The Discovery · Elementary Particle Physics

Nothing about this discovery was a surprise except the mass. The signal’s shape, the channels worth watching and the quantity of data required were all settled before the machine turned on.

🎯 Why this matters

That changes what a discovery is. This one was scheduled rather than stumbled into, and the interesting question moved immediately to whether the object found has exactly the properties predicted for it.

Everything is now in place: a mechanism that predicts a scalar (§9.12), a mass range nobody could reach (§9.13), and a machine built to reach it (§9.14). This section is 4 July 2012.

Making one: gluons, through a quark that is not there

At a $pp$ collider there are few antiquarks, so the $q\bar q$ mechanisms that dominated at the Tevatron are suppressed. What is abundant instead is gluons, and they fuse:

Fig. 9.51 — gluon–gluon fusion, 87 % of Higgs production at the LHC

Click a vertex or an internal line.

Bettini Fig. 9.51. A production mechanism that runs entirely through a virtual particle — and it is the dominant one. Without a heavy top there would be no gluon fusion and the Higgs would have been far harder to make.

💡 What this really says — the two loop-mediated processes are the two that mattered

Notice what the discovery actually rested on.

Production was dominated by gluon–gluon fusion — a loop process, possible only because the top Yukawa is ≈ 1. Detection was dominated by $H\to\gamma\gamma$ — also a loop process, through $W$ and top loops (§9.12), with a branching ratio of 0.2 %.

So the particle that couples to mass was found by making it from massless gluons and watching it decay to massless photons, and both steps work only because virtual heavy particles mediate them.

This is worth pausing on because it inverts the usual intuition about loops. A loop process is normally a small correction to a tree process. Here there is no tree process — the Higgs has no coupling to gluons or photons at any order — so the loop is not a correction, it is the interaction. And that makes both channels unusually sensitive to physics nobody has seen: any new heavy charged or coloured particle would join the loop and shift the rate.

The engineering instinct is right: when a path exists only through an intermediary, the intermediary’s properties are what you are measuring. Both of the LHC’s Higgs workhorses are, in effect, indirect probes of the heaviest things that exist.

Choosing the channel: mass range by mass range

Bettini pp. 411–412. The book walks the whole mass range because before July 2012 nobody knew which row applied.

mass range↕	channel↕	why, and what it costs↕
$M_H < 130$ GeV	$H\to\gamma\gamma$	the hardest region. $b\bar b$ has the largest branching ratio and an overwhelming QCD background. γγ has a branching ratio of only $2\times10^{-3}$ , but it can be reconstructed — so everything depends on the electromagnetic energy resolution of §9.14
$125 < M_H < 180$ GeV	$H\to W^+W^{-*}\to \ell\nu\ell\nu$	a sizeable branching ratio and a clean leptonic final state — but two neutrinos, so no mass peak, only a broad bump
$125 < M_H < 300$ GeV	$H\to Z Z^*\to 4\ell$	the golden channel. Tiny rate, but the four-lepton mass is fully reconstructed and the background is small. One or both $Z$ s off shell
$300 < M_H < 600$ GeV	$H\to ZZ$ , both real	fully available — but the production cross-section has become small, so every $Z$ decay mode must be used to gather rate

The two channels used for the discovery are the two that give a peak: $H\to\gamma\gamma$ and $H\to ZZ^*\to 4\ell$ . The book makes the right point about why both were needed — they are complementary in exactly the two respects that matter.

Bettini p. 413. Neither alone would have been convincing; each covers the other's weakness.

channel↕	BR at 125 GeV↕	$\sigma\times$ BR at 8 TeV↕	resolution↕	background↕
$H\to\gamma\gamma$	$2.3\times10^{-3}$	50 fb	1–2 GeV — excellent	large — irreducible QCD γγ, plus jets faking photons
$H\to ZZ^*\to4\ell$	$1.3\times10^{-4}$	2.8 fb	somewhat worse	small — the ZZ continuum, and little else

Erratum — the top decay channel “opens only at twice its mass, about 345 MeV”

Explaining why $H\to b\bar b$ has the largest branching ratio, the book notes that the $b$ has the largest mass “except top, a decay channel that opens only at twice its mass, about 345 MeV”.

GeV. $2m_t = 2\times172.69 = 345.4$ GeV, which is why the channel is closed for a 125 GeV Higgs — the point the sentence is making. A 345 MeV top would be lighter than a pion, and $H\to t\bar t$ would be wide open.

The number 345 is right; only the unit is wrong. Confirmed on the render of PDF p. 431.

the arithmetic of a discovery

sig7, sig8 = 17.5, 22.3            # pb
L7, L8 = 5.0, 23.0                 # fb^-1
print("Higgs production at the LHC, M_H = 125 GeV")
print(f"  total cross-section   {sig7} pb at 7 TeV,  {sig8} pb at 8 TeV")
print(f"  2011 delivered  ~{L7:.0f} fb^-1 at 7 TeV")
print(f"  2012 delivered  ~{L8:.0f} fb^-1 at 8 TeV")
n7, n8 = sig7*1e3*L7, sig8*1e3*L8
print(f"  -> Higgs bosons produced: {n7:.1e} in 2011, {n8:.1e} in 2012")
print(f"     about SIX HUNDRED THOUSAND Higgs bosons, in total.")

print("\nnow the two channels that give a peak:")
for nm, sb in (('H -> gamma gamma     ', 50.0), ('H -> ZZ* -> 4 leptons', 2.8)):
    print(f"  {nm} sigma x BR = {sb:4.1f} fb  ->  {sb*L8:4.0f} produced in 2012")
print("\n  and those are PRODUCED, not observed.  acceptance and efficiency")
print("  take another factor of two or so.")

print("\ncheck the branching ratios against the book's own cross-sections:")
print(f"  BR(gamma gamma) = 50.0 fb / {sig8*1e3:.0f} fb = {50.0/(sig8*1e3):.2e}    table 9.2: 2.27e-03")
print(f"  BR(ZZ* -> 4l)   =  2.8 fb / {sig8*1e3:.0f} fb = {2.8/(sig8*1e3):.2e}")
print("\n  the second is worth noting: Sec. 9.17 quotes this branching ratio as")
print("  0.18%, but BOTH Zs must decay to e or mu, so it is")
print(f"    BR(H->ZZ*) x BR(Z->ll)^2 = 0.0262 x 0.0673^2 = {0.0262*0.0673**2:.2e}")
print("  which agrees with 1.26e-04 from the cross-sections, not with 0.18%.")

tot4l = 2.2*L7 + 2.8*L8
print("\nwhat 600 000 Higgs bosons buy you, in the golden channel:")
print(f"  produced in 4l over the whole 2011+2012 run:  about {tot4l:.0f}")
print( "  after acceptance and efficiency:              about 10-15 events")
print("\n  a five-sigma discovery of the most sought particle in physics,")
print("  resting on roughly a dozen four-lepton events and a few hundred")
print("  di-photon events above a large background.")

prints

Higgs production at the LHC, M_H = 125 GeV
total cross-section   17.5 pb at 7 TeV,  22.3 pb at 8 TeV
2011 delivered  ~5 fb^-1 at 7 TeV
2012 delivered  ~23 fb^-1 at 8 TeV
-> Higgs bosons produced: 8.8e+04 in 2011, 5.1e+05 in 2012
   about SIX HUNDRED THOUSAND Higgs bosons, in total.

now the two channels that give a peak:
H -> gamma gamma      sigma x BR = 50.0 fb  ->  1150 produced in 2012
H -> ZZ* -> 4 leptons sigma x BR =  2.8 fb  ->    64 produced in 2012

and those are PRODUCED, not observed.  acceptance and efficiency
take another factor of two or so.

check the branching ratios against the book's own cross-sections:
BR(gamma gamma) = 50.0 fb / 22300 fb = 2.24e-03    table 9.2: 2.27e-03
BR(ZZ* -> 4l)   =  2.8 fb / 22300 fb = 1.26e-04

the second is worth noting: Sec. 9.17 quotes this branching ratio as
0.18%, but BOTH Zs must decay to e or mu, so it is
  BR(H->ZZ*) x BR(Z->ll)^2 = 0.0262 x 0.0673^2 = 1.19e-04
which agrees with 1.26e-04 from the cross-sections, not with 0.18%.

what 600 000 Higgs bosons buy you, in the golden channel:
produced in 4l over the whole 2011+2012 run:  about 75
after acceptance and efficiency:              about 10-15 events

a five-sigma discovery of the most sought particle in physics,
resting on roughly a dozen four-lepton events and a few hundred
di-photon events above a large background.

Watching it appear

The golden channel is close to a pure counting experiment — the background is small enough that $S/\sqrt B$ is a fair estimate of the significance. So the history can be replayed on one slider:

H → ZZ* → 4ℓ, replayed against integrated luminosity

4ℓ

integrated luminosity = 5.1 fb⁻¹

signal S

∝ L

background B

∝ L

S/B

2.322

does not move

S/√B

2.1σ

∝ √L

S and B both grow in proportion to the luminosity, so S/B never improves — but S/√B grows as √L. That is the whole economics of a rare-signal search: you cannot make the signal cleaner by running longer, only more significant, and the significance costs quadratically. Going from 3σ to 5σ needs 2.8 times the data.

Yields tuned to the real ones. At 5 fb⁻¹ — all of 2011 — the excess is about 2σ, which is exactly what both experiments reported: 'an excess of events above the expected background at the low end of the explored mass range', with a significance that 'was not enough to establish the existence of a new particle'. Drag to 28 fb⁻¹, the 2011 + 2012 total, and it crosses five.

⚙️ Engineer’s bridge — significance costs quadratically, and that is why 2011 was not enough

Drag the slider and watch which readouts move.

S and B both grow in proportion to $L$ . So $S/B$ — how clean the signal is — never improves at all. Running longer does not make a rare signal less buried; it makes it more certain.

$S/\sqrt B$ grows as $\sqrt L$ . Statistical significance is bought with the square root of the data, which means it costs quadratically: going from 3σ to 5σ needs $(5/3)^2 = 2.8$ times as much data. From 2σ — the 2011 result — to 5σ needs 6.3 times as much. The LHC delivered about 5 fb⁻¹ in 2011 and 23 in 2012, a factor of 5.6, and the discovery arrived just as that arithmetic predicts.

An engineer meets this as coherent averaging: N samples improve SNR by $\sqrt N$ , never by $N$ , because the noise adds in quadrature while the signal adds linearly. It is why a lock-in amplifier’s time constant buys you decibels slowly, and why the last factor of two in any measurement is always the expensive one.

Two consequences worth carrying:

you cannot rescue a bad $S/B$ with time. If the signal is a thousandth of the background, no amount of running changes that — which is exactly why the $b\bar b$ channel was hopeless at a hadron collider no matter how long anyone ran.
and the 5σ convention is expensive on purpose. The extra factor of 2.8 over 3σ is the price of a threshold set high enough that the field’s many simultaneous searches do not produce a false discovery.

Where it breaks: significance grows as √N only while the uncertainty is statistical. Once a systematic floor is reached — the background shape, the energy scale, the luminosity — more data buys nothing, and the curve flattens rather than continuing. That is the usual fate of a mature measurement, and it is why $M_W$ at LEP and the muon anomaly at Fermilab are both quoted with systematics comparable to or larger than their statistical errors. Quadratic cost is the optimistic regime; the pessimistic one is that the cost becomes infinite.

🔬 Experiment card — ATLAS and CMS, CERN LHC, 4 July 2012

Apparatus

Two independently designed general-purpose detectors on the LHC’s 7 and 8 TeV proton–proton collisions (§9.14). Both are onion-shell: silicon pixel and strip trackers, an electromagnetic calorimeter — liquid-argon accordion in ATLAS, lead-tungstate crystals in CMS — a hadron calorimeter, and muon chambers. ATLAS uses a 2 T solenoid plus a huge air-core toroid; CMS a single compact 3.8 T solenoid. Almost no technology is shared.

What is measured

Two fully reconstructable invariant-mass distributions:

m(\gamma\gamma)

, where the resolution is 1–2 GeV and the background large; and

m(4\ell)

from

H\to ZZ^*

, where the background is small and the resolution somewhat worse. A third channel,

H\to WW^*\to\ell\nu\ell\nu

, gives a broad bump rather than a peak because of the two neutrinos, and contributes to the combination.

The result

A narrow excess at 125–127 GeV in both channels and both experiments, from 2011’s 5 fb⁻¹ at 7 TeV plus 2012’s 23 fb⁻¹ at 8 TeV:

$\text{ATLAS: } 5.9\sigma, \qquad \text{CMS: } 5.0\sigma$

The four-lepton channel contributed roughly a dozen events; the di-photon channel a few hundred over a large smooth background.

What it proved

That a neutral boson of mass 125 GeV exists, and that its spin is not 1 (it decays to two photons — §3.5’s Landau–Yang argument). Both collaborations deliberately stopped there, announcing “a new boson compatible with the Higgs” rather than the Higgs itself, because being the Higgs requires

J^P = 0^+

and couplings proportional to mass, neither of which a peak establishes.

Two independent detectors sharing almost no technology is why a common systematic could be excluded. Englert and Higgs received the Nobel Prize the following year.

4 July 2012

Both collaborations announced a new particle in the range 125–127 GeV, at 5.9σ (ATLAS) and 5.0σ (CMS). What could be said immediately, from the observation alone:

Bettini pp. 415–416. Note how much comes from the decay modes alone, before any coupling is measured.

observation↕	conclusion↕
it decays into two pairs of vector bosons with zero net charge	it is a neutral boson
it decays into two photons	its spin is not 1 — a spin-1 particle cannot decay to two photons. This is the Landau–Yang argument, and the site has already made it once, for the π⁰ in §3.5
the signal strengths in the different channels	consistent with the Standard Model Higgs, within uncertainties
the $ZZ^$ decay is not suppressed*	the matrix element cannot carry a high power of the small CM momentum, which disfavours most $J = 2$ assignments — the argument §9.18 completes

⚠️ “A new boson compatible with the Higgs” — the caution was the right call

Both experiments deliberately did not claim to have found the Higgs boson. They announced a new boson compatible with it, and said more data were needed.

That was not excessive modesty. Discovering a 125 GeV neutral boson and discovering the Higgs are different claims, and the second requires two things the first does not:

that it is a scalar — $J^P = 0^+$ , not $0^-$ and not $2^+$ . Settled by the end of Run 1, and the subject of §9.18;
that its couplings are proportional to mass — linearly for fermions, quadratically for bosons (§9.12). That is the specific fingerprint of the BEH mechanism, and any number of other scalars would produce a peak at 125 GeV without it. §9.19 measures it.

The distinction is worth keeping because it is the difference between finding a particle and confirming a mechanism. The peak was the easy part.

🔑 If you remember only three things

Both the making and the seeing go through loops. Neither the dominant production nor the cleanest signature exists at tree level, so the particle was found by processes that are corrections.
Two detectors were designed independently so that a shared mistake would be unlikely. Agreement between them is evidence of a different kind from more data in either one.
The channel had to be chosen without knowing the mass. Different ranges favour different signatures, so the analysis ran in parallel across all of them until one spoke.

Where this goes next

§9.16 takes Run 2’s 150 fb⁻¹ — five times the discovery dataset, and about 8 million Higgs bosons — and separates the production modes and decay channels from each other, which is what makes the coupling measurements possible.

§9.17 then measures the mass, and the width — 4 MeV, against an experimental resolution of 1–2 GeV, by a trick worth waiting for.

✅ Check yourself — the discovery

0/6 answered · 0 correct

1.Gluon fusion is 87 % of Higgs production and H → γγ was a discovery channel. What do those two facts have in common?
2.Why were BOTH γγ and ZZ*→4ℓ needed, rather than whichever was better?
3.Drag the luminosity slider on the 4ℓ histogram. S/B does not improve, but S/√B does. What follows?
4.Observing the new particle decay to two photons immediately ruled out one spin assignment. Which, and why?
5.Both experiments announced 'a new boson compatible with the Higgs' rather than 'the Higgs'. Was that excessive caution?
6.About 600 000 Higgs bosons were produced in 2011–2012. Roughly how many four-lepton events underpinned the discovery in that channel?