The goal of the automation is to handle the full sequence of calculations in an automatic (programmed) way: from the Lagrangian expression describing the physics model up to the cross-sections values and to the event generator software.
In these simple cases, no automatic packages are needed and cross-section analytical expressions can be easily derived at least for the lowest approximation: the Born approximation also called the leading order or the tree level (as Feynman diagrams have only trunk and branches, no loops).
The number of subprocesses describing a given process is so large that automatic tools have been developed to mitigate the burden of hand calculations.
Interactions at HighahEnergih open a large spectrum of possible final states and consequently increase the number of processes to compute.
The automatic packages, once seen as mere teaching support, have become, this last 10 years an essential component of the data simulation and analysis suite for all experiments.
They use values (i.e. for the masses) or expressions (i.e. for the couplings) produced by step I or model specific libraries constructed by hands (usually heavily relying on Computer algebra languages).
The various effects or phenomenon that need to be implemeted are: The interplay or matching of the precise matrix element calculation and the approximations resulting from the simulation of the parton shower gives rise to further complications, either within a given level of precision like at leading order (LO) for the production of n jets or between two levels of precision when tempting to connect matrix element computed at next-to-leading (NLO) (1-loop) or next-to-next-leading order (NNLO) (2-loops) with LO partons shower package.
These are symbolic manipulation codes that automatize the algebraic parts of a matrix element evaluation, like traces on Dirac matrices and contraction of Lorentz indices.
Such codes have evolved quite a lot with applications not only optimized for high-energy physics like FORM but also more general purpose programs like Mathematica and Maple.
One of the first major application of these early developments in this field was the calculation of the anomalous magnetic moments of the electron and the muon[16].
The computational cost of this algorithm grows asymptotically as 3n, where n is the number of particles involved in the process, compared to n!
Additionally, the color and helicity structures are appropriately transformed so the usual summation is replaced by the Monte Carlo techniques.
[11] [12] The integration of the "matrix element" over the multidimensional internal parameters phase space provides the total and differential cross-sections.
For example one scenario is the fact that special functions often need to be calculated in these software packages, both/either algebraically and/or numerically.
Maple, Mathematica often need to consider abstract, mathematical structures in subatomic particle collisions and emissions.
Status: PD: Public Domain, Model: SM: Standard Model, MSSM: Minimal Supersymmetric Standard Model Method: HA: Helicity Amplitude, DS: Dyson Schwinger Output: ME: Matrix Element, CS: Cross-Sections, PEG: Parton level Event Generation, FEG: Full particle level Event Generation