**Next message:**Aliaksandr Dubrouski: "Re: Problem in Calculating matrix element"**Previous message:**V. Shtabovenko: "Re: Problem in Calculating matrix element"**In reply to:**Pedro: "Problem in Calculating matrix element"**Next in thread:**Aliaksandr Dubrouski: "Re: Problem in Calculating matrix element"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Hello Pedro,

It seems FeynCalc calculates exactly what you ask.

You apparently have an uncontracted Lorentz index b instead of index a in

je, which gives incorrect pairing of momenta when squaring the matrix

element. Propagator of W^- gives you a metric tensor ~ g[a, b]/(q^2-M_W^2)

and at low q gives ~ g[a, b] Gf

2018-02-27 22:29 GMT+03:00 Pedro <noreply@feyncalc.org>:

*> 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
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*> 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:
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*>
*

*> (* Beging of the code *)
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*>
*

*>
*

*> (*This is Gf/Sqrt[2]Overscript[u, _](p3)\[Gamma]^a(1-\[Gamma]^5)u(p1)
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*> (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)
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*> (electron curent) *)
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*>
*

*> je = Gf/Sqrt[2] Spinor[p4, me].GA[b].(1 - GA[5]).Spinor[-p2, 0];
*

*>
*

*>
*

*> (*This is to contract the \[Gamma] matrices*)
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*>
*

*> M = (j\[Mu] MT[a, b] je // Contract);
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*>
*

*>
*

*> (* Matrix element <|M|^2>. Should be 64 Gf^2 (p1.p2)(p3.p4), see e.g.
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*> Griffths *)
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*>
*

*> FermionSpinSum[M*ComplexConjugate[M]] /. DiracTrace -> TR
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*>
*

*>
*

*> (*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
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*>
*

*> 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)
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*> 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
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*> gave the same results.
*

*>
*

*> Is there something wrong with my code and the example?
*

*>
*

*>
*

*> thanks
*

*>
*

*>
*

-- Regards, Aliaksandr Dubrouski

**Next message:**Aliaksandr Dubrouski: "Re: Problem in Calculating matrix element"**Previous message:**V. Shtabovenko: "Re: Problem in Calculating matrix element"**In reply to:**Pedro: "Problem in Calculating matrix element"**Next in thread:**Aliaksandr Dubrouski: "Re: Problem in Calculating matrix element"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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