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8.6 — Accelerators, Detectors and What a Discovery Means
To study something you must produce it, and most of the Standard Model vanished from the universe within a nanosecond of the Big Bang. Recreating it means concentrating enough energy in one place to make particles that have not existed naturally in 13.8 billion years.
This chapter covers the machinery: how you accelerate a proton to 6.5 TeV, how you record what comes out of a collision that lasts 10^{-25} s, why the number that matters most is not energy but luminosity, and what "a five sigma discovery" actually means — including why the bar is set so high.
Why accelerators
Two reasons, and they are independent.
To make heavy particles. From E = mc^2 (Chapter 6.4), producing a particle of mass m needs at least mc^2 of energy available in the centre of mass. The Higgs at 125 GeV, the top quark at 173 GeV — these do not exist in nature on Earth and must be manufactured.
To see small things. From de Broglie (Chapter 7.2), \lambda = h/p, and Chapter 5.4 established that you cannot resolve structure smaller than a wavelength.
Worked number. To probe 1 femtometre — the size of a proton:
p = \frac{h}{\lambda} = \frac{6.626\times10^{-34}}{10^{-15}} = 6.6\times10^{-19}\ \text{kg m/s}
pc = 2\times10^{-10}\ \text{J} = 1.2\ \text{GeV}
To probe 10^{-18} m, a thousand times smaller, needs a thousand times more: 1.2 TeV.
This is why accelerators get bigger. Each factor of ten in resolution costs a factor of ten in energy, and energy costs size.
How acceleration works
The principle is one line. A charge q crossing a potential difference V gains energy qV (Chapter 4.3). Do it once and you have 1 MeV; do it ten thousand times and you have 10 GeV.
Van de Graaff generators reach about 25 MV in one gap and stop there, because air breaks down (Chapter 4.1) and even in pressurised gas the limit is a few tens of megavolts.
Linear accelerators (linacs) use a series of gaps with a radio-frequency voltage, timed so the particle always arrives when the field is pushing. SLAC's linac is 3.2 km long and reaches 50 GeV.
Synchrotrons bend the beam into a circle so the same accelerating cavities are used thousands of times per second.
Chapter 4.5 derived the bending:
r = \frac{p}{qB} \quad\Longrightarrow\quad p[\text{GeV/c}] = 0.3\,B[\text{T}]\,r[\text{m}]
This one formula decides the size of every accelerator ever built.
Worked example: the LHC. Its dipole magnets reach 8.33 T and the ring's bending radius is 2804 m:
p = 0.3\times8.33\times2804 = 7006\ \text{GeV} = 7\ \text{TeV}
The LHC's design energy is exactly this number, and it is set by two things and nothing else: the magnetic field the superconductors can hold, and the circumference of the tunnel.
The tunnel was already there. It was dug for LEP, the Large Electron–Positron collider, between 1985 and 1988 — 27 km, 100 m underground, crossing the French–Swiss border. Reusing it saved several billion euros and fixed the LHC's energy.
The magnets are the real limit. 1232 dipoles, each 15 m long, wound with niobium–titanium and cooled to 1.9 K with superfluid helium — colder than deep space, and the largest cryogenic system in the world. At that temperature the cable carries 11,850 A with zero resistance (Chapter 4.4).
Raising the field further requires niobium–tin, which reaches about 11 T and is brittle and much harder to work with. A future 100 km collider at 16 T would reach 100 TeV, and that is the current design study.
Why protons and not electrons
Synchrotron radiation. An accelerating charge radiates (Chapter 4.7), and a particle going in a circle is accelerating. The energy lost per turn:
\Delta E = \frac{4\pi}{3}\frac{q^2\beta^3\gamma^4}{4\pi\varepsilon_0 r} \propto \frac{E^4}{m^4r}
The m^4 is decisive. A proton is 1836 times heavier than an electron, so m^4 is 1.1\times10^{13} — thirteen orders of magnitude less radiation for the same energy and radius.
LEP, running electrons at 104 GeV in the same tunnel, lost 3 GeV per turn and needed enormous radio-frequency power just to stand still. That is why LEP stopped at about 100 GeV per beam and the LHC reaches 6.5 TeV in the identical ring.
The trade-off: a proton is composite, so its 6.5 TeV is shared among quarks and gluons, and a typical parton carries only a fraction. Electron collisions are clean; proton collisions are messy but reach far higher energy. This is why a future electron–positron "Higgs factory" is proposed to study precisely what the LHC discovered.
Colliders versus fixed targets
Chapter 6.P Problem 5 did this arithmetic. In a fixed-target experiment the available energy grows only as \sqrt{E}, because most of the beam energy goes into the centre-of-mass motion of the debris.
\sqrt{s} \approx \sqrt{2E\,m_pc^2}
To match the LHC's 13 TeV with a fixed target would need a beam of about 90,000 TeV.
In a collider with equal and opposite beams, all the energy is available:
\sqrt{s} = 2E
The cost is that hitting two thin beams together is enormously harder than hitting a block of metal.
Luminosity
Energy determines what can be made. Luminosity determines how often.
\boxed{R = \mathcal{L}\times\sigma}
Rate equals luminosity times cross-section. The cross-section \sigma is a property of the physics, measured in barns (10^{-28} m²) and its subdivisions. Luminosity is a property of the machine, in cm⁻²s⁻¹, and it is the number accelerator physicists actually fight for.
\mathcal{L} = \frac{N^2 n_b f}{4\pi\sigma_x\sigma_y}
with N protons per bunch, n_b bunches, f the revolution frequency, and \sigma_{x,y} the beam size at the collision point.
LHC numbers:
| Quantity | Value |
|---|---|
| Protons per bunch | 1.15\times10^{11} |
| Bunches per beam | 2808 |
| Revolution frequency | 11,245 Hz |
| Beam size at collision | 16 μm |
| Bunch crossing interval | 25 ns |
| Peak luminosity | 2\times10^{34} cm⁻²s⁻¹ |
The beams are squeezed to 16 micrometres — a fifth of a human hair — at the interaction point, having travelled 27 km. They cross 40 million times a second, producing about a billion proton–proton interactions per second.
Worked example: how many Higgs bosons?
\sigma_H \approx 50\ \text{pb} = 50\times10^{-36}\ \text{cm}^2
R = (2\times10^{34})(5\times10^{-35}) = 1\ \text{per second}
About one Higgs per second, and roughly 10^{7} per year of running.
But only 0.23 % decay to two photons, the cleanest channel, giving 23,000. And detector acceptance and selection cuts remove most of those, leaving a few hundred usable events — sitting on a background of hundreds of thousands of ordinary two-photon events.
This is why the discovery took two years of running. The Higgs was produced from the first day; extracting it from the background required accumulating enough statistics.
Integrated luminosity is the total collected, in inverse femtobarns. The LHC delivered about 30 fb⁻¹ in Run 1 and 190 fb⁻¹ in Run 2. The High-Luminosity LHC aims for 3000 fb⁻¹ by the 2040s, a tenfold increase, which is what a self-coupling measurement (Chapter 8.4) needs.
Detectors
A detector is a set of nested layers, each measuring something different. Nothing measures a particle directly; everything is inferred from what it leaves behind.
Layer 1: the tracker. Silicon pixels and strips, in a magnetic field. Charged particles ionise as they pass, and the ionisation is read out. From the curvature comes momentum, via p = qBr.
CMS's tracker has 76 million pixels with a resolution of about 10 μm, and it can locate the point where a particle decayed to within 50 μm. That precision is how bottom quarks are identified — a B hadron lives about 1.5 ps, travelling a few millimetres before decaying, so its decay vertex is measurably displaced from the collision point.
Layer 2: the electromagnetic calorimeter. Electrons and photons are stopped, showering into a cascade of pairs and photons. The total light or charge collected is proportional to the energy.
CMS uses 75,848 lead tungstate crystals, a material denser than steel and optically transparent, grown specially for the purpose over ten years.
Layer 3: the hadronic calorimeter. Absorbs protons, neutrons, pions and the jets from quarks and gluons (Chapter 8.3). Alternating layers of brass and scintillator.
Layer 4: the muon system. Muons pass through everything else — they are heavy enough not to shower and do not feel the strong force — so anything reaching the outermost layer is a muon. This is the cleanest identification in the whole detector, and it is why the four-muon Higgs channel is so valuable despite being rare.
Neutrinos are never detected. They are inferred from missing transverse momentum: momentum perpendicular to the beam must sum to zero, so any imbalance implies something invisible left. The same signature would identify dark matter production, which is one of the main searches at the LHC.
The data problem
40 million bunch crossings per second, each producing about 25 interactions and roughly a megabyte of raw data.
40\times10^{6}\times1\ \text{MB} = 40\ \text{TB/s} = 1\ \text{zettabyte per year}
Impossible to record. So the data is filtered in real time by a trigger.
Level 1 is hardware, built from custom electronics and field-programmable gate arrays, deciding within 2.5 microseconds whether an event looks interesting — high-energy leptons, large missing momentum, energetic jets. It cuts 40 MHz to about 100 kHz.
The high-level trigger is a farm of tens of thousands of processor cores running partial reconstruction, cutting 100 kHz to about 1 kHz.
About one event in 40,000 is kept. The rest are gone forever.
This is a genuine risk and everyone knows it. If new physics produces a signature nobody thought to trigger on, it will be discarded in real time and never seen. Trigger menus are designed with this in mind, and "trigger-level analysis" — recording reduced information about many more events — has been introduced partly to cover the gap.
The surviving data still amounts to tens of petabytes a year, distributed to about 170 computing centres worldwide through the Worldwide LHC Computing Grid.
What a discovery means
Particle physics uses a statistical convention that is stricter than most sciences, and the reason is worth understanding.
The p-value is the probability that background alone would produce a fluctuation at least as large as what was seen.
Sigma counts standard deviations of a Gaussian:
| Sigma | p-value (one-sided) | Odds |
|---|---|---|
| 1σ | 0.159 | 1 in 6 |
| 2σ | 0.023 | 1 in 44 |
| 3σ | 0.00135 | 1 in 740 |
| 4σ | 3.2\times10^{-5} | 1 in 31,600 |
| 5σ | 2.9\times10^{-7} | 1 in 3.5 million |
Convention: 3σ is "evidence", 5σ is "discovery".
Why five and not three
Because of the look-elsewhere effect. If you search for a bump anywhere in a spectrum with, say, a thousand independent places it could sit, then a 3σ fluctuation somewhere is not surprising — you expect about one and a half of them by chance.
The correction:
p_{\text{global}} \approx N_{\text{trials}}\times p_{\text{local}}
A 3σ local significance with 1000 trials becomes about 1.35 globally — completely unremarkable.
And because of history. Physics has a long record of 3σ effects that evaporated:
The 750 GeV diphoton excess, December 2015. Both ATLAS and CMS saw a bump at 750 GeV, around 3σ each. Over 500 theory papers were written in six months. With more data in 2016 it vanished entirely. It was a statistical fluctuation, and it is now the standard cautionary tale.
Faster-than-light neutrinos, OPERA, 2011. A 6σ measurement of neutrinos arriving 60 ns early over 730 km. The cause was a loose fibre optic connector, plus a clock calibration error. The collaboration published it as a request for scrutiny rather than a claim, which was the right thing to do, and the two leaders resigned anyway.
Cold fusion, 1989. Announced by press conference before publication. Not reproducible.
BICEP2 primordial gravitational waves, 2014. Announced as a 7σ detection of inflation's signature. It was galactic dust, as Planck data showed within a year.
The 5σ standard exists because of these. It is not that physicists think a 1-in-3.5-million coincidence is impossible; it is that with enough searches, and with unknown systematic errors that are always larger than the statistical ones, a lower bar produces a steady stream of retractions.
Systematic errors are the real problem. Statistical error falls as 1/\sqrt{N} and can always be beaten with more data. Systematic error does not fall at all — it comes from imperfect calibration, imperfect background modelling, and imperfect simulation, and estimating it honestly is the hardest part of any analysis.
Blind analysis is the standard defence: the selection criteria and background model are fixed before anyone looks at the signal region. This prevents the unconscious tuning of cuts until a bump appears, which is a real and documented failure mode.
Counting the neutrinos
Here is a beautiful example of extracting a fundamental fact from a precision measurement.
The Z boson decays into anything light enough, including neutrino pairs. Neutrinos are invisible, so those decays are never seen directly — but each additional neutrino species adds to the Z's total decay rate, which broadens its resonance (Chapter 7.5's energy–time relation).
LEP measured the Z lineshape by scanning the collision energy across the resonance and measuring the cross-section, using 17 million Z bosons.
The measured width:
\Gamma_Z = 2.4952 \pm 0.0023\ \text{GeV}
Subtract the known visible contributions — decays to charged leptons and to hadrons — and what remains is the invisible width. Dividing by the predicted width per neutrino species:
\boxed{N_\nu = 2.984 \pm 0.008}
Exactly three light neutrino species, to a precision of 0.3 %. A fourth would have to be heavier than 45 GeV, and would then not be a "light" neutrino at all.
Three families of matter, established by measuring the width of a spectral line.
Machines around the world
CERN, Geneva. The LHC and its four main experiments. About 17,000 people from over 100 countries.
Fermilab, Illinois. Formerly the Tevatron, which found the top quark in 1995. Now the world centre for neutrino physics, sending a beam to DUNE in South Dakota, and hosting the Muon g−2 experiment.
SLAC, California. The 3.2 km linac, which found the charm quark and the tau lepton. Now largely an X-ray free-electron laser facility.
KEK and J-PARC, Japan. SuperKEKB holds the world luminosity record and studies B mesons and CP violation with the Belle II detector; J-PARC sends the neutrino beam to Super-Kamiokande.
DESY, Hamburg. Formerly HERA, which scattered electrons off protons and mapped the proton's internal structure in detail.
IHEP, Beijing. The Daya Bay reactor experiment measured the last neutrino mixing angle in 2012; a large circular collider is proposed.
Brookhaven, New York. RHIC collides heavy ions to make quark–gluon plasma; the Electron-Ion Collider is under construction.
GSI/FAIR, Germany. Heavy ions and the synthesis of superheavy elements — elements 107 through 112 were made there.
And non-accelerator experiments worldwide: SNOLAB in Canada, Gran Sasso in Italy, Kamioka in Japan, and the China Jinping Underground Laboratory at 2400 m depth, all doing dark matter searches, neutrinoless double beta decay, and neutrino astronomy in places quiet enough to hear them.
Where this shows up in your life
The World Wide Web was invented at CERN in 1989 to share particle physics data.
Medical accelerators. Roughly 30,000 particle accelerators are in operation worldwide, and the overwhelming majority are in hospitals doing radiotherapy or making isotopes. Fewer than one percent are for research.
PET and MRI descend from detector and superconducting magnet technology.
Proton therapy uses accelerators to deposit dose at a controlled depth (the Bragg peak), sparing tissue beyond the tumour.
Synchrotron light sources. The synchrotron radiation that is a nuisance in a collider is the point of about 50 dedicated machines worldwide, producing intense X-rays used for protein structures, battery research, materials science and art conservation. Most protein structures in the Protein Data Bank were solved at a synchrotron.
Touchscreens, semiconductor manufacturing and ion implantation all use accelerator technology.
And grid computing, developed to distribute LHC data, fed directly into modern cloud computing.
What the next chapter fixes
The Standard Model works, and Chapter 8.2 listed what it does not contain: gravity, dark matter, dark energy, the matter–antimatter asymmetry, neutrino masses, and twenty-six unexplained numbers. Chapter 8.7 takes those gaps seriously — what the specific problems are, what supersymmetry was supposed to fix and why its absence matters, what string theory actually says with its mathematics sketched honestly, what loop quantum gravity offers instead, and a clear statement of what is established, what is speculative, and what is currently untestable.