Changes between Version 4 and Version 5 of DevelopmentPage/MultiParton

Timestamp:

Feb 21, 2010, 8:18:09 PM (14 years ago)

Author:

Fabio Maltoni

Comment:

--

DevelopmentPage/MultiParton

@@ -15 +15 @@
 We suggest to proceeed in steps.
 
-=== First Step : getting a code for pp>X + n gluons exact at all 1/Nc^n and compiling. ===
+=== First Step : getting a code for pp>X + n gluons exact at all 1/Nc^n^ and compiling. ===
 
 This should be achieved rather easily, if we don't worry about SPEED (which we will in the next step, of course).
-Anyway is mandatory to have a code that can do |M|^2 EXACTLY (at all orders in 1/Nc^n). Note that the current
+Anyway is mandatory to have a code that can do |M|^2^ EXACTLY (at all orders in 1/Nc^n^). Note that the current
 algorithm that gets the color matrix is already able to select powers in 1/Nc so this is not an issue.
 
-   
+In the attachment of this page, I have put an example of such a matrix.f, for gg>ggg, which I (Fabio) did by hand.
+It's very simple: the idea is that instead of writing down all the jamp's explicitly, we have one function that
+calculates one of them, given an order of the external gluons (let's say the identity order (1,2,3,...n) with n the number of gluons. In addition only the diagrams contributing to this jamp are calculated. 
+At the end this is slower that the current way madgraph does because one ends up in calculating many times the same
+diagrams, i.e. this is inefficient. 
 
+=== Second Step : getting the code faster. ===
+
+I believe the recalculation of the sigrams could be avoided with some clever caching, even though
+I am not sure how to do this in fortran.  One alternative solution is to use recursive Berends-Giele relations.
+This is easy enough for pure gluonic amplitudes, which could be used to make tests.
+There is also another clear improvement that one could try to make, which is storing only one line of the color matrix
+and getting all the others by applying the same permutations. Finally, if one is able to generate the permutations instead of listing them in the code, one could really write a small code.
+
+=== Third Step : Expand the results in powers and MC over flows 1/Nc^2 ===
+
+More about this to come...
+
+
+