The Higgs boson is an elementary particle
in the Standard Model of particle physics,
produced by the quantum excitation of the
Higgs field, one of the fields in particle
physics theory. It is named after physicist
Peter Higgs, who in 1964, along with five
other scientists, proposed the mechanism,
which suggested the existence of such a particle.
Its existence was confirmed by the ATLAS and
CMS collaborations based on collisions in
the LHC at CERN.
On December 10, 2013, two of the physicists,
Peter Higgs and François Englert, were awarded
the Nobel Prize in Physics for their theoretical
predictions. Although Higgs's name has come
to be associated with this theory (the Higgs
mechanism), several researchers between about
1960 and 1972 independently developed different
parts of it.
In mainstream media the Higgs boson has often
been called the "God particle", from a 1993
book on the topic, although the nickname is
strongly disliked by many physicists, including
Higgs himself, who regard it as sensationalistic.
== Introduction ==
=== 
The Standard Model ===
Physicists explain the properties of and forces
between elementary particles in terms of the
Standard Model – a widely accepted framework
for understanding almost everything in the
known universe, other than gravity. (A separate
theory, General Relativity, is used for gravity.)
In this model, the fundamental forces in nature
arise from properties of our universe called
gauge invariance and symmetries. The forces
are transmitted by particles known as gauge
bosons.In the Standard Model, the Higgs particle
is a boson with spin zero, no electric charge
and no colour charge. It is also very unstable,
decaying into other particles almost immediately.
The Higgs field is a scalar field, with two
neutral and two electrically charged components
that form a complex doublet of the weak isospin
SU(2) symmetry. The Higgs field has a "Mexican
hat-shaped" potential. In its ground state,
this causes the field to have a nonzero value
everywhere (including otherwise empty space),
and as a result, below a very high energy
it breaks the weak isospin symmetry of the
electroweak interaction. (Technically the
non-zero expectation value converts the Lagrangian's
Yukawa coupling terms into mass terms.) When
this happens, three components of the Higgs
field are "absorbed" by the SU(2) and U(1)
gauge bosons (the "Higgs mechanism") to become
the longitudinal components of the now-massive
W and Z bosons of the weak force. The remaining
electrically neutral component either manifests
as a Higgs particle, or may couple separately
to other particles known as fermions (via
Yukawa couplings), causing these to acquire
mass as well.
=== The problem of gauge boson mass ===
Field theories had been used with great success
in understanding the electromagnetic field
and the strong force, but by around 1960 all
attempts to create a gauge invariant theory
for the weak force (and its combination with
fundamental force electromagnetism, the electroweak
interaction) had consistently failed, with
gauge theories thereby starting to fall into
disrepute as a result. The problem was that
the symmetry requirements in gauge theory
predicted that both electromagnetism's gauge
boson (the photon) and the weak force's gauge
bosons (W and Z) should have zero mass. Although
the photon is indeed massless, experiments
show that the weak force's bosons have mass.
This meant that either gauge invariance was
an incorrect approach, or something else – unknown
– was giving these particles their mass,
but all attempts to suggest a theory able
to solve this problem just seemed to create
new theoretical issues.
In the late 1950s, physicists had "no idea"
how to resolve these issues, which were significant
obstacles to developing a full-fledged theory
for particle physics.
==== Symmetry breaking ====
By the early 1960s, physicists had realised
that a given symmetry law might not always
be followed under certain conditions, at least
in some areas of physics. This is called symmetry
breaking and was recognised in the late 1950s
by Yoichiro Nambu. Symmetry breaking can lead
to surprising and unexpected results. In 1962
physicist Philip Anderson – an expert in
superconductivity – wrote a paper that considered
symmetry breaking in particle physics, and
suggested that perhaps symmetry breaking might
be the missing piece needed to solve the problems
of gauge invariance in particle physics. If
electroweak symmetry was somehow being broken,
it might explain why electromagnetism's boson
is massless, yet the weak force bosons have
mass, and solve the problems. Shortly afterwards,
in 1963, this was shown to be theoretically
possible, at least for some limited cases.
=== Higgs mechanism ===
Following the 1962 and 1963 papers, three
groups of researchers independently published
the 1964 PRL symmetry breaking papers with
similar conclusions: that the conditions for
electroweak symmetry would be "broken" if
an unusual type of field existed throughout
the universe, and indeed, some fundamental
particles would acquire mass. The field required
for this to happen (which was purely hypothetical
at the time) became known as the Higgs field
(after Peter Higgs, one of the researchers)
and the mechanism by which it led to symmetry
breaking, known as the Higgs mechanism. A
key feature of the necessary field is that
it would take less energy for the field to
have a non-zero value than a zero value, unlike
all other known fields, therefore, the Higgs
field has a non-zero value (or vacuum expectation)
everywhere. It was the first proposal capable
of showing how the weak force gauge bosons
could have mass despite their governing symmetry,
within a gauge invariant theory.
Although these ideas did not gain much initial
support or attention, by 1972 they had been
developed into a comprehensive theory and
proved capable of giving "sensible" results
that accurately described particles known
at the time, and which, with exceptional accuracy,
predicted several other particles discovered
during the following years. During the 1970s
these theories rapidly became the Standard
Model of particle physics. There was not yet
any direct evidence that the Higgs field existed,
but even without proof of the field, the accuracy
of its predictions led scientists to believe
the theory might be true. By the 1980s the
question of whether or not the Higgs field
existed, and therefore whether or not the
entire Standard Model was correct, had come
to be regarded as one of the most important
unanswered questions in particle physics.
==== Higgs field ====
According to the Standard Model, a field of
the necessary kind (the Higgs field) exists
throughout space and breaks certain symmetry
laws of the electroweak interaction. Via the
Higgs mechanism, this field causes the gauge
bosons of the weak force to be massive at
all temperatures below an extreme high value.
When the weak force bosons acquire mass, this
affects their range, which becomes very small.
Furthermore, it was later realised that the
same field would also explain, in a different
way, why other fundamental constituents of
matter (including electrons and quarks) have
mass.
For many decades, scientists had no way to
determine whether or not the Higgs field existed,
because the technology needed for its detection
did not exist at that time. If the Higgs field
did exist, then it would be unlike any other
known fundamental field, but it also was possible
that these key ideas, or even the entire Standard
Model, were somehow incorrect. Only discovering
that the Higgs boson and therefore the Higgs
field existed solved the problem.
Unlike other known fields such as the electromagnetic
field, the Higgs field is scalar and has a
non-zero constant value in vacuum. The existence
of the Higgs field became the last unverified
part of the Standard Model of particle physics,
and for several decades, was considered "the
central problem in particle physics".The presence
of the field, now confirmed by experimental
investigation, explains why some fundamental
particles have mass, despite the symmetries
controlling their interactions implying that
they should be massless. It also resolves
several other long-standing puzzles, such
as the reason for the extremely short range
of the weak force.
Although the Higgs field is non-zero everywhere
and its effects are ubiquitous, proving its
existence was far from easy. In principle,
it can be proved to exist by detecting its
excitations, which manifest as Higgs particles
(the Higgs boson), but these are extremely
difficult to produce and detect. The importance
of this fundamental question led to a 40-year
search, and the construction of one of the
world's most expensive and complex experimental
facilities to date, CERN's Large Hadron Collider,
in an attempt to create Higgs bosons and other
particles for observation and study. On 4
July 2012, the discovery of a new particle
with a mass between 125 and 127 GeV/c2 was
announced; physicists suspected that it was
the Higgs boson. Since then, the particle
has been shown to behave, interact, and decay
in many of the ways predicted for Higgs particles
by the Standard Model, as well as having even
parity and zero spin, two fundamental attributes
of a Higgs boson. This also means it is the
first elementary scalar particle discovered
in nature. As of 2018, in-depth research shows
the particle continuing to behave in line
with predictions for the Standard Model Higgs
boson. More studies are needed to verify with
higher precision that the discovered particle
has all of the properties predicted, or whether,
as described by some theories, multiple Higgs
bosons exist.
==== Higgs boson ====
The hypothesised Higgs mechanism made several
accurate predictions, however to confirm its
existence there was an extensive search for
a matching particle associated with it — the
"Higgs boson". Detecting Higgs bosons was
difficult due to the energy required to produce
them and their very rare production even if
the energy is sufficient. It was therefore
several decades before the first evidence
of the Higgs boson was found. Particle colliders,
detectors, and computers capable of looking
for Higgs bosons took more than 30 years (c.
1980–2010) to develop.
By March 2013, the existence of the Higgs
boson was confirmed, and therefore, the concept
of some type of Higgs field throughout space
is strongly supported. The nature and properties
of this field are now being investigated further,
using more data collected at the LHC.
==== Interpretation ====
Various analogies have been used to describe
the Higgs field and boson, including analogies
with well-known symmetry-breaking effects
such as the rainbow and prism, electric fields,
ripples, and resistance of macro objects moving
through media (such as people moving through
crowds or some objects moving through syrup
or molasses). However, analogies based on
simple resistance to motion are inaccurate,
as the Higgs field does not work by resisting
motion.
== Significance ==
Evidence of the Higgs field and its properties
has been extremely significant for many reasons.
The importance of the Higgs boson is largely
that it is able to be examined using existing
knowledge and experimental technology, as
a way to confirm and study the entire Higgs
field theory. Conversely, proof that the Higgs
field and boson do not exist would have also
been significant.
=== Particle physics ===
==== 
Validation of the Standard Model ====
The Higgs boson validates the Standard Model
through the mechanism of mass generation.
As more precise measurements of its properties
are made, more advanced extensions may be
suggested or excluded. As experimental means
to measure the field's behaviours and interactions
are developed, this fundamental field may
be better understood. If the Higgs field had
not been discovered, the Standard Model would
have needed to be modified or superseded.
Related to this, a belief generally exists
among physicists that there is likely to be
"new" physics beyond the Standard Model, and
the Standard Model will at some point be extended
or superseded. The Higgs discovery, as well
as the many measured collisions occurring
at the LHC, provide physicists a sensitive
tool to parse data for where the Standard
Model fails, and could provide considerable
evidence guiding researchers into future theoretical
developments.
==== Symmetry breaking of the electroweak
interaction ====
Below an extremely high temperature, electroweak
symmetry breaking causes the electroweak interaction
to manifest in part as the short-ranged weak
force, which is carried by massive gauge bosons.
This symmetry breaking is required for atoms
and other structures to form, as well as for
nuclear reactions in stars, such as our Sun.
The Higgs field is responsible for this symmetry
breaking.
==== Particle mass acquisition ====
The Higgs field is pivotal in generating the
masses of quarks and charged leptons (through
Yukawa coupling) and the W and Z gauge bosons
(through the Higgs mechanism).
It is worth noting that the Higgs field does
not "create" mass out of nothing (which would
violate the law of conservation of energy),
nor is the Higgs field responsible for the
mass of all particles. For example, approximately
99% of the mass of baryons (composite particles
such as the proton and neutron), is due instead
to quantum chromodynamics binding energy,
which is the sum of the kinetic energies of
quarks and the energies of the massless gluons
mediating the strong interaction inside the
baryons. In Higgs-based theories, the property
of "mass" is a manifestation of potential
energy transferred to fundamental particles
when they interact ("couple") with the Higgs
field, which had contained that mass in the
form of energy.
==== Scalar fields and extension of the Standard
Model ====
The Higgs field is the only scalar (spin 0)
field to be detected; all the other fields
in the Standard Model are spin ½ fermions
or spin 1 bosons. According to Rolf-Dieter
Heuer, director general of CERN when the Higgs
boson was discovered, this existence proof
of a scalar field is almost as important as
the Higgs's role in determining the mass of
other particles. It suggests that other hypothetical
scalar fields suggested by other theories,
from the inflaton to quintessence, could perhaps
exist as well.
=== Cosmology ===
==== 
Inflaton ====
There has been considerable scientific research
on possible links between the Higgs field
and the inflaton – a hypothetical field
suggested as the explanation for the expansion
of space during the first fraction of a second
of the universe (known as the "inflationary
epoch"). Some theories suggest that a fundamental
scalar field might be responsible for this
phenomenon; the Higgs field is such a field,
and its existence has led to papers analysing
whether it could also be the inflaton responsible
for this exponential expansion of the universe
during the Big Bang. Such theories are highly
tentative and face significant problems related
to unitarity, but may be viable if combined
with additional features such as large non-minimal
coupling, a Brans–Dicke scalar, or other
"new" physics, and they have received treatments
suggesting that Higgs inflation models are
still of interest theoretically.
==== Nature of the universe, and its possible
fates ====
In the Standard Model, there exists the possibility
that the underlying state of our universe
-known as the "vacuum" - is long-lived, but
not completely stable. In this scenario, the
universe as we know it could effectively be
destroyed by collapsing into a more stable
vacuum state. This was sometimes misreported
as the Higgs boson "ending" the universe.
If the masses of the Higgs boson and top quark
are known more precisely, and the Standard
Model provides an accurate description of
particle physics up to extreme energies of
the Planck scale, then it is possible to calculate
whether the vacuum is stable or merely long-lived.
A 125 – 127 GeV Higgs mass seems to be extremely
close to the boundary for stability, but a
definitive answer requires much more precise
measurements of the pole mass of the top quark.
New physics can change this picture.If measurements
of the Higgs boson suggest that our universe
lies within a false vacuum of this kind, then
it would imply – more than likely in many
billions of years – that the universe's
forces, particles, and structures could cease
to exist as we know them (and be replaced
by different ones), if a true vacuum happened
to nucleate. It also suggests that the Higgs
self-coupling λ and its βλ function could
be very close to zero at the Planck scale,
with "intriguing" implications, including
theories of gravity and Higgs-based inflation.
A future electron–positron collider would
be able to provide the precise measurements
of the top quark needed for such calculations.
==== Vacuum energy and the cosmological constant
====
More speculatively, the Higgs field has also
been proposed as the energy of the vacuum,
which at the extreme energies of the first
moments of the Big Bang caused the universe
to be a kind of featureless symmetry of undifferentiated,
extremely high energy. In this kind of speculation,
the single unified field of a Grand Unified
Theory is identified as (or modelled upon)
the Higgs field, and it is through successive
symmetry breakings of the Higgs field, or
some similar field, at phase transitions that
the presently known forces and fields of the
universe arise.The relationship (if any) between
the Higgs field and the presently observed
vacuum energy density of the universe has
also come under scientific study. As observed,
the present vacuum energy density is extremely
close to zero, but the energy density expected
from the Higgs field, supersymmetry, and other
current theories are typically many orders
of magnitude larger. It is unclear how these
should be reconciled. This cosmological constant
problem remains a further major unanswered
problem in physics.
=== Practical and technological impact ===
As yet, there are no known immediate technological
benefits of finding the Higgs particle. However,
a common pattern for fundamental discoveries
is for practical applications to follow later,
and once the discovery has been explored further,
perhaps becoming the basis for new technologies
of importance to society.The challenges in
particle physics have furthered major technological
progress of widespread importance. For example,
the World Wide Web began as a project to improve
CERN's communication system. CERN's requirement
to process massive amounts of data produced
by the Large Hadron Collider also led to contributions
to the fields of distributed and cloud computing.
== History ==
=== Theorization ===
Particle physicists study matter made from
fundamental particles whose interactions are
mediated by exchange particles – gauge bosons
– acting as force carriers. At the beginning
of the 1960s a number of these particles had
been discovered or proposed, along with theories
suggesting how they relate to each other,
some of which had already been reformulated
as field theories in which the objects of
study are not particles and forces, but quantum
fields and their symmetries. However, attempts
to produce quantum field models for two of
the four known fundamental forces – the
electromagnetic force and the weak nuclear
force – and then to unify these interactions,
were still unsuccessful.
One known problem was that gauge invariant
approaches, including non-abelian models such
as Yang–Mills theory (1954), which held
great promise for unified theories, also seemed
to predict known massive particles as massless.
Goldstone's theorem, relating to continuous
symmetries within some theories, also appeared
to rule out many obvious solutions, since
it appeared to show that zero-mass particles
also would have to exist that simply were
"not seen". According to Guralnik, physicists
had "no understanding" how these problems
could be overcome.Particle physicist and mathematician
Peter Woit summarised the state of research
at the time:
Yang and Mills work on non-abelian gauge theory
had one huge problem: in perturbation theory
it has massless particles which don’t correspond
to anything we see. One way of getting rid
of this problem is now fairly well understood,
the phenomenon of confinement realized in
QCD, where the strong interactions get rid
of the massless “gluon” states at long
distances. By the very early sixties, people
had begun to understand another source of
massless particles: spontaneous symmetry breaking
of a continuous symmetry. What Philip Anderson
realized and worked out in the summer of 1962
was that, when you have both gauge symmetry
and spontaneous symmetry breaking, the Nambu–Goldstone
massless mode can combine with the massless
gauge field modes to produce a physical massive
vector field. This is what happens in superconductivity,
a subject about which Anderson was (and is)
one of the leading experts. [text condensed]
The Higgs mechanism is a process by which
vector bosons can acquire rest mass without
explicitly breaking gauge invariance, as a
byproduct of spontaneous symmetry breaking.
Initially, the mathematical theory behind
spontaneous symmetry breaking was conceived
and published within particle physics by Yoichiro
Nambu in 1960, and the concept that such a
mechanism could offer a possible solution
for the "mass problem" was originally suggested
in 1962 by Philip Anderson (who had previously
written papers on broken symmetry and its
outcomes in superconductivity. Anderson concluded
in his 1963 paper on the Yang-Mills theory,
that "considering the superconducting analog...
[t]hese two types of bosons seem capable of
canceling each other out... leaving finite
mass bosons"), and in March 1964, Abraham
Klein and Benjamin Lee showed that Goldstone's
theorem could be avoided this way in at least
some non-relativistic cases, and speculated
it might be possible in truly relativistic
cases.These approaches were quickly developed
into a full relativistic model, independently
and almost simultaneously, by three groups
of physicists: by François Englert and Robert
Brout in August 1964; by Peter Higgs in October
1964; and by Gerald Guralnik, Carl Hagen,
and Tom Kibble (GHK) in November 1964. Higgs
also wrote a short, but important, response
published in September 1964 to an objection
by Gilbert, which showed that if calculating
within the radiation gauge, Goldstone's theorem
and Gilbert's objection would become inapplicable.
(Higgs later described Gilbert's objection
as prompting his own paper.) Properties of
the model were further considered by Guralnik
in 1965, by Higgs in 1966, by Kibble in 1967,
and further by GHK in 1967. The original three
1964 papers demonstrated that when a gauge
theory is combined with an additional field
that spontaneously breaks the symmetry, the
gauge bosons may consistently acquire a finite
mass. In 1967, Steven Weinberg and Abdus Salam
independently showed how a Higgs mechanism
could be used to break the electroweak symmetry
of Sheldon Glashow's unified model for the
weak and electromagnetic interactions, (itself
an extension of work by Schwinger), forming
what became the Standard Model of particle
physics. Weinberg was the first to observe
that this would also provide mass terms for
the fermions.At first, these seminal papers
on spontaneous breaking of gauge symmetries
were largely ignored, because it was widely
believed that the (non-Abelian gauge) theories
in question were a dead-end, and in particular
that they could not be renormalised. In 1971–72,
Martinus Veltman and Gerard 't Hooft proved
renormalisation of Yang–Mills was possible
in two papers covering massless, and then
massive, fields. Their contribution, and the
work of others on the renormalisation group
– including "substantial" theoretical work
by Russian physicists Ludvig Faddeev, Andrei
Slavnov, Efim Fradkin, and Igor Tyutin – was
eventually "enormously profound and influential",
but even with all key elements of the eventual
theory published there was still almost no
wider interest. For example, Coleman found
in a study that "essentially no-one paid any
attention" to Weinberg's paper prior to 1971
and discussed by David Politzer in his 2004
Nobel speech. – now the most cited in particle
physics – and even in 1970 according to
Politzer, Glashow's teaching of the weak interaction
contained no mention of Weinberg's, Salam's,
or Glashow's own work. In practice, Politzer
states, almost everyone learned of the theory
due to physicist Benjamin Lee, who combined
the work of Veltman and 't Hooft with insights
by others, and popularised the completed theory.
In this way, from 1971, interest and acceptance
"exploded" and the ideas were quickly absorbed
in the mainstream.The resulting electroweak
theory and Standard Model have accurately
predicted (among other things) weak neutral
currents, three bosons, the top and charm
quarks, and with great precision, the mass
and other properties of some of these. Many
of those involved eventually won Nobel Prizes
or other renowned awards. A 1974 paper and
comprehensive review in Reviews of Modern
Physics commented that "while no one doubted
the [mathematical] correctness of these arguments,
no one quite believed that nature was diabolically
clever enough to take advantage of them",
adding that the theory had so far produced
accurate answers that accorded with experiment,
but it was unknown whether the theory was
fundamentally correct. By 1986 and again in
the 1990s it became possible to write that
understanding and proving the Higgs sector
of the Standard Model was "the central problem
today in particle physics".
==== Summary and impact of the PRL papers
====
The three papers written in 1964 were each
recognised as milestone papers during Physical
Review Letters's 50th anniversary celebration.
Their six authors were also awarded the 2010
J. J. Sakurai Prize for Theoretical Particle
Physics for this work. (A controversy also
arose the same year, because in the event
of a Nobel Prize only up to three scientists
could be recognised, with six being credited
for the papers.) Two of the three PRL papers
(by Higgs and by GHK) contained equations
for the hypothetical field that eventually
would become known as the Higgs field and
its hypothetical quantum, the Higgs boson.
Higgs' subsequent 1966 paper showed the decay
mechanism of the boson; only a massive boson
can decay and the decays can prove the mechanism.In
the paper by Higgs the boson is massive, and
in a closing sentence Higgs writes that "an
essential feature" of the theory "is the prediction
of incomplete multiplets of scalar and vector
bosons". (Frank Close comments that 1960s
gauge theorists were focused on the problem
of massless vector bosons, and the implied
existence of a massive scalar boson was not
seen as important; only Higgs directly addressed
it.) In the paper by GHK the boson is massless
and decoupled from the massive states. In
reviews dated 2009 and 2011, Guralnik states
that in the GHK model the boson is massless
only in a lowest-order approximation, but
it is not subject to any constraint and acquires
mass at higher orders, and adds that the GHK
paper was the only one to show that there
are no massless Goldstone bosons in the model
and to give a complete analysis of the general
Higgs mechanism. All three reached similar
conclusions, despite their very different
approaches: Higgs' paper essentially used
classical techniques, Englert and Brout's
involved calculating vacuum polarisation in
perturbation theory around an assumed symmetry-breaking
vacuum state, and GHK used operator formalism
and conservation laws to explore in depth
the ways in which Goldstone's theorem may
be worked around. Some versions of the theory
predicted more than one kind of Higgs fields
and bosons, and alternative "Higgsless" models
were considered until the discovery of the
Higgs boson.
=== Experimental search ===
To produce Higgs bosons, two beams of particles
are accelerated to very high energies and
allowed to collide within a particle detector.
Occasionally, although rarely, a Higgs boson
will be created fleetingly as part of the
collision byproducts. Because the Higgs boson
decays very quickly, particle detectors cannot
detect it directly. Instead the detectors
register all the decay products (the decay
signature) and from the data the decay process
is reconstructed. If the observed decay products
match a possible decay process (known as a
decay channel) of a Higgs boson, this indicates
that a Higgs boson may have been created.
In practice, many processes may produce similar
decay signatures. Fortunately, the Standard
Model precisely predicts the likelihood of
each of these, and each known process, occurring.
So, if the detector detects more decay signatures
consistently matching a Higgs boson than would
otherwise be expected if Higgs bosons did
not exist, then this would be strong evidence
that the Higgs boson exists.
Because Higgs boson production in a particle
collision is likely to be very rare (1 in
10 billion at the LHC), and many other possible
collision events can have similar decay signatures,
the data of hundreds of trillions of collisions
needs to be analysed and must "show the same
picture" before a conclusion about the existence
of the Higgs boson can be reached. To conclude
that a new particle has been found, particle
physicists require that the statistical analysis
of two independent particle detectors each
indicate that there is lesser than a one-in-a-million
chance that the observed decay signatures
are due to just background random Standard
Model events—i.e., that the observed number
of events is more than 5 standard deviations
(sigma) different from that expected if there
was no new particle. More collision data allows
better confirmation of the physical properties
of any new particle observed, and allows physicists
to decide whether it is indeed a Higgs boson
as described by the Standard Model or some
other hypothetical new particle.
To find the Higgs boson, a powerful particle
accelerator was needed, because Higgs bosons
might not be seen in lower-energy experiments.
The collider needed to have a high luminosity
in order to ensure enough collisions were
seen for conclusions to be drawn. Finally,
advanced computing facilities were needed
to process the vast amount of data (25 petabytes
per year as of 2012) produced by the collisions.
For the announcement of 4 July 2012, a new
collider known as the Large Hadron Collider
was constructed at CERN with a planned eventual
collision energy of 14 TeV—over seven times
any previous collider—and over 300 trillion
(3×1014) LHC proton–proton collisions were
analysed by the LHC Computing Grid, the world's
largest computing grid (as of 2012), comprising
over 170 computing facilities in a worldwide
network across 36 countries.
==== Search before 4 July 2012 ====
The first extensive search for the Higgs boson
was conducted at the Large Electron–Positron
Collider (LEP) at CERN in the 1990s. At the
end of its service in 2000, LEP had found
no conclusive evidence for the Higgs. This
implied that if the Higgs boson were to exist
it would have to be heavier than 114.4 GeV/c2.The
search continued at Fermilab in the United
States, where the Tevatron—the collider
that discovered the top quark in 1995—had
been upgraded for this purpose. There was
no guarantee that the Tevatron would be able
to find the Higgs, but it was the only supercollider
that was operational since the Large Hadron
Collider (LHC) was still under construction
and the planned Superconducting Super Collider
had been cancelled in 1993 and never completed.
The Tevatron was only able to exclude further
ranges for the Higgs mass, and was shut down
on 30 September 2011 because it no longer
could keep up with the LHC. The final analysis
of the data excluded the possibility of a
Higgs boson with a mass between 147 GeV/c2
and 180 GeV/c2. In addition, there was a small
(but not significant) excess of events possibly
indicating a Higgs boson with a mass between
115 GeV/c2 and 140 GeV/c2.The Large Hadron
Collider at CERN in Switzerland, was designed
specifically to be able to either confirm
or exclude the existence of the Higgs boson.
Built in a 27 km tunnel under the ground near
Geneva originally inhabited by LEP, it was
designed to collide two beams of protons,
initially at energies of 3.5 TeV per beam
(7 TeV total), or almost 3.6 times that of
the Tevatron, and upgradeable to 2 × 7 TeV
(14 TeV total) in future. Theory suggested
if the Higgs boson existed, collisions at
these energy levels should be able to reveal
it. As one of the most complicated scientific
instruments ever built, its operational readiness
was delayed for 14 months by a magnet quench
event nine days after its inaugural tests,
caused by a faulty electrical connection that
damaged over 50 superconducting magnets and
contaminated the vacuum system.Data collection
at the LHC finally commenced in March 2010.
By December 2011 the two main particle detectors
at the LHC, ATLAS and CMS, had narrowed down
the mass range where the Higgs could exist
to around 116-130 GeV (ATLAS) and 115-127
GeV (CMS). There had also already been a number
of promising event excesses that had "evaporated"
and proven to be nothing but random fluctuations.
However, from around May 2011, both experiments
had seen among their results, the slow emergence
of a small yet consistent excess of gamma
and 4-lepton decay signatures and several
other particle decays, all hinting at a new
particle at a mass around 125 GeV. By around
November 2011, the anomalous data at 125 GeV
was becoming "too large to ignore" (although
still far from conclusive), and the team leaders
at both ATLAS and CMS each privately suspected
they might have found the Higgs. On November
28, 2011, at an internal meeting of the two
team leaders and the director general of CERN,
the latest analyses were discussed outside
their teams for the first time, suggesting
both ATLAS and CMS might be converging on
a possible shared result at 125 GeV, and initial
preparations commenced in case of a successful
finding. While this information was not known
publicly at the time, the narrowing of the
possible Higgs range to around 115–130 GeV
and the repeated observation of small but
consistent event excesses across multiple
channels at both ATLAS and CMS in the 124-126
GeV region (described as "tantalising hints"
of around 2-3 sigma) were public knowledge
with "a lot of interest". It was therefore
widely anticipated around the end of 2011,
that the LHC would provide sufficient data
to either exclude or confirm the finding of
a Higgs boson by the end of 2012, when their
2012 collision data (with slightly higher
8 TeV collision energy) had been examined.
==== Discovery of candidate boson at CERN
====
On 22 June 2012 CERN announced an upcoming
seminar covering tentative findings for 2012,
and shortly afterwards (from around 1 July
2012 according to an analysis of the spreading
rumour in social media) rumours began to spread
in the media that this would include a major
announcement, but it was unclear whether this
would be a stronger signal or a formal discovery.
Speculation escalated to a "fevered" pitch
when reports emerged that Peter Higgs, who
proposed the particle, was to be attending
the seminar, and that "five leading physicists"
had been invited – generally believed to
signify the five living 1964 authors – with
Higgs, Englert, Guralnik, Hagen attending
and Kibble confirming his invitation (Brout
having died in 2011).On 4 July 2012 both of
the CERN experiments announced they had independently
made the same discovery: CMS of a previously
unknown boson with mass 125.3 ± 0.6 GeV/c2
and ATLAS of a boson with mass 126.0 ± 0.6
GeV/c2. Using the combined analysis of two
interaction types (known as 'channels'), both
experiments independently reached a local
significance of 5 sigma — implying that
the probability of getting at least as strong
a result by chance alone is less than 1 in
3 million. When additional channels were taken
into account, the CMS significance was reduced
to 4.9 sigma.The two teams had been working
'blinded' from each other from around late
2011 or early 2012, meaning they did not discuss
their results with each other, providing additional
certainty that any common finding was genuine
validation of a particle. This level of evidence,
confirmed independently by two separate teams
and experiments, meets the formal level of
proof required to announce a confirmed discovery.
On 31 July 2012, the ATLAS collaboration presented
additional data analysis on the "observation
of a new particle", including data from a
third channel, which improved the significance
to 5.9 sigma (1 in 588 million chance of obtaining
at least as strong evidence by random background
effects alone) and mass 126.0 ± 0.4 (stat)
± 0.4 (sys) GeV/c2, and CMS improved the
significance to 5-sigma and mass 125.3 ± 0.4
(stat) ± 0.5 (sys) GeV/c2.
==== The 
new particle tested as a possible Higgs boson
====
Following the 2012 discovery, it was still
unconfirmed whether or not the 125 GeV/c2
particle was a Higgs boson. On one hand, observations
remained consistent with the observed particle
being the Standard Model Higgs boson, and
the particle decayed into at least some of
the predicted channels. Moreover, the production
rates and branching ratios for the observed
channels broadly matched the predictions by
the Standard Model within the experimental
uncertainties. However, the experimental uncertainties
currently still left room for alternative
explanations, meaning an announcement of the
discovery of a Higgs boson would have been
premature. To allow more opportunity for data
collection, the LHC's proposed 2012 shutdown
and 2013–14 upgrade were postponed by 7
weeks into 2013.In November 2012, in a conference
in Kyoto researchers said evidence gathered
since July was falling into line with the
basic Standard Model more than its alternatives,
with a range of results for several interactions
matching that theory's predictions. Physicist
Matt Strassler highlighted "considerable"
evidence that the new particle is not a pseudoscalar
negative parity particle (consistent with
this required finding for a Higgs boson),
"evaporation" or lack of increased significance
for previous hints of non-Standard Model findings,
expected Standard Model interactions with
W and Z bosons, absence of "significant new
implications" for or against supersymmetry,
and in general no significant deviations to
date from the results expected of a Standard
Model Higgs boson. However some kinds of extensions
to the Standard Model would also show very
similar results; so commentators noted that
based on other particles that are still being
understood long after their discovery, it
may take years to be sure, and decades to
fully understand the particle that has been
found.These findings meant that as of January
2013, scientists were very sure they had found
an unknown particle of mass ~ 125 GeV/c2,
and had not been misled by experimental error
or a chance result. They were also sure, from
initial observations, that the new particle
was some kind of boson. The behaviours and
properties of the particle, so far as examined
since July 2012, also seemed quite close to
the behaviours expected of a Higgs boson.
Even so, it could still have been a Higgs
boson or some other unknown boson, since future
tests could show behaviours that do not match
a Higgs boson, so as of December 2012 CERN
still only stated that the new particle was
"consistent with" the Higgs boson, and scientists
did not yet positively say it was the Higgs
boson. Despite this, in late 2012, widespread
media reports announced (incorrectly) that
a Higgs boson had been confirmed during the
year.In January 2013, CERN director-general
Rolf-Dieter Heuer stated that based on data
analysis to date, an answer could be possible
'towards' mid-2013, and the deputy chair of
physics at Brookhaven National Laboratory
stated in February 2013 that a "definitive"
answer might require "another few years" after
the collider's 2015 restart. In early March
2013, CERN Research Director Sergio Bertolucci
stated that confirming spin-0 was the major
remaining requirement to determine whether
the particle is at least some kind of Higgs
boson.
==== Confirmation of existence and current
status ====
On 14 March 2013 CERN confirmed that:
"CMS and ATLAS have compared a number of options
for the spin-parity of this particle, and
these all prefer no spin and even parity [two
fundamental criteria of a Higgs boson consistent
with the Standard Model]. This, coupled with
the measured interactions of the new particle
with other particles, strongly indicates that
it is a Higgs boson."This also makes the particle
the first elementary scalar particle to be
discovered in nature.Examples of tests used
to validate that the discovered particle is
the Higgs boson:
==== Findings since 2013 ====
In July 2017, CERN confirmed that all measurements
still agree with the predictions of the Standard
Model, and called the discovered particle
simply "the Higgs boson". As of April 2018,
the Large Hadron Collider has continued to
produce findings that confirm the 2013 understanding
of the Higgs field and particle.
The LHC's experimental work since restarting
in 2015 has included probing the Higgs field
and boson to a greater level of detail, and
confirming whether or not less common predictions
were correct. In particular, exploration since
2015 has provided strong evidence of the predicted
direct decay into fermions such as pairs of
bottom quarks (3.6 σ)—described as an "important
milestone" in understanding its short lifetime
and other rare decays—and also to confirm
decay into pairs of tau leptons (5.9 σ).
This was described by CERN as being "of paramount
importance to establishing the coupling of
the Higgs boson to leptons and represents
an important step towards measuring its couplings
to third generation fermions, the very heavy
copies of the electrons and quarks, whose
role in nature is a profound mystery". Published
results as of 19 Mar 2018 at 13 TeV for ATLAS
and CMS had their measurements of the Higgs
mass at 124.98±0.28 GeV and 125.26±0.21
GeV respectively.
In July 2018, the ATLAS and CMS experiments
reported observing the Higgs boson decay into
a pair of bottom quarks, which makes up approximately
60% of all of its decays.
== Theoretical properties ==
=== 
Theoretical need for the Higgs ===
Gauge invariance is an important property
of modern particle theories such as the Standard
Model, partly due to its success in other
areas of fundamental physics such as electromagnetism
and the strong interaction (quantum chromodynamics).
However, there were great difficulties in
developing gauge theories for the weak nuclear
force or a possible unified electroweak interaction.
Fermions with a mass term would violate gauge
symmetry and therefore cannot be gauge invariant.
(This can be seen by examining the Dirac Lagrangian
for a fermion in terms of left and right handed
components; we find none of the spin-half
particles could ever flip helicity as required
for mass, so they must be massless.) W and
Z bosons are observed to have mass, but a
boson mass term contains terms which clearly
depend on the choice of gauge, and therefore
these masses too cannot be gauge invariant.
Therefore, it seems that none of the standard
model fermions or bosons could "begin" with
mass as an inbuilt property except by abandoning
gauge invariance. If gauge invariance were
to be retained, then these particles had to
be acquiring their mass by some other mechanism
or interaction. Additionally, whatever was
giving these particles their mass had to not
"break" gauge invariance as the basis for
other parts of the theories where it worked
well, and had to not require or predict unexpected
massless particles or long-range forces (seemingly
an inevitable consequence of Goldstone's theorem)
which did not actually seem to exist in nature.
A solution to all of these overlapping problems
came from the discovery of a previously unnoticed
borderline case hidden in the mathematics
of Goldstone's theorem, that under certain
conditions it might theoretically be possible
for a symmetry to be broken without disrupting
gauge invariance and without any new massless
particles or forces, and having "sensible"
(renormalisable) results mathematically. This
became known as the Higgs mechanism.
The Standard Model hypothesises a field which
is responsible for this effect, called the
Higgs field (symbol:
ϕ
{\displaystyle \phi }
), which has the unusual property of a non-zero
amplitude in its ground state; i.e., a non-zero
vacuum expectation value. It can have this
effect because of its unusual "Mexican hat"
shaped potential whose lowest "point" is not
at its "centre". In simple terms, unlike all
other known fields, the Higgs field requires
less energy to have a non-zero value than
a zero value, so it ends up having a non-zero
value everywhere. Below a certain extremely
high energy level the existence of this non-zero
vacuum expectation spontaneously breaks electroweak
gauge symmetry which in turn gives rise to
the Higgs mechanism and triggers the acquisition
of mass by those particles interacting with
the field. This effect occurs because scalar
field components of the Higgs field are "absorbed"
by the massive bosons as degrees of freedom,
and couple to the fermions via Yukawa coupling,
thereby producing the expected mass terms.
When symmetry breaks under these conditions,
the Goldstone bosons that arise interact with
the Higgs field (and with other particles
capable of interacting with the Higgs field)
instead of becoming new massless particles.
The intractable problems of both underlying
theories "neutralise" each other, and the
residual outcome is that elementary particles
acquire a consistent mass based on how strongly
they interact with the Higgs field. It is
the simplest known process capable of giving
mass to the gauge bosons while remaining compatible
with gauge theories. Its quantum would be
a scalar boson, known as the Higgs boson.
=== Properties of the Higgs field ===
In the Standard Model, the Higgs field is
a scalar tachyonic field – scalar meaning
it does not transform under Lorentz transformations,
and tachyonic meaning the field (but not the
particle) has imaginary mass, and in certain
configurations must undergo symmetry breaking.
It consists of four components: two neutral
ones and two charged component fields. Both
of the charged components and one of the neutral
fields are Goldstone bosons, which act as
the longitudinal third-polarisation components
of the massive W+, W−, and Z bosons. The
quantum of the remaining neutral component
corresponds to (and is theoretically realised
as) the massive Higgs boson, this component
can also interact with fermions via Yukawa
coupling to give them mass, as well.
Mathematically, the Higgs field has imaginary
mass and is therefore a tachyonic field. While
tachyons (particles that move faster than
light) are a purely hypothetical concept,
fields with imaginary mass have come to play
an important role in modern physics. Under
no circumstances do any excitations ever propagate
faster than light in such theories — the
presence or absence of a tachyonic mass has
no effect whatsoever on the maximum velocity
of signals (there is no violation of causality).
Instead of faster-than-light particles, the
imaginary mass creates an instability: Any
configuration in which one or more field excitations
are tachyonic must spontaneously decay, and
the resulting configuration contains no physical
tachyons. This process is known as tachyon
condensation, and is now believed to be the
explanation for how the Higgs mechanism itself
arises in nature, and therefore the reason
behind electroweak symmetry breaking.
Although the notion of imaginary mass might
seem troubling, it is only the field, and
not the mass itself, that is quantised. Therefore,
the field operators at spacelike separated
points still commute (or anticommute), and
information and particles still do not propagate
faster than light. Tachyon condensation drives
a physical system that has reached a local
limit – and might naively be expected to
produce physical tachyons – to an alternate
stable state where no physical tachyons exist.
Once a tachyonic field such as the Higgs field
reaches the minimum of the potential, its
quanta are not tachyons any more but rather
are ordinary particles such as the Higgs boson.
=== Properties of the Higgs boson ===
Since the Higgs field is scalar, the Higgs
boson has no spin. The Higgs boson is also
its own antiparticle and is CP-even, and has
zero electric and colour charge.The Standard
Model does not predict the mass of the Higgs
boson. If that mass is between 115 and 180
GeV/c2 (consistent with empirical observations
of 125 GeV/c2), then the Standard Model can
be valid at energy scales all the way up to
the Planck scale (1019 GeV). Many theorists
expect new physics beyond the Standard Model
to emerge at the TeV-scale, based on unsatisfactory
properties of the Standard Model. The highest
possible mass scale allowed for the Higgs
boson (or some other electroweak symmetry
breaking mechanism) is 1.4 TeV; beyond this
point, the Standard Model becomes inconsistent
without such a mechanism, because unitarity
is violated in certain scattering processes.It
is also possible, although experimentally
difficult, to estimate the mass of the Higgs
boson indirectly. In the Standard Model, the
Higgs boson has a number of indirect effects;
most notably, Higgs loops result in tiny corrections
to masses of W and Z bosons. Precision measurements
of electroweak parameters, such as the Fermi
constant and masses of W/Z bosons, can be
used to calculate constraints on the mass
of the Higgs. As of July 2011, the precision
electroweak measurements tell us that the
mass of the Higgs boson is likely to be less
than about 161 GeV/c2 at 95% confidence level
(this upper limit would increase to 185 GeV/c2
if the lower bound of 114.4 GeV/c2 from the
LEP-2 direct search is allowed for). These
indirect constraints rely on the assumption
that the Standard Model is correct. It may
still be possible to discover a Higgs boson
above these masses if it is accompanied by
other particles beyond those predicted by
the Standard Model.
=== Production ===
If Higgs particle theories are valid, then
a Higgs particle can be produced much like
other particles that are studied, in a particle
collider. This involves accelerating a large
number of particles to extremely high energies
and extremely close to the speed of light,
then allowing them to smash together. Protons
and lead ions (the bare nuclei of lead atoms)
are used at the LHC. In the extreme energies
of these collisions, the desired esoteric
particles will occasionally be produced and
this can be detected and studied; any absence
or difference from theoretical expectations
can also be used to improve the theory. The
relevant particle theory (in this case the
Standard Model) will determine the necessary
kinds of collisions and detectors. The Standard
Model predicts that Higgs bosons could be
formed in a number of ways, although the probability
of producing a Higgs boson in any collision
is always expected to be very small—for
example, only 1 Higgs boson per 10 billion
collisions in the Large Hadron Collider. The
most common expected processes for Higgs boson
production are:
Gluon fusion. If the collided particles are
hadrons such as the proton or antiproton—as
is the case in the LHC and Tevatron—then
it is most likely that two of the gluons binding
the hadron together collide. The easiest way
to produce a Higgs particle is if the two
gluons combine to form a loop of virtual quarks.
Since the coupling of particles to the Higgs
boson is proportional to their mass, this
process is more likely for heavy particles.
In practice it is enough to consider the contributions
of virtual top and bottom quarks (the heaviest
quarks). This process is the dominant contribution
at the LHC and Tevatron being about ten times
more likely than any of the other processes.
Higgs Strahlung. If an elementary fermion
collides with an anti-fermion—e.g., a quark
with an anti-quark or an electron with a positron—the
two can merge to form a virtual W or Z boson
which, if it carries sufficient energy, can
then emit a Higgs boson. This process was
the dominant production mode at the LEP, where
an electron and a positron collided to form
a virtual Z boson, and it was the second largest
contribution for Higgs production at the Tevatron.
At the LHC this process is only the third
largest, because the LHC collides protons
with protons, making a quark-antiquark collision
less likely than at the Tevatron. Higgs Strahlung
is also known as associated production.
Weak boson fusion. Another possibility when
two (anti-)fermions collide is that the two
exchange a virtual W or Z boson, which emits
a Higgs boson. The colliding fermions do not
need to be the same type. So, for example,
an up quark may exchange a Z boson with an
anti-down quark. This process is the second
most important for the production of Higgs
particle at the LHC and LEP.
Top fusion. The final process that is commonly
considered is by far the least likely (by
two orders of magnitude). This process involves
two colliding gluons, which each decay into
a heavy quark–antiquark pair. A quark and
antiquark from each pair can then combine
to form a Higgs particle.
=== Decay ===
Quantum mechanics predicts that if it is possible
for a particle to decay into a set of lighter
particles, then it will eventually do so.
This is also true for the Higgs boson. The
likelihood with which this happens depends
on a variety of factors including: the difference
in mass, the strength of the interactions,
etc. Most of these factors are fixed by the
Standard Model, except for the mass of the
Higgs boson itself. For a Higgs boson with
a mass of 125 GeV/c2 the SM predicts a mean
life time of about 1.6×10−22 s.
Since it interacts with all the massive elementary
particles of the SM, the Higgs boson has many
different processes through which it can decay.
Each of these possible processes has its own
probability, expressed as the branching ratio;
the fraction of the total number decays that
follows that process. The SM predicts these
branching ratios as a function of the Higgs
mass (see plot).
One way that the Higgs can decay is by splitting
into a fermion–antifermion pair. As general
rule, the Higgs is more likely to decay into
heavy fermions than light fermions, because
the mass of a fermion is proportional to the
strength of its interaction with the Higgs.
By this logic the most common decay should
be into a top–antitop quark pair. However,
such a decay would only be possible if the
Higgs were heavier than ~346 GeV/c2, twice
the mass of the top quark. For a Higgs mass
of 125 GeV/c2 the SM predicts that the most
common decay is into a bottom–antibottom
quark pair, which happens 57.7% of the time.
The second most common fermion decay at that
mass is a tau–antitau pair, which happens
only about 6.3% of the time.Another possibility
is for the Higgs to split into a pair of massive
gauge bosons. The most likely possibility
is for the Higgs to decay into a pair of W
bosons (the light blue line in the plot),
which happens about 21.5% of the time for
a Higgs boson with a mass of 125 GeV/c2. The
W bosons can subsequently decay either into
a quark and an antiquark or into a charged
lepton and a neutrino. The decays of W bosons
into quarks are difficult to distinguish from
the background, and the decays into leptons
cannot be fully reconstructed (because neutrinos
are impossible to detect in particle collision
experiments). A cleaner signal is given by
decay into a pair of Z-bosons (which happens
about 2.6% of the time for a Higgs with a
mass of 125 GeV/c2), if each of the bosons
subsequently decays into a pair of easy-to-detect
charged leptons (electrons or muons).
Decay into massless gauge bosons (i.e., gluons
or photons) is also possible, but requires
intermediate loop of virtual heavy quarks
(top or bottom) or massive gauge bosons. The
most common such process is the decay into
a pair of gluons through a loop of virtual
heavy quarks. This process, which is the reverse
of the gluon fusion process mentioned above,
happens approximately 8.6% of the time for
a Higgs boson with a mass of 125 GeV/c2. Much
rarer is the decay into a pair of photons
mediated by a loop of W bosons or heavy quarks,
which happens only twice for every thousand
decays. However, this process is very relevant
for experimental searches for the Higgs boson,
because the energy and momentum of the photons
can be measured very precisely, giving an
accurate reconstruction of the mass of the
decaying particle.
=== Alternative models ===
The Minimal Standard Model as described above
is the simplest known model for the Higgs
mechanism with just one Higgs field. However,
an extended Higgs sector with additional Higgs
particle doublets or triplets is also possible,
and many extensions of the Standard Model
have this feature. The non-minimal Higgs sector
favoured by theory are the two-Higgs-doublet
models (2HDM), which predict the existence
of a quintet of scalar particles: two CP-even
neutral Higgs bosons h0 and H0, a CP-odd neutral
Higgs boson A0, and two charged Higgs particles
H±. Supersymmetry ("SUSY") also predicts
relations between the Higgs-boson masses and
the masses of the gauge bosons, and could
accommodate a 125 GeV/c2 neutral Higgs boson.
The key method to distinguish between these
different models involves study of the particles'
interactions ("coupling") and exact decay
processes ("branching ratios"), which can
be measured and tested experimentally in particle
collisions. In the Type-I 2HDM model one Higgs
doublet couples to up and down quarks, while
the second doublet does not couple to quarks.
This model has two interesting limits, in
which the lightest Higgs couples to just fermions
("gauge-phobic") or just gauge bosons ("fermiophobic"),
but not both. In the Type-II 2HDM model, one
Higgs doublet only couples to up-type quarks,
the other only couples to down-type quarks.
The heavily researched Minimal Supersymmetric
Standard Model (MSSM) includes a Type-II 2HDM
Higgs sector, so it could be disproven by
evidence of a Type-I 2HDM Higgs.In other models
the Higgs scalar is a composite particle.
For example, in technicolor the role of the
Higgs field is played by strongly bound pairs
of fermions called techniquarks. Other models,
feature pairs of top quarks (see top quark
condensate). In yet other models, there is
no Higgs field at all and the electroweak
symmetry is broken using extra dimensions.
=== Further theoretical issues and hierarchy
problem ===
The Standard Model leaves the mass of the
Higgs boson as a parameter to be measured,
rather than a value to be calculated. This
is seen as theoretically unsatisfactory, particularly
as quantum corrections (related to interactions
with virtual particles) should apparently
cause the Higgs particle to have a mass immensely
higher than that observed, but at the same
time the Standard Model requires a mass of
the order of 100 to 1000 GeV to ensure unitarity
(in this case, to unitarise longitudinal vector
boson scattering). Reconciling these points
appears to require explaining why there is
an almost-perfect cancellation resulting in
the visible mass of ~ 125 GeV, and it is not
clear how to do this. Because the weak force
is about 1032 times stronger than gravity,
and (linked to this) the Higgs boson's mass
is so much less than the Planck mass or the
grand unification energy, it appears that
either there is some underlying connection
or reason for these observations which is
unknown and not described by the Standard
Model, or some unexplained and extremely precise
fine-tuning of parameters – however at present
neither of these explanations is proven. This
is known as a hierarchy problem. More broadly,
the hierarchy problem amounts to the worry
that a future theory of fundamental particles
and interactions should not have excessive
fine-tunings or unduly delicate cancellations,
and should allow masses of particles such
as the Higgs boson to be calculable. The problem
is in some ways unique to spin-0 particles
(such as the Higgs boson), which can give
rise to issues related to quantum corrections
that do not affect particles with spin. A
number of solutions have been proposed, including
supersymmetry, conformal solutions and solutions
via extra dimensions such as braneworld models.
There are also issues of quantum triviality,
which suggests that it may not be possible
to create a consistent quantum field theory
involving elementary scalar particles. However,
if quantum triviality is avoided, triviality
constraints may set bounds on the Higgs Boson
mass.
== Public discussion ==
=== 
Naming ===
==== 
Names used by physicists ====
The name most strongly associated with the
particle and field is the Higgs boson and
Higgs field. For some time the particle was
known by a combination of its PRL author names
(including at times Anderson), for example
the Brout–Englert–Higgs particle, the
Anderson-Higgs particle, or the Englert–Brout–Higgs–Guralnik–Hagen–Kibble
mechanism, and these are still used at times.
Fuelled in part by the issue of recognition
and a potential shared Nobel Prize, the most
appropriate name was still occasionally a
topic of debate until 2013. Higgs himself
prefers to call the particle either by an
acronym of all those involved, or "the scalar
boson", or "the so-called Higgs particle".A
considerable amount has been written on how
Higgs' name came to be exclusively used. Two
main explanations are offered. The first is
that Higgs undertook a step which was either
unique, clearer or more explicit in his paper
in formally predicting and examining the particle.
Of the PRL papers' authors, only the paper
by Higgs explicitly offered as a prediction
that a massive particle would exist and calculated
some of its properties; he was therefore "the
first to postulate the existence of a massive
particle" according to Nature. Physicist and
author Frank Close and physicist-blogger Peter
Woit both comment that the paper by GHK was
also completed after Higgs and Brout–Englert
were submitted to Physical Review Letters.
and that Higgs alone had drawn attention to
a predicted massive scalar boson, while all
others had focused on the massive vector bosons;
In this way, Higgs' contribution also provided
experimentalists with a crucial "concrete
target" needed to test the theory. However,
in Higgs' view, Brout and Englert did not
explicitly mention the boson since its existence
is plainly obvious in their work, while according
to Guralnik the GHK paper was a complete analysis
of the entire symmetry breaking mechanism
whose mathematical rigour is absent from the
other two papers, and a massive particle may
exist in some solutions. Higgs' paper also
provided an "especially sharp" statement of
the challenge and its solution according to
science historian David Kaiser.The alternative
explanation is that the name was popularised
in the 1970s due to its use as a convenient
shorthand or because of a mistake in citing.
Many accounts (including Higgs' own) credit
the "Higgs" name to physicist Benjamin Lee
(in Korean: Lee Whi-soh). Lee was a significant
populist for the theory in its early stages,
and habitually attached the name "Higgs" as
a "convenient shorthand" for its components
from 1972 and in at least one instance from
as early as 1966. Although Lee clarified in
his footnotes that "'Higgs' is an abbreviation
for Higgs, Kibble, Guralnik, Hagen, Brout,
Englert", his use of the term (and perhaps
also Steven Weinberg's mistaken cite of Higgs'
paper as the first in his seminal 1967 paper)
meant that by around 1975–76 others had
also begun to use the name 'Higgs' exclusively
as a shorthand.
==== Nickname ====
The Higgs boson is often referred to as the
"God particle" in popular media outside the
scientific community. The nickname comes from
the title of the 1993 book on the Higgs boson
and particle physics, The God Particle: If
the Universe Is the Answer, What Is the Question?
by Physics Nobel Prize winner and Fermilab
director Leon Lederman. Lederman wrote it
in the context of failing US government support
for the Superconducting Super Collider, a
part-constructed titanic competitor to the
Large Hadron Collider with planned collision
energies of 2 × 20 TeV that was championed
by Lederman since its 1983 inception and shut
down in 1993. The book sought in part to promote
awareness of the significance and need for
such a project in the face of its possible
loss of funding. Lederman, a leading researcher
in the field, writes that he wanted to title
his book The Goddamn Particle: If the Universe
is the Answer, What is the Question? Lederman's
editor decided that the title was too controversial
and convinced him to change the title to The
God Particle: If the Universe is the Answer,
What is the Question?While media use of this
term may have contributed to wider awareness
and interest, many scientists feel the name
is inappropriate since it is sensational hyperbole
and misleads readers; the particle also has
nothing to do with God, leaves open numerous
questions in fundamental physics, and does
not explain the ultimate origin of the universe.
Higgs, an atheist, was reported to be displeased
and stated in a 2008 interview that he found
it "embarrassing" because it was "the kind
of misuse... which I think might offend some
people". The nickname has been satirised in
mainstream media as well. Science writer Ian
Sample stated in his 2010 book on the search
that the nickname is "universally hate[d]"
by physicists and perhaps the "worst derided"
in the history of physics, but that (according
to Lederman) the publisher rejected all titles
mentioning "Higgs" as unimaginative and too
unknown.Lederman begins with a review of the
long human search for knowledge, and explains
that his tongue-in-cheek title draws an analogy
between the impact of the Higgs field on the
fundamental symmetries at the Big Bang, and
the apparent chaos of structures, particles,
forces and interactions that resulted and
shaped our present universe, with the biblical
story of Babel in which the primordial single
language of early Genesis was fragmented into
many disparate languages and cultures.
Today ... we have the standard model, which
reduces all of reality to a dozen or so particles
and four forces. ... It's a hard-won simplicity
[...and...] remarkably accurate. But it is
also incomplete and, in fact, internally inconsistent...
This boson is so central to the state of physics
today, so crucial to our final understanding
of the structure of matter, yet so elusive,
that I have given it a nickname: the God Particle.
Why God Particle? Two reasons. One, the publisher
wouldn't let us call it the Goddamn Particle,
though that might be a more appropriate title,
given its villainous nature and the expense
it is causing. And two, there is a connection,
of sorts, to another book, a much older one...
Lederman asks whether the Higgs boson was
added just to perplex and confound those seeking
knowledge of the universe, and whether physicists
will be confounded by it as recounted in that
story, or ultimately surmount the challenge
and understand "how beautiful is the universe
[God has] made".
==== Other proposals ====
A renaming competition by British newspaper
The Guardian in 2009 resulted in their science
correspondent choosing the name "the champagne
bottle boson" as the best submission: "The
bottom of a champagne bottle is in the shape
of the Higgs potential and is often used as
an illustration in physics lectures. So it's
not an embarrassingly grandiose name, it is
memorable, and [it] has some physics connection
too."
The name Higgson was suggested as well, in
an opinion piece in the Institute of Physics'
online publication physicsworld.com.
=== Educational explanations and analogies
===
There has been considerable public discussion
of analogies and explanations for the Higgs
particle and how the field creates mass, including
coverage of explanatory attempts in their
own right and a competition in 1993 for the
best popular explanation by then-UK Minister
for Science Sir William Waldegrave and articles
in newspapers worldwide.
An educational collaboration involving an
LHC physicist and a High School Teachers at
CERN educator suggests that dispersion of
light – responsible for the rainbow and
dispersive prism – is a useful analogy for
the Higgs field's symmetry breaking and mass-causing
effect.
Matt Strassler uses electric fields as an
analogy:
Some particles interact with the Higgs field
while others don’t. Those particles that
feel the Higgs field act as if they have mass.
Something similar happens in an electric field
– charged objects are pulled around and
neutral objects can sail through unaffected.
So you can think of the Higgs search as an
attempt to make waves in the Higgs field [create
Higgs bosons] to prove it’s really there.
A similar explanation was offered by The Guardian:
The Higgs boson is essentially a ripple in
a field said to have emerged at the birth
of the universe and to span the cosmos to
this day ... The particle is crucial however:
It is the smoking gun, the evidence required
to show the theory is right.
The Higgs field's effect on particles was
famously described by physicist David Miller
as akin to a room full of political party
workers spread evenly throughout a room: the
crowd gravitates to and slows down famous
people but does not slow down others. He also
drew attention to well-known effects in solid
state physics where an electron's effective
mass can be much greater than usual in the
presence of a crystal lattice.Analogies based
on drag effects, including analogies of "syrup"
or "molasses" are also well known, but can
be somewhat misleading since they may be understood
(incorrectly) as saying that the Higgs field
simply resists some particles' motion but
not others' – a simple resistive effect
could also conflict with Newton's third law.
=== Recognition and awards ===
There was considerable discussion prior to
late 2013 of how to allocate the credit if
the Higgs boson is proven, made more pointed
as a Nobel prize had been expected, and the
very wide basis of people entitled to consideration.
These include a range of theoreticians who
made the Higgs mechanism theory possible,
the theoreticians of the 1964 PRL papers (including
Higgs himself), the theoreticians who derived
from these a working electroweak theory and
the Standard Model itself, and also the experimentalists
at CERN and other institutions who made possible
the proof of the Higgs field and boson in
reality. The Nobel prize has a limit of 3
persons to share an award, and some possible
winners are already prize holders for other
work, or are deceased (the prize is only awarded
to persons in their lifetime). Existing prizes
for works relating to the Higgs field, boson,
or mechanism include:
Nobel Prize in Physics (1979) – Glashow,
Salam, and Weinberg, for contributions to
the theory of the unified weak and electromagnetic
interaction between elementary particles
Nobel Prize in Physics (1999) – 't Hooft
and Veltman, for elucidating the quantum structure
of electroweak interactions in physics
J. J. Sakurai Prize for Theoretical Particle
Physics (2010) – Hagen, Englert, Guralnik,
Higgs, Brout, and Kibble, for elucidation
of the properties of spontaneous symmetry
breaking in four-dimensional relativistic
gauge theory and of the mechanism for the
consistent generation of vector boson masses
(for the 1964 papers described above)
Wolf Prize (2004) – Englert, Brout, and
Higgs
Nobel Prize in Physics (2013) – Peter Higgs
and François Englert, for the theoretical
discovery of a mechanism that contributes
to our understanding of the origin of mass
of subatomic particles, and which recently
was confirmed through the discovery of the
predicted fundamental particle, by the ATLAS
and CMS experiments at CERN's Large Hadron
Collider Englert's co-researcher Robert Brout
had died in 2011 and the Nobel Prize is not
ordinarily given posthumously.Additionally
Physical Review Letters' 50-year review (2008)
recognised the 1964 PRL symmetry breaking
papers and Weinberg's 1967 paper A model of
Leptons (the most cited paper in particle
physics, as of 2012) "milestone Letters".Following
reported observation of the Higgs-like particle
in July 2012, several Indian media outlets
reported on the supposed neglect of credit
to Indian physicist Satyendra Nath Bose after
whose work in the 1920s the class of particles
"bosons" is named (although physicists have
described Bose's connection to the discovery
as tenuous).
== Technical aspects and mathematical formulation
==
In the Standard Model, the Higgs field is
a four-component scalar field that forms a
complex doublet of the weak isospin SU(2)
symmetry:
while the field has charge +½ under the weak
hypercharge U(1) symmetry.
Note: This article uses the scaling convention
where the electric charge, Q, the weak isospin,
T3, and the weak hypercharge, YW, are related
by Q = T3 + YW. A different convention used
in most other Wikipedia articles is Q = T3
+ ½ YW.
The Higgs part of the Lagrangian is
where
W
μ
a
{\displaystyle W_{\mu }^{a}}
and
B
μ
{\displaystyle B_{\mu }}
are the gauge bosons of the SU(2) and U(1)
symmetries,
g
{\displaystyle g}
and
g
′
{\displaystyle g'}
their respective coupling constants,
τ
a
=
1
2
σ
a
{\displaystyle \tau ^{a}={\frac {1}{2}}\sigma
^{a}}
(where
σ
a
{\displaystyle \sigma ^{a}}
are the Pauli matrices) a complete set generators
of the SU(2) symmetry, and
λ
>
0
{\displaystyle \lambda >0}
and
μ
2
>
0
{\displaystyle \mu ^{2}>0}
, so that the ground state breaks the SU(2)
symmetry (see figure). The ground state of
the Higgs field (the bottom of the potential)
is degenerate with different ground states
related to each other by a SU(2) gauge transformation.
It is always possible to pick a gauge such
that in the ground state
ϕ
1
=
ϕ
2
=
ϕ
3
=
0
{\displaystyle \phi ^{1}=\phi ^{2}=\phi ^{3}=0}
. The expectation value of
ϕ
0
{\displaystyle \phi ^{0}}
in the ground state (the vacuum expectation
value or VEV) is then
⟨
ϕ
0
⟩
=
1
2
v
{\displaystyle \langle \phi ^{0}\rangle ={\tfrac
{1}{{\sqrt {2}}\ }}v}
, where
v
=
1
λ
|
μ
|
{\displaystyle v={\tfrac {1}{{\sqrt {\lambda
}}\ }}\left|\mu \right|}
. The 
measured value of this parameter is ~246 GeV/c2.
It has units of mass, and is the only free
parameter of the Standard Model that is not
a dimensionless number. Quadratic terms in
W
μ
{\displaystyle W_{\mu }}
and
B
μ
{\displaystyle B_{\mu }}
arise, which give masses to the W and Z bosons:
with their ratio determining the Weinberg
angle,
cos
⁡
θ
W
=
m
W
m
Z
=
|
g
|
g
2
+
g
′
2
{\displaystyle \cos \theta _{W}={\frac {m_{W}}{m_{Z}}}={\frac
{|g|}{\sqrt {g^{2}+{g'}^{2}}}}}
, and leave a massless U(1) photon,
γ
{\displaystyle \gamma }
. The mass of the Higgs boson itself is given
by
The quarks and the leptons interact with the
Higgs field through Yukawa interaction terms:
where
(
d
,
u
,
e
,
ν
)
L
,
R
i
{\displaystyle (d,u,e,\nu )_{L,R}^{i}}
are left-handed and right-handed quarks and
leptons of 
the ith generation,
λ
u
,
d
,
e
i
j
{\displaystyle \lambda _{u,d,e}^{ij}}
are matrices of Yukawa couplings where h.c.
denotes the hermitian conjugate of all the
preceding terms. In the symmetry breaking
ground state, only the terms containing
ϕ
0
{\displaystyle \phi ^{0}}
remain, giving rise to mass terms for the
fermions. Rotating the quark and lepton fields
to the basis where the matrices of Yukawa
couplings are diagonal, one gets
where the masses of the fermions are
m
u
,
d
,
e
i
=
1
2
λ
u
,
d
,
e
i
v
{\displaystyle m_{u,d,e}^{i}={\tfrac {1}{{\sqrt
{2}}\ }}\lambda _{u,d,e}^{i}v}
, and
λ
u
,
d
,
e
i
{\displaystyle \lambda _{u,d,e}^{i}}
denote the eigenvalues of the Yukawa matrices.
== See also ==
Standard Model Quantum gauge theory
Higgs mechanism
History of quantum field theory
Introduction to quantum mechanics
Noncommutative standard model
and noncommutative geometry
Mathematical formulation of the Standard Model
Standard Model fields overview
mass terms and the Higgs mechanism
W and Z bosons – Elementary particles; gauge
bosons that mediate the weak interactionOther
Bose–Einstein statistics
Dalitz plot
Quantum triviality
ZZ diboson
Scalar boson
Stueckelberg action
Tachyonic field
== Notes
