and the leading collinear singularity are treated exactly with respect to color. In addition, an LC+ shower can start from a state of the color density matrix in which the bra state color and the ket state color do not match.
Initial state evolution in parton shower event generators involves parton distribution functions. We examine the probability for the system to evolve from a higher scale to a lower scale without an initial state splitting. A simple argument suggests that this probability, when multiplied by the ratio of the parton distributions at the two scales, should be independent of the parton distribution functions. We call this the PDF property. We examine whether the PDF property actually holds using Pythia and Deductor. We also test a related property for the Deductor shower and discuss the physics behind the results.
We specify recursive equations that could be used to generate a lowest order parton shower for hard scattering in hadron-hadron collisions. The formalism is based on the factorization soft and collinear interactions from relatively harder interactions in QCD amplitudes. It incorporates quantum interference between different amplitudes in those cases in which the interference diagrams have leading soft or collinear singularities. It incorporates the color and spin information carried by partons emerging from a hard interaction. One motivation for this work is to have a method that can naturally cooperate with next-to-leading order calculations.
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