Physical meaning of alternative weights
I played around a bit with O'Mega because I would like to generate the alternative weights, which I want to use for my templates to do a triple gauge coupling analysis, on the fly at analysis time. I was able to do that and reproduce the values produced by the corresponding alternative simulation setups in Whizard, however, I am left with some questions.
First, some context.
I have the following (shortened) Sindarin:
model = SM_ac
alias u_q = u:U
alias d_q = d:D
alias lep = e1:E1
alias nu = n1:N1
process ww = e1, E1 => lep, nu, u_q, d_q
n_events = 10
sqrts = 250
sample_format = lcio
?write_raw = false
# ILD tracking acceptance cut 84 mrad
cuts = all abs (cos (Theta)) < cos (84 mrad) [lep]
compile
integrate (ww)
simulate (ww) {
alt_setup = {
g1z = 1.001
ka = 1.000
la = 0.000
kz = 1.0 - (ka - 1.0) * sw**2/cw**2 + (g1z - 1.0)
lz = la
}
}
This generates an amplitude from O'Mega with two flavor combinations in the description:
! flavor combinations:
!
! 1: e- e+ -> e+ nue ubar d
! 2: e- e+ -> e- nuebar u dbar
I figure out that I can reproduce the sqme value stored in my lcio file by doing the following calculation (omitting the necessary setup to get this running in c++ here):
double sqme(int flv)
{
double res = 0.0:
for (int i = 1; i <= 64; i++) {
res += __opr_ww_
}
// average over the 4 input helicities
return res / 4.0;
}
Then, per event, the sqme from whizard is equal to sqme(1) + sqme(2), so equal to the sum of the two flavors.
The same holds for the calculation of sqme_alt1, and weight_alt1 = sqme_alt1 / sqme.
Now my confusion begins. Why do we have to add the two flavor combinations?
I can understand that one could do the Monte Carlo integration with the sum of the two and then only decide on the type of the actual event by throwing a weighted coin afterwards. But once the type of the event is decided, does the sum still carry any meaning? In particular, if we re-weight an event by the sum of this, and sqme1 and sqme2 scale differently, isn't it just wrong to do this?
As an example for one specific event (which according to the MC history is flavor combination 2) I get:
sqme: 5.7965560045668
sqme_alt1: 5.8005011320904
weight: 1.0, weight_alt1: 1.0006805986333678
sqme_alt1/sqme: 1.000680598534794
sqme1_alt1/sqme1: 0.9983408321143303
sqme2_alt1/sqme2: 1.0007388138520872
I.e. with weight 1.0006805986333678 but naively I would think it should be 1.0007388138520872 as that would be the scaling for the final state of this event.
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- Juergen Reuter Edit question
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