Standard Model ofparticle physics
Elementary particles of the Standard Model
Background Particle physics Standard Model Quantum field theory Gauge theory Spontaneous symmetry breaking Higgs mechanism
Constituents Electroweak interaction Quantum chromodynamics CKM matrix Standard Model mathematics
Limitations Strong CP problem Hierarchy problem Neutrino oscillations Physics beyond the Standard Model
Scientists Rutherford Thomson Chadwick Bose Sudarshan Davis Jr Anderson Fermi Dirac Feynman Rubbia Gell-Mann Kendall Taylor Friedman Powell Anderson Glashow Iliopoulos Lederman Maiani Meer Cowan Nambu Chamberlain Cabibbo Schwartz Perl Majorana Weinberg Lee Ward Salam Kobayashi Maskawa Mills Yang Yukawa 't Hooft Veltman Gross Pais Pauli Politzer Reines Schwinger Wilczek Cronin Fitch Vleck Higgs Englert Brout Hagen Guralnik Kibble de Mayolo Lattes Zweig
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Quantum field theory
Feynman diagram
History
Background Field theory Electromagnetism Weak force Strong force Quantum mechanics Special relativity General relativity Gauge theory Yang–Mills theory
Symmetries Symmetry in quantum mechanics C-symmetry P-symmetry T-symmetry Lorentz symmetry Poincaré symmetry Gauge symmetry Explicit symmetry breaking Spontaneous symmetry breaking Noether charge Topological charge
Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation value Feynman diagram Lattice field theory LSZ reduction formula Partition function Path Integral Formulation Propagator Quantization Regularization Renormalization Vacuum state Wick's theorem Wightman axioms
Equations Dirac equation Klein–Gordon equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations Schwinger-Dyson equation Renormalization group equation
Standard Model Quantum electrodynamics Electroweak interaction Quantum chromodynamics Higgs mechanism
Incomplete theories String theory Supersymmetry Technicolor Theory of everything Quantum gravity
Scientists Adler Anderson Anselm Bargmann Becchi Belavin Bell Berezin Bethe Bjorken Bleuer Bogoliubov Brodsky Brout Buchholz Cachazo Callan Cardy Coleman Connes Dashen DeWitt Dirac Doplicher Dyson Englert Faddeev Fadin Fayet Fermi Feynman Fierz Fock Frampton Fritzsch Fröhlich Fredenhagen Furry Glashow Gell-Mann Glimm Goldstone Gribov Gross Gupta Guralnik Haag Hagen Han Heisenberg Hepp Higgs 't Hooft Iliopoulos Ivanenko Jackiw Jaffe Jona-Lasinio Jordan Jost Källén Kendall Kinoshita Kim Klebanov Kontsevich Kreimer Kuraev Landau Lee Lee Lehmann Leutwyler Lipatov Łopuszański Low Lüders Maiani Majorana Maldacena Matsubara Migdal Mills Møller Naimark Nambu Neveu Nishijima Oehme Oppenheimer Osborn Osterwalder Parisi Pauli Peccei Peskin Plefka Polchinski Polyakov Pomeranchuk Popov Proca Quinn Rouet Rubakov Ruelle Sakurai Salam Schrader Schwarz Schwinger Segal Seiberg Semenoff Shifman Shirkov Skyrme Sommerfield Stora Stueckelberg Sudarshan Symanzik Takahashi Thirring Tomonaga Tyutin Vainshtein Veltman Veneziano Virasoro Ward Weinberg Weisskopf Wentzel Wess Wetterich Weyl Wick Wightman Wigner Wilczek Wilson Witten Yang Yukawa Zamolodchikov Zamolodchikov Zee Zimmermann Zinn-Justin Zuber Zumino
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TheStandard Model ofparticle physics is agaugequantum field theory containing theinternal symmetries of theunitaryproduct groupSU(3) × SU(2) × U(1). The theory is commonly viewed as describing the fundamental set of particles – theleptons,quarks,gauge bosons and theHiggs boson.

The Standard Model isrenormalizable and mathematically self-consistent;^[1] however, despite having huge and continued successes in providing experimental predictions, it does leave someunexplained phenomena.^[2] In particular, although the physics ofspecial relativity is incorporated,general relativity is not, and the Standard Model will fail at energies or distances where thegraviton is expected to emerge. Therefore, in a modern field theory context, it is seen as aneffective field theory.

The standard model is aquantum field theory, meaning its fundamental objects arequantum fields, which are defined at all points in spacetime. QFT treats particles asexcited states (also calledquanta) of their underlying quantumfields, which are more fundamental than the particles. These fields are

• thefermion fields,ψ, which account for "matter particles";
• theelectroweak boson fields${\displaystyle W_1}$,${\displaystyle W_2}$,${\displaystyle W_3}$, andB;
• thegluon field,G_a; and
• theHiggs field,φ.

That these arequantum rather thanclassical fields has the mathematical consequence that they areoperator-valued. In particular, values of the fields generally do not commute. As operators, they act upon a quantum state (ket vector).

As is common in quantum theory, there is more than one way to look at things. At first the basic fields given above may not seem to correspond well with the "fundamental particles" in the chart above, but there are several alternative presentations that, in particular contexts, may be more appropriate than those that are given above.

Rather than having one fermion fieldψ, it can be split up into separate components for each type of particle. This mirrors the historical evolution of quantum field theory, since the electron componentψ_e (describing theelectron and its antiparticle thepositron) is then the originalψ field ofquantum electrodynamics, which was later accompanied byψ_μ andψ_τ fields for themuon andtauon respectively (and their antiparticles). Electroweak theory added${\displaystyle {\psi }_{{\nu }_{\mathrm{e}}},{\psi }_{{\nu }_{\mu }}}$, and${\displaystyle {\psi }_{{\nu }_{\tau }}}$ for the correspondingneutrinos. Thequarks add still further components. In order to befour-spinors like the electron and otherlepton components, there must be one quark component for every combination offlavor andcolor, bringing the total to 24 (3 for charged leptons, 3 for neutrinos, and 2·3·3 = 18 for quarks). Each of these is a four componentbispinor, for a total of 96 complex-valued components for the fermion field.

An important definition is thebarred fermion field${\displaystyle \overline{\psi }}$, which is defined to be${\displaystyle {\psi }^{†}{\gamma }^0}$, where${\displaystyle †}$ denotes theHermitian adjoint ofψ, andγ⁰ is the zerothgamma matrix. Ifψ is thought of as ann × 1 matrix then${\displaystyle \overline{\psi }}$ should be thought of as a1 × n matrix.

An independent decomposition ofψ is that intochirality components:

where${\displaystyle {\gamma }_5}$ isthe fifth gamma matrix. This is very important in the Standard Model becauseleft and right chirality components are treated differently by the gauge interactions.

In particular, underweak isospinSU(2) transformations the left-handed particles are weak-isospin doublets, whereas the right-handed are singlets – i.e. the weak isospin ofψ_R is zero. Put more simply, the weak interaction could rotate e.g. a left-handed electron into a left-handed neutrino (with emission of aW⁻), but could not do so with the same right-handed particles. As an aside, the right-handed neutrino originally did not exist in the standard model – but the discovery ofneutrino oscillation implies thatneutrinos must have mass, and since chirality can change during the propagation of a massive particle, right-handed neutrinos must exist in reality. This does not however change the (experimentally proven) chiral nature of the weak interaction.

Furthermore,U(1) acts differently on${\displaystyle {\psi }_{\mathrm{e}}^{\mathrm{L}}}$ and${\displaystyle {\psi }_{\mathrm{e}}^{\mathrm{R}}}$ (because they have differentweak hypercharges).

A distinction can thus be made between, for example, the mass and interactioneigenstates of the neutrino. The former is the state that propagates in free space, whereas the latter is thedifferent state that participates in interactions. Which is the "fundamental" particle? For the neutrino, it is conventional to define the "flavor" (ν
_e,ν
_μ, orν
_τ) by the interaction eigenstate, whereas for the quarks we define the flavor (up, down, etc.) by the mass state. We can switch between these states using theCKM matrix for the quarks, or thePMNS matrix for the neutrinos (the charged leptons on the other hand are eigenstates of both mass and flavor).

As an aside, if a complex phase term exists within either of these matrices, it will give rise to directCP violation, which could explain the dominance of matter over antimatter in our current universe. This has been proven for the CKM matrix, and is expected for the PMNS matrix.

Finally, the quantum fields are sometimes decomposed into "positive" and "negative" energy parts:ψ =ψ⁺ +ψ⁻. This is not so common when a quantum field theory has been set up, but often features prominently in the process of quantizing a field theory.

Due to theHiggs mechanism, the electroweak boson fields${\displaystyle W_1}$,${\displaystyle W_2}$,${\displaystyle W_3}$, and${\displaystyle B}$ "mix" to create the states that are physically observable. To retain gauge invariance, the underlying fields must be massless, but the observable states cangain masses in the process. These states are:

The massive neutral(Z) boson:$${\displaystyle Z=\cos {\theta }_{\mathrm{W}}{W}_3-\sin {\theta }_{\mathrm{W}}B}$$The massless neutral boson:$${\displaystyle A=\sin {\theta }_{\mathrm{W}}{W}_3+\cos {\theta }_{\mathrm{W}}B}$$The massive chargedW bosons:$${\displaystyle W^{\pm }=\frac{1}{\sqrt{2}}\left(W_1\mp i{W}_2\right)}$$whereθ_W is theWeinberg angle.

TheA field is thephoton, which corresponds classically to the well-knownelectromagnetic four-potential – i.e. the electric and magnetic fields. TheZ field actually contributes in every process the photon does, but due to its large mass, the contribution is usually negligible.

Much of the qualitative descriptions of the standard model in terms of "particles" and "forces" comes from the perturbativequantum field theory view of the model. In this, theLagrangian is decomposed as${\displaystyle \mathcal{L}={\mathcal{L}}_0+{\mathcal{L}}_{\mathrm{I}}}$ into separatefree field andinteraction Lagrangians. The free fields care for particles in isolation, whereas processes involving several particles arise through interactions. The idea is that the state vector should only change when particles interact, meaning a free particle is one whose quantum state is constant. This corresponds to theinteraction picture in quantum mechanics.

In the more commonSchrödinger picture, even the states of free particles change over time: typically the phase changes at a rate that depends on their energy. In the alternativeHeisenberg picture, state vectors are kept constant, at the price of having the operators (in particular theobservables) be time-dependent. The interaction picture constitutes an intermediate between the two, where some time dependence is placed in the operators (the quantum fields) and some in the state vector. In QFT, the former is called the free field part of the model, and the latter is called the interaction part. The free field model can be solved exactly, and then the solutions to the full model can be expressed as perturbations of the free field solutions, for example using theDyson series.

It should be observed that the decomposition into free fields and interactions is in principle arbitrary. For example,renormalization inQED modifies the mass of the free field electron to match that of a physical electron (with an electromagnetic field), and will in doing so add a term to the free field Lagrangian which must be cancelled by a counterterm in the interaction Lagrangian, that then shows up as a two-line vertex in theFeynman diagrams. This is also how the Higgs field is thought to give particlesmass: the part of the interaction term that corresponds to the nonzero vacuum expectation value of the Higgs field is moved from the interaction to the free field Lagrangian, where it looks just like a mass term having nothing to do with the Higgs field.

Under the usual free/interaction decomposition, which is suitable for low energies, the free fields obey the following equations:

• The fermion fieldψ satisfies theDirac equation;${\displaystyle (i\hslash {\gamma }^{\mu }{\mathrm{\partial }}_{\mu }-m_{\mathrm{f}}c){\psi }_{\mathrm{f}}=0}$ for each type${\displaystyle f}$ of fermion.
• The photon fieldA satisfies thewave equation${\displaystyle {\mathrm{\partial }}_{\mu }{\mathrm{\partial }}^{\mu }{A}^{\nu }=0}$.
• The Higgs fieldφ satisfies theKlein–Gordon equation.
• The weak interaction fieldsZ,W^± satisfy theProca equation.

These equations can be solved exactly. One usually does so by considering first solutions that are periodic with some periodL along each spatial axis; later taking the limit:L → ∞ will lift this periodicity restriction.

In the periodic case, the solution for a fieldF (any of the above) can be expressed as aFourier series of the form$${\displaystyle F(x)=\beta \sum _{\mathbf{p}}\sum _r{E}_{\mathbf{p}}^{-\frac{1}{2}}\left(a_r(\mathbf{p})u_r(\mathbf{p})e^{-\frac{ipx}{\hslash }}+b_r^{†}(\mathbf{p})v_r(\mathbf{p})e^{\frac{ipx}{\hslash }}\right)}$$where:

• β is a normalization factor; for the fermion field${\displaystyle {\psi }_{\mathrm{f}}}$ it is$\sqrt{m_{\mathrm{f}}{c}^2/V}$, where${\displaystyle V=L^3}$ is the volume of the fundamental cell considered; for the photon fieldA^μ it is${\displaystyle \hslash c/\sqrt{2V}}$.
• The sum overp is over all momenta consistent with the periodL, i.e., over all vectors${\displaystyle \frac{2\pi \hslash }{L}(n_1,n_2,n_3)}$ where${\displaystyle n_1,n_2,n_3}$ are integers.
• The sum overr covers other degrees of freedom specific for the field, such as polarization or spin; it usually comes out as a sum from1 to2 or from1 to3.
• E_p is the relativistic energy for a momentump quantum of the field,$=\sqrt{m^2{c}^4+c^2{\mathbf{p}}^2}$ when the rest mass ism.
• a_r(p) and${\displaystyle b_r^{†}(\mathbf{p})}$ areannihilation and creation operators respectively for "a-particles" and "b-particles" respectively of momentump; "b-particles" are theantiparticles of "a-particles". Different fields have different "a-" and "b-particles". For some fields,a andb are the same.
• u_r(p) andv_r(p) are non-operators that carry the vector or spinor aspects of the field (where relevant).
• ${\displaystyle p=(E_{\mathbf{p}}/c,\mathbf{p})}$ is thefour-momentum for a quantum with momentump.${\displaystyle px=p_{\mu }{x}^{\mu }}$ denotes an inner product offour-vectors.

In the limitL → ∞, the sum would turn into an integral with help from theV hidden insideβ. The numeric value ofβ also depends on the normalization chosen for${\displaystyle u_r(\mathbf{p})}$ and${\displaystyle v_r(\mathbf{p})}$.

Technically,${\displaystyle a_r^{†}(\mathbf{p})}$ is theHermitian adjoint of the operatora_r(p) in theinner product space ofket vectors. The identification of${\displaystyle a_r^{†}(\mathbf{p})}$ anda_r(p) ascreation and annihilation operators comes from comparing conserved quantities for a state before and after one of these have acted upon it.${\displaystyle a_r^{†}(\mathbf{p})}$ can for example be seen to add one particle, because it will add1 to the eigenvalue of the a-particlenumber operator, and the momentum of that particle ought to bep since the eigenvalue of the vector-valuedmomentum operator increases by that much. For these derivations, one starts out with expressions for the operators in terms of the quantum fields. That the operators with${\displaystyle †}$ are creation operators and the one without annihilation operators is a convention, imposed by the sign of the commutation relations postulated for them.

An important step in preparation for calculating in perturbative quantum field theory is to separate the "operator" factorsa andb above from their corresponding vector or spinor factorsu andv. The vertices ofFeynman graphs come from the way thatu andv from different factors in the interaction Lagrangian fit together, whereas the edges come from the way that theas andbs must be moved around in order to put terms in the Dyson series on normal form.

The Lagrangian can also be derived without using creation and annihilation operators (the "canonical" formalism) by using apath integral formulation, pioneered by Feynman building on the earlier work of Dirac.Feynman diagrams are pictorial representations of interaction terms. A quick derivation is indeed presented at the article onFeynman diagrams.

We can now give some more detail about the aforementioned free and interaction terms appearing in the Standard ModelLagrangian density. Any such term must be both gauge and reference-frame invariant, otherwise the laws of physics would depend on an arbitrary choice or the frame of an observer. Therefore, theglobalPoincaré symmetry, consisting oftranslational symmetry,rotational symmetry and the inertial reference frame invariance central to the theory ofspecial relativity must apply. ThelocalSU(3) × SU(2) × U(1) gauge symmetry is theinternal symmetry. The three factors of the gauge symmetry together give rise to the three fundamental interactions, after some appropriate relations have been defined, as we shall see.

A free particle can be represented by a mass term, and akinetic term that relates to the "motion" of the fields.

The kinetic term for a Dirac fermion is$${\displaystyle i\overline{\psi }{\gamma }^{\mu }{\mathrm{\partial }}_{\mu }\psi }$$where the notations are carried from earlier in the article.ψ can represent any, or all, Dirac fermions in the standard model. Generally, as below, this term is included within the couplings (creating an overall "dynamical" term).

For the spin-1 fields, first define the field strengthtensor$${\displaystyle F_{\mu \nu }^a={\mathrm{\partial }}_{\mu }{A}_{\nu }^a-{\mathrm{\partial }}_{\nu }{A}_{\mu }^a+g{f}^{abc}{A}_{\mu }^b{A}_{\nu }^c}$$for a given gauge field (here we useA), with gaugecoupling constantg. The quantityf^abc is thestructure constant of the particular gauge group, defined by the commutator$${\displaystyle [t_a,t_b]=i{f}^{abc}{t}_c,}$$wheret_i are thegenerators of the group. In anabelian (commutative) group (such as theU(1) we use here) the structure constants vanish, since the generatorst_a all commute with each other. Of course, this is not the case in general – the standard model includes the non-AbelianSU(2) andSU(3) groups (such groups lead to what is called aYang–Mills gauge theory).

We need to introduce three gauge fields corresponding to each of the subgroupsSU(3) × SU(2) × U(1).

• The gluon field tensor will be denoted by${\displaystyle G_{\mu \nu }^a}$, where the indexa labels elements of the8 representation of colorSU(3). The strong coupling constant is conventionally labelledg_s (or simplyg where there is no ambiguity).The observations leading to the discovery of this part of the Standard Model are discussed in the article inquantum chromodynamics.
• The notation${\displaystyle W_{\mu \nu }^a}$ will be used for the gauge field tensor ofSU(2) wherea runs over the3 generators of this group. The coupling can be denotedg_w or again simplyg. The gauge field will be denoted by${\displaystyle W_{\mu }^a}$.
• The gauge field tensor for theU(1) of weak hypercharge will be denoted byB_μν, the coupling byg′, and the gauge field byB_μ.

The kinetic term can now be written as$${\displaystyle {\mathcal{L}}_{\mathrm{k}\mathrm{i}\mathrm{n}}=-\frac{1}{4}{B}_{\mu \nu }{B}^{\mu \nu }-\frac{1}{2}\mathrm{t}\mathrm{r}{W}_{\mu \nu }{W}^{\mu \nu }-\frac{1}{2}\mathrm{t}\mathrm{r}{G}_{\mu \nu }{G}^{\mu \nu }}$$where the traces are over theSU(2) andSU(3) indices hidden inW andG respectively. The two-index objects are the field strengths derived fromW andG the vector fields. There are also two extra hidden parameters: the theta angles forSU(2) andSU(3).

The next step is to "couple" the gauge fields to the fermions, allowing for interactions.

The electroweak sector interacts with the symmetry groupU(1) × SU(2)_L, where the subscript L indicates coupling only to left-handed fermions.$${\displaystyle {\mathcal{L}}_{\mathrm{E}\mathrm{W}}=\sum _{\psi }\overline{\psi }{\gamma }^{\mu }\left(i{\mathrm{\partial }}_{\mu }-g^{\mathrm{\prime }}\frac{1}{2}{Y}_{\mathrm{W}}{B}_{\mu }-g\frac{1}{2}\mathit{\tau }{\mathbf{W}}_{\mu }\right)\psi }$$whereB_μ is theU(1) gauge field;Y_W is theweak hypercharge (the generator of theU(1) group);W_μ is the three-componentSU(2) gauge field; and the components ofτ are thePauli matrices (infinitesimal generators of theSU(2) group) whose eigenvalues give the weak isospin. Note that we have to redefine a newU(1) symmetry ofweak hypercharge, different from QED, in order to achieve the unification with the weak force. Theelectric chargeQ, third component ofweak isospinT₃ (also calledT_z,I₃ orI_z) and weak hyperchargeY_W are related by$${\displaystyle Q=T_3+\frac{1}{2}{Y}_{\mathrm{W}},}$$(or by thealternative conventionQ =T₃ +Y_W). The first convention, used in this article, is equivalent to the earlierGell-Mann–Nishijima formula. It makes the hypercharge be twice the average charge of a given isomultiplet.

One may then define theconserved current for weak isospin as$${\displaystyle {\mathbf{j}}_{\mu }=\frac{1}{2}{\overline{\psi }}_{\mathrm{L}}{\gamma }_{\mu }\mathit{\tau }{\psi }_{\mathrm{L}}}$$and for weak hypercharge as$${\displaystyle j_{\mu }^Y=2(j_{\mu }^{\mathrm{e}\mathrm{m}}-j_{\mu }^3),}$$where${\displaystyle j_{\mu }^{\mathrm{e}\mathrm{m}}}$ is the electric current and${\displaystyle j_{\mu }^3}$ the third weak isospin current. As explainedabove,these currents mix to create the physically observed bosons, which also leads to testable relations between the coupling constants.

To explain this in a simpler way, we can see the effect of the electroweak interaction by picking out terms from the Lagrangian. We see that the SU(2) symmetry acts on each (left-handed) fermion doublet contained inψ, for example$${\displaystyle -\frac{g}{2}({\overline{\nu }}_e\overline{e}){\tau }^{+}{\gamma }_{\mu }(W^{+}{)}^{\mu }\left(\begin{array}{c}{\nu }_e\\ e\end{array}\right)=-\frac{g}{2}{\overline{\nu }}_e{\gamma }_{\mu }(W^{+}{)}^{\mu }e}$$where the particles are understood to be left-handed, and where

This is an interaction corresponding to a "rotation in weak isospin space" or in other words, a transformation betweene_L andν_eL via emission of aW⁻ boson. TheU(1) symmetry, on the other hand, is similar to electromagnetism, but acts on all "weak hypercharged" fermions (both left- and right-handed) via the neutralZ⁰, as well as thecharged fermions via the photon.

The quantum chromodynamics (QCD) sector defines the interactions betweenquarks andgluons, withSU(3) symmetry, generated byT_a. Since leptons do not interact with gluons, they are not affected by this sector. The Dirac Lagrangian of the quarks coupled to the gluon fields is given by$${\displaystyle {\mathcal{L}}_{\mathrm{Q}\mathrm{C}\mathrm{D}}=i\overline{U}\left({\mathrm{\partial }}_{\mu }-i{g}_s{G}_{\mu }^a{T}^a\right){\gamma }^{\mu }U+i\overline{D}\left({\mathrm{\partial }}_{\mu }-i{g}_s{G}_{\mu }^a{T}^a\right){\gamma }^{\mu }D.}$$whereU andD are the Dirac spinors associated with up and down-type quarks, and other notations are continued from the previous section.

The mass term arising from the Dirac Lagrangian (for any fermionψ) is${\displaystyle -m\overline{\psi }\psi }$, which isnot invariant under the electroweak symmetry. This can be seen by writingψ in terms of left and right-handed components (skipping the actual calculation):$${\displaystyle -m\overline{\psi }\psi =-m({\overline{\psi }}_{\mathrm{L}}{\psi }_{\mathrm{R}}+{\overline{\psi }}_{\mathrm{R}}{\psi }_{\mathrm{L}})}$$i.e. contribution from${\displaystyle {\overline{\psi }}_{\mathrm{L}}{\psi }_{\mathrm{L}}}$ and${\displaystyle {\overline{\psi }}_{\mathrm{R}}{\psi }_{\mathrm{R}}}$ terms do not appear. We see that the mass-generating interaction is achieved by constant flipping of particle chirality. The spin-half particles have no right/left chirality pair with the sameSU(2) representations and equal and opposite weak hypercharges, so assuming these gauge charges are conserved in the vacuum, none of the spin-half particles could ever swap chirality, and must remain massless. Additionally, we know experimentally that the W and Z bosons are massive, but a boson mass term contains the combination e.g.A^μA_μ, which clearly depends on the choice of gauge. Therefore, none of the standard model fermionsor bosons can "begin" with mass, but must acquire it by some other mechanism.

The solution to both these problems comes from theHiggs mechanism, which involves scalar fields (the number of which depend on the exact form of Higgs mechanism) which (to give the briefest possible description) are "absorbed" by the massive bosons as degrees of freedom, and which couple to the fermions via Yukawa coupling to create what looks like mass terms.

In the Standard Model, theHiggs field is a complex scalar field of the groupSU(2)_L:$${\displaystyle \varphi =\frac{1}{\sqrt{2}}\left(\begin{array}{c}{\varphi }^{+}\\ {\varphi }^0\end{array}\right),}$$where the superscripts+ and0 indicate the electric charge (Q) of the components. The weak hypercharge (Y_W) of both components is1.

The Higgs part of the Lagrangian is$${\displaystyle {\mathcal{L}}_{\mathrm{H}}={\left[\left({\mathrm{\partial }}_{\mu }-ig{W}_{\mu }^a{t}^a-i{g}^{\prime }{Y}_{\varphi }{B}_{\mu }\right)\varphi \right]}^2+{\mu }^2{\varphi }^{†}\varphi -\lambda ({\varphi }^{†}\varphi {)}^2,}$$whereλ > 0 andμ² > 0, so that the mechanism ofspontaneous symmetry breaking can be used. There is a parameter here, at first hidden within the shape of the potential, that is very important. In aunitarity gauge one can set${\displaystyle {\varphi }^{+}=0}$ and make${\displaystyle {\varphi }^0}$ real. Then${\displaystyle ⟨{\varphi }^0⟩=v}$ is the non-vanishingvacuum expectation value of the Higgs field.${\displaystyle v}$ has units of mass, and it is the only parameter in the Standard Model that is not dimensionless. It is also much smaller than the Planck scale and about twice the Higgs mass, setting the scale for the mass of all other particles in the Standard Model. This is the only real fine-tuning to a small nonzero value in the Standard Model. Quadratic terms inW_μ andB_μ arise, which give masses to the W and Z bosons:

The mass of the Higgs boson itself is given by$M_{\mathrm{H}}=\sqrt{2{\mu }^2}\equiv \sqrt{2\lambda v^2}.$

TheYukawa interaction terms are$${\displaystyle {\mathcal{L}}_{\text{Yukawa}}=(Y_{\text{u}}{)}_{mn}({\overline{q}}_{\text{L}}{)}_m\tilde{\phi }(u_{\text{R}}{)}_n+(Y_{\text{d}}{)}_{mn}({\overline{q}}_{\text{L}}{)}_m\phi (d_{\text{R}}{)}_n+(Y_{\text{e}}{)}_{mn}({\overline{L}}_{\text{L}}{)}_m\tilde{\phi }(e_{\text{R}}{)}_n+\mathrm{h}.\mathrm{c}.}$$where${\displaystyle Y_{\text{u}}}$,${\displaystyle Y_{\text{d}}}$, and${\displaystyle Y_{\text{e}}}$ are3 × 3 matrices of Yukawa couplings, with themn term giving the coupling of the generationsm andn, and h.c. means Hermitian conjugate of preceding terms. The fields${\displaystyle q_{\text{L}}}$ and${\displaystyle L_{\text{L}}}$ are left-handed quark and lepton doublets. Likewise,${\displaystyle u_{\text{R}}}$,${\displaystyle d_{\text{R}}}$ and${\displaystyle e_{\text{R}}}$ are right-handed up-type quark, down-type quark, and lepton singlets. Finally${\displaystyle \phi }$ is the Higgs doublet and${\displaystyle \tilde{\phi }=i{\tau }_2{\phi }^{\ast }}$

As previously mentioned, evidence shows neutrinos must have mass. But within the standard model, the right-handed neutrino does not exist, so even with a Yukawa coupling neutrinos remain massless. An obvious solution^[4] is to simplyadd a right-handed neutrinoν_R, which requires the addition of a newDirac mass term in the Yukawa sector:$${\displaystyle {\mathcal{L}}_{\nu }^{\text{Dir}}=(Y_{\nu }{)}_{mn}({\overline{L}}_L{)}_m\phi ({\nu }_R{)}_n+\mathrm{h}.\mathrm{c}.}$$

This field however must be asterile neutrino, since being right-handed it experimentally belongs to an isospin singlet (T₃ = 0) and also has chargeQ = 0, implyingY_W = 0 (seeabove) i.e. it does not even participate in the weak interaction. The experimental evidence for sterile neutrinos is currently inconclusive.^[5]

Another possibility to consider is that the neutrino satisfies theMajorana equation, which at first seems possible due to its zero electric charge. In this case a newMajorana mass term is added to the Yukawa sector:$${\displaystyle {\mathcal{L}}_{\nu }^{\text{Maj}}=-\frac{1}{2}m\left({\overline{\nu }}^C\nu +\overline{\nu }{\nu }^C\right)}$$whereC denotes a charge conjugated (i.e. anti-) particle, and the${\displaystyle \nu }$ terms are consistently all left (or all right) chirality (note that a left-chirality projection of an antiparticle is a right-handed field; care must be taken here due to different notations sometimes used). Here we are essentially flipping between left-handed neutrinos and right-handed anti-neutrinos (it is furthermore possible butnot necessary that neutrinos are their own antiparticle, so these particles are the same). However, for left-chirality neutrinos, this term changes weak hypercharge by 2 units – not possible with the standard Higgs interaction, requiring the Higgs field to be extended to include an extra triplet with weak hypercharge = 2^[4] – whereas for right-chirality neutrinos, no Higgs extensions are necessary. For both left and right chirality cases, Majorana terms violatelepton number, but possibly at a level beyond the current sensitivity of experiments to detect such violations.

It is possible to includeboth Dirac and Majorana mass terms in the same theory, which (in contrast to the Dirac-mass-only approach) can provide a “natural” explanation for the smallness of the observed neutrino masses, by linking the right-handed neutrinos to yet-unknown physics around the GUT scale^[6] (seeseesaw mechanism).

Since in any case new fields must be postulated to explain the experimental results, neutrinos are an obvious gateway to searching physicsbeyond the Standard Model.

This section provides more detail on some aspects, and some reference material. Explicit Lagrangian terms are also providedhere.

The Standard Model has the following fields. These describe onegeneration of leptons and quarks, and there are three generations, so there are three copies of each fermionic field. By CPT symmetry, there is a set of fermions and antifermions with opposite parity and charges. If a left-handed fermion spans some representation its antiparticle (right-handed antifermion) spans thedual representation^[7] (note that${\displaystyle \overline{\mathbf{2}}=\mathbf{2}}$ for SU(2), because it ispseudo-real). The column "representation" indicates under whichrepresentations of thegauge groups that each field transforms, in the order (SU(3), SU(2), U(1)) and for the U(1) group, the value of theweak hypercharge is listed. There are twice as many left-handed lepton field components as right-handed lepton field components in each generation, but an equal number of left-handed quark and right-handed quark field components.

Field content of the standard model
Spin 1 – the gauge fields
Symbol	Associated charge	Group	Coupling	Representation[8]
${\displaystyle B}$	Weak hypercharge	U(1)Y	${\displaystyle g^{\prime }}$ or${\displaystyle g_1}$	${\displaystyle (\mathbf{1},\mathbf{1},0)}$
${\displaystyle W}$	Weak isospin	SU(2)L	${\displaystyle g_w}$ or${\displaystyle g_2}$	${\displaystyle (\mathbf{1},\mathbf{3},0)}$
${\displaystyle G}$	color	SU(3)C	${\displaystyle g_s}$ or${\displaystyle g_3}$	${\displaystyle (\mathbf{8},\mathbf{1},0)}$
Spin 1⁄2 – the fermions
Symbol	Name	Baryon number	Lepton number	Representation
${\displaystyle q_{\mathrm{L}}}$	Left-handedquark	${\displaystyle \frac{1}{3}}$	${\displaystyle 0}$	${\displaystyle (\mathbf{3},\mathbf{2},\frac{1}{3})}$
${\displaystyle u_{\mathrm{R}}}$	Right-handed quark (up)	${\displaystyle \frac{1}{3}}$	${\displaystyle 0}$	${\displaystyle (\mathbf{3},\mathbf{1},\frac{4}{3})}$
${\displaystyle d_{\mathrm{R}}}$	Right-handed quark (down)	${\displaystyle \frac{1}{3}}$	${\displaystyle 0}$	${\displaystyle (\mathbf{3},\mathbf{1},-\frac{2}{3})}$
${\displaystyle {\ell }_{\mathrm{L}}}$	Left-handedlepton	${\displaystyle 0}$	${\displaystyle 1}$	${\displaystyle (\mathbf{1},\mathbf{2},-1)}$
${\displaystyle {\ell }_{\mathrm{R}}}$	Right-handed lepton	${\displaystyle 0}$	${\displaystyle 1}$	${\displaystyle (\mathbf{1},\mathbf{1},-2)}$
Spin 0 – the scalar boson
Symbol	Name	Representation
${\displaystyle H}$	Higgs boson	${\displaystyle (\mathbf{1},\mathbf{2},1)}$

This table is based in part on data gathered by theParticle Data Group.^[9]

Left-handed fermions in the Standard Model
Generation 1
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Weak hypercharge	Color charge [lhf 1]	Mass[lhf 2]
Electron	e−	${\displaystyle -1}$	${\displaystyle -\frac{1}{2}}$	${\displaystyle -1}$	${\displaystyle \mathbf{1}}$	511 keV
Positron	e+	${\displaystyle +1}$	${\displaystyle 0}$	${\displaystyle +2}$	${\displaystyle \mathbf{1}}$	511 keV
Electron neutrino	ν e	${\displaystyle 0}$	${\displaystyle +\frac{1}{2}}$	${\displaystyle -1}$	${\displaystyle \mathbf{1}}$	< 0.28 eV[lhf 3][lhf 4]
Electron antineutrino	ν e	${\displaystyle 0}$	${\displaystyle 0}$	${\displaystyle 0}$	${\displaystyle \mathbf{1}}$	< 0.28 eV[lhf 3][lhf 4]
Up quark	u	${\displaystyle +\frac{2}{3}}$	${\displaystyle +\frac{1}{2}}$	${\displaystyle +\frac{1}{3}}$	${\displaystyle \mathbf{3}}$	~ 3 MeV[lhf 5]
Up antiquark	u	${\displaystyle -\frac{2}{3}}$	${\displaystyle 0}$	${\displaystyle -\frac{4}{3}}$	${\displaystyle \overline{\mathbf{3}}}$	~ 3 MeV[lhf 5]
Down quark	d	${\displaystyle -\frac{1}{3}}$	${\displaystyle -\frac{1}{2}}$	${\displaystyle +\frac{1}{3}}$	${\displaystyle \mathbf{3}}$	~ 6 MeV[lhf 5]
Down antiquark	d	${\displaystyle +\frac{1}{3}}$	${\displaystyle 0}$	${\displaystyle +\frac{2}{3}}$	${\displaystyle \overline{\mathbf{3}}}$	~ 6 MeV[lhf 5]
Generation 2
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Weak hypercharge	Color charge [lhf 1]	Mass [lhf 2]
Muon	μ−	${\displaystyle -1}$	${\displaystyle -\frac{1}{2}}$	${\displaystyle -1}$	${\displaystyle \mathbf{1}}$	106 MeV
Antimuon	μ+	${\displaystyle +1}$	${\displaystyle 0}$	${\displaystyle +2}$	${\displaystyle \mathbf{1}}$	106 MeV
Muon neutrino	ν μ	${\displaystyle 0}$	${\displaystyle +\frac{1}{2}}$	${\displaystyle -1}$	${\displaystyle \mathbf{1}}$	< 0.28 eV[lhf 3][lhf 4]
Muon antineutrino	ν μ	${\displaystyle 0}$	${\displaystyle 0}$	${\displaystyle 0}$	${\displaystyle \mathbf{1}}$	< 0.28 eV[lhf 3][lhf 4]
Charm quark	c	${\displaystyle +\frac{2}{3}}$	${\displaystyle +\frac{1}{2}}$	${\displaystyle +\frac{1}{3}}$	${\displaystyle \mathbf{3}}$	~ 1.3 GeV
Charm antiquark	c	${\displaystyle -\frac{2}{3}}$	${\displaystyle 0}$	${\displaystyle -\frac{4}{3}}$	${\displaystyle \overline{\mathbf{3}}}$	~ 1.3 GeV
Strange quark	s	${\displaystyle -\frac{1}{3}}$	${\displaystyle -\frac{1}{2}}$	${\displaystyle +\frac{1}{3}}$	${\displaystyle \mathbf{3}}$	~ 100 MeV
Strange antiquark	s	${\displaystyle +\frac{1}{3}}$	${\displaystyle 0}$	${\displaystyle +\frac{2}{3}}$	${\displaystyle \overline{\mathbf{3}}}$	~ 100 MeV
Generation 3
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Weak hypercharge	Color charge [lhf 1]	Mass[lhf 2]
Tau	τ−	${\displaystyle -1}$	${\displaystyle -\frac{1}{2}}$	${\displaystyle -1}$	${\displaystyle \mathbf{1}}$	1.78 GeV
Antitau	τ+	${\displaystyle +1}$	${\displaystyle 0}$	${\displaystyle +2}$	${\displaystyle \mathbf{1}}$	1.78 GeV
Tau neutrino	ν τ	${\displaystyle 0}$	${\displaystyle +\frac{1}{2}}$	${\displaystyle -1}$	${\displaystyle \mathbf{1}}$	< 0.28 eV[lhf 3][lhf 4]
Tau antineutrino	ν τ	${\displaystyle 0}$	${\displaystyle 0}$	${\displaystyle 0}$	${\displaystyle \mathbf{1}}$	< 0.28 eV[lhf 3][lhf 4]
Top quark	t	${\displaystyle +\frac{2}{3}}$	${\displaystyle +\frac{1}{2}}$	${\displaystyle +\frac{1}{3}}$	${\displaystyle \mathbf{3}}$	171 GeV
Top antiquark	t	${\displaystyle -\frac{2}{3}}$	${\displaystyle 0}$	${\displaystyle -\frac{4}{3}}$	${\displaystyle \overline{\mathbf{3}}}$	171 GeV
Bottom quark	b	${\displaystyle -\frac{1}{3}}$	${\displaystyle -\frac{1}{2}}$	${\displaystyle +\frac{1}{3}}$	${\displaystyle \mathbf{3}}$	~ 4.2 GeV
Bottom antiquark	b	${\displaystyle +\frac{1}{3}}$	${\displaystyle 0}$	${\displaystyle +\frac{2}{3}}$	${\displaystyle \overline{\mathbf{3}}}$	~ 4.2 GeV
^abcThese are not ordinaryabeliancharges, which can be added together, but are labels ofgroup representations ofLie groups. ^abcMass is really a coupling between a left-handed fermion and a right-handed fermion. For example, the mass of an electron is really a coupling between a left-handed electron and a right-handed electron, which is theantiparticle of a left-handedpositron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in theflavor basis or to suggest a left-handed electron antineutrino. ^abcdefThe Standard Model assumes that neutrinos are massless. However, many contemporary experiments prove thatneutrinos oscillate between theirflavor states, which could not happen if all were massless. It is straightforward to extend the model to fit these data but there are many possibilities, so the masseigenstates are stillopen. Seeneutrino mass. ^abcdefYao, W.-M.; et al. (Particle Data Group) (2006)."Review of Particle Physics: Neutrino mass, mixing, and flavor change"(PDF).Journal of Physics G.33 (1): 1.arXiv:astro-ph/0601168.Bibcode:2006JPhG...33....1Y.doi:10.1088/0954-3899/33/1/001.S2CID 117958297. ^abcdThemasses ofbaryons andhadrons and various cross-sections are the experimentally measured quantities. Since quarks can't be isolated because ofQCDconfinement, the quantity here is supposed to be the mass of the quark at therenormalization scale of the QCD scale.

Upon writing the most general Lagrangian with massless neutrinos, one finds that the dynamics depend on 19 parameters, whose numerical values are established by experiment. Straightforward extensions of the Standard Model with massive neutrinos need 7 more parameters (3 masses and 4 PMNS matrix parameters) for a total of 26 parameters.^[10] The neutrino parameter values are still uncertain. The 19 certain parameters are summarized here.

The choice of free parameters is somewhat arbitrary. In the table above, gauge couplings are listed as free parameters, therefore with this choice the Weinberg angle is not a free parameter – it is defined as${\displaystyle \tan {\theta }_{\mathrm{W}}=g_1/g_2}$. Likewise, thefine-structure constant of QED is${\displaystyle \alpha =\frac{1}{4\pi }\frac{(g_1{g}_2{)}^2}{g_1^2+g_2^2}}$. Instead of fermion masses, dimensionless Yukawa couplings can be chosen as free parameters. For example, the electron mass depends on the Yukawa coupling of the electron to the Higgs field, and its value is${\displaystyle m_{\mathrm{e}}=y_{\mathrm{e}}v/\sqrt{2}}$. Instead of the Higgs mass, the Higgs self-coupling strength${\displaystyle \lambda =\frac{m_{\mathrm{H}}^2}{2v^2}}$, which is approximately 0.129, can be chosen as a free parameter. Instead of the Higgs vacuum expectation value, the${\displaystyle {\mu }^2}$ parameter directly from the Higgs self-interaction term${\displaystyle {\mu }^2{\varphi }^{†}\varphi -\lambda ({\varphi }^{†}\varphi {)}^2}$ can be chosen. Its value is${\displaystyle {\mu }^2=\lambda v^2=m_{\mathrm{H}}^2/2}$, or approximately${\displaystyle \mu }$ =88.45 GeV.

The value of thevacuum energy (or more precisely, therenormalization scale used to calculate this energy) may also be treated as an additional free parameter. The renormalization scale may be identified with thePlanck scale or fine-tuned to match the observedcosmological constant. However, both optionsare problematic.^[11]

From the theoretical point of view, the Standard Model exhibits four additional global symmetries, not postulated at the outset of its construction, collectively denotedaccidental symmetries, which are continuousU(1)global symmetries. The transformations leaving the Lagrangian invariant are:$${\displaystyle {\psi }_{\text{q}}\to e^{i\alpha /3}{\psi }_{\text{q}}}$$$${\displaystyle E_{\mathrm{L}}\to e^{i\beta }{E}_{\mathrm{L}}\text{ and }(e_{\mathrm{R}}{)}^{\text{c}}\to e^{i\beta }(e_{\mathrm{R}}{)}^{\text{c}}}$$$${\displaystyle M_{\mathrm{L}}\to e^{i\beta }{M}_{\mathrm{L}}\text{ and }({\mu }_{\mathrm{R}}{)}^{\text{c}}\to e^{i\beta }({\mu }_{\mathrm{R}}{)}^{\text{c}}}$$$${\displaystyle T_{\mathrm{L}}\to e^{i\beta }{T}_{\mathrm{L}}\text{ and }({\tau }_{\mathrm{R}}{)}^{\text{c}}\to e^{i\beta }({\tau }_{\mathrm{R}}{)}^{\text{c}}}$$

The first transformation rule is shorthand meaning that all quark fields for all generations must be rotated by an identical phase simultaneously. The fieldsM_L,T_L and${\displaystyle ({\mu }_{\mathrm{R}}{)}^{\text{c}},({\tau }_{\mathrm{R}}{)}^{\text{c}}}$ are the 2nd (muon) and 3rd (tau) generation analogs ofE_L and${\displaystyle (e_{\mathrm{R}}{)}^{\text{c}}}$ fields.

ByNoether's theorem, each symmetry above has an associatedconservation law: the conservation ofbaryon number,^[12]electron number,muon number, andtau number. Each quark is assigned a baryon number of$\frac{1}{3}$, while each antiquark is assigned a baryon number of$-\frac{1}{3}$. Conservation of baryon number implies that the number of quarks minus the number of antiquarks is a constant. Within experimental limits, no violation of this conservation law has been found.

Similarly, each electron and its associated neutrino is assigned an electron number of +1, while theanti-electron and the associated anti-neutrino carry a −1 electron number. Similarly, the muons and their neutrinos are assigned a muon number of +1 and the tau leptons are assigned a tau lepton number of +1. The Standard Model predicts that each of these three numbers should be conserved separately in a manner similar to the way baryon number is conserved. These numbers are collectively known aslepton family numbers (LF). (This result depends on the assumption made in Standard Model that neutrinos are massless. Experimentally, neutrino oscillations imply that individual electron, muon and tau numbers are not conserved.)^[13][14]

In addition to the accidental (but exact) symmetries described above, the Standard Model exhibits severalapproximate symmetries. These are the "SU(2)custodial symmetry" and the "SU(2) or SU(3) quark flavor symmetry".

For theleptons, the gauge group can be writtenSU(2)_l × U(1)_L × U(1)_R. The twoU(1) factors can be combined intoU(1)_Y × U(1)_l, wherel is thelepton number. Gauging of the lepton number is ruled out by experiment, leaving only the possible gauge groupSU(2)_L × U(1)_Y. A similar argument in the quark sector also gives the same result for the electroweak theory.

The charged currents${\displaystyle j^{\mp }=j^1\pm i{j}^2}$ are$${\displaystyle j_{\mu }^{-}={\overline{U}}_{i\mathrm{L}}{\gamma }_{\mu }{D}_{i\mathrm{L}}+{\overline{\nu }}_{i\mathrm{L}}{\gamma }_{\mu }{l}_{i\mathrm{L}}.}$$These charged currents are precisely those that entered theFermi theory of beta decay. The action contains the charge current piece$${\displaystyle {\mathcal{L}}_{\mathrm{C}\mathrm{C}}=\frac{g}{\sqrt{2}}(j_{\mu }^{+}{W}^{-\mu }+j_{\mu }^{-}{W}^{+\mu }).}$$For energy much less than the mass of the W-boson, the effective theory becomes the current–current contact interaction of theFermi theory,${\displaystyle 2\sqrt{2}{G}_{\mathrm{F}}{J}_{\mu }^{+}{J}^{\mu -}}$.

However, gauge invariance now requires that the component${\displaystyle W^3}$ of the gauge field also be coupled to a current that lies in the triplet of SU(2). However, this mixes with theU(1), and another current in that sector is needed. These currents must be uncharged in order to conserve charge. Soneutral currents are also required,$${\displaystyle j_{\mu }^3=\frac{1}{2}\left({\overline{U}}_{i\mathrm{L}}{\gamma }_{\mu }{U}_{i\mathrm{L}}-{\overline{D}}_{i\mathrm{L}}{\gamma }_{\mu }{D}_{i\mathrm{L}}+{\overline{\nu }}_{i\mathrm{L}}{\gamma }_{\mu }{\nu }_{i\mathrm{L}}-{\overline{l}}_{i\mathrm{L}}{\gamma }_{\mu }{l}_{i\mathrm{L}}\right)}$$$${\displaystyle j_{\mu }^{\mathrm{e}\mathrm{m}}=\frac{2}{3}{\overline{U}}_i{\gamma }_{\mu }{U}_i-\frac{1}{3}{\overline{D}}_i{\gamma }_{\mu }{D}_i-{\overline{l}}_i{\gamma }_{\mu }{l}_i.}$$The neutral current piece in the Lagrangian is then$${\displaystyle {\mathcal{L}}_{\mathrm{N}\mathrm{C}}=e{j}_{\mu }^{\mathrm{e}\mathrm{m}}{A}^{\mu }+\frac{g}{\cos {\theta }_{\mathrm{W}}}(J_{\mu }^3-{\sin }^2{\theta }_{\mathrm{W}}{J}_{\mu }^{\mathrm{e}\mathrm{m}})Z^{\mu }.}$$

This section is an excerpt fromPhysics beyond the Standard Model.[edit]

Beyond the Standard Model
SimulatedLarge Hadron ColliderCMS particle detector data depicting aHiggs boson produced by colliding protons decaying into hadron jets and electrons
Standard Model
Evidence Hierarchy problem Dark matter Dark energy Quintessence Phantom energy Dark radiation Dark photon Cosmological constant problem Strong CP problem Neutrino oscillation
Theories Brans–Dicke theory Cosmic censorship hypothesis Fifth force F-theory Theory of everything Unified field theory Grand Unified Theory Technicolor Kaluza–Klein theory 6D (2,0) superconformal field theory Noncommutative quantum field theory Quantum cosmology Brane cosmology String theory Superstring theory M-theory Mathematical universe hypothesis Mirror matter Randall–Sundrum model N = 4 supersymmetric Yang–Mills theory Twistor string theory Dark fluid Doubly special relativity de Sitter invariant special relativity Causal fermion systems Black hole thermodynamics Unparticle physics Graviphoton Graviscalar Graviton Gravitino Massive gravity Gauge gravitation theory Gauge theory gravity CPT symmetry
Supersymmetry MSSM NMSSM Superstring theory M-theory Supergravity Supersymmetry breaking Extra dimensions Large extra dimensions
Quantum gravity False vacuum String theory Spin foam Quantum foam Quantum geometry Loop quantum gravity Quantum cosmology Loop quantum cosmology Causal dynamical triangulation Causal fermion systems Causal sets Canonical quantum gravity Semiclassical gravity Superfluid vacuum theory
Experiments ANNIE Gran Sasso INO LHC SNO Super-K Tevatron NOvA
v t e

Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of theStandard Model, such as the inability to explain the fundamental parameters of the standard model, thestrong CP problem,neutrino oscillations,matter–antimatter asymmetry, and the nature ofdark matter anddark energy.^[15] Another problem lies within themathematical framework of the Standard Model itself: the Standard Model is inconsistent with that ofgeneral relativity, and one or both theories break down under certain conditions, such asspacetime singularities like theBig Bang andblack holeevent horizons.

Theories that lie beyond the Standard Model include various extensions of the standard model throughsupersymmetry, such as theMinimal Supersymmetric Standard Model (MSSM) andNext-to-Minimal Supersymmetric Standard Model (NMSSM), and entirely novel explanations, such asstring theory,M-theory, andextra dimensions. As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the "best step" towards aTheory of Everything, can only be settled via experiments, and is one of the most active areas of research in boththeoretical andexperimental physics.^[16]

• Overview ofStandard Model ofparticle physics
• Fundamental interaction
• Noncommutative standard model
• Open questions:CP violation,Neutrino masses,Quark matter
• Physics beyond the Standard Model
• Strong interactions
  • Flavor
  • Quantum chromodynamics
  • Quark model
• Weak interactions
  • Electroweak interaction
  • Fermi's interaction
• Weinberg angle
• Symmetry in quantum mechanics
• Quantum Field Theory in a Nutshell by A. Zee