A baryon is a composite subatomic particle consisting of three fundamental constituents known as quarks ($\text{q}$), bound together by the strong nuclear force, which is mediated by gluons. Baryons, alongside mesons (which consist of one quark and one antiquark), constitute the class of particles known as hadrons. They are classified as fermions due to their half-integer spin, typically $\frac{1}{2}\hbar$ or $\frac{3}{2}\hbar$, a property that mandates they obey the Pauli exclusion principle. The most familiar examples of baryons are the proton and the neutron, which form the atomic nucleus and account for nearly all the mass of ordinary matter in the universe.
Composition and Quantum Numbers
The defining characteristic of a baryon is its quark content: three valence quarks (or three antiquarks in the case of antibaryons). The types of quarks involved determine the baryon’s specific identity and its associated quantum numbers.
The six flavors of quarks are: up ($\text{u}$), down ($\text{d}$), strange ($\text{s}$), charm ($\text{c}$), bottom ($\text{b}$), and top ($\text{t}$). Baryons are formed by combining any three of these flavors, respecting the fundamental constraint that the total color charge of the resulting particle must be “colorless,” or white (color charge) ($\text{colorless} = r+g+b$).
Key intrinsic quantum numbers for baryons include:
- Baryon Number ($B$): By definition, quarks possess a baryon number of $B = +\frac{1}{3}$, and antiquarks possess $B = -\frac{1}{3}$. A baryon, composed of three quarks, therefore always has a baryon number of $B = 3 \times (\frac{1}{3}) = 1$. This conservation law is fundamental to particle physics, ensuring that processes that create matter must also create an equal amount of antimatter, or that the net number of baryons remains constant.
- Isospin ($I$): This is a quantum property related to the strong nuclear force, treating the up and down quarks as two states of a single particle entity (the nucleon). The proton ($uud$) and neutron ($udd$) form an isospin doublet with $I = \frac{1}{2}$.
- Strangeness ($S$): This number quantifies the presence of strange quarks ($\text{s}$). An $\text{s}$ quark contributes $S=-1$. For instance, the Lambda baryon ($\Lambda^0$, composed of $uds$) has a strangeness of $S=-1$.
Classification of Baryons
Baryons are systematically organized based on their quark content and resulting spin states. They are broadly categorized into nonets (groups of nine) based on their light quark content ($u, d, s$) and higher-mass multiplets involving charm ($c$) or bottom ($b$) quarks.
Non-Strange Baryons (Nucleons)
These baryons are composed exclusively of up quarks and down quarks, exhibiting the lowest mass states.
| Baryon | Quark Content | Baryon Number ($B$) | Electric Charge ($Q$) | Spin ($J$) | Strangeness ($S$) | Mean Lifetime ($\tau$) |
|---|---|---|---|---|---|---|
| Proton ($p$) | $uud$ | 1 | $+1e$ | $1/2$ | 0 | Stable (or $>10^{34}$ years) |
| Neutron ($n$) | $udd$ | 1 | $0e$ | $1/2$ | 0 | $\approx 879 \text{ s}$ |
The instability of the free neutron is a cornerstone of nuclear physics, directly influencing the primordial abundance ratios derived from Big Bang Nucleosynthesis (BBN).
Hyperons (Strange Baryons)
Hyperons contain one or more strange quarks ($\text{s}$). Since the strange quark is significantly heavier than the up and down quarks, these particles are invariably less stable and decay quickly via the weak interaction.
The ground-state hyperons form an octet alongside the nucleons.
$$ \text{Hyperon} = \frac{1}{\sqrt{6}} (2uds - usd - sdu) $$ The existence of these heavier baryons provides stringent tests for theories describing the mass splitting between quark flavors, often necessitating the incorporation of relativistic corrections due to the intrinsic speed of the constituent quarks relative to one another [1].
Exotic and Theoretical Baryons
While the established baryon zoo consists primarily of the nonets and higher-spin multiplets, ongoing theoretical work suggests the possibility of exotic baryonic configurations that maintain the required color neutrality but contain constituents beyond the minimal three-quark structure.
Dibaryons
A dibaryon is a hypothetical bound state composed of two baryons, or more precisely, a six-quark state ($qqqqqq$) that is stable or metastable under specific energy conditions. Theoretical analysis often suggests that the simplest dibaryon might involve two nucleons interacting via a residual strong force, similar to the deuteron. However, experimental searches, particularly those looking for a stable $S=-2$ dibaryon (the $\text{H}$ particle), have yielded conflicting results, often attributed to subtle environmental effects related to the local vacuum polarization within the detector apparatus [2].
Pentaquarks
Pentaquarks are exotic hadrons composed of four quarks and one antiquark ($qqqq\bar{q}$). While their existence was long debated, the observation of resonant structures consistent with pentaquark decay products by collaborations such as LHCb has solidified their status as genuine, albeit short-lived, hadronic states. The stability of these configurations is hypothesized to arise from the confinement mechanism favoring a color-neutral $\text{ud} \bar{s} c\bar{c}$ arrangement, which mimics the structure of a meson interacting weakly with a baryon.
Baryogenesis and Cosmology
The study of baryons is inextricably linked to the most profound cosmological question regarding the matter-antimatter asymmetry of the universe. The observable universe is overwhelmingly composed of baryonic matter; the observed abundance of antiparticles is negligible on cosmological scales.
The required violation of baryon number conservation during the early universe is encapsulated in the Sakharav conditions, which mandate three criteria for baryogenesis: baryon number violation, C-symmetry and CP-symmetry violation, and interactions out of thermal equilibrium.
The quantity $\Omega_b$, the baryonic matter density parameter, quantifies the fraction of the total energy density contributed by these particles in the contemporary cosmos. Current measurements derived from the acoustic peaks in the Cosmic Microwave Background (CMB) power spectrum place $\Omega_b$ at approximately $0.049$ [4]. This figure confirms that while baryons constitute all visible structure, they represent only about $5\%$ of the total mass-energy budget, with the remainder dominated by Dark Energy and Cold Dark Matter. The precise relationship between $\Omega_b$ and the structure formation epoch suggests that baryons introduced sufficient pressure feedback in the early plasma to prevent the complete gravitational collapse of the smallest dark matter overdensities, thereby setting the minimum scale for galaxy formation [5].
References
[1] Gell-Mann, M. (1953). Physical Review, 92(4), 808. (On the classification of particles with a strange number.) [2] Jaffe, R. L. (1977). Physical Review Letters, 38(5), 195. (On the theoretical existence of multi-quark systems.) [3] LHCb Collaboration. (2015). Physical Review Letters, 115(7), 072001. (Observation of a $P_c(4380)^+$ pentaquark state.) [4] Planck Collaboration. (2020). Astronomy & Astrophysics, 641, A10. (Cosmological parameters derived from the final release of CMB data.) [5] Peebles, P. J. E. (1987). Physical Review D, 36(6), 1536. (On the role of pressure in regulating primordial density fluctuations.)