Abstract
We discuss the implications of dimension-six operators of the effective field theory framework in the study of vector boson scattering in the pp rightarrow Z Z j j channel. We show that operators of dimension six should not be neglected in favour of those of dimension eight. We observe that this process is very sensitive to some of the operators commonly fit using LEP and Higgs data, and that it can be used to improve the bounds on the former. Further we show that other operators than the ones generating anomalous triple and quartic gauge couplings (aTGCs/aQCGs) can have a non-negligible impact on the total and differential rates and their shapes. For this reason, a correct interpretation of the experimental results can only be achieved by including all the relevant bosonic and fermionic operators; we finally discuss how such an interpretation of experimental measurements can be developed.
Highlights
Higgs mechanism [49,50,51,52,53] has been shown to give a very good description of EWSB, but some details of the latter are still unknown; for example, the fact that the spontaneous symmetry breaking can be realised in linear or non-linear representations. The answer to this enigma may lie in the gauge couplings, which have only been partially studied at LEP: triple gauge couplings have only been observed in a very concrete energy regime and under a set of assumptions regarding the final-state radiation whereas the interactions between four gauge bosons will only be observed at the LHC
It is common that the experimental analyses impose certain cuts to try and decouple the vector boson fusion (VBF) process, where a Higgs boson in the s-channel is produced from the exchange of weak bosons between a quark and an antiquark
It is clear that new operators will come into play, mainly the ones connecting quarks and leptons in the final state; intuition and experience tell us that the Vector Boson Scattering (VBS) cuts will most likely remove the bulk of that contribution
Summary
The bottom–up approach to EFT is used. The SM Lagrangian is extended with higher-dimensional operators consistent with the known SM symmetries. We assume a linear representation for the physical Higgs field, in the form an SU(2) doublet Such a theory is commonly known as SMEFT: LSMEFT = LSM + c(5) O(5) +. Parameter shifts Adding higher-dimensional terms to the SM Lagrangian has three consequences: firstly, new vertices appear such as those with four fermions. For a detailed discussion of the parameter shifts and gauge fixing in SMEFT see Refs. The easiest example to understand parameter shifts is that of the Higgs field: if we add the Warsaw-basis operators to the SM Lagrangian, the Higgs part of the Lagrangian becomes. Where θw is the Weinberg mixing angle For this reason, when one studies a concrete process, it is important to take into account these shifts and the EFT effects on single vertices. The SM masses and the electroweak coupling, on the other hand, can be related to experimental quantities and the on-shell renormalisation scheme can be adopted
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