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Register a new userSolving QCD evolution equations in rapidity space with Markovian Monte Carlo
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This work covers methodology of solving QCD evolution equation of the parton distribution using Markovian Monte Carlo (MMC) algorithms in a class of models ranging from DGLAP to CCFM. One of the purposes of the above MMCs is to test the other more sophisticated Monte Carlo programs, the so-called Constrained Monte Carlo (CMC) programs, which will be used as a building block in the parton shower MC. This is why the mapping of the evolution variables (eikonal variable and evolution time) into four-momenta is also defined and tested. The evolution time is identified with the rapidity variable of the emitted parton. The presented MMCs are tested independently, with ~0.1% precision, against the non-MC program APCheb especially devised for this purpose.
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A model for the production of large rapidity gaps being implemented in the Monte Carlo event generator PHOJET is discussed. In this model, high-mass diffraction dissociation exhibits properties similar to hadron production in non-diffractive hadronic collisions at high energies. Hard diffraction is described using leading-order QCD matrix elements together with a parton distribution function for the pomeron and pomeron-flux factorization. Since this factorization is imposed on Born graph level only, unitarity corrections lead to a non-factorizing flux function. Rapidity gaps between jets are obtained by soft color reconnection. It was previously shown that this model is able to describe data on diffractive hadron production from the CERN-SPS collider and from the HERA lepton-proton collider. In this work we focus on the model predictions for rapidity gap events in p-p collisions at sqrt{s} = 1800 GeV and compare to TEVATRON data.
In this talk I gave a brief summary of leading order, next-to-leading order and shower calculations. I discussed the main ideas and approximations of the shower algorithms and the related matching schemes. I tried to focus on QCD issues and open questions instead of making a inventory of the existing programs.
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions. Finally, comparison of solutions obtained numerically are presented.
Some of the most arduous and error-prone aspects of precision resummed calculations are related to the partonic hard process, having nothing to do with the resummation. In particular, interfacing to parton-distribution functions, combining various channels, and performing the phase space integration can be limiting factors in completing calculations. Conveniently, however, most of these tasks are already automated in many Monte Carlo programs, such as MadGraph, Alpgen or Sherpa. In this paper, we show how such programs can be used to produce distributions of partonic kinematics with associated color structures representing the hard factor in a resummed distribution. These distributions can then be used to weight convolutions of jet, soft and beam functions producing a complete resummed calculation. In fact, only around 1000 unweighted events are necessary to produce precise distributions. A number of examples and checks are provided, including $e^+e^-$ two- and four-jet event shapes, $n$-jettiness and jet-mass related observables at hadron colliders. Attached code can be used to modify MadGraph to export the relevant leading-order hard functions and color structures for arbitrary processes.
We report on the first global QCD analysis of the quark transversity distributions in the nucleon from semi-inclusive deep-inelastic scattering (SIDIS), using a new Monte Carlo method based on nested sampling and constraints on the isovector tensor charge $g_T$ from lattice QCD. A simultaneous fit to the available SIDIS Collins asymmetry data is compatible with $g_T$ values extracted from a comprehensive reanalysis of existing lattice simulations, in contrast to previous analyses which found significantly smaller $g_T$ values. The contributions to the nucleon tensor charge from $u$ and $d$ quarks are found to be $delta u = 0.3(2)$ and $delta d = -0.7(2)$ at a scale $Q^2 = 2$ GeV$^2$.
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