1000 Solved Problems in Modern Physics

540 10 Particle Physics – II

The TCP theorem: A lagrangian which is invariant under proper Lorentz transfor-

mation is invariant with respect to the combined operation CPT, taken in any order.

The predictions of the TCP theorem which have been verified are

(i) the existence of an anti particle for every particle.

(ii) The equality of masses, lifetimes, and magnetic moments of particles and anti

particles.

Table 10.5Conservation laws for the three types of interactions

Quantity Strong Electromagnetic Weak

1. Q (Charge) Yes Yes Yes


2. B (Baryon no.) Yes Yes Yes


3. J (Angular momentum) Yes Yes Yes


4. Mass+Energy Yes Yes Yes


5. Linear momentum Yes Yes Yes


6. I (Isospin) Yes No No


7. I 3 (Third component of I) Yes Yes NoΔI 3 =± 1 / 2


8. S (Strangeness) Yes Yes NoΔS=± 1


9. p (parity) Yes Yes No


10. C (Charge conjugation) Yes Yes No


11. G (G-parity) Yes No No


12. L (Lepton number) Yes Yes Yes

Quarksare the structureless fermions from which all the strongly interacting parti-

cles (hadrons) are built. The quarks occur with fractional baryon number,B=^13

and charges+^23 eor−^13 e. Baryons are built with three quarks (u, d, s) and mesons

with a quark-antiquark pair. Their characteristics are shown in Table 10.6.

Table 10.6Characteristics of quarks

Quark Symbol Mass(GeV/c^2 ) Q/e I SCB∗ T

Down d ∼ 0. 3 −

1

3

(^1) / 2 0000
Up u ∼ 0. 3 +
2
3
(^1) / 2 0000
Strange s 0. 5 −
1
3
0 − 1000
Charmed c 1. 6 +
2
3
00 + 100
Bottom b 4. 5 −
1
3
000 − 10
Top t 175 +
2
3
0000 + 1
For all the quarks spin-parityJp =^1 / 2 +. The quark structure of some of the
hadrons is as follows.
p=uud;n=udd;π+=ud ̄;π−=ud ̄ ;Σ+=uus;k ̄◦=d ̄s;
Ξ−=dss;Ω−=sss;K+=u ̄s;D+=cd ̄;π^0 =
uu ̄−dd
√
2
;Δ++=uuu