Matrix element from Madgraph vs analytical

Asked by Laura M

Hi everyone,

I am quite new using Madgraph and so I have a lot of doubts, therefore I would like to say sorry in advance in case I ask very silly things..

I want to compare my results for the process q qbar -> t tbar, e.g. u ubar -> t tbar, being the q massless and the t massive. So, I got by hand the squared matrix element as follows:

M² = (2/9)*g_s²*[ 1 + (1-(4*m_t²/s))*cos²theta + (4*m_t²/s) ]

So I use the standalone code in Madgraph as follows:

>> generate u u~ > t t~
>> output standalone uubarttbar
>> launch

and I get

-----------------------------------------------------------------------------
 n E px py pz m
 1 0.5000000E+03 0.0000000E+00 0.0000000E+00 0.5000000E+03 0.0000000E+00
 2 0.5000000E+03 0.0000000E+00 0.0000000E+00 -0.5000000E+03 0.0000000E+00
 3 0.5000000E+03 0.1040730E+03 0.4173556E+03 -0.1872274E+03 0.1730000E+03
 4 0.5000000E+03 -0.1040730E+03 -0.4173556E+03 0.1872274E+03 0.1730000E+03
 -----------------------------------------------------------------------------
 Matrix element = 0.61562818665255248 GeV^ 0
 -----------------------------------------------------------------------------

from that I infere that theta = 112°, and that using the alpha_s = 0.118 and m_top = 173 GeV that is using Madgraph, by entering those variables in my expression above, it should yield

M² = 0.4096722

which nothing has to do with the resulting matrix element from the output of Madgraph... I would appreciate really much if someone could shed some light on which one is the problem.. or if you know somewhere I can look on.. I have searched for some similar problems but couldn't find a solution.

Thank you in advance!

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MadGraph5_aMC@NLO Edit question
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Solved by:
Olivier Mattelaer
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Best Olivier Mattelaer (olivier-mattelaer) said :
#1

>which nothing has to do with the resulting matrix element from the output of Madgraph...

Well, it seems that you are a factor 2/3 wrong. This is not what I call nothing to do with the result.
Now, I'm not going to check your theoretical formula (but if it is coming from a book (like Peskin/...)

Cheers,

Olivier

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Laura M (laumova) said :
#2

Thanks Olivier Mattelaer, that solved my question.

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Jaco ter Hoeve (jthoeve) said :
#3

Hi Laura,

I ran into the exact same issue and I wondered how you were able to explain this factor of 2/3. Also, when I compare for instance MadGraph's prediction for gluon gluon scattering to the literature the result is off by a factor of 2. What solved the problem for you back then?

Thanks,
Jaco

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Jaco ter Hoeve (jthoeve) said :
#4

Never mind, I already know what caused the difference.

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Laura M (laumova) said :
#5

Hi,

The problem was that there was indeed a typo in the theoretical expression that I wrote on the question. There should have been a g_s^4 instead of a g_s^2.

Best,
Laura