The
Contents 1 Non-technical summary 1.1 The Standard Model 1.2 The problem of gauge boson mass 1.2.1 Symmetry breaking 1.3 Higgs mechanism 1.3.1 Higgs field 1.3.2 Higgs boson 1.3.3 Interpretation 2 Significance 2.1
2.1.1 Validation of the Standard Model
2.1.2
2.2 Cosmology 2.2.1 Inflation
2.2.2 Nature of the universe, and its possible fates
2.2.3
2.3 Practical and technological impact 3 History 3.1 Summary and impact of the PRL papers 4 Theoretical properties 4.1 Theoretical need for the Higgs 4.2 Properties of the Higgs field 4.3 Properties of the Higgs boson 4.4 Production 4.5 Decay 4.6 Alternative models 4.7 Further theoretical issues and hierarchy problem 5 Experimental search 5.1 Search before 4 July 2012 5.2 Discovery of candidate boson at CERN 5.3 The new particle tested as a possible Higgs boson 5.4 Confirmation of existence and current status 6 Public discussion 6.1 Naming 6.1.1 Names used by physicists 6.1.2 Nickname 6.1.3 Other proposals 6.2 Media explanations and analogies 6.3 Recognition and awards 7 Technical aspects and mathematical formulation 8 See also 9 Notes 10 References 11 Further reading 12 External links 12.1 Popular science, mass media, and general coverage 12.2 Significant papers and other 12.3 Introductions to the field Non-technical summary[edit]
Background
Constituents
Electroweak interaction
Limitations Strong CP problem Hierarchy problem Neutrino oscillations Physics beyond the Standard Model Scientists Rutherford · Thomson · Chadwick · Bose · Sudarshan · Koshiba · Davis Jr. · Anderson · Fermi · Dirac · Feynman · Rubbia · Gell-Mann · Kendall · Taylor · Friedman · Powell · P. W. Anderson · Glashow · Iliopoulos · Maiani · Meer · Cowan · Nambu · Chamberlain · Cabibbo · Schwartz · Perl · Majorana · Weinberg · Lee · Ward · Salam · Kobayashi · Maskawa · Yang · Yukawa · 't Hooft · Veltman · Gross · Politzer · Wilczek · Cronin · Fitch · Vleck · Higgs · Englert · Brout · Hagen · Guralnik · Kibble · Ting · Richter v t e The Standard Model[edit]
Physicists explain the properties and forces between elementary
particles in terms of the
This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (January 2015) (Learn how and when to remove this template message) This section possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed. (January 2015) (Learn how and when to remove this template message) Evidence of the
Diagram showing the
In the Standard Model, there exists the possibility that 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.[31][32][33][34][35] This was sometimes
misreported as the
The six authors of the 1964 PRL papers, who received the 2010 J. J.
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.[51] [text condensed] The
2010
The three papers written in 1964 were each recognised as milestone
papers during
"
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
Summary of interactions between certain particles described by the Standard Model. Properties of the Higgs field[edit]
In the Standard Model, the
Feynman diagrams for Higgs production
Higgs Strahlung
Top fusion 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
Decay[edit] The
The
Since it interacts with all the massive elementary particles of the
SM, the
A one-loop
Further theoretical issues and hierarchy problem[edit]
Main articles:
Feynman diagrams showing the cleanest channels associated with the
low-mass (~125 GeV)
On 22 June 2012
Confirmation of existence and current status[edit]
On 14 March 2013
"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
This also makes the particle the first elementary scalar particle to
be discovered in nature.[14]
In July 2017,
Requirement How tested / explanation Current status (July 2017) Zero spin Examining decay patterns. Spin-1 had been ruled out at the time of initial discovery by the observed decay to two photons (γ γ), leaving spin-0 and spin-2 as remaining candidates. Spin-0 confirmed.[5][4][156][157] The spin-2 hypothesis is excluded with a confidence level exceeding 99.9%.[157] Even (Positive) parity Studying the angles at which decay products fly apart. Negative parity was also disfavoured if spin-0 was confirmed.[158] Even parity tentatively confirmed.[4][156][157] The spin-0 negative parity hypothesis is excluded with a confidence level exceeding 99.9%.[156][5] Decay channels (outcomes of particle decaying) are as predicted
The
γ γ, τ τ, WW and ZZ observed; evidence for bb seen. All observed signal strengths are consistent with the Standard Model prediction.[159][1] Couples to mass (i.e., strength of interaction with Standard Model
particles proportional to their mass)
Higher energy results remain consistent After the LHC's 2015 restart at the higher energy of 13 TeV, searches for multiple Higgs particles (as predicted in some theories) and tests targeting other versions of particle theory continued. These higher energy results must continue to give results consistent with Higgs theories Analysis of collisions up to July 2017 do not show deviations from the Standard Model, with experimental precisions better than results at lower energies.[1] Public discussion[edit]
Naming[edit]
Names used by physicists[edit]
The name most strongly associated with the particle and field is the
Higgs boson[82]:168 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,[Note
17] and these are still used at times.[54][161] Fuelled in part by the
issue of recognition and a potential shared Nobel Prize,[161][162] the
most appropriate name was still occasionally a topic of debate until
2013.[161] 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".[162]
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;[82]:167[163] he was therefore
"the first to postulate the existence of a massive particle" according
to Nature.[161] Physicist and author
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
Lederman asks whether the
Photograph of light passing through a dispersive prism: the rainbow effect arises because photons are not all affected to the same degree by the dispersive material of the prism. An educational collaboration involving an
Symmetry breaking in optics In a vacuum, light of all colours (or photons of all wavelengths) travels at the same velocity, a symmetrical situation. In some substances such as glass, water or air, this symmetry is broken (See: Photons in matter). The result is that light of different wavelengths have different velocities. Symmetry breaking
in particle physics
In 'naive' gauge theories, gauge bosons and other fundamental
particles are all massless – also a symmetrical situation. In the
presence of the
Matt Strassler uses electric fields as an analogy:[198] Some particles interact with the
A similar explanation was offered by The Guardian:[199] The
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.[Note 18] 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.[200]
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.[202]
Recognition and awards[edit]
There was considerable discussion prior to late 2013 of how to
allocate the credit if the
Additionally
ϕ = 1 2 ( ϕ 1 + i ϕ 2 ϕ 0 + i ϕ 3 ) , displaystyle phi = frac 1 sqrt 2 left( begin array c phi ^ 1 +iphi ^ 2 \phi ^ 0 +iphi ^ 3 end array right);,
(1) while the field has charge +½ under the weak hypercharge U(1) symmetry.[209] 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 articles is Q = T3 + ½ YW.[210] [211] [212] The potential for the Higgs field, plotted as function of ϕ 0 displaystyle phi ^ 0 and ϕ 3 displaystyle phi ^ 3 . It has a Mexican-hat or champagne-bottle profile at the ground. The Higgs part of the Lagrangian is[209] L H =
( ∂ μ − i g W μ a τ a − i 1 2 g ′ B μ ) ϕ
2 + μ 2 ϕ † ϕ − λ ( ϕ † ϕ ) 2 , displaystyle mathcal L _ H =leftleft(partial _ mu -igW_ mu ^ a tau ^ a -i frac 1 2 g'B_ mu right)phi right^ 2 +mu ^ 2 phi ^ dagger phi -lambda (phi ^ dagger phi )^ 2 ,
(2) where W μ a displaystyle W_ mu ^ a and B μ displaystyle B_ mu are the gauge bosons of the
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
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 leftmu right . The measured value of this parameter is
~7002246000000000000♠246 GeV/c2.[104] It has units of mass, and
is the only free parameter of the
W μ displaystyle W_ mu and B μ displaystyle B_ mu arise, which give masses to the W and Z bosons:[209] m W = 1 2 v g , displaystyle m_ W = tfrac 1 2 vleftgright,
(3) m Z = 1 2 v g 2 + g ′ 2 , displaystyle m_ Z = tfrac 1 2 v sqrt g^ 2 + g' ^ 2 ,
(4) 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
γ displaystyle gamma . The mass of the
m H = 2 μ 2 ≡ 2 λ v 2 . displaystyle m_ H = sqrt 2mu ^ 2 equiv sqrt 2lambda v^ 2 .
(5) The quarks and the leptons interact with the
L Y = − λ u i j ϕ 0 − i ϕ 3 2 u ¯ L i u R j + λ u i j ϕ 1 − i ϕ 2 2 d ¯ L i u R j − λ d i j ϕ 0 + i ϕ 3 2 d ¯ L i d R j − λ d i j ϕ 1 + i ϕ 2 2 u ¯ L i d R j − λ e i j ϕ 0 + i ϕ 3 2 e ¯ L i e R j − λ e i j ϕ 1 + i ϕ 2 2 ν ¯ L i e R j + h.c. , displaystyle begin aligned mathcal L _ Y =&-lambda _ u ^ ij frac phi ^ 0 -iphi ^ 3 sqrt 2 overline u _ L ^ i u_ R ^ j +lambda _ u ^ ij frac phi ^ 1 -iphi ^ 2 sqrt 2 overline d _ L ^ i u_ R ^ j \&-lambda _ d ^ ij frac phi ^ 0 +iphi ^ 3 sqrt 2 overline d _ L ^ i d_ R ^ j -lambda _ d ^ ij frac phi ^ 1 +iphi ^ 2 sqrt 2 overline u _ L ^ i d_ R ^ j \&-lambda _ e ^ ij frac phi ^ 0 +iphi ^ 3 sqrt 2 overline e _ L ^ i e_ R ^ j -lambda _ e ^ ij frac phi ^ 1 +iphi ^ 2 sqrt 2 overline nu _ L ^ i e_ R ^ j + textrm h.c. ,end aligned
(6) 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 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 L m = − m u i u ¯ L i u R i − m d i d ¯ L i d R i − m e i e ¯ L i e R i + h.c. , displaystyle mathcal L _ m =-m_ u ^ i overline u _ L ^ i u_ R ^ i -m_ d ^ i overline d _ L ^ i d_ R ^ i -m_ e ^ i overline e _ L ^ i e_ R ^ i + textrm h.c. ,
(7) 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.[209] See also[edit] Standard Model Book: Particles of the Standard Model
W and Z bosons Other Bose–Einstein statistics
Dalitz plot
Notes[edit] ^ Note that such events also occur due to other processes. Detection involves a statistically significant excess of such events at specific energies. ^ a b In the Standard Model, the total decay width of a Higgs boson with a mass of 7002125000000000000♠125 GeV/c2 is predicted to be 6987652085830209000♠4.07×10−3 GeV.[3] The mean lifetime is given by τ = ℏ / Γ displaystyle tau =hbar /Gamma .
^ It is quite common for a law of physics to hold true only if certain
assumptions held true or only under certain conditions. For example,
"the "radiation gauge" condition ∇⋅A(x) = 0 is clearly noncovariant, which means that if we wish to maintain transversality of the photon in all Lorentz frames, the photon field Aμ(x) cannot transform like a four-vector. This is no catastrophe, since the photon field is not an observable, and one can readily show that the S-matrix elements, which are observable have covariant structures .... in gauge theories one might arrange things so that one had a symmetry breakdown because of the noninvariance of the vacuum; but, because the Goldstone et al. proof breaks down, the zero mass Goldstone mesons need not appear." [Emphasis in original] Bernstein (1974) contains an accessible and comprehensive background and review of this area, see external links ^ A field with the "Mexican hat" potential V ( ϕ ) = μ 2 ϕ 2 + λ ϕ 4 displaystyle V(phi )=mu ^ 2 phi ^ 2 +lambda phi ^ 4 and μ 2 < 0 displaystyle mu ^ 2 <0 has a minimum not at zero but at some non-zero value ϕ 0 displaystyle phi _ 0 . By expressing the action in terms of the field ϕ ~ = ϕ − ϕ 0 displaystyle tilde phi =phi -phi _ 0 (where ϕ 0 displaystyle phi _ 0 is a constant independent of position), we find the Yukawa term has a component g ϕ 0 ψ ¯ ψ displaystyle gphi _ 0 bar psi psi . Since both g and ϕ 0 displaystyle phi _ 0 are constants, this looks exactly like the mass term for a fermion of mass g ϕ 0 displaystyle gphi _ 0 . The field ϕ ~ displaystyle tilde phi is then the Higgs field. ^ In the Standard Model, the mass term arising from the Dirac Lagrangian for any fermion ψ displaystyle psi is − m ψ ¯ ψ displaystyle -m bar psi psi . This is not invariant under the electroweak symmetry, as can be seen by writing ψ displaystyle psi in terms of left and right handed components: − m ψ ¯ ψ = − m ( ψ ¯ L ψ R + ψ ¯ R ψ L ) displaystyle -m bar psi psi ;=;-m( bar psi _ L psi _ R + bar psi _ R psi _ L ) i.e., contributions from ψ ¯ L ψ L displaystyle bar psi _ L psi _ L and ψ ¯ R ψ R displaystyle bar psi _ R psi _ R terms do not appear. We see that the mass-generating interaction is
achieved by constant flipping of particle chirality. Since the
spin-half particles have no right/left helicity pair with the same
References[edit] ^ a b c d e "
"Something we cannot yet detect and which, one might say, has been put
there to test and confuse us ... The issue is whether physicists will
be confounded by this puzzle or whether, in contrast to the unhappy
Babylonians, we will continue to build the tower and, as Einstein put
it, 'know the mind of God'."
"And the Lord said, Behold the people are un-confounding my
confounding. And the Lord sighed and said, Go to, let us go down, and
there give them the
^ Sample, Ian (12 June 2009). "Higgs competition: Crack open the
bubbly, the
Peskin, Michael E.; Schroeder, Daniel V. (1995). Introduction to
Further reading[edit] Nambu, Yoichiro; Jona-Lasinio, Giovanni (1961). "Dynamical Model of
Elementary Particles Based on an Analogy with Superconductivity".
Physical Review. 122: 345–358. Bibcode:1961PhRv..122..345N.
doi:10.1103/PhysRev.122.345.
Klein, Abraham; Lee, Benjamin W. (1964). "Does Spontaneous Breakdown
of Symmetry Imply Zero-Mass Particles?".
The Higgs
External links[edit] Wikimedia Commons has media related to Higgs boson. Look up higgs boson in Wiktionary, the free dictionary. Popular science, mass media, and general coverage[edit] Hunting the Higgs
Higgs, Peter (2010). "My Life as a Boson" (PDF).
Cartoon about the search Cham, Jorge (2014-02-19). "True Tales from the Road: The Higgs Boson Re-Explained". Piled Higher and Deeper. Retrieved 2014-02-25. Significant papers and other[edit] "Observation of a new particle in the search for the Standard Model
Introductions to the field[edit] For a pedagogic introduction to electroweak symmetry breaking with
step by step derivations, not found in texts, of many key relations,
see http://www.quantumfieldtheory.info/Electroweak_Sym_breaking.pdf
Spontaneous symmetry breaking, gauge theories, the
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Bosons Gauge Photon Gluon W and Z bosons Scalar Higgs boson Others Ghosts Hypothetical Superpartners Gauginos Gluino Gravitino Photino Others Higgsino
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Axino
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