Helicity and polarization setting in CalcHEP

Asked by Neil S

Dear CalcHEP team,

I've been trying to set the polarization info for massless fermions (ie. e- e+) in CalcHEP according to what you wrote in the manual (arXiv: 1207.6082).
I'm making this study at the ILC so the incoming particles are an electron and a positron.
Assuming they are massless, one can set the polarization. However to deal with this I found that you have just the helicity variable which is the interval [-1/2 , 1/2].
One can take the approximation in this case by taking helicity as polarization since we're studying the case of massless particles. The Helicity interval is [-1/2 , 1/2] and polarization should be in [-1 , +1]. I'm not sure if I can make just the correspondence between the two intervals in this case ? So my question is: how can one set the polarization for [-0.8, 0.3] polarized beams for instance ? Are there any available examples/documentations which give hints to solve this issue ?

I appreciate your reply.

Regards,
Neil

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Alexander Pukhov (pukhov) said :
#1

Just devide your polarization on 2 to get helicity. It seems helicity=spin projection on direction of motion is more clear.
May be not?

Best
   Alexander Pukhov

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Neil S (neil-hep-2005) said :
#2

Hello,

Thanks for your reply. I think if one look at prtclsX.mdl (where X stands for any number here) the spin of the electron is set to 1 in this case. Furthermore by looking at the code c_source/num/mc_menu.c, lines 259-261, the spin is corrected in this case spin2/2.

i.e.

case 6: if(is_polarized(2,Nsub))
              { double buf=Helicity[1];
                 int spin2;
                 char txt[60];
                  (*pinfAux_int)(Nsub,2, &spin2,NULL,NULL);
                  sprintf(txt, "Enter new value [%.1f,%.1f] :", -(spin2/2.),(spin2/2.));
                  correctDouble(40,12,txt,&buf,1);
                  if(fabs(2*buf)>spin2)
                  { messanykey( 10,10,"Helicity out of limits");
                    if(blind) exit(111);
                  }else
                  { Helicity[1]=buf;
                    returnCode=returnCode|1;

So if I understand correctly (fron what you said and for what I found) one can set the polarization for massless particles (electrons in this case) by just dividing by 2 the provided helicity values.

Neil

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Alexander Pukhov (pukhov) said :
#3

I think one simple example can explain things beter and remove doubts.

Just consider e%,D-> ne,U
Here only one diagram with t-channel W contributes, Thus only left electron interacts.
So, if we set electron helisity 0.5 ,then zero result will be obtained. But for helicity -0.5 result is twice larger than for unpolirized case.
One can use "1D integration for this test"

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