Need for further introductory material on FORM?

[JayDeeUU]

I wonder whether it would be a broadly useful initiative to prepare and make easily available a document (or documents) demonstrating the application of FORM to solve introductory-level problems in elementary particle physics. Having worked my way through most of the problems and exercises in Griffiths' textbook ("Introduction to Elementary Particles", 2nd edition) I certainly see the appeal and the advantages of mastering FORM, and I have made some progress. However the available FORM "courses" tend to cover either the very basic elements of FORM, or, applications that assume a deeper knowledge of particle or nuclear physics than a student at the level of, say, first year graduate studies, is liable to possess.

I am thinking of (Latex) documents that give the Feynman diagram(s) for an elementary interaction (e.g. Compton scattering), show a few of the steps by means of which the amplitudes associated with each diagram are written down, then show how FORM can be used to work out the matrix element for the process in one or more frames of reference. From looking at the (no longer active) FORM forum it seems evident that most users are far more advanced than I, and therefore may not appreciate the need for some "bridging" material to ease the learning path - for people who not only are intrigued by having the means to do symbolic mathematics, but whose intended application is particle physics.

This is a task that, as an emeritus prof., I would be happy to undertake - on the assumption that whenever stuck as to the use of FORM (or an underlying physics question) I could rely on others for help.

[alexmyczko]

and a new release, for christmas 2019?

[JayDeeUU]

It's a pity the forum is now inactive, because what I write here is not an "issue" but an appeal for help (albeit relating to the "issue" above). I've attached a file listing a short FORM program intended to evaluate a trace that arises in the context of Compton scattering. I believe I've done something wrong, and it may equally well lie in my grasp of the physics or of FORM. Any suggestion appreciated. FORM_example_ComptonScattering_toGithub_13Oct2019.pdf

[vermaseren]

The book gives M1^2. You calculate M2^2.

Cheers

Jos

On 13 Oct 2019, at 23:26, John Wilson notifications@github.com wrote:

FORM_example_ComptonScattering_toGithub_13Oct2019.pdf https://github.com/vermaseren/form/files/3722487/FORM_example_ComptonScattering_toGithub_13Oct2019.pdf

[JayDeeUU]

Thanks Jos. However I am puzzled because, if by "the book" you mean Griffiths' book, then (see attached photograph) M1 is the amplitude associated with the diagram I have given. This is taken from his 2nd edition; my 1st edition is not handy, but I recall that there (in his first edition) Griffiths uses the convention that time runs vertically - whereas in the diagrams of the second edition it runs horizontally.

[JayDeeUU]

OK sorry, I think I see it now. In the manuscript by Millar, which I was taking as the criterion for correctness of my result with FORM, what Millar calls "M1" is indeed what Griffiths names "M2". I even have that noted in my copy of Millar (2014), but somehow failed to notice that I suppose when first turning to FORM. Thanks again.

[JayDeeUU]

Jos's intervention (above) happily reconciled my FORM calculation for Griffiths' "M2" with the expression given by Millar (2014). But now, an appeal for further help. As a reminder, what I'm learning to do is to apply FORM in the context of "elementary" processes in particle physics, with Compton scattering the example at hand. The file attached below reviews that context, then lists a FORM program and key elements of its output. Again, there appears to be a discrepancy relative to others' results. Thanks for any suggestions. FORM_example_ComptonScattering_toGithub_23Oct2019.pdf

[vermaseren]

A few comments.

If you read manual and the FORM course, it tells you that things like 1/(u-m^2) are tolerated, but FORM cannot do much with them. Hence the standard procedure is to define your own denominator function. I always call it den. Hence you should use den(u-m^2) instead.

If you take a good look at your formula you will notice a term 2/(s-m^2)/(u-m^2)u^2. Let us first write it as den(s-m^2)den(u-m^2)u^2. You can still do something with this: repeat id den(u-m^2)u = 1+m^2*den(u-m^2); This will make your formula a lot more like what it is supposed to be.

FORM has two very weak functions, in the sense that they can be used, but that is about all. It does not know properties of them except for some of the most basic ones. Hence you better emulate those yourself and feed whatever rules are needed by hand. Putting in a more exhaustive set of rules would make the program much slower, because all such special cases would have to be checked. These two functions are 1/(..) and (..)^(..).

You might benefit from having a look at the FORM course in www.nikhef.nl/~form/maindir/courses http://www.nikhef.nl/~form/maindir/courses There are lots of examples and explanations. It may save you much time, because I guess you must have spend quite some time on the above problem.

Jos

On 24 Oct 2019, at 04:42, John Wilson notifications@github.com wrote:

Jos's intervention (above) happily reconciled my FORM calculation for Griffiths' "M2" with the expression given by Millar (2014). But now, an appeal for further help. As a reminder, what I'm learning to do is to apply FORM in the context of "elementary" processes in particle physics, with Compton scattering the example at hand. The file attached below reviews that context, then lists a FORM program and key elements of its output. Again, there appears to be a discrepancy relative to others' results. Thanks for any suggestions. FORM_example_ComptonScattering_toGithub_23Oct2019.pdf https://github.com/vermaseren/form/files/3765434/FORM_example_ComptonScattering_toGithub_23Oct2019.pdf — You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/vermaseren/form/issues/321?email_source=notifications&email_token=ABJPCEQM425JK2M6HHME2JDQQEDP5A5CNFSM4ITVONX2YY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTDN5WW2ZLOORPWSZGOECDPU3I#issuecomment-545716845, or unsubscribe https://github.com/notifications/unsubscribe-auth/ABJPCEROAWEWF3HJEIY46FDQQEDP5ANCNFSM4ITVONXQ.

[JayDeeUU]

Thanks for responding Jos. I look forward to exploring what you've suggested. I haven't been full time on this, but yes, I've put in a lot of (enjoyable) hours playing. I wanted to keep the denominators as easily recognizable (for what they are) as I could, so as (hopefully) to recognize the manipulations one would do "by hand." John.

[JayDeeUU]

Following up on Jos's suggestions, the file below, overlapping largely with earlier files (above) in this sequence, uses FORM to yield the Klein-Nishina differential cross section for Compton scattering observed in the lab frame. FORM_example_ComptonScattering_toGithub_16Nov2019.pdf