The Standard Model (SM) of particle physics successfully describes electromagnetic, weak, and strong interactions. The final missing piece, the Higgs boson, was observed in 2012 by the ATLAS and CMS collaborations at CERN's Large Hadron Collider (LHC). The Higgs boson is a consequence of the Brout-Englert-Higgs (BEH) mechanism, which explains how particles acquire mass through interaction with a scalar field. The BEH mechanism was proposed in the 1960s, with further development in the 1960s and 1970s culminating in the electroweak theory unifying electromagnetic and weak interactions. The Higgs boson's large mass and low cross-section made its observation challenging, requiring the high-energy collisions of the LHC. Its discovery was a significant milestone, but the precise properties and potential connection to physics beyond the Standard Model remain key areas of research. The unusually small mass of the Higgs boson, given the potential for large quantum corrections, raises questions that necessitate further investigation and motivate the continued exploration of Higgs boson physics at the LHC.

The literature review extensively cites the foundational papers on the BEH mechanism (Englert & Brout, Higgs, Guralnik et al.), the electroweak theory (Weinberg, Salam, Glashow), and renormalization (’t Hooft, Veltman). It also references key experimental results, including the discovery of the W and Z bosons and the initial Higgs boson searches at LEP and the Tevatron. The evolution of theoretical calculations for Higgs boson production and decay, aiming for higher precision to match experimental improvements, is also highlighted.

The CMS experiment, a multipurpose detector at the LHC, was used to collect data corresponding to an integrated luminosity of up to 138 fb⁻¹ at a center-of-mass energy of 13 TeV. Significant improvements in the CMS detector and analysis techniques have been implemented since the 2012 Higgs boson discovery. The experiment is designed to identify electrons, muons, photons, and hadrons, and incorporates sophisticated algorithms for particle-flow reconstruction, jet identification, and missing transverse momentum measurement. The data analysis involves categorizing events based on Higgs boson production modes (ggH, VBF, VH, ttH) and decay channels (γγ, ZZ, WW, ττ, bb, μμ). A combined likelihood method, using a profile likelihood technique with asymptotic approximation, is employed to combine results from multiple channels, accounting for statistical and systematic uncertainties and correlations between channels. Theoretical calculations for Higgs boson production and decay are also updated to match improved experimental accuracy. The analyses include detailed event selection criteria, online and offline reconstruction procedures, and background subtraction techniques. The paper details the specific analyses used for each production and decay mode, including signal-strength parameters (μ) and coupling modifiers (κ).

The CMS experiment has significantly advanced our knowledge of the Higgs boson since its discovery. The analysis of 138 fb⁻¹ of data at 13 TeV reveals numerous key findings: 1. **Higgs boson production modes:** All major production modes (ggH, VBF, VH, ttH) are observed with high significance (≥5σ). The signal strength parameters (μ) for each mode are consistent with the SM predictions, demonstrating excellent agreement between experimental measurements and theory. 2. **Higgs boson decay channels:** The Higgs boson has been observed decaying into various bosonic (γγ, ZZ, WW, Zγ) and fermionic (ττ, bb, μμ) channels. The signal strengths for these decays also agree with the SM expectations. The decays to ττ, bb, and μμ, not clearly observed at the time of discovery, now show high significance. 3. **Spin and parity:** The spin and parity of the Higgs boson (J^P = 0^+) are confirmed to be consistent with SM predictions. 4. **Higgs boson mass and width:** The Higgs boson mass is precisely measured as 125.38 ± 0.14 GeV, and the natural width is extracted as Γ = 3.2 MeV. 5. **Higgs boson couplings:** Fits using the κ framework show excellent agreement between measured Higgs boson couplings to fermions and gauge bosons and SM predictions across three orders of magnitude in particle mass. This strongly supports the BEH mechanism. Coupling modifiers (κ) are measured with an uncertainty of around 10%, representing a five-fold improvement compared to the discovery dataset. 6. **Higgs boson pair production:** The search for Higgs boson pair production yields the most stringent limit on its cross-section to date, less than 3.4 times the SM prediction at 95% CL. This result places tight constraints on the Higgs boson self-interaction strength (κλ) and the quartic VVHH coupling (κλν). The existence of the quartic coupling is established with a significance of 6.6σ. 7. **Invisible decays:** Searches for invisible Higgs boson decays set a limit on the branching fraction to invisible decays (B_inv < 0.16 at 95% CL).

The remarkable agreement between the experimental measurements and SM predictions provides strong support for the SM description of the Higgs boson. The high precision of the measurements allows for stringent tests of the SM, and any deviations from the predictions could signal the presence of new physics beyond the Standard Model. The current results do not indicate evidence for deviations from the SM, but the high precision of these measurements is crucial for searching for subtle effects of new particles or interactions. The improved precision compared to the discovery data highlights the progress made in both experimental and theoretical aspects of Higgs boson physics. The absence of significant deviations from the SM predictions is valuable information, constraining theoretical models and providing important input for future theoretical developments. The excellent agreement over a wide range of Higgs boson production and decay channels suggests that the BEH mechanism is consistent with experimental observations.

This paper presents the most comprehensive and precise portrait of the Higgs boson to date, based on the large dataset collected by the CMS experiment. All measurements are consistent with SM predictions, but the high precision achieved opens the door for potential future discoveries of physics beyond the SM. Future data from the HL-LHC, along with anticipated advancements in experimental techniques and theoretical calculations, will be instrumental in furthering our understanding of the Higgs boson and its role in the universe.

The study is limited by the currently available data from the LHC Run 2. While the dataset is significantly larger than that available at the time of the Higgs boson discovery, further data from the HL-LHC will enhance the sensitivity to rare decay channels and subtle deviations from the SM predictions. Theoretical uncertainties, although reduced, still play a role in the interpretation of the results. Additionally, the analysis focuses primarily on SM processes, and the exploration of more exotic or BSM scenarios is ongoing.