|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{Standard model of particle physics|cTopic=Some models}}
| | The ac1st16.dll error is annoying plus pretty common with all sorts of Windows computers. Not only does it make a computer run slower, but it can also avoid we from using a range of programs, including AutoCAD. To fix this issue, you need to use a simple system to cure all of the potential issues that cause it. Here's what you should do...<br><br>You may find which there are registry cleaners which are free plus those which you'll have to pay a nominal sum for. Some registry cleaners provide a bare bones program for free with all the way of upgrading to a more advanced, effective version of the same program.<br><br>Over time a disk can furthermore receive fragmented. Fragmentation causes the computer to slow down because it takes windows much longer to obtain a files place. Fortunately, your PC has a built in disk defragmenter. We can run this system by clicking "Start" - "All Programs" - "Accessories" - "System Tools" - "Disk Defragmenter". You can today have the option to choose that drives or partition we want to defragment. This action may take you certain time so it is actually advised to do this on a regular basis thus as to avoid further fragmentation and to speed up a windows XP computer.<br><br>Windows errors will be caused by any number of factors, but there's almost constantly 1 cause. There's a hidden part of your system which is responsible for creating 90% of all Windows errors, and it's called the 'registry'. This is the central database for a system plus is where your computer stores all its program files and settings. It's a really important piece of Windows, which is must be able to function. However, it's moreover one of the biggest causes of issues on your PC.<br><br>The [http://bestregistrycleanerfix.com/regzooka regzooka] could come because standard with a back up plus restore facility. This ought to be an easy to apply process.That means that should you encounter a problem with a PC following using a registry cleaning we can simply restore the settings.<br><br>The most probable cause of the trouble is the program problem - Registry Errors! That is the reason why individuals whom already have more than 2 G RAM on their computers are nevertheless constantly bothered by the problem.<br><br>Google Chrome is my lifeline and for this day fortunately. My all settings and analysis associated bookmarks were saved in Chrome plus stupidly I didn't synchronize them with all the Gmail to shop them online. I could not afford to install modern version plus sacrifice all my work settings. There was no means to retrieve the older settings. The only choice left for me was to miraculously fix it browser in a method that all information and settings stored inside it are recovered.<br><br>By changing the technique we use the internet we can have access more of the valuable bandwidth. This will eventually provide we a quicker surfing experience. Here is a link to 3 techniques to personalize your PC speed on the net. |
| In [[particle physics]], the '''electroweak interaction''' is the [[unified field theory|unified description]] of two of the four known [[fundamental interaction]]s of nature: [[electromagnetism]] and the [[weak interaction]]. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the [[electroweak scale|unification energy]], on the order of 100 [[GeV]], they would merge into a single '''electroweak force'''. Thus if the universe is hot enough (approximately 10<sup>15</sup> [[Kelvin|K]], a temperature exceeded until shortly after the [[Big Bang]]) then the electromagnetic force and weak force merge into a combined electroweak force. During the [[electroweak epoch]], the electroweak force separated from the [[strong force]]. During the [[quark epoch]], the electroweak force split into the electromagnetic and [[weak force]].
| |
| | |
| For contributions to the unification of the weak and electromagnetic interaction between [[elementary particle]]s, [[Abdus Salam]], [[Sheldon Lee Glashow|Sheldon Glashow]] and [[Steven Weinberg]] were awarded the [[Nobel Prize in Physics]] in 1979.<ref>
| |
| {{cite book
| |
| |author=S. Bais
| |
| |year=2005
| |
| |title=The Equations: Icons of knowledge
| |
| |page=84
| |
| |publisher=
| |
| |isbn=0-674-01967-9
| |
| }}</ref><ref>
| |
| {{cite web
| |
| |url=http://nobelprize.org/nobel_prizes/physics/laureates/1979/
| |
| |title=The Nobel Prize in Physics 1979
| |
| |publisher=[[The Nobel Foundation]]
| |
| |accessdate=2008-12-16
| |
| }}</ref> The existence of the electroweak interactions was experimentally established in two stages, the first being the discovery of [[neutral current]]s in neutrino scattering by the [[Gargamelle]] collaboration in 1973, and the second in 1983 by the [[UA1]] and the [[UA2]] collaborations that involved the discovery of the [[W and Z bosons|W and Z]] [[gauge boson]]s in proton–antiproton collisions at the converted [[Super Proton Synchrotron]]. In 1999, [[Gerardus 't Hooft]] and [[Martinus Veltman]] were awarded the Nobel prize for showing that the electroweak theory is [[renormalizable]].
| |
| | |
| ==Formulation==
| |
| [[File:Electroweak.svg|300px|right|thumb|The pattern of [[weak isospin]], T<sub>3</sub>, and [[weak hypercharge]], Y<sub>W</sub>, of the known elementary particles, showing electric charge, Q, along the [[weak mixing angle]]. The neutral Higgs field (circled) breaks the electroweak symmetry and interacts with other particles to give them mass. Three components of the Higgs field become part of the massive W and Z bosons.]]
| |
| | |
| Mathematically, the unification is accomplished under an [[SU(2)|''SU''(2)]] × [[U(1)|''U''(1)]] [[gauge theory|gauge group]]. The corresponding [[gauge boson]]s are the '''three''' W bosons of [[weak isospin]] from SU(2) ({{SubatomicParticle|W boson+}}, {{SubatomicParticle|W boson0}}, and {{SubatomicParticle|W boson-}}), and the {{SubatomicParticle|B boson0}} boson of [[weak hypercharge]] from U(1), respectively, all of which are massless.
| |
| | |
| In the [[Standard Model]], the [[W and Z bosons|{{SubatomicParticle|W boson+-}} and {{SubatomicParticle|Z boson0}} bosons]], and the photon, are produced by the [[spontaneous symmetry breaking]] of the '''electroweak symmetry''' from ''SU''(2) × ''U''(1)<sub>''Y''</sub> to ''U''(1)<sub>em</sub>, caused by the [[Higgs mechanism]] (see also [[Higgs boson]]).<ref>
| |
| {{cite journal
| |
| | author=F. Englert, R. Brout
| |
| | year=1964
| |
| | title=Broken Symmetry and the Mass of Gauge Vector Mesons
| |
| | journal=[[Physical Review Letters]]
| |
| | volume=13 | pages=321–323
| |
| | doi=10.1103/PhysRevLett.13.321
| |
| | bibcode=1964PhRvL..13..321E
| |
| | issue=9
| |
| }}</ref><ref name="Peter W. Higgs 1964 508-509">
| |
| {{cite journal
| |
| | author=P.W. Higgs
| |
| | year=1964
| |
| | title=Broken Symmetries and the Masses of Gauge Bosons
| |
| | journal=[[Physical Review Letters]]
| |
| | volume=13 | pages=508–509
| |
| | doi=10.1103/PhysRevLett.13.508
| |
| | bibcode=1964PhRvL..13..508H
| |
| | issue=16
| |
| }}</ref><ref>
| |
| {{cite journal
| |
| | author=G.S. Guralnik, C.R. Hagen, T.W.B. Kibble
| |
| | year=1964
| |
| | title=Global Conservation Laws and Massless Particles
| |
| | journal=[[Physical Review Letters]]
| |
| | volume=13 | pages=585–587
| |
| | doi=10.1103/PhysRevLett.13.585
| |
| | bibcode=1964PhRvL..13..585G
| |
| | issue=20
| |
| }}</ref><ref>
| |
| {{cite journal
| |
| | author=G.S. Guralnik
| |
| | year=2009
| |
| | title=The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles
| |
| | journal=[[International Journal of Modern Physics A]]
| |
| | volume=24 | pages=2601–2627
| |
| | doi=10.1142/S0217751X09045431
| |
| | arxiv=0907.3466
| |
| |bibcode = 2009IJMPA..24.2601G
| |
| | issue=14 }}</ref> ''U''(1)<sub>''Y''</sub> and ''U''(1)<sub>em</sub> are different copies of ''U''(1); the [[generating set|generator]] of ''U''(1)<sub>em</sub> is given by ''Q'' = ''Y''/2 + ''I''<sub>3</sub>, where ''Y'' is the generator of ''U''(1)<sub>''Y''</sub> (called the [[weak hypercharge]]), and ''I''<sub>3</sub> is one of the ''SU''(2) generators (a component of [[weak isospin]]).
| |
| | |
| The spontaneous symmetry breaking causes the {{SubatomicParticle|W boson0}} and {{SubatomicParticle|B boson0}} bosons to coalesce together into two different bosons – the {{SubatomicParticle|Z boson0}} boson, and the photon (γ) as follows:
| |
| | |
| : <math> \begin{pmatrix}
| |
| \gamma \\
| |
| Z^0 \end{pmatrix} = \begin{pmatrix}
| |
| \cos \theta_W & \sin \theta_W \\
| |
| -\sin \theta_W & \cos \theta_W \end{pmatrix} \begin{pmatrix}
| |
| B^0 \\
| |
| W^0 \end{pmatrix} </math>
| |
| | |
| Where θ<sub>W</sub> is the ''[[weak mixing angle]]''. The axes representing the particles have essentially just been rotated, in the ({{SubatomicParticle|W boson0}}, {{SubatomicParticle|B boson0}}) plane, by the angle θ<sub>W</sub>. This also introduces a discrepancy between the mass of the {{SubatomicParticle|Z boson0}} and the mass of the {{SubatomicParticle|W boson+-}} particles (denoted as M<sub>Z</sub> and M<sub>W</sub>, respectively);
| |
| | |
| :<math>M_Z=\frac{M_W}{\cos\theta_W}</math>
| |
| | |
| The distinction between electromagnetism and the weak force arises because there is a (nontrivial) linear combination of ''Y'' and ''I''<sub>3</sub> that vanishes for the Higgs boson (it is an eigenstate of both ''Y'' and ''I''<sub>3</sub>, so the coefficients may be taken as −''I''<sub>3</sub> and ''Y''): ''U''(1)<sub>em</sub> is defined to be the group generated by this linear combination, and is unbroken because it does not interact with the Higgs.
| |
| | |
| ==Lagrangian==
| |
| | |
| ===Before electroweak symmetry breaking===
| |
| The [[Lagrangian]] for the electroweak interactions is divided into four parts before [[electroweak symmetry breaking]]
| |
| :<math>\mathcal{L}_{EW} = \mathcal{L}_g + \mathcal{L}_f + \mathcal{L}_h + \mathcal{L}_y.</math>
| |
| | |
| The <math>\mathcal{L}_g</math> term describes the interaction between the three W particles and the B particle. | |
| :<math>\mathcal{L}_g = -\frac{1}{4}W^{a\mu\nu}W_{\mu\nu}^a - \frac{1}{4}B^{\mu\nu}B_{\mu\nu}</math>, | |
| where <math>W^{a\mu\nu}</math> (<math>a=1,2,3</math>) and <math>B^{\mu\nu}</math> are the [[field strength tensor]]s for the weak isospin and weak hypercharge fields.
| |
| | |
| <math>\mathcal{L}_f</math> is the kinetic term for the Standard Model fermions. The interaction of the gauge bosons and the fermions are through the [[gauge covariant derivative]].
| |
| :<math>\mathcal{L}_f = \overline{Q}_i iD\!\!\!\!/\; Q_i+ \overline{u}_i iD\!\!\!\!/\; u_i+ \overline{d}_i iD\!\!\!\!/\; d_i+ \overline{L}_i iD\!\!\!\!/\; L_i+ \overline{e}_i iD\!\!\!\!/\; e_i </math>,
| |
| where the subscript <math>i</math> runs over the three generations of fermions, <math>Q</math>, <math>u</math>, and <math>d</math> are the left-handed doublet, right-handed singlet up, and right handed singlet down quark fields, and <math>L</math> and <math>e</math> are the left-handed doublet and right-handed singlet electron fields.
| |
| | |
| The ''h'' term describes the Higgs field F.
| |
| :<math>\mathcal{L}_h = |D_\mu h|^2 - \lambda \left(|h|^2 - \frac{v^2}{2}\right)^2</math>
| |
| | |
| The ''y'' term gives the [[Yukawa interaction]] that generates the fermion masses after the Higgs acquires a vacuum expectation value.
| |
| :<math>\mathcal{L}_y = - y_{u\, ij} \epsilon^{ab} \,h_b^\dagger\, \overline{Q}_{ia} u_j^c - y_{d\, ij}\, h\, \overline{Q}_i d^c_j - y_{e\,ij} \,h\, \overline{L}_i e^c_j + h.c.</math>
| |
| | |
| ===After electroweak symmetry breaking===
| |
| The Lagrangian reorganizes itself after the Higgs boson acquires a vacuum expectation value. Due to its complexity, this Lagrangian is best described by breaking it up into several parts as follows.
| |
| | |
| :<math>\mathcal{L}_{EW} = \mathcal{L}_K + \mathcal{L}_N + \mathcal{L}_C + \mathcal{L}_H + \mathcal{L}_{HV} + \mathcal{L}_{WWV} + \mathcal{L}_{WWVV} + \mathcal{L}_Y</math>
| |
| | |
| The kinetic term <math>\mathcal{L}_K</math> contains all the quadratic terms of the Lagrangian, which include the dynamic terms (the partial derivatives) and the mass terms (conspicuously absent from the Lagrangian before symmetry breaking) | |
| | |
| :<math> \begin{align}
| |
| \mathcal{L}_K = \sum_f \overline{f}(i\partial\!\!\!/\!\;-m_f)f-\frac14A_{\mu\nu}A^{\mu\nu}-\frac12W^+_{\mu\nu}W^{-\mu\nu}+m_W^2W^+_\mu W^{-\mu}
| |
| \\
| |
| \qquad -\frac14Z_{\mu\nu}Z^{\mu\nu}+\frac12m_Z^2Z_\mu Z^\mu+\frac12(\partial^\mu H)(\partial_\mu H)-\frac12m_H^2H^2
| |
| \end{align}</math>
| |
| | |
| where the sum runs over all the fermions of the theory (quarks and leptons), and the fields <math>A_{\mu\nu}^{}</math>, <math>Z_{\mu\nu}^{}</math>, <math>W^-_{\mu\nu}</math>, and <math>W^+_{\mu\nu}\equiv(W^-_{\mu\nu})^\dagger</math> are given as
| |
| | |
| :<math>X_{\mu\nu}=\partial_\mu X_\nu - \partial_\nu X_\mu + g f^{abc}X^{b}_{\mu}X^{c}_{\nu}</math>, (replace X by the relevant field, and ''f''<sup>abc</sup> with the structure constants for the gauge group).
| |
| | |
| The neutral current <math>\mathcal{L}_N</math> and charged current <math>\mathcal{L}_C</math> components of the Lagrangian contain the interactions between the fermions and gauge bosons.
| |
| | |
| :<math>\mathcal{L}_{N} = e J_\mu^{em} A^\mu + \frac g{\cos\theta_W}(J_\mu^3-\sin^2\theta_WJ_\mu^{em})Z^\mu</math>,
| |
| | |
| where the electromagnetic current <math>J_\mu^{em}</math> and the neutral weak current <math>J_\mu^3</math> are
| |
| | |
| :<math>J_\mu^{em} = \sum_f q_f\overline{f}\gamma_\mu f</math>,
| |
| | |
| and
| |
| | |
| :<math>J_\mu^3 = \sum_f I^3_f\overline{f} \gamma_\mu\frac{1-\gamma^5}{2} f</math>
| |
| | |
| <math>q_f^{}</math> and <math>I_f^3</math> are the fermions' electric charges and weak isospin.
| |
| | |
| The charged current part of the Lagrangian is given by
| |
| | |
| :<math>\mathcal{L}_C=-\frac g{\sqrt2}\left[\overline u_i\gamma^\mu\frac{1-\gamma^5}2M^{CKM}_{ij}d_j+\overline\nu_i\gamma^\mu\frac{1-\gamma^5}2e_i\right]W_\mu^++h.c.</math>
| |
| | |
| <math>\mathcal{L}_H</math> contains the Higgs three-point and four-point self interaction terms.
| |
| | |
| :<math>\mathcal{L}_H=-\frac{gm_H^2}{4m_W}H^3-\frac{g^2m_H^2}{32m_W^2}H^4</math>
| |
| | |
| <math>\mathcal{L}_{HV}</math> contains the Higgs interactions with gauge vector bosons.
| |
| | |
| :<math>\mathcal{L}_{HV}=\left(gm_WH+\frac{g^2}4H^2\right)\left(W_\mu^+W^{-\mu}+\frac1{2\cos^2\theta_W}Z_\mu Z^\mu\right)</math>
| |
| | |
| <math>\mathcal{L}_{WWV}</math> contains the gauge three-point self interactions.
| |
| | |
| :<math>\mathcal{L}_{WWV}=-ig[(W_{\mu\nu}^+W^{-\mu}-W^{+\mu}W_{\mu\nu}^-)(A^\nu\sin\theta_W-Z^\nu\cos\theta_W)+W_\nu^-W_\mu^+(A^{\mu\nu}\sin\theta_W-Z^{\mu\nu}\cos\theta_W)]</math>
| |
| | |
| <math>\mathcal{L}_{WWVV}</math> contains the gauge four-point self interactions
| |
| | |
| :<math>\begin{align}
| |
| \mathcal{L}_{WWVV} = -\frac{g^2}4 \Big\{&[2W_\mu^+W^{-\mu} + (A_\mu\sin\theta_W - Z_\mu\cos\theta_W)^2]^2
| |
| \\
| |
| &- [W_\mu^+W_\nu^- + W_\nu^+W_\mu^- + (A_\mu\sin\theta_W - Z_\mu\cos\theta_W) (A_\nu\sin\theta_W - Z_\nu\cos\theta_W)]^2\Big\}
| |
| \end{align}</math>
| |
| | |
| and <math>\mathcal{L}_Y</math> contains the Yukawa interactions between the fermions and the Higgs field. | |
| | |
| :<math>\mathcal{L}_Y = -\sum_f \frac{gm_f}{2m_W}\overline ffH</math>
| |
| | |
| Note the <math>\frac{1-\gamma^5}{2}</math> factors in the weak couplings: these factors project out the left handed components of the spinor fields. This is why electroweak theory (after symmetry breaking) is commonly said to be a [[chiral theory]].
| |
| | |
| ==See also==
| |
| *[[Fundamental force]]s
| |
| *[[Standard model (basic details)|Formulation of the standard model]]
| |
| *[[Weinberg angle]]
| |
| *[[Unitarity gauge]]
| |
| | |
| == References ==
| |
| <references/>
| |
| | |
| ===General readers===
| |
| *{{cite book
| |
| |author=B.A. Schumm
| |
| |year=2004
| |
| |title=Deep Down Things: The Breathtaking Beauty of Particle Physics
| |
| |publisher=[[Johns Hopkins University Press]]
| |
| |isbn=0-8018-7971-X
| |
| }} Conveys much of the [[Standard Model]] with no formal mathematics. Very thorough on the weak interaction.
| |
| | |
| === Texts ===
| |
| *{{cite book
| |
| | author=D.J. Griffiths
| |
| | year=1987
| |
| | title=Introduction to Elementary Particles
| |
| | publisher=[[John Wiley & Sons]]
| |
| | isbn=0-471-60386-4
| |
| }}
| |
| *{{cite book
| |
| | author=W. Greiner, B. Müller
| |
| | year=2000
| |
| | title=Gauge Theory of Weak Interactions
| |
| | publisher=[[Springer (publisher)|Springer]]
| |
| | isbn=3-540-67672-4
| |
| }}
| |
| *{{cite book
| |
| | author=G.L. Kane
| |
| | year=1987
| |
| | title=Modern Elementary Particle Physics
| |
| | publisher=[[Perseus Books]]
| |
| | isbn=0-201-11749-5
| |
| }}
| |
| | |
| === Articles ===
| |
| *{{cite journal
| |
| |author=E.S. Abers, B.W. Lee
| |
| |year=1973
| |
| |title=Gauge theories
| |
| |journal=[[Physics Reports]]
| |
| |volume=9 |pages=1–141
| |
| |doi=10.1016/0370-1573(73)90027-6
| |
| |bibcode = 1973PhR.....9....1A }}
| |
| *{{cite journal
| |
| |author=Y. Hayato ''et al.''
| |
| |year=1999
| |
| |title=Search for Proton Decay through p → νK<sup>+</sup> in a Large Water Cherenkov Detector
| |
| |journal=[[Physical Review Letters]]
| |
| |volume=83 |pages=1529
| |
| |doi=10.1103/PhysRevLett.83.1529
| |
| |bibcode=1999PhRvL..83.1529H
| |
| |arxiv = hep-ex/9904020
| |
| |issue=8 }}
| |
| *{{cite journal
| |
| |author=J. Hucks
| |
| |year=1991
| |
| |title=Global structure of the standard model, anomalies, and charge quantization
| |
| |journal=[[Physical Review D]]
| |
| |volume=43 |pages=2709–2717
| |
| |doi=10.1103/PhysRevD.43.2709
| |
| |bibcode = 1991PhRvD..43.2709H
| |
| |issue=8 }}
| |
| * {{cite arxiv
| |
| |author=S.F. Novaes
| |
| |year=2000
| |
| |title=Standard Model: An Introduction
| |
| |class=hep-ph
| |
| |eprint=hep-ph/0001283
| |
| }}
| |
| *{{cite arxiv
| |
| |author=D.P. Roy
| |
| |year=1999
| |
| |title=Basic Constituents of Matter and their Interactions — A Progress Report
| |
| |class=hep-ph
| |
| |eprint=hep-ph/9912523
| |
| }}
| |
| | |
| <!--Categories-->
| |
| [[Category:Particle physics]]
| |
| [[Category:Electroweak theory]]
| |