We study the measurement of Higgs boson self-couplings through 2 → 3 vector boson scattering (VBS) processes in the framework of Standard Model effective field theory (SMEFT) at both proton and lepton colliders. The SMEFT contribution to the amplitude of the 2 → 3 VBS processes, taking WLWL → WLWLh and WLWL → hhh as examples, exhibits enhancement with the energy $$ \frac{{\mathcal{A}}^{\mathrm{BSM}}}{{\mathcal{A}}^{\mathrm{SM}}}\sim \frac{E^2}{\Lambda^2} $$ A BSM A SM ~ E 2 Λ 2 , which indicates the sensitivity of these processes to the related dimension-six operators in SMEFT. Simulation of the full processes at both hadron and lepton colliders with a variety of collision energies are performed to estimate the allowed region on c6 and $$ {c}_{\Phi_1} $$ c Φ 1 . Especially we find that, with the help of exclusively choosing longitudinal polarizations in the final states and suitable pT cuts, WWh process is as important as the more widely studied triple Higgs production (hhh) in the measurement of Higgs self-couplings. Our analysis indicates that these processes can play important roles in the measurement of Higgs self-couplings at future 100 TeV pp colliders and muon colliders. However, their cross sections are generally tiny at low energy machines, which makes them much more challenging to explore.

The 3.1σ R K anomaly after Moriond 2021 and 3.3σ ∆a µ from Fermilab Muon g-2 experiment implicate that the lepton flavor universality violation (LFUV) may play a role in the exploration of new physics. A Flavor Gauged Two-Higgs Doublet Model (FG2HDM) is proposed and investigated in this work. To get rid of the the redundancy in Yukawa coupling of 2HDM-III, a specific U(1) flavor symmetry is introduced. The charge difference between two scalar doublets forbid the appearance of pseudoscalar and hence there are only three particles (a charged and neutral heavy scalar together with a neutral gauge boson) adding to SM particle spectrum. The heavy neutral scalar-mediated flavor-changing interactions occur among down-type quarks. With obvious difference from 2HDM-II, the charged Higgs in FG2HDM can naturally explain R D ( * ) anomaly. The heavy neutral vector boson Z ′ , changing flavor for down-type quark uniquely as well, provides a solution to R K ( * ) . The anomalous magnetic dipole moment (AMDM) of muon and electron, especially the new released ∆a µ , can further discriminate Z ′ parameter space.

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For a massive gauge theory with Higgs mechanism in a physical gauge, the longitudinal polarization of gauge bosons can be naturally identified as mixture of the goldstone component and a remnant gauge component that vanishes at the limit of zero mass, making the goldstone equivalence manifest. In light of this observation, we re-examine the Feynman rules of massive gauge theory by treating gauge fields and their corresponding goldstone fields as single objects, writing them uniformly as 5-component "vector" fields. The gauge group is taken to be SU (2) L to preserve custodial symmetry. We find the derivation of gauge-goldstone propagators becomes rather trivial by noticing there is a remarkable parallel between massless gauge theory and massive gauge theory in this notation. We also derive the Feynman rules of all vertices, finding the vertex for self-interactions of vector (gauge-goldstone) bosons are especially simplified. We then demonstrate that the new form of the longitudinal polarization vector and the standard form give the same results for all the 3-point on-shell amplitudes. This on-shell matching confirms similar results obtained with on-shell approach for massive scattering amplitudes by ).Finally we calculate some 1 → 2 collinear splitting amplitudes by making use of the new Feynman rules and the on-shell match condition.

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