Standard Model

Standard Model

The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions together with the elementary particles that take part in these interactions. These particles make up all matter in the universe except for the dark matter. The standard model is a non-abelian gauge theory of the electroweak and strong interactions with the symmetry group "SU(3)×SU(2)×U(1)". To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions.

The Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction.

The recent observation of neutrino oscillations will result in certain modifications of some of the parameters of the standard model.

Historical background

The formulation of the unification of the electromagnetic and weak interactions in the Standard Model is due to Steven Weinberg, Abdus Salam and, subsequently, Sheldon Glashow. The unification model was initially proposed by Steven Weinberg in 1967, [S. Weinberg "Phys. Rev.Lett." 19 1264–1266 (1967).] and completed integrating it with the proposals by P. Higgs, [cite web|url=|title=Broken Symmetries and the Masses of Gauge Bosons] G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, [cite web|url=|title=Global Conservation Laws and Massless Particles] and F. Englert and R. Brout [cite web|url=|title=Broken Symmetry and the Mass of Gauge Vector Mesons] of spontaneous symmetry breaking which gives origin to the masses of all particles described in the model.

After the discovery, made at CERN of the existence of neutral weak currents, [F. J. Hasert "et al." "Phys. Lett." 46B 121 (1973).] [F. J. Hasert "et al." "Phys. Lett." 46B 138 (1973).] [F. J. Hasert "et al." "Nucl. Phys." B73 1(1974).] [cite web|url=|title=The discovery of the weak neutral currents|date=2004-10-04|publisher=CERN courier|accessdate=2008-05-08] mediated by the SubatomicParticle|Z boson boson, foreseen in the Standard Model, Glashow, Salam, and Weinberg received the Nobel Prize in Physics in 1979.


In physics, the dynamics of both matter and energy in nature is presently best understood in terms of the kinematics and interactions of fundamental particles. To date, science has managed to reduce the laws which seem to govern the behavior and interaction of all types of matter and energy we are aware of, to a small core of fundamental laws and theories. A major goal of physics is to find the 'common ground' that would unite all of these into one integrated model of everything, in which all the other laws we know of would be special cases, and from which the behavior of all matter and energy can be derived (at least in principle). "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." (Feynman's lectures on Physics, Vol 1. 2–7)

The standard model is a grouping of two major theories — quantum electroweak and quantum chromodynamics — which provides an internally consistent theory describing interactions between all experimentally observed particles. Technically, quantum field theory provides the mathematical framework for the standard model. The standard model describes each type of particle in terms of a mathematical field. For a technical description of the fields and their interactions, see standard model (mathematical formulation).

Particle Content

The particles of the standard model are organized into three classes according to their spin: fermions (spin-½ particles of matter), gauge bosons (spin-1 force-mediating particles), and the (spin-0) Higgs boson.

Particles of matter

All fermions in the Standard Model are spin-½, and follow the Pauli Exclusion Principle in accordance with the spin-statistics theorem.

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) imesSU(2) imesU(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.

The QCD sector

The electroweak sector

The electroweak sector is a Yang-Mills gauge theory with the symmetry group U(1) imes SU(2)_L,:mathcal{L}_{EW}=sum_psiarpsigamma^muleft(ipartial_mu-g'{1over2}Y_WB_mu-g{1over2}vec au_Lvec W_mu ight)psi +mathcal{L}_{YM}(B_mu)+mathcal{L}_{YM}(vec W_mu),where B_mu is the U(1) gauge field; Y_W is the weak hypercharge — the generator of the U(1) group; vec{W}_mu is thethree-component SU(2) gauge field; vec{ au}_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.

The Higgs sector

In the standard model the Higgs field is a complex spinor of thegroup SU(2)_L,:varphi={1oversqrt{2left(egin{array}{c}varphi^+ \ varphi^0end{array} ight);,where the indexes {}^+ and {}^0 indicate the Q-charges of thecomponents; the Y_W-charge of both components is equal 1.

Before the symmetry breaking the Higgs Lagrangian is given as

mathcal{L}_H=varphi^daggerleft(stackrel{leftarrow}{partial_mu}-ig'{1over2}Y_WB_mu-ig{1over2}vec auvec W_mu ight)left(partial_mu+ig'{1over2}Y_WB_mu+ig{1over2}vec auvec W_mu ight)varphi-{lambda^2over4}left(varphi^daggervarphi-v^2 ight)^2

Additional Symmetries of the Standard Model

From the theoretical point of view, the standard model exhibits additional global symmetries that were not postulated at the outset of its construction. There are four such symmetries and are collectively called accidental symmetries, all of which are continuous U(1) global symmetries. The transformations leaving the Lagrangian invariant are:psi_ ext{q}(x) ightarrow e^{ialpha/3}psi_ ext{q}:E_L ightarrow e^{ieta}E_L ext{ and }(e_R)^c ightarrow e^{ieta}(e_R)^c:M_L ightarrow e^{ieta}M_L ext{ and }(mu_R)^c ightarrow e^{ieta}(mu_R)^c:T_L ightarrow e^{ieta}T_L ext{ and }( au_R)^c ightarrow e^{ieta}( au_R)^c.The first transformation rule is shorthand to mean 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, ( au_R)^c are the 2nd (muon) and 3rd (tau) generation analogs of E_L and (e_R)^c fields.

By Noether's theorem, each of these symmetries yields an associated conservation law. They are the conservation of baryon number, "electron number", "muon number", and "tau number". Each quark carries 1/3 of a baryon number, while each antiquark carries -1/3 of a baryon number. The conservation law implies that the total number of quarks minus number of antiquarks stays constant throughout time. Within experimental limits, no violation of this conservation law has been found.

Similarly, each electron and its associated neutrino carries +1 electron number, while the antielectron and the associated antineutrino carry -1 electron number, the muons carry +1 muon number and the tau leptons carry +1 tau number. The standard model predicts that each of these three numbers should be conserved separately in a manner similar to the baryon number. These numbers are collectively known as lepton family numbers (LF). The difference in the symmetry structures between the quark and the lepton sectors is due to the masslessness of neutrinos in the standard model. However, it was recently found that neutrinos have small mass, and oscillate between flavors, signaling the violation of these three quantum numbers.

In addition to the accidental (but exact) symmetries described above, the standard model exhibits a set of approximate symmetries. These are the "SU(2) Custodial Symmetry" and the "SU(2) or SU(3) quark flavor symmetry."

Tests and predictions

The Standard Model predicted the existence of W and Z bosons, the gluon, the top quark and the charm quark before these particles had been observed. Their predicted properties were experimentally confirmed with good precision.

The Large Electron-Positron Collider at CERN tested various predictions about the decay of Z bosons, and found them confirmed.

To get an idea of the success of the Standard Model a comparison between the measured and the predicted values of some quantities are shown in the following table:

Challenges to the standard model

The Standard Model of particle physics has been empirically determined through experiments over the past fifty years. Currently the Standard Model predicts that there is one more particle to be discovered, the Higgs boson. One of the reasons for building the Large Hadron Collider is that the increase in energy is expected to make the Higgs observable. However, as of August 2008, there are only indirect experimental indications for the existence of the Higgs boson and it can not be claimed to be found.

There has been a great deal of both theoretical and experimental research exploring whether the Standard Model could be extended into a complete theory of everything. This area of research is often described by the term 'Beyond the Standard Model'. There are several motivations for this research. First, the Standard Model does not attempt to explain gravity, and it is unknown how to combine quantum field theory which is used for the Standard Model with general relativity which is the best physical model of gravity. This means that there is not a good theoretical model for phenomena such as the early universe.

Another avenue of research is related to the fact that the standard model seems very "ad-hoc" and inelegant. For example, the theory contains many seemingly unrelated parameters of the theory — 21 in all (18 parameters in the core theory, plus G, c and h; there are believed to be an additional 7 or 8 parameters required for the neutrino masses, although neutrino masses are outside the standard model and the details are unclear). Research also focuses on the Hierarchy problem (why the weak scale and Planck scale are so disparate), and attempts to reconcile the emerging Standard Model of Cosmology with the Standard Model of particle physics. Many questions relate to the initial conditions that led to the presently observed Universe. Examples include: Why is there a matter/antimatter asymmetry? Why is the Universe isotropic and homogeneous at large distances?

ee also

*The theoretical formulation of the standard model
*Weak interactions, Fermi theory of beta decay and electroweak theory
*Strong interactions, flavour, quark model and quantum chromodynamics
*For open questions, see quark matter, CP violation and neutrino masses
*Beyond the Standard Model
*noncommutative standard model



Introductory textbooks

*cite book | author=Griffiths, David J. | title=Introduction to Elementary Particles | publisher=Wiley, John & Sons, Inc | year=1987 | id=ISBN 0-471-60386-4
*cite book | author=D.A. Bromley | title=Gauge Theory of Weak Interactions | publisher=Springer | year=2000 | id=ISBN 3-540-67672-4
*cite book | author=Gordon L. Kane | title=Modern Elementary Particle Physics | publisher=Perseus Books | year=1987 | id=ISBN 0-201-11749-5

Advanced textbooks

*cite book | author = Cheng, Ta Pei; Li, Ling Fong | title=Gauge theory of elementary particle physics | publisher = Oxford University Press | id=ISBN 0-19-851961-3
*:"— introduction to all aspects of gauge theories and the Standard Model."
*cite book | author = Donoghue, J. F.; Golowich, E.; Holstein, B. R. | title=Dynamics of the Standard Model | publisher = Cambridge University Press | id=ISBN 978-0521476522
*:"— highlights dynamical and phenomenological aspects of the Standard Model."
*cite book | author = O'Raifeartaigh, L. | title=Group structure of gauge theories | publisher = Cambridge University Press | id=ISBN 0-521-34785-8
*:"— highlights group-theoretical aspects of the Standard Model."

Journal articles

* S.F. Novaes, "Standard Model: An Introduction", [ hep-ph/0001283]
* D.P. Roy, "Basic Constituents of Matter and their Interactions — A Progress Report", [ hep-ph/9912523]
* Y. Hayato "et al.", "Search for Proton Decay through p → νK+ in a Large Water Cherenkov Detector". Phys. Rev. Lett. 83, 1529 (1999).
* Ernest S. Abers and Benjamin W. Lee, "Gauge theories". Physics Reports (Elsevier) C9, 1–141 (1973).

External links

* [ New Scientist story: Standard Model may be found incomplete]
* [ "The Universe Is A Strange Place", a lecture by Frank Wilczek]
* [ "Observation of the Top Quark" at Fermilab]
* [ PDF version of the Standard Model Lagrangian (after electroweak symmetry breaking, with no explicit Higgs boson)]
* [ PDF, PostScript, and LaTeX version of the Standard Model Lagrangian with explicit Higgs terms]
* [ The particle adventure.]

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