Particle accelerators or colliders produce collisions (interactions) of particles (like the
electron or the
proton). The colliding particles form the
Initial State. In the collision, particles can be annihilated or/and exchanged producing possibly different sets of particles, the
Final States. The Initial and Final States of the interaction relate through the so-called scattering matrix (
S-matrix). For example, at
LEP, , or are processes where the
initial state is an electron and a positron colliding to produce an electron and a positron or two muons of opposite charge: the
final states. 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). But particle physics is now requiring much more complex calculations like at
LHC p p \rarr n_\text{jets} where p are protons and n_\text{jets} is the number of
jets of particles initiated by proton constituents (
quarks and
gluons). 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. High precision experiments impose the calculation of
higher order calculation, namely the inclusion of subprocesses where more than one
virtual particle can be created and annihilated during the interaction lapse creating so-called
loops which induce much more involved calculations. Finally new theoretical models like the
supersymmetry model (
MSSM in its minimal version) predict a flurry of new processes. 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 help constructing
event generators and are sometimes viewed as
generators of event generators or
Meta-generators. A particle physics model is essentially described by its
Lagrangian. To simulate the production of events through
event generators, 3 steps have to be taken. The Automatic Calculation project is to create the tools to make those steps as automatic (or programmed) as possible:
I Feynman rules, coupling and mass generation • LanHEP is an example of
Feynman rules generation. • Some model needs an additional step to compute, based on some parameters, the mass and coupling of new predicted particles.
II Matrix element code generation: Various
methods are used to automatically produce the
matrix element expression in a computer language (
Fortran,
C/C++). 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). When this expression is integrated (usually numerically) over the internal degrees of freedom it will provide the total and differential cross-sections for a given set of initial parameters like the
initial state particle energies and
polarization.
III Event generator code generation: This code must them be interfaced to other packages to fully provide the actual
final state. The various effects or phenomenon that need to be implemented are: •
Initial state radiation and
beamstrahlung for initial states. •
Parton distribution functions describing the actual content in terms of
gluons and
quarks of the p or p-bar initial state particles •
Parton showering describing the way final state quarks or gluons due to the
QCD confinement generate additional quark/gluon pairs generating a so-called shower of
partons before transforming into hadrons. •
Hadronization describing how the final quark pairs/triplets form the visible and detectable hadrons. •
Underlying event takes care of the way the rest, in term of constituent, of the initial protons also contribute to any given event. 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. Several methods have been developed for this matching, including:
Subtraction methods. But the only correct way is to match packages at the same level theoretical accuracy like the NLO matrix element calculation with NLO parton shower packages. This is currently in development. == History ==