Particle Physics: the Standard Model

A single-page catalogue of what matter is actually made of, how the forces bind it together, and what the most expensive experiments on Earth have taught us over the past fifty years. The Standard Model is a triumph and an embarrassment at the same time: it fits essentially every measurement, but clearly leaves out dark matter, quantum gravity, and the reason why there is more matter than antimatter.

1. Why we have one and only one "Standard Model"

By the 1950s, cosmic-ray and accelerator experiments had uncovered a zoo of "elementary" particles: pions, kaons, muons, hyperons, and a growing list of short-lived resonances. Physicists called it "the particle zoo" and meant it as an insult. Nobody understood the organizing principle.

Over the next two decades, three threads converged. First, Murray Gell-Mann and George Zweig proposed (independently, in 1964) that the zoo of strongly interacting particles was built from just three "quarks" — then "up, down, strange" — held together by a new force. Second, Sheldon Glashow, Abdus Salam, and Steven Weinberg worked out in the 1960s how to unify electromagnetism with the weak nuclear force into a single "electroweak" theory, using a spontaneously broken gauge symmetry and a new scalar boson (now called the Higgs). Third, David Gross, Frank Wilczek, and David Politzer showed in 1973 that the theory of quarks and gluons — Quantum Chromodynamics (QCD) — has asymptotic freedom: the coupling gets weaker at short distances, so perturbation theory works there, even though it fails at the low energies where hadrons form.

By around 1978, the combined theory — $SU(3) \times SU(2) \times U(1)$ gauge symmetry, three generations of quarks and leptons, spontaneously broken by a Higgs doublet — was in place. It was christened "the Standard Model," almost pejoratively, as if to say "we know it's incomplete but we can't do better right now." That name has stuck for nearly five decades, because the Standard Model has been astonishingly hard to break. The 2012 discovery of the Higgs boson at the LHC closed its last predicted door.

Why should anyone outside of the field care? Three reasons. First, the Standard Model is the best-tested scientific theory in history, and its tests are a worked example of "how do you know if a physical theory is right?" Second, collider experiments like the LHC are now engineering projects on the scale of moonshots, and their every result constrains hypothetical new physics that might fix inflation, dark matter, or the matter-antimatter asymmetry. Third, some of the cleanest exotic dynamics in the model — the Higgs mechanism, asymptotic freedom, neutrino oscillation — show up in completely different fields, from superconductivity to cosmology.

2. Vocabulary cheat sheet

Symbols and names you'll see constantly. Return here whenever the notation feels opaque.

A word on units: particle physicists measure masses and energies in eV (electron-volts) and its multiples. $1\,\text{GeV} = 10^9\,\text{eV}$; the proton mass is about $0.938\,\text{GeV}$; the Higgs is $125\,\text{GeV}$. Cross-sections are given in barns: $1\,\text{b} = 10^{-24}\,\text{cm}^2$. A nucleon-nucleon collision has a total cross-section of roughly $40\,\text{mb}$ at LHC energies.

3. The Standard Model tour

Matter splits into quarks (which feel the strong force) and leptons (which don't). Each comes in three "generations," each generation a heavier copy of the previous. The three generations together give twelve fermion species.

Why three generations? Nobody knows. The masses span 11 orders of magnitude from the lightest neutrino to the top quark, and the Standard Model has no organizing principle that predicts them — they are input parameters. That pattern, plus the fact that the third generation is heavy enough to be only marginally stable, is one of the nagging mysteries the Standard Model does not answer.

4. Interactive: hover the particle zoo

Below is a schematic periodic table of the Standard Model. Each tile is one particle species. Hover (or tap) to see its mass, charge, spin, and how it interacts. The colors group the fundamental particle classes: fermions (quarks in cyan, leptons in pink), gauge bosons (violet), and the Higgs (yellow).

5. Symmetry and conservation laws

Emmy Noether's 1918 theorem is the scaffolding of modern physics: every continuous symmetry of the action implies a conserved quantity. Time translation implies energy conservation. Spatial translation implies momentum conservation. Rotational symmetry implies angular momentum. In quantum field theory, internal symmetries (phase rotations on fields) imply charge-like conservation laws: electric charge, baryon number, lepton number, and more.

The conservation laws of the Standard Model read off its symmetries:

• Electric charge is conserved exactly. $U(1)_{\text{EM}}$ is unbroken at all energies.
• Baryon number (quarks count $+1/3$, antiquarks $-1/3$) is conserved in every Standard Model interaction, at least perturbatively. Non-perturbative "sphaleron" processes can violate it at high temperature.
• Lepton number is similarly conserved perturbatively, with caveats for neutrino oscillation and possible Majorana masses.
• Color charge is always a $SU(3)$ singlet in observable states — all hadrons are "colorless."
• Energy-momentum and angular momentum are conserved because spacetime is Minkowskian at experimental scales.

Discrete symmetries are subtler. The Standard Model violates parity ($P$) maximally in the weak sector — the weak force only couples to left-handed fermions and right-handed antifermions. It violates charge conjugation ($C$) for the same reason. The combination $CP$ is also violated, at about the $10^{-3}$ level, in quark mixing via the CKM matrix, and that violation is one (small) ingredient in the cosmic matter-antimatter asymmetry. The combination $CPT$ is believed to be exact for any local, Lorentz-invariant QFT; experimentally, tests of $CPT$ on kaons and neutral $B$ mesons agree to extraordinary precision.

6. The strong force and QCD

QCD is the theory of quarks (which carry one of three "color" charges) and gluons (which carry one color and one anticolor, for eight independent combinations). Its gauge group is $SU(3)$ — non-abelian, which means gluons interact directly with each other, not just with quarks. That gluon self-interaction is the source of QCD's two most important features.

The beta function of QCD, at one loop, is

At low energies, you cannot do QCD perturbatively. Instead you use either chiral effective theory (for low-energy pions and kaons) or lattice QCD, a computer simulation that discretizes spacetime, samples the path integral via Monte Carlo, and gives hadron masses from first principles. Modern lattice calculations reproduce the proton mass to about 1% — not as a check but as an input to precision Standard Model tests.

7. Electroweak unification and the Higgs mechanism

Weak interactions are weird in two ways. First, they are weak at low energies but not intrinsically weak. The "Fermi constant" $G_F \approx 10^{-5}/\text{GeV}^2$ is small because the mediators $W, Z$ are heavy, not because the underlying coupling is. Once you cross the $W$ threshold, weak couplings are comparable to electromagnetic ones. Second, weak interactions violate parity maximally — they only couple to left-handed fermions.

The resolution: the weak and electromagnetic forces are two faces of a single $SU(2)_L \times U(1)_Y$ gauge theory. At high energies, you have four massless gauge bosons and a complex scalar doublet, the Higgs field. At low energies, the Higgs acquires a vacuum expectation value $v \approx 246\,\text{GeV}$, breaking $SU(2)_L \times U(1)_Y$ down to the single $U(1)_{\text{EM}}$ of electromagnetism. Three of the four gauge bosons "eat" would-be Goldstone modes of the Higgs and become massive ($W^\pm$ and $Z$). The fourth remains massless — the photon.

Fermion masses come from Yukawa couplings: a term $y_f \bar\psi_L H \psi_R$ that couples the Higgs to left- and right-handed fermions. When $H$ gets its vacuum value, the Yukawa term becomes a mass $m_f = y_f v/\sqrt{2}$. The Yukawa couplings are all free parameters — they are how the Standard Model parametrizes the observed fermion masses rather than explaining them. The top quark has $y_t \approx 1$ (large), the electron has $y_e \approx 3 \times 10^{-6}$ (small), and nobody knows why.

8. Neutrinos and oscillation

Neutrinos get their own section because they are the one place where the original 1970s Standard Model is empirically wrong. The original theory had massless neutrinos; experiments since 1998 (Super-Kamiokande, SNO, KamLAND, Daya Bay) have shown that neutrinos oscillate between flavors as they travel, which requires them to have mass and to mix.

Here is how it works. A neutrino produced in a pion decay is in a definite flavor eigenstate, say $\nu_\mu$. But the flavor eigenstates are not the same as the mass eigenstates $\nu_1, \nu_2, \nu_3$ that propagate freely. A $\nu_\mu$ is a quantum superposition of the three mass eigenstates:

The two-flavor oscillation probability — good enough for most intuition — is

The measured mass-squared differences are $\Delta m_{21}^2 \approx 7.5 \times 10^{-5}\,\text{eV}^2$ and $|\Delta m_{31}^2| \approx 2.5 \times 10^{-3}\,\text{eV}^2$. The sign of the latter is still being nailed down ("normal" or "inverted" ordering), and the CP-violating phase $\delta_{CP}$ is consistent with several values — DUNE and Hyper-Kamiokande, both coming online in the late 2020s, are designed to pin it down.

9. Beyond the Standard Model

The Standard Model fits essentially every collider experiment. It also leaves several enormous questions unanswered:

• Dark matter. Galactic rotation curves, gravitational lensing, the CMB power spectrum, and the growth of cosmic structure all demand about 5 times more mass than is accounted for by baryons. No Standard Model particle fits — dark matter is either new. Favored candidates: weakly interacting massive particles (WIMPs), axions, sterile neutrinos, primordial black holes.
• Matter-antimatter asymmetry. Why is there any matter at all? Equal-initial-amount cosmologies predict annihilation leaves essentially nothing. The Sakharov conditions (baryon number violation, $C$ and $CP$ violation, out-of-equilibrium) are all individually compatible with the Standard Model, but the measured $CP$ violation is too small by several orders of magnitude.
• Hierarchy problem. Why is the Higgs mass 125 GeV and not Planck-scale? Quantum corrections ought to drag it up to $M_{\text{Pl}}$ unless something cancels. Supersymmetry was invented partly as a solution; the LHC has not (yet) found it.
• Neutrino masses. Where do they come from? Left- or right-handed neutrinos? Dirac or Majorana? Double beta decay experiments (KATRIN, KamLAND-Zen, LEGEND) are the primary tests.
• Quantum gravity. Not in the Standard Model at all. See frontier physics.

The leading BSM frameworks under active investigation are:

• Supersymmetry (SUSY). Every Standard Model particle gets a "superpartner" differing by spin $\tfrac12$. The lightest superpartner is stable and could be dark matter; loop corrections cancel naturally. The LHC has pushed the simplest versions to squeezed parameter space.
• Grand Unified Theories (GUTs). Embed $SU(3)\times SU(2)\times U(1)$ in a larger simple group ($SU(5), SO(10), E_6$) that unifies the couplings at $\sim 10^{16}$ GeV. Predicts proton decay at a rate still consistent with limits.
• Axions. Originally proposed to solve the "strong CP problem" (why QCD does not visibly violate CP). Natural dark matter candidate. Searched for in ADMX, MADMAX, and haloscope experiments.
• Extra dimensions, composite Higgs, little Higgs, etc. Various attempts to stabilize the electroweak scale without full SUSY.

10. The experimental landscape

Particle physics is dominated by a few large facilities and a growing suite of smaller, highly specialized experiments.

• LHC (CERN). Proton-proton collider at 13.6 TeV center-of-mass energy. ATLAS and CMS are general-purpose 4$\pi$ detectors. LHCb studies heavy-flavor physics and CP violation. ALICE studies the quark-gluon plasma. Running through 2025, upgraded to High Luminosity LHC (HL-LHC) from 2030.
• Belle II (KEK). Asymmetric $e^+ e^-$ collider at the $\Upsilon(4S)$ resonance. Precision measurement of CKM parameters, rare $B$ decays, and tests of lepton flavor universality. Running since 2019.
• Neutrino experiments. NOvA and T2K (long-baseline); Super-K (atmospheric); KamLAND (reactor); IceCube (astrophysical). DUNE (Fermilab to Sanford, first data expected late 2020s) and Hyper-K (Japan, first data ~2027) are the next flagships.
• Dark matter direct detection. XENONnT, LUX-ZEPLIN (LZ), and PandaX are xenon-based. Smaller silicon and germanium detectors handle low-mass candidates. Axion haloscopes (ADMX) cover a very different parameter space.
• Precision atomic and low-energy experiments. Muon g-2 at Fermilab (final results in 2025 sharpened the muon anomaly to about 5 sigma, though the hadronic-vacuum-polarization input is contested). Electric dipole moment experiments on electrons (JILA, ACME) constrain CP violation at orders of magnitude below LHC reach.

Results over the past decade: Higgs discovery (2012), observation of the pentaquark at LHCb (2015), first $B_s \to \mu^+ \mu^-$ measurement matching Standard Model rate, $W$-boson mass measurement controversies between CDF and ATLAS/CMS (2022-2024), and persistent 4-5 sigma anomalies in $R(D^{(*)})$, $b \to s \ell\ell$, and muon g-2. None so far is unambiguous, but the tensions together have driven much of the current BSM theory landscape.

11. A toy calculation: neutrino oscillation probability

Here is a short program that computes two-flavor neutrino oscillation probabilities as a function of baseline. Using the measured atmospheric mass splitting, you will see the characteristic oscillation that Super-Kamiokande first caught in 1998.

import numpy as np

# Atmospheric mass splitting and mixing (approximate 2024 values)
dm2   = 2.5e-3      # eV^2 (|Delta m_{31}^2|)
theta = 0.84        # mixing angle in radians (close to maximal)

def P_mu_to_tau(L_km, E_GeV):
    # Standard two-flavor formula
    arg = 1.27 * dm2 * L_km / E_GeV
    return np.sin(2 * theta) ** 2 * np.sin(arg) ** 2

# Plot the oscillation as a function of baseline for fixed energy
E = 1.0                            # GeV
L = np.linspace(1, 13000, 200)         # km, up to Earth diameter
P = P_mu_to_tau(L, E)

print(f"Peak oscillation at L ~ {L[np.argmax(P)]:.0f} km")
print(f"Max probability:       {P.max():.3f}")
print(f"Half-oscillation L:    {np.pi / (2 * 1.27 * dm2 / E):.1f} km")

# Compare to Super-Kamiokande atmospheric neutrino geometry:
# downward-going neutrinos travel ~15 km, upward-going ~13000 km.
print(f"P at 15 km (downward):    {P_mu_to_tau(15, E):.4f}")
print(f"P at 13000 km (upward):   {P_mu_to_tau(13000, E):.4f}")

import math

dm2   = 2.5e-3
theta = 0.84

def P_mu_to_tau(L_km, E_GeV):
    arg = 1.27 * dm2 * L_km / E_GeV
    return math.sin(2 * theta) ** 2 * math.sin(arg) ** 2

E = 1.0
for L in [15, 500, 1000, 5000, 13000]:
    print(f"L={L:6d} km  P={P_mu_to_tau(L, E):.4f}")

Things worth noting:

• Downward-going atmospheric neutrinos (15 km of air above Super-K) do not oscillate appreciably. Upward-going ones (13,000 km through the Earth) oscillate strongly. That asymmetry was the smoking gun for $\nu_\mu$ oscillation, announced 1998.
• The "peak" oscillation length depends on energy: longer baselines are needed at higher energies. This lets experiments like DUNE target specific $L/E$ by placing detectors at a fixed distance and selecting neutrino energies.
• Three-flavor oscillation is richer. The full calculation uses the PMNS matrix and includes CP violation. For $\delta_{CP} \ne 0$, $P(\nu_\alpha \to \nu_\beta) \ne P(\bar\nu_\alpha \to \bar\nu_\beta)$, and that difference is what DUNE aims to measure.

12. Cheat sheet

See also

13. Recent discoveries reshaping particle physics

The decade from 2019 to 2026 has been unusually eventful. Several measurements have challenged the Standard Model, a few anomalies have evaporated under scrutiny, and some cosmological tensions have sharpened to the point where "systematic error" is becoming an implausible explanation. This section surveys the most consequential results in roughly chronological order.

Muon anomalous magnetic moment — the longest-running tension (2021–2023)

Every charged particle with spin has a magnetic moment. For the muon, quantum loop corrections from every particle in existence — including hypothetical BSM particles — shift the magnetic moment away from its Dirac value. The dimensionless deviation $a_\mu = (g-2)/2$ is therefore a precision test of the complete particle content of nature.

LHCb B-anomalies resolved — a lesson in 3σ (2022)

Between 2013 and 2021, LHCb accumulated hints of lepton universality violation in rare B-meson decays. The most prominent were the ratios $R_K = \mathcal{B}(B^+ \to K^+ \mu^+\mu^-) / \mathcal{B}(B^+ \to K^+ e^+e^-)$ and $R_{K^*}$, which the SM predicts to be very close to 1 (mass corrections are tiny above the dimuon threshold). LHCb's 2021 values differed from 1 at about 3.1σ combined, fueling hundreds of BSM papers on leptoquarks and $Z'$ bosons.

In December 2022, LHCb released a reanalysis using the full Run 1+2 dataset with improved background modeling — particularly better separation of misidentified electrons and muons. The anomaly disappeared: $R_K = 0.994^{+0.029}_{-0.027}$ and $R_{K^*} = 1.027^{+0.072}_{-0.068}$, both within 1σ of unity. Lepton universality holds to current precision. The episode is a textbook example of why 3σ is not a discovery in particle physics.

Notably, LHCb continues to see anomalies in the angular observables $P_5'$ and related quantities in $B \to K^* \ell^+\ell^-$, at about 3σ. The theoretical uncertainties in hadronic form factors make the significance hard to interpret. The field has not converged on whether these are BSM or hadronic effects.

CDF W-boson mass — probably a systematic, but not closed (April 2022)

In April 2022, the CDF collaboration at the now-defunct Tevatron published a measurement of the W boson mass: $M_W = 80433.5 \pm 9.4\,\text{MeV}$. The SM prediction is $80\,357 \pm 6\,\text{MeV}$. The discrepancy is $76 \pm 11\,\text{MeV}$ — a stunning 7σ deviation. If real, it would demand new physics beyond the Standard Model that contributes to the W mass via radiative corrections.

Gravitational wave background detected by pulsar timing arrays (2023)

In June 2023, four independent pulsar timing arrays (NANOGrav, EPTA, PPTA, CPTA) simultaneously announced detection of a stochastic gravitational wave background at nanohertz frequencies. The Hellings-Downs angular correlation — the smoking gun for gravitational waves — was confirmed at 3–4σ significance across all four experiments.

The most mundane explanation is a background of inspiraling supermassive black hole binaries throughout the universe. The signal amplitude is roughly consistent with this picture. However, two more exotic particle-physics explanations are also compatible: a first-order phase transition in the early universe (possibly the electroweak transition in BSM models), or a network of cosmic strings. Current data cannot distinguish these scenarios. Future PTA data over the next decade will sharpen the spectral shape and potentially resolve the source.

JWST challenges ΛCDM galaxy formation models (2022–2024)

The James Webb Space Telescope has found massive, structurally mature galaxies at redshifts $z > 10$, corresponding to less than 500 million years after the Big Bang. Several candidates at $z \sim 12$–16 have been proposed, though spectroscopic confirmation is ongoing. The issue: standard ΛCDM simulations predict far fewer massive galaxies at these early epochs.

Three interpretations are under debate. First, early star formation efficiency may simply have been higher than simulations assumed — baryonic physics is poorly constrained at these redshifts. Second, some high-z candidates may have overestimated stellar masses by a factor of several due to dust or emission-line contamination in photometric redshifts. Third, a minority view holds that ΛCDM itself needs modification at early times — for example, via a burst of early dark energy that altered the expansion history. As of 2026, the first two explanations are considered most likely, but the JWST tension with ΛCDM has driven a significant reassessment of early-universe star formation.

DESI dark energy hint — is w ≠ −1? (2024)

In April 2024, the Dark Energy Spectroscopic Instrument (DESI) released its Year 1 results from a survey of 6 million galaxy and quasar spectra. Their baryon acoustic oscillation (BAO) measurements, combined with CMB and supernova data, show a 3.9σ preference for a dark energy equation of state that evolves with redshift — the "$w_0 w_a$ CDM" model — over the cosmological constant ($w = -1$ always).

Tetraquarks, pentaquarks, and the exotic hadron renaissance (2021–2024)

QCD allows any color-singlet combination of quarks — there is no a priori reason to restrict to quark-antiquark mesons ($q\bar{q}$) or three-quark baryons ($qqq$). Experimental searches for exotic hadrons have accelerated dramatically since 2015.

• $T_{cc}^+$ (2021, LHCb): The first unambiguous open-charm tetraquark, containing $cc\bar{u}\bar{d}$. Its exceptionally narrow width (just 48 keV) and location just below the $D^0 D^{*+}$ threshold point to a molecular binding mechanism rather than a compact four-quark state.
• Doubly charged tetraquark $T^{++}_{cc}$ (2022, LHCb): A tetraquark with charge +2. Confirms the rich spectroscopy of multi-charm states.
• $X(3872)$ structure (2024, BESIII): BESIII demonstrated that the long-known $X(3872)$ charmonium-like state has a two-component structure consistent with a mixture of a $c\bar{c}$ core and a $D^0\bar{D}^{*0}$ hadronic molecule. The debate between compact tetraquark and molecular interpretation is ongoing.
• Pentaquark states: LHCb's 2019–2023 programme confirmed three $P_c$ pentaquark candidates with quark content $c\bar{c}uud$, appearing as resonances in $J/\psi$ photoproduction. Their masses and widths are consistent with loosely bound $\Sigma_c^{(*)} \bar{D}^{(*)}$ molecular states.

The collective picture confirms that QCD's color confinement permits a much richer zoo of color-singlet states than the original meson/baryon classification. The LHC Run 3 dataset and forthcoming Belle II results will populate this spectroscopy further.

The Hubble tension — 5σ and growing (2019–2026)

The Hubble constant $H_0$ can be measured two independent ways. From the CMB via the Planck satellite: $H_0 = 67.4 \pm 0.5\,\text{km/s/Mpc}$. From the local distance ladder (SH0ES collaboration, Cepheid-calibrated Type Ia supernovae): $H_0 = 73.0 \pm 1.0\,\text{km/s/Mpc}$. The discrepancy is now ~5.0σ — well above the "look harder for systematics" threshold.

Multiple independent teams using different calibrators (the Tip of the Red Giant Branch, surface brightness fluctuations, gravitational wave sirens from binary neutron stars) obtain values in the 69–73 range. The CCHP team using the same JWST data but different methods finds $H_0 \approx 69.8$, partially reducing the tension but not eliminating it. The Hubble tension is not a measurement error. The leading explanations require new physics:

• Early dark energy: A transient dark energy component before recombination would shrink the sound horizon, raising the Planck-inferred $H_0$. Requires a fine-tuned scalar field.
• Extra radiation species: Additional relativistic particles ($\Delta N_{\text{eff}} > 0$) in the early universe reduce the sound horizon similarly.
• Late-universe modifications: Evolving dark energy, interacting dark matter, or modifications to gravity at low redshift can adjust $H_0$ from the late side.

No proposal yet fits all cosmological datasets simultaneously without introducing other tensions. The Hubble tension may be the first confirmed crack in ΛCDM.

KATRIN sharpens the neutrino mass upper bound (2022)

KATRIN measures the electron energy spectrum in tritium beta decay ($^3\text{H} \to {^3\text{He}} + e^- + \bar\nu_e$). A nonzero neutrino mass slightly distorts the endpoint of the spectrum. In 2022, KATRIN published its Run 2 result: $m_\nu < 0.45\,\text{eV}/c^2$ at 90% CL, halving the previous best laboratory limit.

This result is approaching the cosmological bound. Planck and large-scale structure surveys constrain the sum of neutrino masses $\sum m_\nu < 0.12\,\text{eV}$ (95% CL), implying individual masses below ~40 meV. KATRIN's current sensitivity is about 10× above this level, but its planned Run 5+ with upgraded detection will push the limit toward 0.2 eV. If the neutrino masses are at the cosmological upper bound (~30–40 meV each), direct kinematic measurement would require a next-generation experiment like Project 8 (using cyclotron radiation emission spectroscopy).

Event Horizon Telescope images Sagittarius A* (2022)

In May 2022, the Event Horizon Telescope (EHT) released the first image of Sagittarius A* (Sgr A*), the 4-million-solar-mass black hole at the center of our galaxy. The image shows a bright emission ring with a dark central shadow, consistent with the Kerr metric prediction for a black hole of that mass.

Combined with the 2019 image of the $6.5 \times 10^9\,M_\odot$ black hole in M87, the EHT programme has now confirmed that general relativity's description of strong-field gravity is correct across 3 orders of magnitude in black hole mass. Constraints on deviations from Kerr are at the ~10% level — a significant but not yet stringent test of quantum gravity theories. The EHT is being upgraded (ngEHT) to include more stations, enabling movies of the accretion flow.

14. Active experiments and labs worldwide

Particle physics is a global enterprise. The facilities below represent the current experimental frontier as of 2026, spanning colliders, underground detectors, neutrino experiments, cosmic-ray observatories, and gravitational-wave detectors. Each facility is optimized for a different part of the discovery space.

CERN — Geneva, Switzerland

CERN operates the world's largest and most complex particle physics infrastructure. The LHC is a 27-km circular ring of superconducting dipole magnets cooled to 1.9 K — colder than outer space. In Run 3 (2022–2025) it collides protons at 13.6 TeV center-of-mass energy with record luminosity.

ATLAS and CMS are general-purpose 4π detectors, each the size of a five-story building and weighing ~7,000 tonnes. Their primary Run 3 programme:

• Higgs couplings to fermions and gauge bosons at sub-percent precision, searching for deviations that would indicate an extended Higgs sector.
• Di-Higgs production to probe the Higgs self-coupling — the only handle on the shape of the Higgs potential, which determines whether the electroweak phase transition was first-order (relevant for baryogenesis).
• Searches for BSM particles: stops, gluinos, electroweakinos, leptoquarks, $Z'$ bosons, and dark matter via missing transverse energy (MET).

LHCb is a forward spectrometer optimized for beauty and charm physics. Its silicon VELO pixel detector (upgraded in 2022) reconstructs B-meson decay vertices with ~20 μm precision. Current programme: measuring all angles and sides of the CKM unitarity triangle, searching for new sources of CP violation, and rare FCNC decays. In 2024, LHCb announced the first observation of time-reversal violation in charm mesons, a first in the charm sector.

ALICE studies the quark-gluon plasma (QGP) in Pb-Pb collisions. A landmark 2023 result: ALICE measured the QGP shear viscosity-to-entropy ratio $\eta/s$ and found it consistent with the holographic lower bound $\eta/s = \hbar/4\pi k_B$ predicted by AdS/CFT holography. The QGP is the most perfect fluid ever measured.

NA62 at the CERN SPS beam measures the extremely rare decay $K^+ \to \pi^+ \nu\bar\nu$. The SM branching ratio is $(8.4 \pm 1.0) \times 10^{-11}$ — one in a hundred billion. Any significant excess would be an unambiguous signal of new physics. NA62's latest measurement is consistent with the SM at about 1σ, but statistics are still limited.

Fermilab — Batavia, Illinois, USA

The flagship US national laboratory for particle physics. The Muon g-2 experiment, described in the previous section, uses a 14-meter diameter superconducting storage ring. Muons at 3.09 GeV complete ~10 million orbits in 700 μs, and the precession of their spin relative to their momentum reveals the anomalous magnetic moment. The 2023 result combined all Run 1–4 data. A final combination with Run 5 is expected in 2025.

NOvA is a long-baseline neutrino oscillation experiment, 810 km from Fermilab to Minnesota. Its current constraints on $\theta_{23}$ favor near-maximal mixing ($\theta_{23}$ close to $\pi/4$), and it has placed some constraints on $\delta_{CP}$, though degeneracies make interpretation difficult without the companion DUNE measurement.

DUNE (Deep Underground Neutrino Experiment) is the centerpiece of the US neutrino programme. A 1300-km baseline from Fermilab to the Sanford Underground Research Facility (SURF) in South Dakota provides the optimal lever arm for measuring $\delta_{CP}$ and the mass ordering. The near detector is at Fermilab; the far detector consists of four 17,000-tonne liquid argon time projection chambers (LArTPCs) underground at SURF. First beam is expected ~2028. The detector will also serve as a supernova neutrino detector, capable of detecting thousands of events from a galactic core-collapse supernova.

PIP-II (Proton Improvement Plan II) is a new 800 MeV superconducting linear accelerator at Fermilab, currently under construction. It will deliver the highest-power proton beam in the world to produce the DUNE neutrino flux. Several of PIP-II's cryomodules are being built at partner institutions in the UK and India in the first major international in-kind contribution to a US accelerator.

Mu2e searches for muon-to-electron conversion in the field of an aluminum nucleus. If a single conversion is observed in ~$10^{17}$ stopped muons, it is unambiguous new physics. Mu2e is under construction with first data around 2026–2027.

KEK and J-PARC — Japan

Belle II at SuperKEKB is an asymmetric $e^+e^-$ collider running at the $\Upsilon(4S)$ resonance, which decays almost exclusively to $B\bar{B}$ pairs. This "B factory" environment allows measurements of time-dependent CP asymmetries with high purity. Belle II's dataset as of early 2026 is ~400 fb⁻¹; the target is 50 ab⁻¹ by 2035, ~50× the full Belle dataset. The experiment is particularly powerful for searching for light dark matter mediators and dark photons in the GeV mass range, complementary to the LHC.

T2K shoots a muon neutrino beam from J-PARC (Tokai) to Super-Kamiokande (295 km). The 2020 T2K result using $\nu_\mu \to \nu_e$ vs $\bar\nu_\mu \to \bar\nu_e$ comparison showed a 2.0σ preference for maximal CP violation ($\delta_{CP} \approx -\pi/2$) — the strongest hint to date of leptonic CP violation. T2K is being upgraded and will feed beam to Hyper-Kamiokande (260 kt water Cherenkov, operational ~2027), which will nail down $\delta_{CP}$ to within ~20° with a decade of data.

IHEP / BEPCII — Beijing, China

BEPCII (Beijing Electron-Positron Collider II) runs at center-of-mass energies of 2–4.6 GeV, covering the charmonium and charm threshold regions. The BESIII experiment is the world's leading facility for precision charm physics and has produced a series of results on exotic charmonium-like states.

The 2024 BESIII observation of the internal structure of the $X(3872)$ state revealed it has both a compact charmonium-like component and a hadronic molecule component near the $D^0\bar{D}^{*0}$ threshold. This dual nature has resolved part of a decade-long debate.

China has approved in principle the CEPC (Circular Electron-Positron Collider), a 100-km ring that would serve first as a Tera-Z factory (10¹² Z bosons) and then as a Higgs factory at 240 GeV producing ~800,000 Higgs bosons per year. This directly competes with CERN's FCC-ee proposal. Both laboratories are seeking domestic and international support for projects that would run in the 2040s.

GSI / FAIR — Darmstadt, Germany

The Facility for Antiproton and Ion Research (FAIR) is a major new accelerator complex adjacent to the existing GSI facility. FAIR came online in 2024–2025 after more than a decade of construction. Its four main experimental programmes:

• CBM (Compressed Baryonic Matter): Studies nuclear matter at densities several times higher than normal, relevant to neutron star interiors. Uses a fixed-target setup with heavy ion beams at up to 11 GeV/u (SIS100 synchrotron). Searching for the QCD critical point and onset of deconfinement.
• PANDA (antiProton ANnihilations at DArmstadt): Uses a stored antiproton beam for precise spectroscopy of charmonium states and searches for exotic hadrons in antiproton-proton annihilation.
• HADES: Measures dilepton (electron-positron pair) spectra in heavy-ion collisions to probe strangeness production and chiral symmetry restoration.
• NuSTAR: Nuclear structure and astrophysics with exotic radioactive beams relevant to the r-process in neutron star mergers.

Gran Sasso National Laboratory (LNGS) — Italy

The largest underground physics laboratory in the world, located beneath 1,400 meters of rock in the Gran Sasso mountains, providing ~3,800 meters-water-equivalent shielding against cosmic rays. Three active particle physics programmes of particular note:

XENONnT is the current flagship liquid xenon dark matter experiment, with a 5.9-tonne active liquid xenon TPC. Its 2022–2023 result set the world's most stringent spin-independent WIMP-nucleon cross section limit of $\sigma_{\text{SI}} < 2.4 \times 10^{-47}\,\text{cm}^2$ at 28 GeV WIMP mass (90% CL). This is now ~10⁻¹⁰ times smaller than a proton cross-section. The experiment continues to run, and no signal has been found.

LEGEND-200 searches for neutrinoless double beta decay (0νββ) using 200 kg of germanium-76 detectors. If the Majorana neutrino mass is above ~50 meV, LEGEND-200 should observe a signal. The planned LEGEND-1000 upgrade (1,000 kg) would reach the inverted hierarchy parameter space definitively.

DarkSide-20k, a 20-tonne liquid argon TPC, is under construction and will provide a complementary dark matter search to xenon-based experiments. Argon has different sensitivity characteristics and a natural radioactive background from ³⁹Ar that must be reduced using underground-sourced argon depleted in cosmogenic isotopes.

SNOLAB (Canada) and SURF (USA)

SNOLAB in Sudbury, Ontario (2 km underground, 6 km water-equivalent shielding) houses several key experiments. SNO+ is the successor to the SNO experiment that confirmed neutrino flavor transformation. Currently in a phase loading tellurium-130 into its liquid scintillator for a 0νββ search, SNO+ aims to complement LEGEND and KamLAND-Zen. The DEAP-3600 argon dark matter detector completed its run; its data analysis established competitive limits on WIMP-argon scattering.

SURF (Sanford Underground Research Facility, 1.5 km deep in the former Homestake mine) is home to LUX-ZEPLIN (LZ), currently the world's most sensitive dark matter detector with 7 tonnes of active liquid xenon. LZ's 2023 first science run results set the most stringent WIMP limits at WIMP masses above ~9 GeV, with $\sigma_{\text{SI}} < 6.0 \times 10^{-48}\,\text{cm}^2$ at 40 GeV. SURF also hosts the first DUNE far detector module, currently under excavation, and the MAJORANA DEMONSTRATOR (enriched Ge-76 0νββ detector, completed and being incorporated into LEGEND).

IceCube — South Pole, Antarctica

IceCube is a cubic kilometer of Antarctic ice instrumented with 5,160 digital optical modules (DOMs) drilled into boreholes at 1.45–2.45 km depth, where the ice is exceptionally clear. High-energy neutrinos (TeV–PeV) interact in or near the detector and produce Cherenkov light from charged secondaries — tracks from muons (pointing back to the source), or cascades from electron and tau neutrinos.

Pierre Auger Observatory (Argentina) and Telescope Array (Utah, USA)

These two observatories detect ultra-high-energy cosmic rays (UHECRs) by observing the extensive air showers they produce in the atmosphere. The Auger Observatory covers 3,000 km² of Argentine pampas with 1,660 water Cherenkov detectors and 27 fluorescence telescopes. It can measure cosmic ray energies up to $\sim 10^{20}\,\text{eV}$ — 40 million times the LHC's maximum.

In 2023, Auger published a result showing anisotropy in cosmic ray arrival directions at energies above 40 EeV that correlates with the positions of starburst galaxies (particularly Centaurus A and the Centaurus A region). This supports the hypothesis that at least some of the highest-energy cosmic rays come from starburst-driven outflows, though the deflection by intergalactic magnetic fields makes source identification probabilistic. The Telescope Array (TA) in Utah has reported a "hotspot" in the northern sky, now being investigated with the expanded TA×4.