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{{more footnotes|date=February 2014}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
{{Flavour quantum numbers}}


The '''weak hypercharge''' in [[particle physics]] is a [[quantum number]] relating the [[electric charge]] and the third component of [[weak isospin]]. It is [[Conservation law (physics)|conserved]](only terms that are overall weak-hypercharge neutral are allowed in the Lagrangian) and is similar to the [[Gell-Mann–Nishijima formula]] for the [[hypercharge]] of strong interactions (which is not conserved in weak interactions). It is frequently denoted ''Y''<sub>W</sub> and corresponds to the [[gauge symmetry]] [[U(1)]].<ref>{{cite book|title=Dynamics of the standard model|pages=52|author=J. F. Donoghue, E. Golowich, B. R. Holstein|publisher=Cambridge University Press|year=1994|isbn=0-521-47652-6}}</ref>
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


==Definition==
Registered users will be able to choose between the following three rendering modes:
Weak hypercharge is the generator of the U(1) component of the [[electroweak]] gauge group, {{gaps|SU(2)|×|U(1)}} and its associated [[quantum field]] ''B'' mixes with the ''W''<sup>3</sup> electroweak quantum field to produce the observed {{subatomic particle|Z boson|link=yes}} gauge boson and the [[photon]] of [[quantum electrodynamics]].


Weak hypercharge, usually written as ''Y''<sub>W</sub>, satisfies the equality:
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


:<math>\qquad Q = T_3 + {Y_{\rm W} \over 2}</math>
<!--'''PNG''' (currently default in production)
where ''Q'' is the electrical charge (in [[elementary charge]] units) and ''T''<sub>3</sub> is the third component of [[weak isospin]]. Rearranging, the weak hypercharge can be explicitly defined as:
:<math forcemathmode="png">E=mc^2</math>
:<math>\qquad Y_{\rm W} = 2(Q - T_3)</math>


{| class = "wikitable" style = "text-align: center"
'''source'''
!
:<math forcemathmode="source">E=mc^2</math> -->
! left-handed
! el. charge<br>''Q''
! weak isospin<br>''T''<sub>3</sub>
! style="border-right:medium solid" | weak<br>hyper-<br>charge<br>''Y''<sub>W</sub>
! right-handed
! el. charge<br>''Q''
! weak isospin<br>''T''<sub>3</sub>
! weak<br>hyper-<br>charge<br>''Y''<sub>W</sub>
|- style="border-top: 2pt black solid"
|-
| rowspan = "2" | Leptons
| {{subatomic particle|electron neutrino|link=yes}}, {{subatomic particle|muon neutrino|link=yes}}, {{subatomic particle|tau neutrino|link=yes}}
| 0
| +1/2
| style="border-right:medium solid" | −1
| colspan=4 align=center | Do not interact (if exist at all)
|- style="border-bottom: 2pt black solid"
| {{subatomic particle|electron|link=yes}}, {{subatomic particle|muon|link=yes}}, {{subatomic particle|tau|link=yes}}
| −1
| −1/2
| style="border-right:medium solid" | −1
| {{physics particle|e|TR=−|BR=R}}, {{physics particle|μ|TR=−|BR=R}}, {{physics particle|τ|TR=−|BR=R}}
| −1
| 0
| −2
|-
| rowspan = "2" | Quarks
| {{subatomic particle|up quark|link=yes}}, {{subatomic particle|charm quark|link=yes}}, {{subatomic particle|top quark|link=yes}}
| +2/3
| +1/2
| style="border-right:medium solid" | +1/3
| {{physics particle|u|BR=R}}, {{physics particle|c|BR=R}}, {{physics particle|t|BR=R}}
| +2/3
| 0
| +4/3
|-
| [[down quark|d]], [[strange quark|s]], [[bottom quark|b]]<div style="font-size:60%"></div>
| −1/3
| −1/2
| style="border-right:medium solid" | +1/3
| {{physics particle|d|BR=R}}, {{physics particle|s|BR=R}}, {{physics particle|b|BR=R}}
| −1/3
| 0
| −2/3
|}


Note: sometimes weak hypercharge is scaled so that 
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
:<math>\qquad Y_{\rm W} = Q - T_3</math>
although this is a minority usage.<ref>{{cite book|title=The mathematical theory of cosmic strings|author=M. R. Anderson|pages=12|publisher=CRC Press|year=2003|isbn=0-7503-0160-0}}</ref>


Hypercharge assignments in the [[Standard Model]] are determined up to a twofold ambiguity by demanding cancellation of all anomalies.
==Demos==


==Baryon and lepton number==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
Weak hypercharge is related to [[B − L|baryon number minus lepton number]] via:


:<math>X + 2Y_{\rm W} = 5(B - L) \,</math>


where ''[[X (charge)|X]]'' is a [[Grand Unification Theory|GUT]]-associated conserved quantum number. Since weak hypercharge is also conserved{{clarify|reason=In which interactions?|date=February 2014}} this implies that baryon number minus lepton number is also conserved, within the [[Standard Model]] and most extensions.{{clarify|reason=In which interactions?|date=February 2014}}
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


===Neutron decay===
==Test pages ==
:{{SubatomicParticle|neutron|link=yes}}  &rarr; {{SubatomicParticle|proton|link=yes}}  + {{SubatomicParticle|electron}}  + {{SubatomicParticle|electron antineutrino}}


Hence neutron decay conserves [[baryon number]] ''B'' and [[lepton number]] ''L'' separately, so also the difference ''B''&nbsp;−&nbsp;''L'' is conserved.
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


===Proton decay===
*[[Inputtypes|Inputtypes (private Wikis only)]]
[[Proton decay]] is a prediction of many [[Grand unification theory|grand unification theories]].
*[[Url2Image|Url2Image (private Wikis only)]]
:{{SubatomicParticle|proton+}}  &rarr; {{SubatomicParticle|antielectron|link=yes}}  + {{SubatomicParticle|pion0|link=yes}} &rarr; {{SubatomicParticle|antielectron}}  + 2{{SubatomicParticle|photon|link=yes}}
==Bug reporting==
 
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
Hence proton decay conserves ''B''&nbsp;−&nbsp;''L'', even though it violates both [[lepton number]] and [[baryon number]] conservation.
 
== See also ==
* [[Standard Model (mathematical formulation)]]
 
== Notes ==
<references/>
 
[[Category:Particle physics]]
[[Category:Nuclear physics]]
[[Category:Standard Model]]
[[Category:Electroweak theory]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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