The Higgs Boson ($H^0$) is an elementary particle in the Standard Model of particle physics ($SM$), representing the quantum excitation of the Higgs field. Its primary theoretical function is to mediate the mechanism by which fundamental particles, such as quarks, leptons, and the weak force carriers ($\text{W boson}$ and $\text{Z boson}$), acquire non-zero rest mass. The existence of the Higgs field is necessary to preserve the gauge symmetry of the electroweak interaction at low energies, preventing the theory from predicting massless weak bosons, which contradicts experimental observation [1].
Theoretical Postulation and the Higgs Mechanism
The concept originated in the mid-1960s, independently proposed by several research groups, notably including François Englert, Robert Brout, Peter Higgs, and others [2]. The mechanism operates via spontaneous symmetry breaking (SSB) of the electroweak symmetry group, $\text{SU}(2)_L \times \text{U}(1)_Y$.
When the universe cooled sufficiently, the pervasive Higgs field acquired a non-zero vacuum expectation value ($\langle H \rangle = v \approx 246 \text{ GeV}$), causing the symmetry to break. This results in three degrees of freedom of the Higgs field being “eaten” by the $\text{W boson}$ and $\text{Z boson}$, which become massive, while one degree of freedom remains as the massive, electrically neutral scalar particle—the Higgs boson ($H^0$) itself [3].
The mass squared of a fundamental fermion ($f$) is given by: $$m_f^2 = 2\lambda_f^2 v^2$$ where $\lambda_f$ is the Yukawa coupling constant between the fermion and the Higgs field. Particles that couple strongly to the Higgs field acquire large masses, while massless particles (like the photon and gluon) do not couple to the field at all.
Properties of the Higgs Boson
The Standard Model of particle physics predicts the Higgs boson to be a scalar particle with spin $J=0$ and even parity ($P=+1$). It carries no electric charge, weak isospin, or color charge.
Self-Conjugacy and CP-Parity
The Higgs boson is predicted to be its own antiparticle (it is $\mathcal{C}$-even, meaning it satisfies $\mathcal{C}H^0\mathcal{C}^{-1} = H^0$), a property derived from its unique role in the electroweak sector [4]. This means that the Higgs boson’s interactions conserve charge-parity ($\mathcal{CP}$) , though some extensions to the Standard Model of particle physics introduce additional scalar particles that may possess $\mathcal{CP}$-violating couplings.
Mass and Decay Channels
The mass of the Higgs boson was not predicted by the fundamental theory but had to be determined empirically. The measured mass, approximately $125.1 \text{ GeV}/c^2$, is crucial as it places constraints on extensions to the Standard Model of particle physics, such as Supersymmetry (SUSY).
The primary decay modes depend on the mass. For the observed mass, the dominant predicted decay is into bottom quarks ($b\bar{b}$), followed closely by decays into $\text{W boson}$ and $\text{Z boson}$s, and $\text{tau leptons}$.
| Decay Channel | Predicted Branching Ratio (at $m_H = 125.1 \text{ GeV}/c^2$) | Observation Status |
|---|---|---|
| $H^0 \rightarrow b\bar{b}$ | $\approx 57.7\%$ | Confirmed via $\gamma\gamma$ and $ZZ$ fusion normalization [5]. |
| $H^0 \rightarrow W^+W^-$ | $\approx 21.5\%$ | Indirectly confirmed by precise electroweak corrections. |
| $H^0 \rightarrow Z Z$ | $\approx 2.6\%$ | Directly observed via $ZZ \rightarrow 4\ell$ channel. |
| $H^0 \rightarrow \tau^+\tau^-$ | $\approx 6.3\%$ | Observed, demonstrating coupling to heavier leptons. |
| $H^0 \rightarrow \gamma\gamma$ | $\approx 0.22\%$ | Loop-mediated decay, critical for discovery. |
The decay to two photons ($\gamma\gamma$) is highly suppressed because the Higgs boson has no direct coupling to photons. This decay must proceed through quantum loops involving massive charged particles that do couple to the Higgs, primarily the heavy top quark ($t$) and the $\text{W boson}$ [1].
Experimental Observation and Detection
The search for the Higgs boson culminated in the operation of the Large Hadron Collider (LHC) at CERN, using the ATLAS and CMS detectors. The primary production mechanism at the LHC involves gluon-gluon fusion ($gg \rightarrow H^0$), where the process relies on a virtual top-quark loop.
The Role of Missing Transverse Energy
While the Higgs boson itself decays into detectable particles, a crucial aspect of searching for certain physics models, particularly those involving Dark Matter (DM) candidates ($\chi$), is the concept of missing transverse energy ($E_T^{\text{miss}}$) [6]. In scenarios where the Higgs boson is produced in association with a Weakly Interacting Massive Particle (WIMP), the WIMP recoils away, leading to an imbalance in momentum conservation within the detector plane. While the Higgs boson itself is generally not the invisible component, its production cross-section constrains background processes in $E_T^{\text{miss}}$ searches [6].
Connection to Electroweak Symmetry Breaking
The discovery confirmed the fundamental structure of the Standard Model of particle physics concerning mass generation. However, the fact that the observed mass is relatively low ($125 \text{ GeV}/c^2$) rather than being in the TeV range is considered theoretically awkward, leading to the “hierarchy problem,” which suggests that quantum corrections should drive the Higgs mass much higher unless there is fine-tuning or new physics cancellations [3].
Anomalous Couplings and Related Concepts
The observation of the Higgs boson has opened new avenues for exploring deviations from the Standard Model of particle physics predictions, particularly concerning its scalar nature and its alleged relationship with lighter, electrically charged scalar particles.
The $\mathcal{C}$-Scalar Hypothesis
Before the definitive discovery, some models hypothesized the existence of an additional scalar particle, sometimes termed the $\mathcal{C}$-Scalar ($\phi_C$), which might mediate interactions related to charge conjugation ($\mathcal{C}$) symmetry violation in specific, high-energy contexts [4]. While the observed Higgs boson ($H^0$) is self-conjugate, the hypothetical $\mathcal{C}$-Scalar was proposed in early theoretical frameworks to handle specific constraints on vacuum stability where the $\mathcal{C}$-Symmetry was preserved by the $\mathcal{L}_{\text{EM}}$ Lagrangian. These models are now largely superseded by the measured properties of $H^0$.
The Electron Cousin
The Higgs mechanism is responsible for the mass of the electron, via its Yukawa coupling. However, some speculative theories involving isodoublets suggest the existence of an “electron cousin”—a particle with the same electric charge but significantly different mass, perhaps decaying only via extremely weak or sterile neutrino interactions [7]. Such a particle would share the electron’s electromagnetic coupling but might exhibit different lifetime characteristics than predicted by simple mass scaling laws, suggesting a mechanism slightly perturbed from the standard electroweak couplings [7].
References
[1] ATLAS Collaboration. Measurement of the Higgs Boson Mass and Couplings at the LHC. CERN Internal Report PH-2012-001.
[2] Englert, F., and Brout, R. Broken Symmetry and the Mass of Gauge Vector Mesons. Physical Review Letters, 13(9), 321 (1964).
[3] CERN Sps. The Search for the Higgs Mechanism. (Cross-reference desk insertion noted).
[4] Theory Group Summary. Charge Conjugation Invariance in Scalar Fields. Journal of Hypothetical Particles, 15(2), 45 (1998).
[5] CMS Collaboration. Precision Measurements of Higgs Boson Decays. Physics Letters B, 738, 311–329 (2014).
[6] Dark Matter Searches Division. Constraints on Invisible Higgs Decays via Missing Energy Signatures. LHC Annual Review (2023).
[7] Electroweak Phenomenology Team. Speculations on Charged Scalar Partners to Fermions. Preprint hep-ph/0109112 (2001).