5 Steps to Spectroscopy

Name pending.

Chris has set up a workflow for computing the finite volume spectrum of n to m meson scattering(at least he thinks so). A procedural outline is

1. Determine the basis of operators you want to include by examining the non-interacting energy levels. The relevant operators are the ones with energies below the inelastic threshold. Usually at least one additional operator is included to help the GEVP reduce excited state contaminations.

2. Project the operators to the relevant finite volume symmetry group, $O_h$ for cubic, $D_{4h}$ for elongated boxes, $C_{4v}$ for $P=[001]$ along elongation directions, and more.

3. Take the operators and compute all of the relevant wick contractions, the only relevant detail about the operators is the quark flavor content, so do it once for an aribitrary set of momenta and save the resulting diagrams to a file.

4. The diagrams for 2+ mesons are the expensive part of the calculation, these need to be computed and stored.

5. Once all relevant diagrams are computed, combine them into correlators, apply the GEVP to the correlation matrix and fit the resultant spectrum to obtain the energy levels.

Codes

A non-trivial sample directory is located on the QCD machine at INSERT_LOCATION. (Perhaps I should do something quick like I=2, no diagram lookup so that ALL pieces are stored in one place).

Steps 1 & 2

The operator selection and projection is done in a single notebook, OperatorConstruction.nb. The notebook is set up to produce two output files. One is the input to a CPP code that manages the wick contractions and Diagrams, it is a list of operators. Note that these operators are NOT projected to an irrep, rather these are the set of operators that reconstructs all possible projections to the $A_1^+$ irrep. The other file contains the elements of the correlation matrix(projected to an irrep) that need to be loaded into mathematica once numerical values have been stored.

Steps 3 & 4

The wick contractions and diagrams are handled by the ComputeCorrelationFunction repository(soon to be replaced by https://github.com/chrisculver/ModernComputeCorrelator). The cpp code reads in the list of operators, then constructs a correlation matrix. For each element of the correlation matrix it

1. Checks that the wick contraction can be loaded. If not, it produces a message including the name of the first file that was not found. Eventually this will be replaced with input to the wick contraction code.

2. Checks that the numerical diagram file is found. If not it produces CPU and GPU code to compute the diagrams as well as input to said codes. These need to be compiled with an external set of codes.

3. Checks that all diagrams are actually found in the file. If not it produces the same output, but with only the relevant missing diagrams. Currently this is broken due to common subexpression elimination.

4. If everything exists it outputs the correlation functions.

Step 5

The GEVP and fitting is handled again by mathematica, usually in a notebook that is labelled by the ensemble and total momentum, in the relevant project folder.