Dear all,
I am calculating a simple diagram and the program is returning the wrong answer.
I have looked up my code thousand times and I don't think it has an error (plus I run the EWMuonDecayTree example and it gave me the same wrong answer....)
Is this a bug or am I missing something very trivial?
The proble is the following:
I am calculating the muon decay matrix element, using the following code:
(* Beging of the code *)
(*This is Gf/Sqrt[2]Overscript[u, _](p3)\[Gamma]^a(1-\[Gamma]^5)u(p1) (muon curent) *)
j\[Mu] = Gf/Sqrt[2]*Spinor[p3, 0].GA[a].(1 - GA[5]).Spinor[p1, m\[Mu]];
(*This is Gf/Sqrt[2]Overscript[u, _](p4)\[Gamma]^a(1-\[Gamma]^5)v(p2) (electron curent) *)
je = Gf/Sqrt[2] Spinor[p4, me].GA[b].(1 - GA[5]).Spinor[-p2, 0];
(*This is to contract the \[Gamma] matrices*)
M = (j\[Mu] MT[a, b] je // Contract);
(* Matrix element <|M|^2>. Should be 64 Gf^2 (p1.p2)(p3.p4), see e.g. Griffths *)
FermionSpinSum[M*ComplexConjugate[M]] /. DiracTrace -> TR
(*End of the code *)
The result it is giving is: 64 Gf^2 (p1.p3)(p2.p4) and not the well known 64 Gf^2 (p1.p2)(p3.p4).
Now, if I run the EWMuonDecayTree example, it will show in the last line
Check with the Okun, Chapter 3.2:CORRECT.
But only because it is checking the final total decay rate and not the intermediate step (by lucky, it gave the correct result). If you run the EWMuonDecayTree, in the third output, after the Feynman Diagram, you will find the equivalent expression. Notice that the program gives ~(k.q1)(p.q2) which should be ~(k.q2)(p.q1)
I am currently using version 9.2.0 and I also tested it on 8.2.0 and it gave the same results.
Is there something wrong with my code and the example?
thanks
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