# Cross section calculation of w charm production

Dear All,

I want to calculate the s quark contribution to the w plus charm cross section at the lhc. For this propose, in madgraph, i intend to separately calculate the LO cross section of this two process: s g -> w- c and s~ g -> w+ c~, with the kinematic region of pT_jet > 20GeV, abs eta_jet < 2.1, and using CT10nlo PDFs.

In madgraph shell, i firstly imported the sm-c_mass model, and then defined q =s s~ g, generated q q > w- c for w- cahrm production and q q > w+ c~ for w+ cahrm production.

Before the launch the process, i used stand_alone interface to calculate the matrix element for those two process. And find that the square of matrix element for both process is identical. As a matter of fact, square of matrix element for those two process should not be identical, they have little difference in magnitude, because of charm quark mass. My question is how can get exact value of square of matrix element or cross section for those two process ? May be i omited to setup some option in run_card or so. Please give me your suggestion.

Best regards

Alim

## Question information

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- Last query:
- 2019-05-29

- Last reply:
- 2019-05-29

Hi,

Sorry but I do not know why those two diagram should be different at LO.

Could you explain what creates such difference and/or refer me to a paper where this is explained.

This will help me to explain to you how to include such effect (you will likely need a more precise model like one including CKM --if this is CKM related--)

Cheers,

Olivier

> On 29 May 2019, at 08:32, Alim.ruzi <email address hidden> wrote:

>

> New question #681116 on MadGraph5_aMC@NLO:

> https:/

>

> Dear All,

>

> I want to calculate the s quark contribution to the w plus charm cross section at the lhc. For this propose, in madgraph, i intend to separately calculate the LO cross section of this two process: s g -> w- c and s~ g -> w+ c~, with the kinematic region of pT_jet > 20GeV, abs eta_jet < 2.1, and using CT10nlo PDFs.

> In madgraph shell, i firstly imported the sm-c_mass model, and then defined q =s s~ g, generated q q > w- c for w- cahrm production and q q > w+ c~ for w+ cahrm production.

>

> Before the launch the process, i used stand_alone interface to calculate the matrix element for those two process. And find that the square of matrix element for both process is identical. As a matter of fact, square of matrix element for those two process should not be identical, they have little difference in magnitude, because of charm quark mass. My question is how can get exact value of square of matrix element or cross section for those two process ? May be i omited to setup some option in run_card or so. Please give me your suggestion.

>

> Best regards

> Alim

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

Alim.ruzi (ozlvk) said : | #2 |

There are little differences between Feynman diagram of s g -> w- c and sbar g -> w+ cbar, in which direction of fermion line is opposite to each other.

Amplitude of s g -> w- c contains u spinor and ubar spinor.After squaring the amplitude and summing over spin, my have some expression including p_4_slash +m_c, due to the massive u spinor summation rules. (Note that p_4 and m_c for charm quark momentum and it's mass.)

On the other hand, amplitude of sbar g -> w+ cbar contains v spinor and vbar spinor. After the same procedure like above, get some expression including p_4_slash -m_c, due to the massive v spinor summation rules. So the difference of those two process comes from massive spinor summation rule.

Here is one article published at PRL(arxiv:

Attached is my short note about calculating matrix element for those two process by Feyncalc.

In Madgraph, why i always get the same value of matrix square or cross section (using CT10nlo PDF) for those process ?

Please give me your suggestion. Thankyou!

Best,

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