538 10 Particle Physics – II
Strangeness and strange particles: Heavy unstable particles such as kaons and
hyperons which are produced copiously but decay slowly are named as strange
particles. A new quantum numberS, strangeness is introduced to distinguish them
from other particles. Gellmann’s formula
Q
e=T 3 +
S+B
2
(10.2)
where B is the baryon number.K+andK^0 are assignedS=+1, whileK−andK^0
haveS=−1. TheΣhyperons andΛhyperons haveS=− 1 , Ξ−andΞ^0 have
S=− 2 ,Ω−hasS=−3. The ordinary particles,n,p,π+,π^0 ,π−haveS=0.
The anti particles have opposite strangeness. StrangenessSis an additive quantum
number. Table 10.3 summarises the strangenessSfor various hadron multiplets.
Table 10.3TandSassignments
T/S − 3 − 2 −10 1 2 3
0 Ω− Λ Λ Ω+
p
Ξ^0 K− nK+ Ξ^0(^1) / 2 Ξ− K^0 p K^0 Ξ+
n
Σ+ π+ Σ
−
1 Σ^0 π^0 Σ^0
Σ− π− Σ
- StrangenessSis conserved in strong and electromagnetic interactions, that is
ΔS =0, but breaks down in weak interactions, such as decays, the rule being
ΔS=±1.
Leptons: The electron, the muon and the tauon and their respective neutrinos as well
as their antiparticles constitute the family of leptons. Leptons are assigned lepton
number,L =+1 and antileptons,L =−1. The numbersLe, LμandLτare
separately conserved in all the three types of interactions. The lepton numbers are
shown in Table 10.4.
Table 10.4Lepton numbers
Q/eLe= 1 Lμ= 1 Lτ= 1
0
− 1
(
νe
e−
)(
νμ
μ−
)(
ντ
τ−
)
Q/eLe=− 1 Lμ=− 1 Lτ=− 1
0 - 1
(
νe
e+
)(
νμ
μ+
)(
ντ
τ+
)
Helicity or handedness: The helicityHis defined as the ratioJz/JwhereJzis
the component of spin along the momentum vector of the particle andJis the
total spin. Massless particles have spin componentsJz=+Jonly. ThusH=+ 1
or−1. Neutrinos haveH =−1 (left-handed) and anti-neutrinos haveH =+ 1
(right-handed). Massive particles are not in pure helicity eigen states and contain
both LH and RH components.