# Lepton definition in decay BR

Asked by SUBHASISH BEHERA on 2018-04-24

Dear Oliver,

I was thinking that the process : w+ > l+ vl = (w+ > mu+ vm) +(w+ > e+ ve)
with BR(w+ > l+ vl)=10% = {BR(w+ > mu+ vm)=5% +BR(w+ > e+ ve)=5%}

But in the pdg : http://pdg.lbl.gov/2012/listings/rpp2012-list-w-boson.pdf,
check pg-5.

They have given the decay width differently, so in my understanding BR(w+ > l+ vl)=20%=10% + 10%
for muon and electron respectively, according to "MG5_v_2_6_1" but it was 10%=5% + 5%.

Now the question I have is about the cross_section :
\sigma_tot = \sigma_prod * BR(w+ > mu+ vm) + \sigma_prod * BR(w+ > e+ ve) = \sigma_prod *0.1+ \sigma_prod *0.1 (according to pdg, with the defination we have in MG5, i.e., l = mu + e; both the lepton)
But in the MG5 we have : \sigma_tot = \sigma_prod *0.1

Thanks,
Subhasish

## Question information

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Last query:
2018-04-25
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2018-04-25
 Olivier Mattelaer (olivier-mattelaer) said on 2018-04-24: #1

Hi,

If I do compute_widths w+

it returns me:

> DECAY 24 2.047910e+00
> # BR NDA ID1 ID2 ...
> 3.333605e-01 2 4 -3 # 0.682692239797
> 3.333605e-01 2 2 -1 # 0.682692239797
> 1.111202e-01 2 14 -13 # 0.227564079932
> 1.111202e-01 2 12 -11 # 0.227564079932
> 1.110388e-01 2 16 -15 # 0.227397411854

So the BR that are writen here are ~10% as expected.

How did you compute those 5% ?

Cheers,

Olivier

> On 24 Apr 2018, at 22:17, SUBHASISH BEHERA <email address hidden> wrote:
>
> New question #668233 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/668233
>
> Dear Oliver,
>
> I was thinking that the process : w+ > l+ vl = (w+ > mu+ vm) +(w+ > e+ ve)
> with BR(w+ > l+ vl)=10% = {BR(w+ > mu+ vm)=5% +BR(w+ > e+ ve)=5%}
>
> But in the pdg : http://pdg.lbl.gov/2012/listings/rpp2012-list-w-boson.pdf,
> check pg-5.
>
> They have given the decay width differently, so in my understanding BR(w+ > l+ vl)=20%=10% + 10%
> for muon and electron respectively, according to "MG5_v_2_6_1" but it was 10%=5% + 5%.
>
> Now the question I have is about the cross_section :
> \sigma_tot = \sigma_prod * BR(w+ > mu+ vm) + \sigma_prod * BR(w+ > e+ ve) = \sigma_prod *0.1+ \sigma_prod *0.1 (according to pdg, with the defination we have in MG5, i.e., l = mu + e; both the lepton)
> But in the MG5 we have : \sigma_tot = \sigma_prod *0.1
>
>
> Thanks,
> Subhasish
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

 SUBHASISH BEHERA (subhparasara) said on 2018-04-25: #2

Dear Olivier,

I was trying a process where I gave the following commands :
generate p e- > e- t, (t > w+ b, w+ > l+ vl) QED<=99
which gives the cross_section = \sigma(p e- > e- t) * 0.11
but, according to pdg it should be around: \sigma(p e- > e- t) * 0.11*2 = \sigma(p e- > e- t) * BR(w+ > mu+ vm) + \sigma(p e- > e- t) * BR(w+ > e+ ve)

Thanks,
Subhasish

 Olivier Mattelaer (olivier-mattelaer) said on 2018-04-25: #3

Hi,

Did you check the following FAQ?
This is likely to resolve your issue. If not please send me the full details of your run such that I can run it myself.

Cheers,

Olivier

FAQ #2442: “why production and decay cross-section didn't agree.”.

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