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| {{Flavour_quantum_numbers}}
| | 29 year old Slaughterer Efrain Nadel from Aberdeen, has several passions including house repair, diet and soccer. Preceding year very recently made a journey Viñales Valley. |
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| The '''weak hypercharge''' in [[particle physics]] is a conserved quantum number relating the [[electrical charge]] and the third component of [[weak isospin]], and is similar to the [[Gell-Mann–Nishijima formula]] for the [[hypercharge]] of strong interactions (which is not conserved). 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>
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| ==Definition==
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| It is the generator of the U(1) component of the [[electroweak]] gauge group, SU(2)xU(1) and its associated quantum field ''B'' mixes with the ''W<sup>3</sup>'' [[electroweak]] quantum field to produce the observed ''Z<sup>0</sup>'' gauge boson and the [[photon]] of [[quantum electrodynamics]].
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| Weak hypercharge, usually written as ''Y<sub>W</sub>'', is defined as:
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| :<math>\qquad Q = T_3 + {Y_W \over 2}</math>
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| 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 expressed as:
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| :<math>\qquad Y_W = 2(Q - T_3)</math>
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| {| class = "wikitable" style = "text-align: center"
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| !
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| ! left-handed
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| ! el. charge<br><math>Q</math>
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| ! weak isospin<br><math>T_3</math>
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| ! style="border-right:medium solid" | weak hypercharge<br><math>Y_W</math>
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| ! right-handed
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| ! el. charge<br><math>Q</math>
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| ! weak isospin<br><math>T_3</math>
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| ! weak hypercharge<br><math>Y_W</math>
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| |- style="border-top: 2pt black solid"
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| |-
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| | rowspan = "2" | Leptons
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| | <math> \nu_e, \nu_{\mu}, \nu_{\tau} </math>
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| | 0
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| | +½
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| | style="border-right:medium solid" | -1
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| | -
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| | -
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| | -
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| | -
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| |- style="border-bottom: 2pt black solid"
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| | <math> e^-, \mu^-, \tau^- </math>
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| | -1
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| | -½
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| | style="border-right:medium solid" | -1
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| | <math> e_R^-, \mu_R^-, \tau_R^- </math>
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| | -1
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| | 0
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| | -2
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| |-
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| | rowspan = "2" | Quarks
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| | <math> u, c, t </math>
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| | +2/3
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| | +½
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| | style="border-right:medium solid" | +1/3
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| | <math> u_R, c_R, t_R </math>
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| | +2/3
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| | 0
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| | +4/3
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| |-
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| | <math> d', s', b' </math>
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| | -1/3
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| | -½
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| | style="border-right:medium solid" | +1/3
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| | <math> d_R, s_R, b_R </math>
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| | -1/3
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| | 0
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| | -2/3
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| |}
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| Note: sometimes weak hypercharge is scaled so that
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| :<math>\qquad Y_W = Q - T_3</math>
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| 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>
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| ==Baryon and lepton number==
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| Weak hypercharge is related to [[B−L|baryon number - lepton number]] via:
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| :<math>X + 2Y_W = 5(B - L) \,</math>
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| where [[X (charge)|X]] is a [[Grand unification theory|GUT]]-associated conserved [[quantum number]]. Since weak hypercharge is also conserved this implies that baryon number minus lepton number is also conserved, within the [[Standard Model]] and most extensions.
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| ===Neutron decay===
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| :{{SubatomicParticle|neutron|link=yes}} → {{SubatomicParticle|proton|link=yes}} + {{SubatomicParticle|electron|link=yes}} + {{SubatomicParticle|electron antineutrino|link=yes}}
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| Hence neutron decay conserves [[baryon number]] B and [[lepton number]] L separately, so also the difference [[B-L]] is conserved.
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| ===Proton decay===
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| [[Proton decay]] is a prediction of many [[Grand unification theory|grand unification theories]].
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| :{{SubatomicParticle|proton+|link=yes}} → {{SubatomicParticle|antielectron|link=yes}} + {{SubatomicParticle|pion0|link=yes}} → {{SubatomicParticle|antielectron|link=yes}} + 2{{SubatomicParticle|photon|link=yes}}
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| Hence proton decay conserves [[B-L]], even though it violates both [[lepton number]] and [[baryon number]] conservation.
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| == See also ==
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| * [[Standard Model (mathematical formulation)]]
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| == Notes ==
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| <references/>
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| [[Category:Particle physics]]
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| [[Category:Nuclear physics]]
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| [[Category:Standard Model]]
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| [[Category:Electroweak theory]]
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29 year old Slaughterer Efrain Nadel from Aberdeen, has several passions including house repair, diet and soccer. Preceding year very recently made a journey Viñales Valley.