This is a summary of the theoretical contributions to the QCD session of the 47th Rencontre de Moriond, including some perspectives on the implications of the reported experimental results on the status of our theoretical understanding.
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 num
ber 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.
We introduce shower deconstruction, a method to look for new physics in a hadronic environment. The method aims to be a full information approach using small jets. It assigns to each event a number chi that is an estimate of the ratio of the probabil
ity for a signal process to produce that event to the probability for a background process to produce that event. The analytic functions we derive to calculate these probabilities mimic what full event generators like Pythia or Herwig do and can be depicted in a diagrammatic way. As an example, we apply this method to a boosted Higgs boson produced in association with a Z-boson and show that this method can be useful to discriminate this signal from the Z+jets background.
The signal for a highly boosted heavy resonance competing against a background of light parton jets at the LHC can be enhanced by analyzing subjets in the fat jet that possibly contains the heavy resonance. Three methods for doing this are known as f
iltering, pruning, and trimming. We study the possibility of combining these methods using a relative likelihood approach. We find that, because the methods are not the same, one achieves an enhanced statistical power by combining them. We illustrate the possibilities first with a simple problem of combining trimming and pruning to enhance the signal for finding a boosted top quark. We then study the more difficult problem of disentangling from the background the signal for the production of a Higgs boson in association with a Z-boson. For this problem, we combine filtering, trimming, and pruning.
Cross sections for physical processes that involve very different momentum scales in the same process will involve large logarithms of the ratio of the momentum scales when calculated in perturbation theory. One goal of calculations using parton show
ers is to sum these large logarithms. We ask whether this goal is achieved for the transverse momentum distribution of a Z-boson produced in hadron-hadron collisions when the shower is organized with higher virtuality parton splittings coming first, followed successively by lower virtuality parton splittings. We find that the virtuality ordered shower works well in reproducing the known QCD result.
We study a parton shower description, based on a dipole picture, of the final state in electron-positron annihilation. In such a shower, the distribution function describing the inclusive probability to find a quark with a given energy depends on the
shower evolution time. Starting from the exclusive evolution equation for the shower, we derive an equation for the evolution of the inclusive quark energy distribution in the limit of strong ordering in shower evolution time of the successive parton splittings. We find that, as expected, this is the DGLAP equation. This paper is a response to a recent paper of Dokshitzer and Marchesini that raised troubling issues about whether a dipole based shower could give the DGLAP equation for the quark energy distribution.
One approach to the calculation of cross sections for infrared-safe observables in high energy collisions at next-to-leading order is to perform all of the integrations, including the virtual loop integration, by Monte Carlo numerical integration. In
a previous paper, two of us have shown how one can perform such a virtual loop integration numerically after first introducing a Feynman parameter representation. In this paper, we perform the integration directly, without introducing Feynman parameters, after suitably deforming the integration contour. Our example is the N-photon scattering amplitude with a massless electron loop. We report results for N = 6 and N = 8.
It is useful to describe a leading order parton shower as the solution of a linear equation that specifies how the state of the partons evolves. This description involves an essential approximation of a strong ordering of virtualities as the shower p
rogresses from a hard interaction to softer interactions. If this is to be the only approximation, then the partons should carry color and spin and quantum interference graphs should be included. We explain how the evolution equation for this kind of a shower can be formulated. We discuss briefly our efforts to implement this evolution equation numerically.
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 state
s, 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 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 interaction
s 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.
