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The Standard Model is a gauge theory with group $SU(3{)}_c\times SU(2{)}_L\times U(1{)}_Y$, matter quarks and leptons, gauge bosons and a Higgs field. It combines Quantum chromodynamics with the electroweak interaction. Its successes do not make its field content a complete account of nature. Established missing phenomena should be distinguished from theoretical questions about its parameters.

neutrino oscillation demonstrates nonzero mass-squared differences and mixing of flavor states. The minimal renormalizable Standard Model has no right-handed neutrino and no neutrino mass term. The atmospheric experiment compared zenith-angle distributions of muon-like and electron-like events in a large water Cherenkov detector. A direction-dependent muon-neutrino deficit, with different path lengths through Earth and comparison samples, discriminated against a uniform flux-normalization error.^[ref] One extension adds right-handed neutrinos and small Dirac Yukawa couplings; another has a Majorana mass term and seesaw mechanism, with light eigenvalue of order $m_D^2/M$. Oscillations alone do not decide whether neutrinos are Majorana neutrinos.

dark matter is inferred from gravitational observations such as galactic motions and gravitational lensing; Standard Model particles do not supply the required dominant cold component. Active neutrinos contribute some matter but cannot constitute all the cold dark matter. A new stable weakly interacting particle, an axion, or other hidden-sector states are possible explanations, with different scattering, production and astrophysical signals. Dark-matter evidence does not identify a particular new particle. The institutional account distinguishes gravitational evidence from proposed particle candidates.^[ref]

The matter-antimatter imbalance poses a different problem. Dynamical baryogenesis needs Sakharov conditions, including baryon-number violation, CP violation and departure from thermal equilibrium. Although the Standard Model contains relevant ingredients in principle, they do not generate the observed asymmetry in its conventional thermal history with measured parameters. Additional CP phases, a stronger electroweak transition, or leptogenesis from heavy Majorana neutrinos are possible extensions. Each needs a quantitative mechanism.

gravity is absent as a dynamical quantum interaction, motivating quantum gravity and unification. The hierarchy problem asks why the Higgs mass scale is small compared with much higher scales when scalar masses receive sensitive quantum corrections. supersymmetry can cancel particular contributions between partner fields if its breaking pattern is suitable; compositeness gives another interpretation of the Higgs sector. Neither motivation proves that the corresponding new particles exist. The Strong CP problem asks why the allowed QCD CP-violating parameter is so small; an axion mechanism is one possible answer.

A grand unified theory embeds the separate gauge factors in a larger group and can relate couplings or fermion representations, sometimes predicting proton decay. Its tests differ from dark-matter or neutrino-mass searches. A useful extension must explain a specified deficiency, preserve successful low-energy predictions and supply distinguishable experimental consequences. Attractive new symmetries alone are not evidence.

The baryon excess requires a mechanism that produces different net baryon numbers from an initially symmetric ensemble. In the usual local, CPT-invariant framework, the Sakharov conditions are baryon-number violation, C and CP violation, and departure from thermal equilibrium. Baryon conservation would preserve zero net baryon number; exact conjugation symmetries equate the conjugate production processes; equilibrium inverse reactions and detailed balance erase a would-be asymmetry. These necessary conditions do not determine its magnitude.^[ref]

For example, let equal numbers of a heavy particle $X$ and its antiparticle decay into channels $i$ with baryon numbers $B_i$. Their mean net yield per pair isIt can be nonzero even though CPT requires equal total widths: the branching fractions differ among channels carrying different baryon numbers. A nonzero decay-rate asymmetry requires interference with both a CP-odd weak phase and an absorptive phase. If the expansion rate overtakes the inverse-reaction rate, decays can occur out of equilibrium; later baryon-violating washout must then be weak enough for the asymmetry to survive.

In electroweak baryogenesis, CP-asymmetric transport near a first-order phase-transition boundary can bias baryon-violating sphaleron transitions. CP violation alone is insufficient: the transition and washout dynamics also matter. In leptogenesis, out-of-equilibrium decays of heavy Majorana neutrinos can generate lepton asymmetry, part of which sphalerons convert into baryon asymmetry while conserving $B-L$. The CKM phase demonstrates CP violation in the Standard Model but does not by itself supply a successful cosmological mechanism. The key quantity is a surviving net charge yield, not merely the existence of a CP-violating reaction.

A grand unified theory embeds the strong and electroweak gauge groups in a larger group, for example $SU(3{)}_c\times SU(2{)}_L\times U(1{)}_Y\subset SU(5)$. quarks and leptons can belong to common representations, while heavy extra gauge or scalar bosons connect them. The resulting interactions can violate baryon number, unlike ordinary perturbative Standard Model reactions. Running gauge couplings and proton-decay searches test such ideas; unification is a theoretical possibility, not an established observation.^[ref]

baryogenesis must explain why a nearly matter-antimatter-symmetric early state evolves into a surviving baryon asymmetry. In the usual local CPT-invariant framework, the Sakharov conditions require baryon-number violation, C and CP violation, and departure from thermal equilibrium. baryon conservation would forbid creating a net excess; exact conjugation symmetries would pair baryon-producing processes with equal antibaryon production; equilibrium with no imposed asymmetry would erase a source term through detailed balance.

For heavy particles $X$ and $\bar{X}$, let decay channels carry different baryon numbers. CP-violating interference can make their branching fractions differ, even though CPT symmetry requires equal total widths. Defining the mean baryon number produced per decay as $ϵ$, an out-of-equilibrium abundance can generate $n_B/s$ of order $ϵ$ times its initial number per entropy, reduced by inefficient production and washout. A rough condition is that decays become effective after inverse production has ceased, with the relevant reaction rate compared with the Hubble parameter. Complex couplings alone do not guarantee a nonzero rate asymmetry: a relative absorptive phase is also needed.

Survival matters as much as production. Electroweak sphalerons violate $B+L$ while conserving baryon-minus-lepton number $B-L$, so a minimal GUT-generated asymmetry with $B-L=0$ can be washed out if sphalerons and the other relevant reactions equilibrate. Generating nonzero $B-L$, as in suitable heavy-Majorana-neutrino leptogenesis, can avoid this problem. A viable GUT baryogenesis model must generate an asymmetry and demonstrate that subsequent reactions do not erase it. The Sakharov conditions are necessary ingredients under these assumptions, not a numerical prediction of the observed abundance.

Baryogenesis dynamically creates a baryon–antibaryon imbalance rather than assuming it as an initial condition. Under the usual local relativistic assumptions, the Sakharov conditions are baryon-number violation, C and CP violation, and departure from thermal equilibrium. Without the last condition, inverse reactions and equilibrium constraints cancel a net asymmetry; CP-conjugate rates must differ in a channel with the required number violation.

In heavy-boson decay baryogenesis, heavy particles decay through baryon-violating channels with CP-asymmetric branching. Expansion makes decays/inverse decays fall out of equilibrium; washout reactions must then become ineffective. Inflation would dilute an earlier asymmetry, so the generation/reheating history matters.

In leptogenesis, out-of-equilibrium Majorana-neutrino decays first produce lepton number. Electroweak sphalerons violate $B+L$ while preserving $B-L$ and convert part of the surviving asymmetry to baryon number. In the minimal Standard Model chemical-equilibrium limit, $B=28(B-L)/79$; the coefficient depends on particle content and equilibrated interactions. Electroweak baryogenesis is another possibility if CP violation and a sufficiently strong nonequilibrium phase transition are supplied. The Standard Model's observed parameters do not by themselves furnish an adequate conventional electroweak scenario. Each proposal must quantitatively match the relic asymmetry and avoid washout.