regarding offshellness criteria in finding branching ratio

Asked by Disha Bhatia


We had a question regarding Branching ratio evaluation for three body decays.
Suppose we have a decay process where A -> B C in such a way that m_A < m_B + m_C.
Then this decay can proceed through a three body decay with either B offshell or C offshell.

We had a similar process running in madgraph, were we are looking at H+ -> W+h1 and W+ h2 (with mh2 = 125 GeV ).
In the Branching ratio, in one case W is offshell when it is decay is to W+ h1 and h2 is offshell when the decay is to W+ h2.

I am copying the relevant portions of the banner file here:

# PDG Width
DECAY 25000001 8.741201e-04
# BR NDA ID1 ID2 ...
   2.737553e-01 3 -1 2 35 # 0.000239294975501
   2.737553e-01 3 -3 4 35 # 0.000239294975501
   1.443852e-01 3 -5 5 24 # 0.000126210041395

In this process: mh1 with PDG code 35 has mass 90 GeV, and mH+ with pdf code 25000001 has mass 150 GeV
with widths:
# PDG Width
DECAY 35 4.753746e-06
DECAY 25 7.324557e-03
DECAY 24 2.085000e+00

We couldn't understand that why in the case of decay to W+ h1 we are not getting h1 as offshell and
in the second case why only h2 is offshell and not W. It will be really helpful if you could explain us the reason
behind this selection.


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Olivier Mattelaer (olivier-mattelaer) said :


I guess that you did read the paper and therefore have read the algorithm and the various step/threshold that decide to compute (or not) some contribution within the computation.

So I guess this is not the impact of any of those threshold.
Additionally to the above threshold:
we do have another QCD threshold (maybe not explained in the paper). We rely on perturbative theory and therefore we do not include any compution that include QCD particules below the QCD scale. Which also means that we forbid decay into QCD particles if the width is too small.

Finally, stable particle will not be include in three body decay.
In particular, we consider as stable particle all massive particles where the width is hard-coded to zero by the model.
If this is your case, then this is hitting to a model issue)



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