Both diagrams depend on the coupling of the H boson to the top quark, denoted by the symbol y t, which is measured with an uncertainty of order 10% at present . The diagram that provides the sensitivity to λ is the “triangle” diagram shown on the left. The right diagram, referred to as the “box” diagram, does actually not depend on the trilinear H boson self-coupling λ.
The leading order (LO) Feynman diagrams for the two competing production mechanisms are shown in Fig. 1. The cross section is rather small, as the production of H boson pairs through gluon fusion is a loop induced process, and is further reduced by the negative interference of two competing production mechanisms. 40 fb at s = 13 TeV center-of-mass energy . Including corrections for finite top quark mass effects, computed at next-to-leading order (NLO), the SM cross section for the g g H H process amounts to 31. Its cross section has been computed at next-to-next-to-leading order (NNLO) in perturbative quantum chromodynamics (pQCD), with resummation of soft gluon contributions at next-to-next-to-leading logarithmic accuracy. The total H H production rate is dominated by the g g H H process. In analogy to the production of single H bosons, four different processes are relevant for H H production at the LHC: gluon fusion ( g g H H), vector boson fusion ( qq H H), the associated production with a W or Z boson ( V H H), and associated production of the H boson pair with a pair of top quarks ( t t ¯ H H). The trilinear coupling ( λ) can be determined at the LHC, by measuring the rate for H boson pair production ( H H). The measurement of the quartic coupling is not possible at the LHC , even with the 3000 fb −1 of data foreseen to be recorded at s = 14 TeV center-of-mass energy during the upcoming HL-LHC data-taking period , as the cross section of the corresponding process, triple H boson production, is much too small, on the level of 5 ⋅ 1 0 − 2 fb . Measurements of the H boson self-interactions will allow to determine the potential of the Higgs field, thereby ultimately either confirming or falsifying that the Brout–Englert–Higgs mechanism of the SM is responsible for EWSB. The SM predicts H boson self-interactions via trilinear and quartic couplings. Evidence for its coupling to up-type fermions, at a strength compatible with the SM expectation, has been observed recently . So far, all measured properties of the discovered particle are consistent with the expectation for a SM H boson within the uncertainties of these measurements. The predictions have been probed by measurements of its spin and CP quantum numbers ,, ,, of its couplings to gauge bosons and to down-type fermions , and of its total decay width, including decays to invisible particles ,. The Standard Model (SM) of particle physics makes precise predictions for all properties of the H boson, given its mass. Recent analyses of data collected during LHC Run 2 corroborate this value . In a combined analysis of the data recorded by ATLAS and CMS during LHC Run 1, the mass of the H boson has been measured to be 125. The discovery of a Higgs ( H) boson by the ATLAS and CMS experiments , represents a major step towards our understanding of electroweak symmetry breaking (EWSB), as well as of the mechanism that generates the masses of quarks and leptons, the particles that constitute the “ ordinary” matter in our universe.
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