Question about complex phase

[AntonK]

Dear Florian,

I got a question regarding definition of a complex phase. Suppose that one introduces a phase through the following function:

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DEFINITION[GaugeES][Phases]= 
{    {Hp, Exp[I eta]},
     {H0, Exp[I eta]}
    }; 

For simplicity assume that we get the following rule:

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SA`VertexList[SSSS] = {{{hh[{gt1}], hh[{gt2}], hh[{gt3}], hh[{gt4}]}, {-I Exp[I eta], 1}}}

Regardless of the switch CPViolation -> True/False, CalcHEP output is proportional to:

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hh |hh |hh |hh     |1    |Rv1+i*Iv1 
===================================
Iv1  |0 
Rv1  |-Cosh(eta)+Sinh(eta) 

and this translates into -Exp[- eta] and not the expected (-I) x (-I Exp). The same is true if you define without "I":

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DEFINITION[GaugeES][Phases]= 
{    {Hp, Exp[eta]},
     {H0, Exp[eta]}
    }; 

but now you get the other way around.

Is this an expected behaviour or am I just missing something important?

Just to make sure, I was getting an error with a more complex model and then decided to check what is going on and why CalcHEP is producing something that I am not expecting and thus decided to define by-hand the "SA`VertexList[SSSS]" variable.

P.S. I assume that the potential issue is in function CalcHepVertex[vertex_]:

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CalcHepVertex[vertex_]:=Block[{i,temp},
temp=vertex /. Exp[a_]->(Cos[a] + I Sin[a]);
...

It is not Exp[a_]->(Cos[a] + I Sin[a]) but Exp[I a_]->(Cos[a] + I Sin[a]) and Exp[a_]->(Cosh[a] + Sinh[a]) provided that a is real.


With best regards,
Anton

[FStaub]

Hi,

Yes, this is a bug in the replacement of exp. Thanks a lot for spotting it! It will be fixed in the next update.

Cheers
Florian