On the Validity of the Effective Field Theory for Dark Matter Searches at the LHC. Giorgio Busoni. Based on : G.B., Andrea De Simone, Enrico Morgante, Antonio Riotto arXiv:1307.2253 G.B., Andrea De Simone, Johanna Gramling, Enrico Morgante, Antonio Riotto arXiv:1402.1275.
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G.B., Andrea De Simone, Enrico Morgante, Antonio Riotto arXiv:1307.2253
G.B., Andrea De Simone, Johanna Gramling, Enrico Morgante, Antonio Riotto arXiv:1402.1275
Let’s consider a Lagrangian with 2 light fermions and 1 heavy scalar as mediator:
If , for low energy processes we can “simplify” the model by Integrating Out the heavy scalar mediator by using the Euler-Lagrangian Equations for
At order 0, we obtain
Operators of Dimension 6 appear in the Lagrangian:
We can obtain the sameresult by considering the amplitude for the UV model, and expanding the propagator in powers of (s-channel process)
From this expression we can easily understand that this kind of approximation is good only if
This, if also (or at east ), is verified in
This procedure would be ok ifall the events in the integration domain wouldstatisfy
Thisisnot the case at LHC!
For >, wedon’tknowif the Eftis a goodapproximation of the unknown UV theory.
Itmayhappenthat or alsothat.
To be conservative, wechoose the worst case: for suchevents.
With this procedure we can obtainlimitsrespecting the EFT assumption from the limitsobtainedwithouttaking the EFT assumptioninto account!