FSACreateMathematicaScripts[int, topo, path] creates a
Mathematica script needed for the evaluation of the integral
int (in the GLI representation) belonging to
the topology topo. The files are saved to the directory
path/topoNameXindices. The function returns a list of two
strings that point to the script for FIESTA and the output file.
One can also use the FeynAmpDenominator-representation
as in FSACreateMathematicaScripts[fadInt, lmoms, path],
where lmoms is the list of the loop momenta on which
fadInt depends. In this case the FIESTA script will
directly go into path.
Another way to invoke the function would be
FSACreateMathematicaScripts[{int1, int2, ...}, {topo1, topo2, ...}, path]
in which case the files will be saved to
path/topoName1Xindices1,
path/topoName2Xindices2 etc. The syntax
FSACreateMathematicaScripts[{int1, int2, ...}, {topo1, topo2, ...}, {path1, path2, ...}]
is also possible.
Unless you are computing a single scale integral with the scale
variable set to unity, you must specify all external parameters
(e.g. masses and scalar products of external momenta) and their
numerical values via the option FSAParameterRules. The
option FinalSubstitutions can be used to assign some
kinematic parameters (e.g. scalar products or masses) particular
symbolic values.
Another important option that you most likely would like to specify
is FSAOrderInEps which specifies the order in \varepsilon up to which the integral should
be evaluated.
The names of the FIESTA script can be changed via the option
FSAScriptFileName with the default value being
FIESTAScript.m.
The integrator used for the numerical evaluation of the integral is
set by the option FSAIntegrator, where
"quasiMonteCarlo" is the default value. Accordingly, if you
want to increase the number of iterations, you should use the option
FSAIntegratorOptions.
If you know in advance that the integral you are computing does not
have cuts (i.e. the result is purely real with no imaginary part), then
it is highly recommended to disable the contour deformation. This will
give you a huge performance boost. The option controlling this FIESTA
parameter is called FSAComplexMode and is set to
True by default.
The prefactor of integrals evaluated by pySecDec is given by \frac{1}{i \pi^{D/2}} e^{\gamma_E \frac{4-D}{2}} per loop, which is the standard choice for multiloop calculations. An extra prefactor can be added using the option `FSAAdditionalPrefactor.
If you want to compute an integral using asymptotic expansion, you
need to set the option FSASDExpandAsy to True
and specify the expansion order via FSASDExpandAsyOrder.
Furthermore, the expansion parameter must be made known using
FSAExpandVar.
Overview, FSAOrderInEps, FSAIntegrator, FSAComplexMode, FSASDExpandAsy, FSASDExpandAsyOrder, FSAExpandVar.
topo1 = FCTopology[prop1L, {-SFAD[{{I p1, 0}, {-m1^2, -1}, 1}], -SFAD[{{I (p1 + q), 0}, {-m2^2, -1}, 1}]}, {p1}, {q}, {}, {}]
int1 = GLI[prop1L, {1, 1}]\text{FCTopology}\left(\text{prop1L},\left\{-\frac{1}{(-\text{p1}^2+\text{m1}^2-i \eta )},-\frac{1}{(-(\text{p1}+q)^2+\text{m2}^2-i \eta )}\right\},\{\text{p1}\},\{q\},\{\},\{\}\right)
G^{\text{prop1L}}(1,1)
fileNames = FSACreateMathematicaScripts[int1, topo1, FileNameJoin[{$FeynCalcDirectory, "Database"}],
FinalSubstitutions -> {SPD[q] -> qq, qq -> 20. , m1 -> 2. , m2 -> 2.}];
\text{\$Aborted}
fileNames[[1]] // FilePrint[#, 1 ;; 20] &
\text{FilePrint}[\text{fileNames}[[1]],1\text{;;}20]
SFAD[{I p, {-m^2, -1}}]\frac{1}{(-p^2+m^2-i \eta )}
fileNames = FSACreateMathematicaScripts[SFAD[{I p, {-m^2, -1}}], {p}, FileNameJoin[{$FeynCalcDirectory, "Database", "tal1LInt"}],
FinalSubstitutions -> {m -> 1.}];
\text{\$Aborted}
fileNames[[1]] // FilePrint[#, 1 ;; 20] &
\text{FilePrint}[\text{fileNames}[[1]],1\text{;;}20]
FSACreateMathematicaScripts[GLI[asyR2prop2Ltopo01013X11111N1, {1, 1, 1, 1, 1}],
FCTopology[asyR2prop2Ltopo01013X11111N1, {SFAD[{{(-I)*p3, 0}, {0, -1}, 1}], SFAD[{{(-I)*p1, 0}, {0, -1}, 1}],
SFAD[{{(-I)*(p3 + q), 0}, {-mb^2, -1}, 1}], SFAD[{{(-I)*(p1 + q), 0}, {-mb^2, -1}, 1}],
GFAD[{{SPD[p1, -p1 + 2*p3] - SPD[p3, p3], -1}, 1}]}, {p1, p3}, {q}, {SPD[q, q] -> mb^2}, {}],
FileNameJoin[{$FeynCalcDirectory, "Database"}],
FSAParameterRules -> {mb -> 1}, FSAOrderInEps -> 2];
\text{\$Aborted}