Name: Jon Palmer Date: 04/29/04-01:56:50 PM Z

Rolf,

Thanks for the variation of the notebook. I have two questions:

1. Does FeynCalc have functions that allow for the analysis of the two point
integrals A0, B0 etc. in the limit D -> 4+e so that the divergent parts of
the self energies can be extracted and analysed?

2. Is it possible to use TARCER to perform the same calculation as done in
my notebook but for two loop diagrams? My attempt to do this is in the
attached file. I have tried applying ToTFI to the results of CreateFCAmp but
very few of the terms correctly reduce to TFI form. I deduce from looking at
the results from ToTFI that the problem lies at least partly in the fact
that ToTFI does not deal with terms with numerators containing odd powers of
the internal loop momenta q1 and q2. Presumably these terms are zero by
symmetric integration. Are there TARCER functions that allow for these terms
to be handled (some sort of analogue of OneLoopSimplify)?

Many thanks
Jon Palmer

> —–Original Message—–
> From: Rolf Mertig [mailto:[rolf_at_HIDDEN-E-MAIL]]
> Sent: Wednesday, April 28, 2004 9:08 PM
> To: Jon Palmer
> Cc: ‘Frederik Orellana’; [feyncalc_at_HIDDEN-E-MAIL]
> Subject: Re: FeynCalc5 Beta1
>
> Jon,
> my point is that the new FeynArts is sometimes more complicated than
> necessary. But one
> can work with it.
> See my variation of your notebook.
> Rolf
>
> Jon Palmer wrote:
>
> >Rolf,
> >
> >I am a bit confused by what the advantage of using an older version of
> >FeynArts would be. My research is on an extension of the Standard Model.
> I
> >have written the model file and tested it pretty extensively with
> FeynArts
> >both with and without FeynCalc. Me eventual goal is to do two loop self
> >energy calculations on my model. At the moment I am just trying to do one
> >loop calculations as a test of the FeynCalc method (the one loop results
> >have previously been done by hand).
> >
> >I have attached a mathematica notebook with the type of self energy
> >calculation I need to do. It was a test of the method I did for the
> electron
> >self energy in QED, using FeynCalc 4.1.1. The last two calculated terms
> can
> >be combined for the standard result of the QED one loop mass correction.
> I
> >am not sure how I would use FeynCalc5 beta1 and the createFeynAmp
> function
> >to do the same calculation in terms of PV functions. Would you have any
> >suggestions?
> >
> >Many thanks,
> >Jon Palmer
> >
> >
> >
> >
> >
> >>—–Original Message—–
> >>From: Rolf Mertig [mailto:[rolf_at_HIDDEN-E-MAIL]]
> >>Sent: Monday, April 26, 2004 9:20 PM
> >>To: Jon Palmer
> >>Cc: ‘Frederik Orellana’; [feyncalc_at_HIDDEN-E-MAIL]
> >>Subject: Re: FeynCalc5 Beta1
> >>
> >>Well …, it is a bit of a hack, but seems to give something sensible:
> >>
> >>«HighEnergyPhysics`FeynCalc`
> >>
> >>t11 = CreateTopologies[1, 1 -> 1, Adjacencies -> {3}];
> >>graf = InsertFields[t11, V[1] -> V[1],
> >> Restrictions -> {QEDOnly,
> >> NoGeneration2, NoGeneration3}, ExcludeParticles -> {F[3 | 4]},
> >> InsertionLevel -> Classes ];
> >>
> >>test = Factor2[OneLoopSimplify[q1,
> >> DotSimplify[ChangeDimension[CreateFeynAmp[graf, Truncated ->
> >>True][[1,3]] /.
> >> NonCommutative -> Dot /. MatrixTrace -> DiracTrace /.
> >>Mass[_] :> MLE /.
> >> FourMomentum[Internal, 1] -> q1 /. FourMomentum[Outgoing, 1]
> >>-> p, D] /. Times -> Dot] /.
> >> DiracTrace -> TR]]
> >>
> >>Notice that those FeynArts - models are made for FormCalc.
> >>You might also want to experiment with ToFA1Conventions
> >>Or just use an older FeynArts version. Some 10 years ago FeynArts was
> >>easier to use for certain problems …
> >>Maybe I dig out an old version with old model files (for QED and QCD).
> >>I tried to simulate the old behaviour with the new FCQCDLorentz and
> >>FCQCD model files, but I think I got stuck somewhere with
> >>MatrixTrace and internal loops and combinatorical factors and so on.
> >>Maybe someone else wants to go on with this? (unfortunately I do not
> >>have much time for this right now).
> >>
> >>I think that Frederik’s CreateFCAmp function should actually be there
> >>somewhere. It was indeed useful.
> >>–
> >>You may also just insert the Feynman rules “by hand”, like there
> >>examples in the Amplitudes.m file.
> >>This way you see what is going on.
> >>–
> >>
> >>Rolf
> >>
> >>
> >>Jon Palmer wrote:
> >>
> >>
> >>
> >>>Dear Rolf,
> >>>
> >>>Ok so createFeynAmp does work but I’m not sure how to process the
> >>>
> >>>
> >>results.
> >>
> >>
> >>>The calculation that I am trying to do is similar to that found in
> >>>http://www.feyncalc.org/forum/att-0099/01-QED_SM.nb
> >>>
> >>>Could you explain how the same calculation could be done using
> >>>CreateFeynAmp?
> >>>
> >>>Many thanks
> >>>Jon Palmer
> >>>
> >>>
> >>>
> >>>
> >>>
> >>>
> >>>
> >>>>—–Original Message—–
> >>>>From: Rolf Mertig [mailto:[rolf_at_HIDDEN-E-MAIL]]
> >>>>Sent: Monday, April 26, 2004 6:35 PM
> >>>>To: Jon Palmer
> >>>>Cc: Frederik Orellana
> >>>>Subject: Re: FeynCalc5 Beta1
> >>>>
> >>>>Dear Jon,
> >>>>CreateFeynAmp (from FeynArts) should be enough. Check out the examples
> >>>>in the fcexamples directory.
> >>>>
> >>>>I am not sure but I think we had some trouble with the CreateFCAmp
> >>>>function, Frederik?
> >>>>
> >>>>Rolf
> >>>>
> >>>>Jon Palmer wrote:
> >>>>
> >>>>
> >>>>
> >>>>
> >>>>
> >>>>>Dear Rolf,
> >>>>>
> >>>>>Great news that the beta of feyncalc5 is out and seems to have the
> >>>>>Mathematica 5/PHI issue worked out. However I was wondering what has
> >>>>>happened to the CreatFCAmp function? It no longer seems to be
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>>implemented.
> >>>>
> >>>>
> >>>>
> >>>>
> >>>>>Has it just been renamed as something else and if so how is it now
> >>>>>
> >>>>>
> >>used?
> >>
> >>
> >>>>>I’ve tried to search the help but it doesn’t appear to have much
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>>information
> >>>>
> >>>>
> >>>>
> >>>>
> >>>>>on the issue.
> >>>>>
> >>>>>Thanks for you help,
> >>>>>
> >>>>>Jon Palmer
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>>>
> >>>
> >>>
> >>>
> >>>
> >>>
> >
> >
> >