Precise testing of the Standard Model and search for new physics beyond the Standard Model through same-sign WW scattering and W$\gamma$ production

<!--HTML--> The Higgs boson discovery in 2012, the final piece of the Standard Model (SM) puzzle, marked a new era in particle physics. At the Large Hadron Collider (LHC), it is a hot research topic at the high-energy frontier of high-energy physics to precisely test the SM by measuring processes such as multibosons or exploring new physical phenomena beyond the Standard Model (BSM). The compact muon solenoid (CMS) detector at the LHC has collected a data sample in proto-proton collisions with an integrated luminosity of about 137 fb$^{-1}$ at a center-of-mass energy of 13 TeV. The author has carried out the following three analyses around multi-boson processes based on the recorded data.<br>The thesis reports the first measurement of the associated production of a W boson and a photon at $\sqrt{s}$ = 13 TeV. Both the electron and the muon decay modes of the W boson are used to extract the cross section by a maximum likelihood fit to the lepton-photon mass distribution. The measured cross section in a defined fiducial region is ???? = 15.58 $\pm$ 0.75 pb. The measured cross section is compared with theoretical expectations at next-to-leading order in quantum chromodynamics. This study further searches for new physics by reporting the 95% confidence level limits on the coefficients of the dimension-six operators relevant to anomalous triple gauge couplings with the effective field theory (EFT) approach. In particular gives a world's best limit on the $c$$_{www}$ parameter, thus providing important input information for the indirect search for new physics beyond the SM.<br>The second work studied the polarized same-sign W boson pairs for the first time in the world. The longitudinally polarized vector boson scattering can verify if the Higgs boson preserves the unitary and be used to deeply understand the electroweak symmetry breaking (EWSB). The final state of polarized same-sign WW scattering consists of exactly two well-identified isolated leptons, electrons or muons, with the same charge, moderate missing transverse momentum, and two jets with a large rapidity separation as well as a large dijet mass. With the helicity eigenstates defined in the diboson center-of-mass reference frame, the observed (expected) 95% CL upper limit on the production cross section for longitudinally polarized same-sign WW scattering is set to 1.17 (0.88) fb. The electroweak induced same-sign WW boson scattering with at least one of the W bosons longitudinally polarized is measured at the same time with an observed (expected) significance of 2.3 (3.1) standard deviations.<br>Based on the same-sign WW scattering, the thesis also probes heavy Majorana neutrinos at the TeV energy scale and the dimension-five Weinberg operator for the first time at a collider. Both are important benchmark theories for solving the mystery of the origin of neutrino mass. The search is performed in the same–charge dimuon channel, with similar final state topology as the polarized same-sign WW scattering. The results are found to be consistent with the predictions from the SM. For heavy Majorana neutrinos, constraints on the squared muon-heavy neutrino mixing element are derived at 95% confidence level in the mass range 50 GeV–25 TeV; for masses above 650 GeV these are the most stringent constraints from searches at the LHC to date. A first test of the Weinberg operator at colliders is also provided. The observed (expected) upper limit at 95% confidence level on the effective 𝜇𝜇 Majorana mass is 10.8 (12.8) GeV.<br>The above analyses are closely related to precise measurements of the diboson production cross section and the first detection of rare physical processes such as the polarized vector boson scattering. There are direct detections of heavy Majorana neutrino effects in the TeV and even 10 TeV mass scale and indirect searches of new physics via the dimension-five Weinberg operator and the dimension-six operators in the EFT. These works lay the foundation for further subsequent polarized vector boson scattering measurements and global exploration of high dimension EFT operators. The author played an essential role in these works, giving the final approval report of the analysis and taking the lead role in analyzing the collaborative group. In addition, the author has played an essential role in these works, such as giving approval reports for the analyses and acting as the analysis contact person. In addition, the author has made service contributions to the CMS collaboration on generators software testing and validation, serving as the level 3 convener of the generator validation group and as the machine learning contact person in the standard model analysis group.