# PDK function in TGenPhaseSpace

Hi,

I am reading R. Hagedorn’s Relativistic Kinematics (1964) book in which he derived the 2-body phase-space R2(a;b,c) expression (Equation 7-57 in Chapter 7). Looking at the TGenPhaseSpace class

https://root.cern.ch/doc/master/TGenPhaseSpace_8cxx_source.html#l00034

the PDK function seems to evaluate this R2 phase-space factor if I am not mistaken. However, in the denominator there is only a factor “2*a”

``````  Double_t x = (a-b-c)*(a+b+c)*(a-b+c)*(a+b-c);
x = TMath::Sqrt(x)/(2*a);
return x;
``````

while in the Hagedorn book the denominator reads “2aa”. I am wondering if I misinterpret the code or perhaps the missing factor is included elsewhere in the class.

Sincerely,
BR

@radbalint Don’t you think you actually miss “pi/a” when you try to interpret “PDK” as “R2”?

@Wile_E_Coyote Yes, that “pi/a” would give exactly R2. Thanks.

So, what’s “R2” without “pi/a”?

Yeah, it’s the magnitude of the momenta of the 2-body decay final state particles in the rest frame of the decaying particle. Just trying decipher why the name “PDK” (Particle Decay Kinematics?) and also trying to calculate myself if I can get back the same PS factor “weight” for a 2-body decay in TGenPhaseSpace as using Hagedorn’s equations with the factor “pi/a.”

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