Topness

51 years old Sportspersons Rusty from Wrigley, spends time with pastimes which includes beach, property agent in singapore developers in singapore and surf fishing. Continues to be inspired how enormous the earth is after making vacation to Saloum Delta.

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_W and corresponds to the gauge symmetry U(1).

Definition

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 W³ electroweak quantum field to produce the observed Z⁰ gauge boson and the photon of quantum electrodynamics.

Weak hypercharge, usually written as Y_W, is defined as:

$\qquad Q=T_{3}+{Y_{W} \over 2}$

where Q is the electrical charge (in elementary charge units) and T₃ is the third component of weak isospin. Rearranging, the weak hypercharge can be expressed as:

$\qquad Y_{W}=2(Q-T_{3})$

	left-handed	el. charge $Q$	weak isospin $T_{3}$	weak hypercharge $Y_{W}$	right-handed	el. charge $Q$	weak isospin $T_{3}$	weak hypercharge $Y_{W}$
Leptons	$\nu _{e},\nu _{\mu },\nu _{\tau }$	0	+½	-1	-	-	-	-
	$e^{-},\mu ^{-},\tau ^{-}$	-1	-½	-1	$e_{R}^{-},\mu _{R}^{-},\tau _{R}^{-}$	-1	0	-2
Quarks	$u,c,t$	+2/3	+½	+1/3	$u_{R},c_{R},t_{R}$	+2/3	0	+4/3
	$d',s',b'$	-1/3	-½	+1/3	$d_{R},s_{R},b_{R}$	-1/3	0	-2/3

Note: sometimes weak hypercharge is scaled so that

$\qquad Y_{W}=Q-T_{3}$

although this is a minority usage.

Baryon and lepton number

Weak hypercharge is related to baryon number - lepton number via:

$X+2Y_{W}=5(B-L)\,$

where X is a 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.

Neutron decay

Template:SubatomicParticle → Template:SubatomicParticle + Template:SubatomicParticle + Template:SubatomicParticle

Hence neutron decay conserves baryon number B and lepton number L separately, so also the difference B-L is conserved.

Proton decay

Proton decay is a prediction of many grand unification theories.

Template:SubatomicParticle → Template:SubatomicParticle + Template:SubatomicParticle → Template:SubatomicParticle + 2Template:SubatomicParticle

Hence proton decay conserves B-L, even though it violates both lepton number and baryon number conservation.

See also

• Standard Model (mathematical formulation)