Multiplication by Infinity: CERN Announces July 4 Press Conference re Higgs Boson

Today CERN announced there will be an announcement regarding the progress in verifying the existence of The Higgs Boson on July 4, 2012. "Born on the 4th of July" is how one scientist describes it. Well perhaps, we shall see. But it looks good. ;-)

A diagram summarizing the tree-level interactions between elementary particles described in the Standard Model. Vertices (darkened circles) represent types of particles, and edges (blue arcs) connecting them represent interactions that can take place. The organization of the diagram is as follows: the top row of vertices (leptons and quarks) are the matter particles; the second row of vertices (photon, W/Z, gluons) are the force mediating particles; and the bottom row is the Higgs boson.

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon experimental confirmation of the existence ofquarks. Since then, discoveries of the bottom quark (1977), the top quark (1995) and the tau neutrino (2000) have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as a "theory of almost everything".

The Standard Model falls short of being a complete theory of fundamental interactions because it does not incorporate the physics of dark energy nor of the full theory of gravitation as described by general relativity. The theory does not contain any viable dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not correctly account for neutrino oscillations (and their non-zero masses). Although the Standard Model is believed to be theoretically self-consistent, it has several apparently unnatural properties giving rise to puzzles like the strong CP problem and the hierarchy problem.

Nevertheless, the Standard Model is important to theoretical and experimental particle physicists alike. For theorists, the Standard Model is a paradigmatic example of a quantum field theory, which exhibits a wide range of physics including spontaneous symmetry breaking, anomalies, non-perturbative behavior, etc. It is used as a basis for building more exotic models that incorporate hypothetical particles, extra dimensions, and elaborate symmetries (such as supersymmetry) in an attempt to explain experimental results at variance with the Standard Model, such as the existence of dark matter and neutrino oscillations. In turn, experimenters have incorporated the Standard Model into simulators to help search for new physics beyond the Standard Model.

Recently, the Standard Model has found applications in fields besides particle physics, such as astrophysics, cosmology, and nuclear physics.

[edit]Historical background

The first step towards the Standard Model was Sheldon Glashow's discovery in 1960 of a way to combine the electromagnetic and weak interactions.^[1] In 1967 Steven Weinberg^[2] and Abdus Salam^[3] incorporated the Higgs mechanism^[4]^[5]^[6] into Glashow's electroweak theory, giving it its modern form.

The Higgs mechanism is believed to give rise to the masses of all the elementary particles in the Standard Model. This includes the masses of the W and Z bosons, and the masses of the fermions, i.e. the quarks and leptons.

After the neutral weak currents caused by Z boson exchange were discovered at CERN in 1973,^[7]^[8]^[9]^[10] the electroweak theory became widely accepted and Glashow, Salam, and Weinberg shared the 1979 Nobel Prize in Physics for discovering it. The W and Z bosons were discovered experimentally in 1981, and their masses were found to be as the Standard Model predicted.

The theory of the strong interaction, to which many contributed, acquired its modern form around 1973–74, when experiments confirmed that the hadrons were composed of fractionally charged quarks.

[edit]Overview

At present, matter and energy are best understood in terms of the kinematics and interactions of elementary particles. To date, physics has reduced the laws governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. A major goal of physics is to find the "common ground" that would unite all of these theories into one integrated theory of everything, of which all the other known laws would be special cases, and from which the behavior of all matter and energy could be derived (at least in principle).^[11]

The Standard Model groups two major extant theories—quantum electroweak and quantum chromodynamics—into an internally consistent theory that describes the interactions between all known particles in terms of quantum field theory. For a technical description of the fields and their interactions, see Standard Model (mathematical formulation).

[edit]Particle content

[edit]Fermions

Organization of Fermions
	Charge	First generation		Second generation		Third generation
Quarks	+2/3	Up	u	Charm	c	Top	t
Quarks	−1/3	Down	d	Strange	s	Bottom	b
Leptons	−1	Electron	e−	Muon	μ−	Tau	τ−
Leptons	0	Electron neutrino	ν e	Muon neutrino	ν μ	Tau neutrino	ν τ

The Standard Model includes 12 elementary particles of spin ${}_\frac{1}{2}$ known as fermions. According to the spin-statistics theorem, fermions respect the Pauli exclusion principle. Each fermion has a corresponding antiparticle.

The fermions of the Standard Model are classified according to how they interact (or equivalently, by what charges they carry). There are six quarks (up, down, charm, strange,top, bottom), and six leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino). Pairs from each classification are grouped together to form a generation, with corresponding particles exhibiting similar physical behavior (see table).

The defining property of the quarks is that they carry color charge, and hence, interact via the strong interaction. A phenomenon called color confinement results in quarks being perpetually (or at least since very soon after the start of the Big Bang) bound to one another, forming color-neutral composite particles (hadrons) containing either a quark and an antiquark (mesons) or three quarks (baryons). The familiar proton and the neutron are the two baryons having the smallest mass. Quarks also carry electric charge and weak isospin. Hence they interact with other fermions both electromagnetically and via the weak interaction.

The remaining six fermions do not carry colour charge and are called leptons. The three neutrinos do not carry electric charge either, so their motion is directly influenced only by the weak nuclear force, which makes them notoriously difficult to detect. However, by virtue of carrying an electric charge, the electron, muon, and tau all interact electromagnetically.

Each member of a generation has greater mass than the corresponding particles of lower generations. The first generation charged particles do not decay; hence all ordinary (baryonic) matter is made of such particles. Specifically, all atoms consist of electrons orbiting atomic nuclei ultimately constituted of up and down quarks. Second and third generations charged particles, on the other hand, decay with very short half lives, and are observed only in very high-energy environments. Neutrinos of all generations also do not decay, and pervade the universe, but rarely interact with baryonic matter.

[edit]Gauge bosons

Summary of interactions between particles described by the Standard Model.

The above interactions form the basis of the standard model. Feynman diagrams in the standard model are built from these vertices. Modifications involving Higgs boson interactions and neutrino oscillations are commonly added. The charge of the W bosons are dictated by the fermions they interact with.

In the Standard Model, gauge bosons are defined as force carriers that mediate the strong, weak, and electromagnetic fundamental interactions.

Interactions in physics are the ways that particles influence other particles. At a macroscopic level, electromagnetism allows particles to interact with one another via electric and magnetic fields, and gravitation allows particles with mass to attract one another in accordance with Einstein's theory ofgeneral relativity. The Standard Model explains such forces as resulting from matter particlesexchanging other particles, known as force mediating particles (strictly speaking, this is only so if interpreting literally what is actually an approximation method known as perturbation theory)^{[citation needed]}. When a force mediating particle is exchanged, at a macroscopic level the effect is equivalent to a force influencing both of them, and the particle is therefore said to havemediated (i.e., been the agent of) that force. The Feynman diagram calculations, which are a graphical representation of the perturbation theory approximation, invoke "force mediating particles", and when applied to analyze high-energy scattering experiments are in reasonable agreement with the data. However, perturbation theory (and with it the concept of a "force-mediating particle") fails in other situations. These include low-energy quantum chromodynamics, bound states, and solitons.

The gauge bosons of the Standard Model all have spin (as do matter particles). The value of the spin is 1, making them bosons. As a result, they do not follow the Pauli exclusion principle that constrains fermions: thus bosons (e.g. photons) do not have a theoretical limit on their spatial density (number per volume). The different types of gauge bosons are described below.

Photons mediate the electromagnetic force between electrically charged particles. The photon is massless and is well-described by the theory of quantum electrodynamics.

The W+, W−, and Z gauge bosons mediate the weak interactions between particles of different flavors (all quarks and leptons). They are massive, with the Z being more massive than the W±. The weak interactions involving the W± exclusively act on left-handed particles and right-handed antiparticles only. Furthermore, the W± carries an electric charge of +1 and −1 and couples to the electromagnetic interaction. The electrically neutral Z boson interacts with both left-handed particles and antiparticles. These three gauge bosons along with the photons are grouped together, as collectively mediating theelectroweak interaction.

The eight gluons mediate the strong interactions between color charged particles (the quarks). Gluons are massless. The eightfold multiplicity of gluons is labeled by a combination of color and anticolor charge (e.g. red–antigreen).^{[nb 1]} Because the gluon has an effective color charge, they can also interact among themselves. The gluons and their interactions are described by the theory of quantum chromodynamics.

The interactions between all the particles described by the Standard Model are summarized by the diagrams on the right of this section.

[edit]Higgs boson

Main article: Higgs boson

The Higgs particle is a hypothetical massive scalar elementary particle theorized by Robert Brout, François Englert, Peter Higgs, Gerald Guralnik, C. R. Hagen, and Tom Kibble in 1964 (see 1964 PRL symmetry breaking papers) and is a key building block in the Standard Model.^[12]^[13]^[14]^[15] It has no intrinsic spin, and for that reason is classified as a boson (like the gauge bosons, which have integer spin). Because an exceptionally large amount of energy and beam luminosity are theoretically required to observe a Higgs boson in high energy colliders, it is the only fundamental particle predicted by the Standard Model that has yet to be observed.

The Higgs boson plays a unique role in the Standard Model, by explaining why the other elementary particles, except thephoton and gluon, are massive. In particular, the Higgs boson would explain why the photon has no mass, while the W and Z bosons are very heavy. Elementary particle masses, and the differences between electromagnetism (mediated by the photon) and the weak force (mediated by the W and Z bosons), are critical to many aspects of the structure of microscopic (and hence macroscopic) matter. In electroweak theory, the Higgs boson generates the masses of the leptons (electron, muon, and tau) and quarks.

As yet, no experiment has conclusively detected the existence of the Higgs boson. It is hoped that the Large Hadron Collider at CERN will confirm the existence of this particle. As of August 2011, a significant portion of the possible masses for the Higgs have been excluded at 95% confidence level: CMS has excluded the mass ranges 145–216 GeV,226–288 GeV and 310–400 GeV,^[16] while the ATLAS experiment has excluded 146–232 GeV, 256–282 GeV and 296–466 GeV.^[17] Note that these exclusions apply only to the Standard Model Higgs, and that more complex Higgs sectors which are possible in Beyond the Standard Model scenarios may be significantly more difficult to characterize. CERN director general Rolf Heuer has predicted that by the end of 2012 either the Standard Model Higgs boson will be observed, or excluded in all mass ranges, implying that the Standard Model is not the whole story.^[18]

On December 13, 2011 CERN announced that both ATLAS and CMS experiments had detected 'hints' of the Higgs boson in at approximately 124 GeV. These results were not sufficiently strong to announce that the Higgs boson had been found (ATLAS showed a 2.3 sigma level of certainty for an excess at 126 GeV, while CMS showed a 1.9 sigma level excess at 124 GeV) but the fact that two separate experiments show excesses in the same energy range has led to much excitement in the particle physics world.^[19]

[edit]Field content

The Standard Model has the following fields:

[edit]Spin 1

A U(1) gauge field B_μν with coupling g′ (weak U(1), or weak hypercharge)
An SU(2) gauge field W_μν with coupling g (weak SU(2), or weak isospin)
An SU(3) gauge field G_μν with coupling g_s (strong SU(3), or color charge)

[edit]Spin ¹⁄₂

The spin ${}_{\frac{1}{2}}$ particles are in representations of the gauge groups. For the U(1) group, we list the value of the weak hypercharge instead. The left-handed fermionic fields are:

An SU(3) triplet, SU(2) doublet, with U(1) weak hypercharge ${}_{\frac{1}{3}}$ (left-handed quarks)
An SU(3) triplet, SU(2) singlet, with U(1) weak hypercharge ${}_{\frac{2}{3}}$ (left-handed down-type antiquark)
An SU(3) singlet, SU(2) doublet with U(1) weak hypercharge −1 (left-handed lepton)
An SU(3) triplet, SU(2) singlet, with U(1) weak hypercharge ${}_{-\frac{4}{3}}$ (left-handed up-type antiquark)
An SU(3) singlet, SU(2) singlet with U(1) weak hypercharge 2 (left-handed antilepton)

By CPT symmetry, there is a set of right-handed fermions with the opposite quantum numbers.

This describes one generation of leptons and quarks, and there are three generations, so there are three copies of each field. Note that there are twice as many left-handed lepton field components as left-handed antilepton field components in each generation, but an equal number of left-handed quark and antiquark fields.

[edit]Spin 0

An SU(2) doublet H with U(1) hyper-charge +1 (Higgs field)

Note that ${}_{\left|H\right|^2}$ , summed over the two SU(2) components, is invariant under both SU(2) and under U(1), and so it can appear as a renormalizable term in the Lagrangian, as can its square.^{[clarification needed]}

This field acquires a vacuum expectation value, leaving a combination of the weak isospin, ${}_{I^3}$ , and weak hypercharge unbroken. This is the electromagnetic gauge group, and the photon remains massless. The standard formula for the electric charge (which defines the normalization of the weak hypercharge, ${}_Y$ , which would otherwise be somewhat arbitrary) is:^{[nb 2]}

$Q = I_\mathrm{3} + \frac{Y}{2}.$

[edit]Lagrangian

The Lagrangian for the spin 1 and spin ¹⁄₂ fields is the most general renormalizable gauge field Lagrangian with no fine tunings:

Spin 1:

$\int - {1\over 4} B_{\mu\nu} B^{\mu\nu} - {1\over 4}\mathrm{tr} W_{\mu\nu}W^{\mu\nu} - {1\over 4} \mathrm{tr}G_{\mu\nu} G^{\mu\nu}$

where the traces are over the SU(2) and SU(3) indices hidden in W and G respectively. The two-index objects are the field strengths derived from W and G the vector fields. There are also two extra hidden parameters: the theta angles for SU(2) and SU(3).

The spin-¹⁄₂ particles can have no mass terms because there is no right/left helicity pair with the same SU(2) and SU(3) representation and the same weak hypercharge. This means that if the gauge charges were conserved in the vacuum, none of the spin ¹⁄₂ particles could ever swap helicity, and they would all be massless.

For a neutral fermion, for example a hypothetical right-handed lepton N (or N^α in relativistic two-spinor notation), with no SU(3), SU(2) representation and zero charge, it is possible to add the term:^{[clarification needed]}

$\int M N^\alpha N^\beta \epsilon_{\alpha\beta} + \bar{N_\dot{\alpha}}\bar{N_\dot{\beta}}\epsilon^{\dot\alpha\dot\beta}.$

This term gives the neutral fermion a Majorana mass. Since the generic value for M will be of order 1, such a particle would generically be unacceptably heavy. The interactions are completely determined by the theory – the leptons introduce no extra parameters.

[edit]Higgs mechanism

Main article: Higgs mechanism

The Lagrangian for the Higgs includes the most general renormalizable self interaction:

$S_{\mathrm{Higgs}} = \int d^4x\left[(D_\mu H)^*(D^\mu H) + \lambda(|H|^2 - v^2)^2\right].$

The parameter v² has dimensions of mass squared, and it gives the location where the classical Lagrangian is at a minimum. In order for the Higgs mechanism to work, v² must be a positive number. v has units of mass, and it is the only parameter in the Standard Model which is not dimensionless. It is also much smaller than the Planck scale; it is approximately equal to the Higgs mass, and sets the scale for the mass of everything else. This is the only real fine-tuning to a small nonzero value in the Standard Model, and it is called the Hierarchy problem.

It is traditional to choose the SU(2) gauge so that the Higgs doublet in the vacuum has expectation value (v,0).

[edit]Masses and CKM matrix

Main article: Cabibbo–Kobayashi–Maskawa matrix

The rest of the interactions are the most general spin-0 spin-¹⁄₂ Yukawa interactions, and there are many of these. These constitute most of the free parameters in the model. The Yukawa couplings generate the masses and mixings once the Higgs gets its vacuum expectation value.

The terms L^*HR^{[clarification needed]} generate a mass term for each of the three generations of leptons. There are 9 of these terms, but by relabeling L and R, the matrix can be diagonalized. Since only the upper component of H is nonzero, the upper SU(2) component of L mixes with R to make the electron, the muon, and the tau, leaving over a lower massless component, the neutrino. Note: Neutrino oscillations show neutrinos have mass.^[20] See also: Pontecorvo–Maki–Nakagawa–Sakata matrix.

The terms QHU^{[clarification needed]} generate up masses, while QHD^{[clarification needed]} generate down masses. But since there is more than one right-handed singlet in each generation, it is not possible to diagonalize both with a good basis for the fields, and there is an extra CKM matrix.

[edit]Theoretical aspects

[edit]Construction of the Standard Model Lagrangian

Parameters of the Standard Model
Symbol	Description	Renormalization scheme (point)	Value
m_e	Electron mass		511 keV
m_μ	Muon mass		105.7 MeV
m_τ	Tau mass		1.78 GeV
m_u	Up quark mass	μ_MS = 2 GeV	1.9 MeV
m_d	Down quark mass	μ_MS = 2 GeV	4.4 MeV
m_s	Strange quark mass	μ_MS = 2 GeV	87 MeV
m_c	Charm quark mass	μ_MS = m_c	1.32 GeV
m_b	Bottom quark mass	μ_MS = m_b	4.24 GeV
m_t	Top quark mass	On-shell scheme	172.7 GeV
θ₁₂	CKM 12-mixing angle		13.1°
θ₂₃	CKM 23-mixing angle		2.4°
θ₁₃	CKM 13-mixing angle		0.2°
δ	CKM CP-violating Phase		0.995
g₁ or g'	U(1) gauge coupling	μ_MS = m_Z	0.357
g₂ or g	SU(2) gauge coupling	μ_MS = m_Z	0.652
g₃ or g_s	SU(3) gauge coupling	μ_MS = m_Z	1.221
θ_QCD	QCD vacuum angle		~0
μ	Higgs quadratic coupling		Unknown
λ	Higgs self-coupling strength		Unknown

Technically, quantum field theory provides the mathematical framework for the Standard Model, in which a Lagrangian controls the dynamics and kinematics of the theory. Each kind of particle is described in terms of a dynamical field that pervades space-time. The construction of the Standard Model proceeds following the modern method of constructing most field theories: by first postulating a set of symmetries of the system, and then by writing down the most general renormalizable Lagrangian from its particle (field) content that observes these symmetries.

The global Poincaré symmetry is postulated for all relativistic quantum field theories. It consists of the familiar translational symmetry, rotational symmetry and the inertial reference frame invariance central to the theory of special relativity. The local SU(3)×SU(2)×U(1) gauge symmetry is an internal symmetry that essentially defines the Standard Model. Roughly, the three factors of the gauge symmetry give rise to the three fundamental interactions. The fields fall into different representations of the various symmetry groups of the Standard Model (see table). Upon writing the most general Lagrangian, one finds that the dynamics depend on 19 parameters, whose numerical values are established by experiment. The parameters are summarized in the table at right.

[edit]Quantum chromodynamics sector

Main article: Quantum chromodynamics

The quantum chromodynamics (QCD) sector defines the interactions between quarks and gluons, with SU(3) symmetry, generated by T^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

$\mathcal{L}_{QCD} = i\overline U (\partial_\mu-ig_sG_\mu^a T^a)\gamma^\mu U + i\overline D (\partial_\mu-i g_s G_\mu^a T^a)\gamma^\mu D.$

$G_\mu^a$ is the SU(3) gauge field containing the gluons, $\gamma^\mu$ are the Dirac matrices, D and U are the Dirac spinors associated with up- and down-type quarks, and g_s is the strong coupling constant.

[edit]Electroweak sector

Main article: Electroweak interaction

The electroweak sector is a Yang–Mills gauge theory with the symmetry group U(1)×SU(2)_L,

$\mathcal{L}_\mathrm{EW} = \sum_\psi\bar\psi\gamma^\mu \left(i\partial_\mu-g^\prime{1\over2}Y_\mathrm{W}B_\mu-g{1\over2}\vec\tau_\mathrm{L}\vec W_\mu\right)\psi$

where B_μ is the U(1) gauge field; Y_W is the weak hypercharge—the generator of the U(1) group; $\vec{W}_\mu$ is the three-component SU(2) gauge field; $\vec{\tau}_\mathrm{L}$ are the Pauli matrices—infinitesimal generators of the SU(2) group. The subscript L indicates that they only act on left fermions; g′ and g are coupling constants.

[edit]Higgs sector

In the Standard Model, the Higgs field is a complex spinor of the group SU(2)_L:

$\varphi={1\over\sqrt{2}} \left( \begin{array}{c} \varphi^+ \\ \varphi^0 \end{array} \right)\;,$

where the indexes + and 0 indicate the electric charge (Q) of the components. The weak isospin (Y_W) of both components is 1.

Before symmetry breaking, the Higgs Lagrangian is:

$\mathcal{L}_\mathrm{H} = \varphi^\dagger \left({\partial^\mu}- {i\over2} \left( g'Y_\mathrm{W}B^\mu + g\vec\tau\vec W^\mu \right)\right) \left(\partial_\mu + {i\over2} \left( g'Y_\mathrm{W}B_\mu +g\vec\tau\vec W_\mu \right)\right)\varphi \ - \ {\lambda^2\over4}\left(\varphi^\dagger\varphi-v^2\right)^2\;,$

which can also be written as:

$\mathcal{L}_\mathrm{H} = \left| \left(\partial_\mu + {i\over2} \left( g'Y_\mathrm{W}B_\mu +g\vec\tau\vec W_\mu \right)\right)\varphi\right|^2 \ - \ {\lambda^2\over4}\left(\varphi^\dagger\varphi-v^2\right)^2\;.$

[edit]Additional symmetries of the Standard Model

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 continuous U(1) global symmetries. The transformations leaving the Lagrangian invariant are:

$\psi_\text{q}(x)\rightarrow e^{i\alpha/3}\psi_\text{q}$

$E_L\rightarrow e^{i\beta}E_L\text{ and }(e_R)^c\rightarrow e^{i\beta}(e_R)^c$

$M_L\rightarrow e^{i\beta}M_L\text{ and }(\mu_R)^c\rightarrow e^{i\beta}(\mu_R)^c$

$T_L\rightarrow e^{i\beta}T_L\text{ and }(\tau_R)^c\rightarrow e^{i\beta}(\tau_R)^c.$

The first transformation rule is shorthand meaning that all quark fields for all generations must be rotated by an identical phase simultaneously. The fields $M_L$ , $T_L$ and $(\mu_R)^c$ , $(\tau_R)^c$ are the 2nd (muon) and 3rd (tau) generation analogs of $E_L$ and $(e_R)^c$ fields.

By Noether's theorem, each symmetry above has an associated conservation law: the conservation of baryon number, electron number, muon number, and tau 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 the anti-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 as lepton family numbers (LF).

Symmetry works differently for quarks than for leptons, mainly because the Standard Model predicts (incorrectly) that neutrinos are massless. However, in 2002 it was discovered that neutrinos have mass (now established to be not greater than 0.28 electron volts), and as neutrinos oscillate between flavors (muon neutrinos have been observed changing to tau neutrinos) the discovery of neutrino mass indicates that the conservation of lepton family number is violated.^[21]

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

Symmetries of the Standard Model and Associated Conservation Laws
Symmetry	Lie Group	Symmetry Type	Conservation Law
Poincaré	Translations ×SO(3,1)	Global symmetry	Energy, Momentum, Angular momentum
Gauge	SU(3)×SU(2)×U(1)	Local symmetry	Color charge, Weak isospin, Electric charge, Weak hypercharge
Baryon phase	U(1)	Accidental Global symmetry	Baryon number
Electron phase	U(1)	Accidental Global symmetry	Electron number
Muon phase	U(1)	Accidental Global symmetry	Muon number
Tau phase	U(1)	Accidental Global symmetry	Tau number

Field content of the Standard Model
Field (1st generation)		Spin	Gauge group Representation	Baryon Number	Electron Number
Left-handed quark	$Q_\text{L}\,$	$\frac{1}{2}$	(3, 2, +¹⁄₃)	$\frac{1}{3}$	$0\,$
Left-handed up antiquark	$\bar u_\text{L} \equiv (u_\text{R})^c\,$	$\frac{1}{2}$	$\left(\bar{\mathbf{3}}, \mathbf{1}, -\frac{4}{3}\right)$	$-\frac{1}{3}$	$0\,$
Left-handed down antiquark	$\bar d_\text{L} \equiv (d_\text{R})^c\,$	$\frac{1}{2}$	$\left(\bar{\mathbf{3}}, \mathbf{1}, -\frac{2}{3}\right)$	$-\frac{1}{3}$	$0\,$
Left-handed lepton	$L_\text{L}\,$	$\frac{1}{2}$	( $\mathbf{1}\,$ , $\mathbf{2}\,$ , $-1\,$ )	$0\,$	$1\,$
Left-handed antielectron	$\bar e_\text{L} \equiv (e_\text{R})^c\,$	$\frac{1}{2}$	( $\mathbf{1}\,$ , $\mathbf{1}\,$ , $+2\,$ )	$0\,$	$-1\,$
Hypercharge gauge field	$B_\mu\,$	$1\,$	( $\mathbf{1}\,$ , $\mathbf{1}\,$ , $0\,$ )	$0\,$	$0\,$
Isospin gauge field	$W_\mu\,$	$1\,$	( $\mathbf{1}\,$ , $\mathbf{3}\,$ , $0\,$ )	$0\,$	$0\,$
Gluon field	$G_\mu\,$	$1\,$	( $\mathbf{8}\,$ , $\mathbf{1}\,$ , $0\,$ )	$0\,$	$0\,$
Higgs field	$H\,$	$0\,$	( $\mathbf{1}\,$ , $\mathbf{2}\,$ , $+1\,$ )	$0\,$	$0\,$

[edit]List of Standard Model fermions

This table is based in part on data gathered by the Particle Data Group.^[22]

**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	$e^-\,$	$-1\,$	$-1/2\,$	$-1\,$	$\bold{1}\,$	511 keV
Positron	$e^+\,$	$+1\,$	$0\,$	$+2\,$	$\bold{1}\,$	511 keV
Electron neutrino	$\nu_e\,$	$0\,$	$+1/2\,$	$-1\,$	$\bold{1}\,$	< 0.28 eV^{[lhf 3]}^{[lhf 4]}
Electron antineutrino	$\bar\nu_e\,$	$0\,$	$0\,$	$0\,$	$\bold{1}\,$	< 0.28 eV^{[lhf 3]}^{[lhf 4]}
Up quark	$u\,$	$+2/3\,$	$+1/2\,$	$+1/3\,$	$\bold{3}\,$	~ 3 MeV^{[lhf 5]}
Up antiquark	$\bar{u}\,$	$-2/3\,$	$0\,$	$-4/3\,$	$\bold{\bar{3}}\,$	~ 3 MeV^{[lhf 5]}
Down quark	$d\,$	$-1/3\,$	$-1/2\,$	$+1/3\,$	$\bold{3}\,$	~ 6 MeV^{[lhf 5]}
Down antiquark	$\bar{d}\,$	$+1/3\,$	$0\,$	$+2/3\,$	$\bold{\bar{3}}\,$	~ 6 MeV^{[lhf 5]}

Generation 2
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Weak hypercharge	Color charge ^{[lhf 1]}	Mass ^{[lhf 2]}
Muon	$\mu^-\,$	$-1\,$	$-1/2\,$	$-1\,$	$\bold{1}\,$	106 MeV
Antimuon	$\mu^+\,$	$+1\,$	$0\,$	$+2\,$	$\bold{1}\,$	106 MeV
Muon neutrino	$\nu_\mu\,$	$0\,$	$+1/2\,$	$-1\,$	$\bold{1}\,$	< 0.28 eV^{[lhf 3]}^{[lhf 4]}
Muon antineutrino	$\bar\nu_\mu\,$	$0\,$	$0\,$	$0\,$	$\bold{1}\,$	< 0.28 eV^{[lhf 3]}^{[lhf 4]}
Charm quark	$c\,$	$+2/3\,$	$+1/2\,$	$+1/3\,$	$\bold{3}\,$	~ 1.337 GeV
Charm antiquark	$\bar{c}\,$	$-2/3\,$	$0\,$	$-4/3\,$	$\bold{\bar{3}}\,$	~ 1.3 GeV
Strange quark	$s\,$	$-1/3\,$	$-1/2\,$	$+1/3\,$	$\bold{3}\,$	~ 100 MeV
Strange antiquark	$\bar{s}\,$	$+1/3\,$	$0\,$	$+2/3\,$	$\bold{\bar{3}}\,$	~ 100 MeV

Generation 3
Fermion (left-handed)	Symbol	Electric charge	Weak isospin	Weak hypercharge	Color charge^{[lhf 1]}	Mass^{[lhf 2]}
Tau	$\tau^-\,$	$-1\,$	$-1/2\,$	$-1\,$	$\bold{1}\,$	1.78 GeV
Antitau	$\tau^+\,$	$+1\,$	$0\,$	$+2\,$	$\bold{1}\,$	1.78 GeV
Tau neutrino	$\nu_\tau\,$	$0\,$	$+1/2\,$	$-1\,$	$\bold{1}\,$	< 0.28 eV^{[lhf 3]}^{[lhf 4]}
Tau antineutrino	$\bar\nu_\tau\,$	$0\,$	$0\,$	$0\,$	$\bold{1}\,$	< 0.28 eV^{[lhf 3]}^{[lhf 4]}
Top quark	$t\,$	$+2/3\,$	$+1/2\,$	$+1/3\,$	$\bold{3}\,$	171 GeV
Top antiquark	$\bar{t}\,$	$-2/3\,$	$0\,$	$-4/3\,$	$\bold{\bar{3}}\,$	171 GeV
Bottom quark	$b\,$	$-1/3\,$	$-1/2\,$	$+1/3\,$	$\bold{3}\,$	~ 4.2 GeV
Bottom antiquark	$\bar{b}\,$	$+1/3\,$	$0\,$	$+2/3\,$	$\bold{\bar{3}}\,$	~ 4.2 GeV
^ ^a ^b ^c These are not ordinary abelian charges, which can be added together, but are labels of group representations of Lie groups. ^ ^a ^b ^c Mass 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 the antiparticle of a left-handed positron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left-handed electron antineutrino. ^ ^a ^b ^c ^d ^e ^f The Standard Model assumes that neutrinos are massless. However, several contemporary experiments prove that neutrinos oscillate between their flavour 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 mass eigenstates are still open. See neutrino mass. ^ ^a ^b ^c ^d ^e ^f W.-M. Yao et al. (Particle Data Group) (2006). "Review of Particle Physics: Neutrino mass, mixing, and flavor change". Journal of Physics G 33: 1. arXiv:astro-ph/0601168. Bibcode 2006JPhG...33....1Y. DOI:10.1088/0954-3899/33/1/001. ^ ^a ^b ^c ^d The masses of baryons and hadrons and various cross-sections are the experimentally measured quantities. Since quarks can't be isolated because of QCD confinement, the quantity here is supposed to be the mass of the quark at the renormalization scale of the QCD scale.

Log plot of masses in the Standard Model.

[edit]Tests and predictions

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. (April 2008)

The Standard Model (SM) predicted the existence of the W and Z bosons, gluon, and the top andcharm quarks before these particles were observed. Their predicted properties were experimentally confirmed with good precision. To give an idea of the success of the SM, the following table compares the measured masses of the W and Z bosons with the masses predicted by the SM:

Quantity	Measured (GeV)	SM prediction (GeV)
Mass of W boson	80.387 ± 0.019	80.390 ± 0.018
Mass of Z boson	91.1876 ± 0.0021	91.1874 ± 0.0021

The SM also makes several predictions about the decay of Z bosons, which have been experimentally confirmed by the Large Electron-Positron Collider at CERN.

In May 2012 BaBar Collaboration reported that their recently analyzed data may suggest possible flaws in the Standard Model of particle physics.^[23]^[24] These data show that a particular type of particle decay called "B to D-star-tau-nu" happens more often than the Standard Model says it should. In this type of decay, a particle called the B-bar meson decays into a D meson, an antineutrino and a tau-lepton. While the level of certainty of the excess (3.4 sigma) is not enough to claim a break from the Standard Model, the results are a potential sign of something amiss and are likely to impact existing theories, including those attempting to deduce the properties of Higgs bosons.^[25]

[edit]Challenges

Unsolved problems in physics
What gives rise to the Standard Model of particle physics? Why do particle masses and coupling constantshave the values that we measure? Does the Higgs boson really exist? Why are there three generations of particles? Why is there more matter than antimatter in the universe? Where does Dark Matter fit into the model? Is it even a new particle?

[edit]See also

Mathematics portal

	Book: Particles of the Standard Model
Wikipedia books are collections of articles that can be downloaded or ordered in print.

[edit]Notes and references

[edit]Notes

^ Technically, there are nine such color–anticolor combinations. However, there is one color-symmetric combination that can be constructed out of a linear superposition of the nine combinations, reducing the count to eight.
^ The normalization ${}_{Q=I^3+Y}$ is sometimes used instead.

[edit]References

^ S.L. Glashow (1961). "Partial-symmetries of weak interactions". Nuclear Physics 22(4): 579–588. Bibcode 1961NucPh..22..579G. DOI:10.1016/0029-5582(61)90469-2.
^ S. Weinberg (1967). "A Model of Leptons". Physical Review Letters 19 (21): 1264–1266. Bibcode 1967PhRvL..19.1264W. DOI:10.1103/PhysRevLett.19.1264.
^ A. Salam (1968). N. Svartholm. ed. Elementary Particle Physics: Relativistic Groups and Analyticity. Eighth Nobel Symposium. Stockholm: Almquvist and Wiksell. pp. 367.
^ F. Englert, R. Brout (1964). "Broken Symmetry and the Mass of Gauge Vector Mesons". Physical Review Letters 13 (9): 321–323. Bibcode 1964PhRvL..13..321E.DOI:10.1103/PhysRevLett.13.321.
^ P.W. Higgs (1964). "Broken Symmetries and the Masses of Gauge Bosons".Physical Review Letters 13 (16): 508–509. Bibcode 1964PhRvL..13..508H.DOI:10.1103/PhysRevLett.13.508.
^ G.S. Guralnik, C.R. Hagen, T.W.B. Kibble (1964). "Global Conservation Laws and Massless Particles". Physical Review Letters 13 (20): 585–587. Bibcode 1964PhRvL..13..585G. DOI:10.1103/PhysRevLett.13.585.
^ F.J. Hasert et al. (1973). "Search for elastic muon-neutrino electron scattering".Physics Letters B 46: 121. Bibcode 1973PhLB...46..121H. DOI:10.1016/0370-2693(73)90494-2.
^ F.J. Hasert et al. (1973). "Observation of neutrino-like interactions without muon or electron in the gargamelle neutrino experiment". Physics Letters B 46: 138. Bibcode 1973PhLB...46..138H. DOI:10.1016/0370-2693(73)90499-1.
^ F.J. Hasert et al. (1974). "Observation of neutrino-like interactions without muon or electron in the Gargamelle neutrino experiment". Nuclear Physics B 73: 1. Bibcode 1974NuPhB..73....1H. DOI:10.1016/0550-3213(74)90038-8.
^ D. Haidt (4 October 2004). "The discovery of the weak neutral currents". CERN Courier. Retrieved 8 May 2008.
^ "Details can be worked out if the situation is simple enough for us to make an approximation, which is almost never, but often we can understand more or less what is happening." from The Feynman Lectures on Physics, Vol 1. pp. 2–7
^ F. Englert, R. Brout (1964). "Broken Symmetry and the Mass of Gauge Vector Mesons". Physical Review Letters 13 (9): 321–323. Bibcode 1964PhRvL..13..321E.DOI:10.1103/PhysRevLett.13.321.
^ P.W. Higgs (1964). "Broken Symmetries and the Masses of Gauge Bosons".Physical Review Letters 13 (16): 508–509. Bibcode 1964PhRvL..13..508H.DOI:10.1103/PhysRevLett.13.508.
^ G.S. Guralnik, C.R. Hagen, T.W.B. Kibble (1964). "Global Conservation Laws and Massless Particles". Physical Review Letters 13 (20): 585–587. Bibcode 1964PhRvL..13..585G. DOI:10.1103/PhysRevLett.13.585.
^ G.S. Guralnik (2009). "The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles". International Journal of Modern Physics A 24 (14): 2601–2627. arXiv:0907.3466. Bibcode 2009IJMPA..24.2601G. DOI:10.1142/S0217751X09045431.
^ http://cms.web.cern.ch/cms/News/2011/LP11/
^ http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2011-135/
^ http://www.zdnet.co.uk/news/emerging-tech/2011/07/25/cern-higgs-boson-answer-to-come-by-end-of-2012-40093510/
^ http://news.cnet.com/8301-30685_3-57342044-264/cern-physicists-find-hint-of-higgs-boson/
^ http://operaweb.lngs.infn.it/spip.php?rubrique14 31May2010 Press Release.
^ "Neutrino 'ghost particle' sized up by astronomers". BBC News. 22 June 2010.
^ W.-M. Yao et al. (Particle Data Group) (2006). "Review of Particle Physics: Quarks". Journal of Physics G 33: 1. arXiv:astro-ph/0601168. Bibcode 2006JPhG...33....1Y. DOI:10.1088/0954-3899/33/1/001.
^ BABAR Data in Tension with the Standard Model (SLAC press-release).
^ BaBar Collaboration, Evidence for an excess of B -> D(*) Tau Nu decays,arXiv:1205.5442.
^ BaBar data hint at cracks in the Standard Model (EScienceNews.com).
^ CERN Press Release

[edit]Further reading

R. Oerter (2006). The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics. Plume.
B.A. Schumm (2004). Deep Down Things: The Breathtaking Beauty of Particle Physics. Johns Hopkins University Press. ISBN 0-8018-7971-X.

Introductory textbooks

I. Aitchison, A. Hey (2003). Gauge Theories in Particle Physics: A Practical Introduction.. Institute of Physics. ISBN 978-0-585-44550-2.
W. Greiner, B. Müller (2000). Gauge Theory of Weak Interactions. Springer. ISBN 3-540-67672-4.
G.D. Coughlan, J.E. Dodd, B.M. Gripaios (2006). The Ideas of Particle Physics: An Introduction for Scientists. Cambridge University Press.
D.J. Griffiths (1987). Introduction to Elementary Particles. John Wiley & Sons. ISBN 0-471-60386-4.
G.L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5.

Advanced textbooks

T.P. Cheng, L.F. Li (2006). Gauge theory of elementary particle physics. Oxford University Press. ISBN 0-19-851961-3. Highlights the gauge theory aspects of the Standard Model.
J.F. Donoghue, E. Golowich, B.R. Holstein (1994). Dynamics of the Standard Model. Cambridge University Press. ISBN 978-0-521-47652-2. Highlights dynamical andphenomenological aspects of the Standard Model.
L. O'Raifeartaigh (1988). Group structure of gauge theories. Cambridge University Press. ISBN 0-521-34785-8. Highlights group-theoretical aspects of the Standard Model.

Journal articles

E.S. Abers, B.W. Lee (1973). "Gauge theories". Physics Reports 9: 1–141. Bibcode 1973PhR.....9....1A. DOI:10.1016/0370-1573(73)90027-6.
Y. Hayato et al. (1999). "Search for Proton Decay through p → νK⁺ in a Large Water Cherenkov Detector". Physical Review Letters 83 (8): 1529. arXiv:hep-ex/9904020.Bibcode 1999PhRvL..83.1529H. DOI:10.1103/PhysRevLett.83.1529.
S.F. Novaes (2000). "Standard Model: An Introduction". arXiv:hep-ph/0001283 [hep-ph].
D.P. Roy (1999). "Basic Constituents of Matter and their Interactions — A Progress Report.". arXiv:hep-ph/9912523 [hep-ph].
F. Wilczek (2004). "The Universe Is A Strange Place". Nuclear Physics B - Proceedings Supplements 134: 3. arXiv:astro-ph/0401347. Bibcode 2004NuPhS.134....3W.DOI:10.1016/j.nuclphysbps.2004.08.001.

[edit]External links

"LHC sees hint of lightweight Higgs boson" "New Scientist".
"Standard Model may be found incomplete," New Scientist.
"Observation of the Top Quark" at Fermilab.
"The Standard Model Lagrangian." After electroweak symmetry breaking, with no explicit Higgs boson.
"Standard Model Lagrangian" with explicit Higgs terms. PDF, PostScript, and LaTeX versions.
"The particle adventure." Web tutorial.
Nobes, Matthew (2002) "Introduction to the Standard Model of Particle Physics" on Kuro5hin: Part 1, Part 2, Part 3a, Part 3b.

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Multiplication by Infinity

Friday, June 22, 2012

CERN Announces July 4 Press Conference re Higgs Boson

Contents

[edit]Historical background

[edit]Overview

[edit]Particle content

[edit]Fermions

[edit]Gauge bosons

[edit]Higgs boson

[edit]Field content

[edit]Spin 1

[edit]Spin ¹⁄₂

[edit]Spin 0

[edit]Lagrangian

[edit]Higgs mechanism

[edit]Masses and CKM matrix

[edit]Theoretical aspects

[edit]Construction of the Standard Model Lagrangian

[edit]Quantum chromodynamics sector

[edit]Electroweak sector

[edit]Higgs sector

[edit]Additional symmetries of the Standard Model

[edit]List of Standard Model fermions

[edit]Tests and predictions

[edit]Challenges

[edit]See also

[edit]Notes and references

[edit]Notes

[edit]References

[edit]Further reading

[edit]External links

No comments:

Friday, June 22, 2012

CERN Announces July 4 Press Conference re Higgs Boson

Contents

[edit]Historical background

[edit]Overview

[edit]Particle content

[edit]Fermions

[edit]Gauge bosons

[edit]Higgs boson

[edit]Field content

[edit]Spin 1

[edit]Spin 1⁄2

[edit]Spin 0

[edit]Lagrangian

[edit]Higgs mechanism

[edit]Masses and CKM matrix

[edit]Theoretical aspects

[edit]Construction of the Standard Model Lagrangian

[edit]Quantum chromodynamics sector

[edit]Electroweak sector

[edit]Higgs sector

[edit]Additional symmetries of the Standard Model

[edit]List of Standard Model fermions

[edit]Tests and predictions

[edit]Challenges

[edit]See also

[edit]Notes and references

[edit]Notes

[edit]References

[edit]Further reading

[edit]External links

No comments:

[edit]Spin ¹⁄₂