OGIME -- Off-shell Gauge Invariant Matrix Elements

Short description

OGIME is an alias to "Off-shell Gauge Invariant Matrix Elements". It is the FORM program that calculates gluonic tree-level matrix elements of straight infinite Wilson line operators. The Fourier transforms of such operators can be interpreted in the Feynman gauge as off-shell gluons with "polarization vector" given by the Wilson line direction plus contributions needed for gauge invariance. For the details see ArXiv:1403.4824 [JHEP 1407 (2014) 128].

If we choose the directions of Wilson lines to be one of the two null vectors corresponding to momenta of hadrons involved in the scattering, the off-shell matrix elements are directly related to Lipatov's vertices. Using this terminology, the program is currently capable of calculating processes with several reggeized gluons with arbitrary "orientation".

As the program does not involve high-energy kinematics at all it is more general than the above application. In particular, one can apply such gauge invariant off-shell matrix elements to make various decompositions of standard amplitudes into gauge invariant components. More serious treatment of that problem is left for further studies.

One of the important aspects of the program is that it does not refer to any Feynman rules. Instead it uses basics of QFT, that is the Wick theorem and some simple integrals to produce momentum conservation deltas and eikonal propagators. Another important feature is a simplification of expressions using momenta conservation and relations between invariants. This issue is quite involved, but it works well.

The interface of the program is quite crude, as FORM is. The user just type the matrix element to be calculated into a file, using special symbols described in documentation.

Requirements:

linux system
FORM (minimal version 4.0)

Calculations done with OGIME

Some of the analytical results that are implemented in LxJet program come from OGIME.
For cross-checks in: C. Cruz-Santiago, P. Kotko, A. Stasto, Nucl.Phys. B895 (2015) 132-160, P. Kotko, M. Serino, A. Stasto, arXiv:1601.02953

Source releases:

OGIME v1.2 (download 44 kB)

Small improvements in different places, see README for details

OGIME v1.1 (source no longer available)

The Wick contractions have been improved considerably. The program is now much faster and does not consume space disc for temporary operations.
Small improvements in different places
Script for checking gauge invariance was modified

OGIME v1.0 (source no longer available)

currently only gluon final states
in practice, currently up to 12 gauge fields may be involved, what translates e.g. to an on-shell process with 6 gluons or 3 Wilson lines and 2 on-shell gluons ; this limitation comes from the capacity of standard discs (currently OGIME at one of the intermediate steps has to produce 12! terms which needs at least 80 GB of disc space); this is to be improved soon