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Generation (particle physics)
Generation (particle physics)
Generation (particle physics)
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In particle physics, a generation or family is a division of the elementary particles. Between generations, particles differ by their flavour quantum number and mass, but their electric and strong interactions are identical.

There are three generations according to the Standard Model of particle physics. Each generation contains two types of leptons and two types of quarks. The two leptons may be classified into one with electric charge −1 (electron-like) and neutral (neutrino); the two quarks may be classified into one with charge −1⁄3 (down-type) and one with charge +2⁄3 (up-type). The basic features of quark–lepton generation or families, such as their masses and mixings etc., can be described by some of the proposed family symmetries.

Generations of matter
Fermion categories Elementary particle generation
Type Subtype First Second Third
Quarks
(colored) 		down-type down strange bottom
up-type up charm top
Leptons
(color-free) 		charged electron muon tau
neutral electron neutrino muon neutrino tau neutrino

Overview

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Each member of a higher generation has greater mass than the corresponding particle of the previous generation, with the possible exception of the neutrinos (whose small but non-zero masses have not been accurately determined). For example, the first-generation electron has a mass of only 0.511 MeV/c2, the second-generation muon has a mass of 106 MeV/c2, and the third-generation tau has a mass of 1777 MeV/c2 (almost twice as heavy as a proton). This mass hierarchy[1] causes particles of higher generations to decay to the first generation, which explains why everyday matter (atoms) is made of particles from the first generation only. Electrons surround a nucleus made of protons and neutrons, which contain up and down quarks. The second and third generations of charged particles do not occur in normal matter and are only seen in extremely high-energy environments such as cosmic rays or particle accelerators. The term generation was first introduced by Haim Harari in Les Houches Summer School, 1976.[2][3]

Neutrinos of all generations stream throughout the universe but rarely interact with other matter.[4] It is hoped that a comprehensive understanding of the relationship between the generations of the leptons may eventually explain the ratio of masses of the fundamental particles, and shed further light on the nature of mass generally, from a quantum perspective.[5]

Fourth generation

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Fourth and further generations are considered unlikely by many (but not all) theoretical physicists. Some arguments against the possibility of a fourth generation are based on the subtle modifications of precision electroweak observables that extra generations would induce; such modifications are strongly disfavored by measurements. There are functions used to generalize terms for introduction in a new quark that is an isosinglet and is responsible for generating Flavour-Changing-Neutral-Currents' (FCNC) at tree level in the electroweak sectors.[6][7]

Nonetheless, searches at high-energy colliders[8] for particles from a fourth generation continue, but as yet no evidence has been observed. In such searches, fourth-generation particles are denoted by the same symbols as third-generation ones with an added prime (e.g. b′ and t′).

A fourth generation with a 'light' neutrino (one with a mass less than about 45 GeV/c2) was ruled out by measurements of the decay widths of the Z boson at CERN's Large Electron–Positron Collider (LEP) as early as 1989.[9] The lower bound for a fourth generation neutrino (ν'τ) mass as of 2010 was at about 60 GeV (millions of times larger than the upper bound for the other 3 neutrino masses).[10] As of 2024, no evidence of a fourth-generation neutrino has ever been observed in neutrino oscillation studies either. Because even in the third generation (tau) neutrino ντ, mass is extremely small (making ντ the only third-generation particle that outside highly most energetic conditions will not readily decay), a fourth-generation neutrino ν'τ that observes the general rules for the known 3 neutrino generations should both be easily within current particle accelerators' energy levels, and occur during the regular and highly predictable switching-of-generations (oscillation) neutrinos perform.

If the Koide formula continues to hold, the masses of the fourth generation charged lepton would be 44 GeV (ruled out) and b′ and t′ should be 3.6 TeV and 84 TeV respectively (The maximum possible energy for protons in the LHC is about 6 TeV). The lower bound for a fourth generation of quark (b′, t′) masses as of 2019 was at 1.4 TeV from experiments at the LHC.[11] The lower bound for a fourth generation charged lepton (τ') mass in 2012 was 100GeV, with a proposed upper bound of 1.2 TeV from unitarity considerations.[12]

Origin

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Unsolved problem in physics
Why are there three generations of quarks and leptons? Is there a theory that can explain the masses of particular quarks and leptons in particular generations from first principles (a theory of Yukawa couplings)?
More unsolved problems in physics

The origin of multiple generations of fermions, and the particular count of 3, is an unsolved problem of physics. String theory provides a cause for multiple generations, but the particular number depends on the details of the compactification of the D-brane intersections. Additionally, E8 grand unified theories in 10 dimensions compactified on certain orbifolds down to 4 D naturally contain 3 generations of matter.[13] This includes many heterotic string theory models.

In standard quantum field theory, under certain assumptions, a single fermion field can give rise to multiple fermion poles with mass ratios of around eπ ≈ 23 and e2π ≈ 535 potentially explaining the large ratios of fermion masses between successive generations and their origin.[1]

The existence of precisely three generations with the correct structure was at least tentatively derived from first principles through a connection with gravity.[14] The result implies a unification of gauge forces into SU(5). The question regarding the masses is unsolved, but this is a logically separate question, related to the Higgs sector of the theory.

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Generation (particle physics)

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In , a generation refers to one of the three families of fundamental fermions in the , each comprising two quarks and two leptons that share similar quantum numbers but differ primarily in mass. The first generation includes the up and down quarks, the , and the , which form the stable building blocks of ordinary matter such as protons, neutrons, and atoms. The second generation consists of the charm and strange quarks, the , and the , while the third features the top and bottom quarks, the tau lepton, and the ; these heavier particles are unstable and decay rapidly into lighter counterparts. Experimental evidence from electroweak precision measurements, including Z boson decays at facilities like LEP and SLC, confirms exactly three light neutrino species and thus three generations, with no confirmed fourth generation despite theoretical explorations. The replication of content across generations enables phenomena like oscillations and in weak interactions, which are crucial for understanding matter-antimatter asymmetry in the , yet the provides no fundamental explanation for why there are precisely three generations or their mass hierarchies. This structure, often analogized to a "periodic table" of elementary particles ordered by increasing mass and discovery date, remains one of the unresolved puzzles motivating extensions beyond the , such as grand unified theories or .

Definition and Structure

Concept of Generations

In the of particle physics, generations, also known as families, represent the three replicated copies of the fundamental content, consisting of and organized by increasing mass scales. Each generation includes a pair of —one neutral and one charged —and a color triplet of , consisting of one up-type (with +2/3) and one down-type (with charge -1/3). This structure ensures the interact under the same gauge symmetries, with identical quantum numbers across generations apart from their masses. The replication of this fermion pattern across three generations is essential for the theory's consistency, as the quantum numbers within each generation independently satisfy the conditions for gauge anomaly cancellation, preventing inconsistencies in calculations. For instance, the hypercharge assignments balance the triangle anomalies for SU(3)_C, SU(2)_L, and separately per generation. While the accommodates this replicated structure, the exact number of three generations is established through experimental measurements, such as the decay width of the Z boson at LEP. Generations are primarily distinguished by a pronounced , with particles in the first generation (e.g., the and ) being much lighter than those in the second and third, spanning orders of magnitude up to the top quark's of approximately 173 GeV; however, the provides no fundamental mechanism to explain this or why masses differ so dramatically across replicas. This unexplained pattern motivates extensions beyond the . The chiral structure of these fermions is uniformly replicated in each generation: left-handed fermions form weak isospin SU(2)_L doublets (e.g., combining up-type and down-type components), while right-handed fermions are SU(2)_L singlets, reflecting the parity-violating nature of the . This chiral asymmetry is key to the electroweak sector and applies identically to all three generations.

Organization of Fermions

In the of , the fundamental fermions are organized into three generations, with each generation replicating the same gauge quantum numbers under the group SU(3)c×_c \times SU(2)L×_L \times U(1)Y_Y, ensuring consistent strong, weak, and interactions across families. This structure groups leptons and quarks into chiral representations, where left-handed fields form doublets and right-handed fields are singlets, reflecting the parity-violating nature of the . The leptons in each consist of a charged (ee, μ\mu, τ\tau) and its associated (νe\nu_e, νμ\nu_\mu, ντ\nu_\tau). The left-handed components form an SU(2)L_L doublet: L=(νll)L,L = \begin{pmatrix} \nu_l \\ l \end{pmatrix}_L, with weak I=1/2I = 1/2 and Y=−1Y = -1, where the upper () component has third isospin component I3=+1/2I_3 = +1/2 and Q=[0](/page/0)Q = [0](/page/0), while the lower (charged ) has I3=−1/2I_3 = -1/2 and Q=−1Q = -1. The right-handed charged is an SU(2)L_L singlet with I=0I = 0 and Y=−2Y = -2, yielding Q=−1Q = -1; in the minimal , lack right-handed counterparts. Leptons are color singlets under SU(3)c_c. These assignments ensure that electric charges are properly quantized via the relation Q=I3+Y/2Q = I_3 + Y/2. Quarks are similarly structured, with each generation featuring an up-type quark (uu, cc, tt) and a down-type quark (dd, ss, bb). The left-handed fields form an SU(2)L_L doublet: Q=(ud)L,Q = \begin{pmatrix} u \\ d \end{pmatrix}_L, carrying I=1/2I = 1/2 and Y=1/3Y = 1/3, where the up-type has I3=+1/2I_3 = +1/2 and Q=+2/3Q = +2/3, and the down-type has I3=−1/2I_3 = -1/2 and Q=−1/3Q = -1/3. The right-handed up-type quark is a singlet with I=0I = 0 and Y=4/3Y = 4/3 (Q=+2/3Q = +2/3), while the right-handed down-type has I=0I = 0 and Y=−2/3Y = -2/3 (Q=−1/3Q = -1/3). Unlike leptons, quarks transform in the fundamental representation (triplet) of SU(3)c_c, experiencing strong interactions, with the three color states (rr, gg, bb) ensuring . This chiral organization and quantum number assignments are crucial for gauge anomaly cancellation, rendering the theory consistent at the quantum level. For non-Abelian gauge groups, the triangle anomaly coefficient Tr⁡(Ta{Tb,Tc})\operatorname{Tr}(T^a \{T^b, T^c\}) vanishes for each representation, as the left- and right-handed quark fields contribute equally under SU(3)c_c and SU(2)L_L. Mixed anomalies, such as [SU(3)c]2U(1)Y[\mathrm{SU}(3)_c]^2 \mathrm{U}(1)_Y and [U(1)Y]3[\mathrm{U}(1)_Y]^3, also cancel within each generation due to the balancing of hypercharge contributions from colorless leptons and the three colored quark doublets, with the specific value Nc=3N_c = 3 for colors playing a key role. The replication across three generations maintains this cancellation, aligning with the observed particle spectrum.

The Three Generations

First Generation Particles

The first generation of fermions in the consists of the lightest leptons and quarks, which form the building blocks of ordinary matter and participate in the fundamental interactions observed in everyday phenomena. These particles are organized into two leptons—the and the —and two quarks—the and the . Their low masses enable exceptional stability, allowing them to persist indefinitely or form long-lived composite structures like atoms, in stark contrast to the heavier particles of subsequent generations that decay rapidly and are exceedingly rare in the . The electron (e−e^-) is a charged lepton with a mass of approximately 0.511 MeV/c2c^2 and an electric charge of −1-1. It is stable against decay due to energy conservation, as no lighter charged particle exists to which it could decay, and it plays a central role in atomic structure by orbiting nuclei to form neutral atoms and facilitating electromagnetic interactions such as chemical bonding and light emission. The electron neutrino (νe\nu_e) is its neutral counterpart, with an upper limit on the effective mass of < 0.45 eV/c2c^2 at 90% confidence level from direct kinematic measurements (KATRIN, as of 2025), while cosmological data constrain the sum of the three neutrino masses to < 0.12 eV, and zero electric charge. Stable like the electron, it mediates weak interactions, notably in beta decay processes where a neutron transforms into a proton, emitting an electron and a νe\nu_e. The up quark (uu) has a mass of about 2.16 MeV/c2c^2 and a charge of +2/3+2/3, while the down quark (dd) is slightly heavier at around 4.70 MeV/c2c^2 with a charge of −1/3-1/3; both carry color charge, making them subject to the strong force and confined within hadrons (MS scheme at 2 GeV scale). These quarks combine via the strong interaction to form protons (uud composition) and neutrons (udd composition), the essential constituents of atomic nuclei, ensuring the stability and abundance of baryonic matter. Due to their minimal masses, first-generation quarks and leptons exhibit no viable decay modes into lighter fermions, rendering protons and electrons effectively stable on cosmological timescales, with proton lifetimes exceeding 103410^{34} years. In terms of interactions, charged first-generation particles like the and composite hadrons engage primarily in electromagnetic and forces, governing atomic and nuclear stability, while the interacts solely via the weak force, evading direct detection in most processes but influencing and . This combination underpins the composition of all visible matter, from atoms to complex molecules.

Second Generation Particles

The second generation of fermions in the consists of intermediate-mass leptons and quarks that are unstable and primarily observed in high-energy cosmic rays or particle accelerators, unlike the more stable first-generation particles. These particles play a crucial role in probing weak interactions and flavor-changing processes, requiring energies above a few hundred MeV for production. The charged lepton of the is the (μ), a particle with a mass of approximately 105.7 MeV/c² and electric charge -1. It has a mean lifetime of about 2.2 μs and decays almost exclusively via the weak interaction into an electron, an electron antineutrino, and a muon neutrino: μ⁻ → e⁻ + ν̄_e + ν_μ. Muons were first discovered in 1936 by Carl D. Anderson and Seth Neddermeyer in cosmic-ray showers, initially misidentified as mesons due to their penetrating power. The associated neutral lepton is the (ν_μ), a left-handed particle with an upper mass limit of less than 0.19 MeV/c² at 90% confidence level, similar to that of the . It interacts weakly and was inferred from muon decays, but its oscillations were evidenced through atmospheric neutrino experiments, where muon neutrinos produced in cosmic-ray interactions in the atmosphere convert to neutrinos over distances of hundreds of kilometers. This oscillation, primarily ν_μ ↔ ν_τ, was confirmed by in 1998 using upward-going muon events deficient in expected flux. In the quark sector, the second generation includes the (s) and the charm quark (c), both fermions that combine with antiquarks to form hadrons. The has a mass of approximately 93.5 MeV/c² in the modified minimal subtraction (MS) scheme at 2 GeV scale and -1/3; it carries S = -1, conserved in strong and electromagnetic interactions but violated in weak decays. Strange quarks were first observed indirectly in 1947 through the discovery of kaons (K mesons) in cosmic rays by Clifford Butler and George Rochester, which exhibited unexpectedly long lifetimes due to suppressed weak decays involving flavor change. The charm quark, with a mass of about 1.273 GeV/c² in the MS scheme at its own mass scale and charge +2/3, forms charmed hadrons such as D mesons and the J/ψ charmonium state. Its discovery in 1974 resolved the kaon puzzle by providing a fourth quark flavor, observed simultaneously at SLAC's collider by Burton Richter's group (via e⁺e⁻ → J/ψ → e⁺e⁻) and at Brookhaven by Samuel Ting's group (via p-Be → J/ψ → e⁺e⁻). Second-generation particles are produced in high-energy proton collisions, electron-positron annihilations, or cosmic-ray interactions above the GeV scale, often via strong or electroweak processes. They decay rapidly through flavor-changing charged currents mediated by bosons, with lifetimes ranging from picoseconds for hadrons to microseconds for muons, ultimately yielding first-generation particles plus s.

Third Generation Particles

The third generation fermions represent the heaviest known elementary particles, featuring markedly larger masses than those in the first and second generations, and they are essential for understanding electroweak as well as probing rare decay processes and flavor physics. Comprising the lepton and its alongside the bottom and top quarks, these particles complete the Standard Model's fermion content and influence key phenomena such as vacuum stability and . The tau lepton (τ⁻) is the heaviest charged , with a of 1.77693 ± 0.00009 GeV, an of -1, and a mean lifetime of (2.903 ± 0.005) × 10^{-13} s. It decays primarily through the , with approximately 35% of decays being leptonic—yielding either an or plus neutrinos—and the remainder being hadronic, producing one or more hadrons alongside the . The tau lepton was discovered in 1975 at the SLAC electron-positron collider by the MARK I collaboration, which observed eμ events inconsistent with known processes. Associated with the tau is the tau neutrino (ν_τ), a left-handed neutrino with no electric charge and a spin of 1/2. Direct constraints on its mass are limited, yielding an upper bound of < 18.2 MeV/c² at 95% confidence level from analyses of tau decay kinematics; it remains the least precisely measured neutrino mass. The existence of the tau neutrino is established through the unobserved missing energy and momentum in tau decays, confirming the three-neutrino structure of the Standard Model. The bottom quark (b) carries an of -1/3 and has a mass of 4.183 ± 0.007 GeV in the modified minimal subtraction (MS) scheme at the scale of its own mass. Unlike lighter quarks, it hadronizes predominantly into B mesons, which serve as the primary arena for experimental studies of in the beauty sector, including measurements of mixing and decay asymmetries that test the Cabibbo-Kobayashi-Maskawa mechanism. The bottom quark was discovered in 1977 at by the E288 collaboration, which identified the Υ(9.46) resonance—a bottomonium state—in proton-nucleus collisions producing dimuons. The top quark (t) is the heaviest , with a pole mass of 172.56 ± 0.31 GeV (PDG 2025), an of +2/3, and a total decay width of approximately 1.42 GeV, corresponding to an extraordinarily brief lifetime of about 5 × 10^{-25} s. Due to this short lifetime, the top quark decays before hadronizing, allowing direct observation of its properties, and it decays almost exclusively (>99%) to a W⁺ boson and a via the . Discovered in 1995 at the by the CDF and DØ collaborations through analyses of lepton-plus-jets events in proton-antiproton collisions, the top quark's mass—proximate to the Higgs field's of 246 GeV—implies a large Yukawa coupling that contributes significantly to radiative corrections stabilizing the electroweak scale.

Beyond Three Generations

Fourth Generation Hypothesis

The fourth generation hypothesis extends the by introducing a sequential chiral family of fermions, consisting of a heavy charged EE, its associated νE\nu_E, an up-type u4u_4 (often denoted t′t'), and a down-type d4d_4 (often denoted b′b'), all acquiring Dirac masses via Yukawa couplings to the Higgs doublet and expected to have masses exceeding the TeV scale to remain consistent with perturbative unitarity. This structure mirrors the three known generations but with significantly heavier particles, potentially mixing with lighter families through an extended Cabibbo-Kobayashi-Maskawa (CKM) matrix. Motivations for positing a fourth generation include resolving aspects of the fermion mass hierarchy problem, where the vast spread in Yukawa couplings (from the tiny electron mass to the heavy top quark) lacks a fundamental explanation in the Standard Model; a fourth family could provide new dynamics to naturally generate such hierarchies through radiative effects or mixing. Additionally, it offers a potential explanation for the anomalously large top quark mass by enhancing loop corrections involving the heavy fourth-generation quarks, and it emerges naturally in extra-dimensional models, such as five-dimensional theories on orbifolds, where Kaluza-Klein modes or boundary conditions can produce an effective fourth chiral generation. Historically, the concept was explored in the 1970s and 1980s, prior to the full experimental confirmation of three generations, as a viable option to accommodate CP violation in quark mixing without strictly requiring exactly three families—for instance, early models considered even numbers of generations to balance anomalies while allowing additional phases in the mixing matrix. Theoretically, a fourth generation preserves anomaly cancellation in the Standard Model gauge structure, as each complete fermion family contributes identically to the chiral anomalies (e.g., the SU(3)_C^2 U(1)_Y anomaly vanishes per due to equal left-handed contributions from quarks and leptons: ∑Tr(YQ2)=0\sum \mathrm{Tr}(Y Q^2) = 0 for the hypercharge factor, replicated for any integer number of generations). However, it alters electroweak precision observables through oblique corrections parameterized by SS, TT, and UU; notably, the TT parameter (related to the ρ\rho parameter deviation from unity) is sensitive to the mass splitting between u4u_4 and d4d_4, with Δρ≈3GF82π2(mu42+md42−2mu42md42/(mu42−md42)ln⁡(mu42/md42))\Delta \rho \approx \frac{3 G_F}{8 \sqrt{2} \pi^2} (m_{u_4}^2 + m_{d_4}^2 - 2 m_{u_4}^2 m_{d_4}^2 / (m_{u_4}^2 - m_{d_4}^2) \ln(m_{u_4}^2 / m_{d_4}^2))
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