1000 Solved Problems in Modern Physics

10.1 Basic Concepts and Formulae 537

Table 10.2Characteristics of the fundamental interactions

Strong Electromagnetic Weak Gravitational

Carrier of field

spin-parity(Jp)of

quantum

Gluon 1− Photon 1− W±,Z^01 −, 1 + Gravitation? 2+

Coupling constant αs≤ 1

α=

e^2

4 πc

=

1

137

G

(

Mc^2

) 2

(c)^3

GNM^2

4 πc

= 5 × 10 −^40

Mass 0 0 80, 90 GeV 0

Relative strength 1 10 −^2 ≤^10 −^510 −^38

Time scale 10 −^23 s10−^18 − 10 −^20 s > 10 −^13 s

Range ≤ 10 −^15 m ∞ 10 −^18 m ∞

Source Colour charge Electric charge Weak charge Mass

Standard model: As of today, the physics embodied in electrodynamics, chromo
dynamics and electro-weak interaction is termed as the standard model of elemen-
tary particles.
Resonancesor resonant states are the analogs of excited states of atoms. They are the
excited states of familiar hadrons. Some of them are so short lived (∼ 10 −^23 − 10 −^24 s)
that their direct detection is not possible. They ultimately decay into more familiar
particles, like nucleons, mesons, leptons and photons. Because of their short lives
their energy (mass) spread is enormous, due to uncertainty principle.
Baryon number (B)is the generalization of mass number. For nucleons and hyperons
B=+1, for anti baryons,B=−1, for pions, kaons and other particlesB= 0 .Bis
an additive quantum and is conserved in all the three types of interactions.
Isospin (T or I)is a quantum number applicable to hadrons and is conserved in
strong interactions. It results from the near equality of u and d-quarks. This is
reflected in the near equality of masses of charged multiplets such as (n,p),(π+,π^0 ,
π−),(K+,K^0 ) etc, as well as for the atomic nuclei once the coulomb interaction
is removed. It is thus named because its mathematical description is entirely analo-
gous to ordinary spin or angular momentum in quantum mechanics. The tables for
Clebsch – Gordon coefficients for the addition of angular momenta (displayed in the
summary of Chap. 3) can be directly used for the isospins.Tis the additive quantum
number. The charge multiplicity is given by 2T+1. The antiparticle has the sameT
as the particle but oppositeT 3 .T 3 is analogous to Lzfor angular momentum. Total
isospin (I) is conserved in strong interactions but breaks down in em and weak
interactions. The third component (I 3 ) of a system of hadrons is conserved in strong
and em interactions but is violated in weak interactions

(

ΔI 3 =±^1

/

2

)

.

The generalized pauli principle

(− 1 )l+s+I=− 1 (10.1)

wherelis the orbital angular momentum,sthe spin andIthe isospin.