[secs 16.1 dunlap]

15
[Secs 16.1 Dunlap] Conservation Laws - II [Secs 2.2, 2.3, 16.4, 16.5 Dunlap]

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Conservation Laws - II. [Secs 16.1 Dunlap]. [Secs 2.2, 2.3, 16.4, 16.5 Dunlap]. ISO-SPIN in strong interaction: - PowerPoint PPT Presentation

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Page 1: [Secs 16.1   Dunlap]

[Secs 16.1 Dunlap]

Conservation Laws - II

[Secs 2.2, 2.3, 16.4, 16.5 Dunlap]

Page 2: [Secs 16.1   Dunlap]

Isospin Conservation

ISO-SPIN in strong interaction:

It originates from the observation that the NUCLEON can be considered as being the same particle in 2-states – (i) isospin up = proton . (ii) isospin down = neutron.

NUCLEON

T=1/2

Tz= +1/2

Tz= -1/2

Page 3: [Secs 16.1   Dunlap]

NUCLEON

T=1/2

Tz= +1/2

Tz= -1/2

Isospin Conservation

J=1/2

B-field

Ordinary spin (ang. mom) Iso-spin

12 .NE g B

12 .NE g B

Without a B-field the nucleon’s spin states Jz=±1/2 cannot be distinguished –

A B-field breaks the symmetry causing the Jz =+1/2 state to have a different energy to the Jz = -1/2 state

Jz= +1/2

Jz= -1/2

The analogy between conventional SPIN and ISOSPIN

J is conserved

Without a EM -field the nucleon’s isospin states Tz=±1/2 cannot be distinguished – i.e. same mass

The EM -field breaks the symmetry causing the Tz =+1/2 state to have a different energy to the Tz = -1/2 state. n is slightly heavier than p

p

n

T is conserved

Page 4: [Secs 16.1   Dunlap]

Iso-spin Conservation

T=1/2

Tz= -1/2 Tz=+1/2

Page 5: [Secs 16.1   Dunlap]

Isospin conservationWhat is the isospin of the pion?

Well that’s easy.

140

139

138

137

136

135

134

MeV

0Tz=-1 Tz=0 Tz=+1

Clearly the pion is a T=1 particle state. The reason that the π ± states are higher in energy is that the EM force between 2 quarks decreases binding energy (anti-binding).

Page 6: [Secs 16.1   Dunlap]

Isospin ConservationLets look at some examples:

1 11 1 1

2 21 3 1 3 5

, , ,2 2 2 2 2

p n

T=

Thus T is conserved and this reaction could proceed via the S.I. It does.

However, take a look at this decay:

1 1 1

21

(0,1,2) 2

K

T=

This reaction can proceed through the T=1/2 and T=3/2 channels

This reaction cannot proceed by any T channels and is absolutely forbidden via the S.I. However the reaction does occur – but not by the S.I

Page 7: [Secs 16.1   Dunlap]

Baryon number conservation

B=±

B=0

Baryon no is +1 for Baryons

Baryon no is -1 for Anti-Baryons (i.e. anti-protons)

Baryon no is strictly conserved.

Page 8: [Secs 16.1   Dunlap]

Baryon number conservation

0 - p e

1 +1 0 0en

Take some examples

Neutron decay

B=

Thus this reaction is allowed

(1)

(2) p p p p p p

+1 +1 +1 +1 +1 -1

+1 +1 +1 +1 +1 -1

Anti – proton production.Q =

B =This reaction is thus allowed

(3) 0

1 +1 0 0

-1 0 +1 0

p n

Q = B =

This reaction violates B conservation and is strictly forbidden

Page 9: [Secs 16.1   Dunlap]

Lepton number conservation

L=± 1

L=0

Leptons have L= +1

Anti-Leptons have L= -1

All other types of particle have L=0

Page 10: [Secs 16.1   Dunlap]

Lepton number conservation

1st generation 2nd generation 3rd generation

Lepton no= +1 e -

e

-

-

Lepton no= -1

e

e

Lepton numbers are defined according to

Example (1)

0 +1 -1

Lμ=

Pion decay

-e e

0 +1 0 -1

+1 0 +1 0

Muon decay

Example (2)

Le=

L μ =

Page 11: [Secs 16.1   Dunlap]

Conservation of Strangeness

In the early 1950s physicists discovered in proton-neutron collisions some Baryons and Mesons that behaved “strangely” – They had much too long lifetimes! We are talking about mesons called Kaons (K-mesons) and Baryons called Hyperons such as 0 and 0. Since such particles were produced in large quantities in proton-neutron collisions they had to be classified as strongly interacting particles [i.e Hadronic matter]. If they were hadronic particles, though, they should decay very quickly into pions (within the time it takes for a nucleon to emit a pion ~ 10-23s) but their lifetimes were typically 10-8 to 10-11s. It is possible to explain this in terms of a new conservation law: the conservation of strangeness.

Page 12: [Secs 16.1   Dunlap]

Conservation of Strangeness

Murray Gell-Mann Kazuhiko Nishijima

In 1953 two physicists, one in the USA and one in Japan, simultaneously understood the reason why the Λ and K particles were living so long – i.e. why they were decaying through the WEAK interaction and NOT THE STRONG. These were Murray Gell-Mann and Kazuhiko Nismijima. They saw that the explanation lay in a new conservation law - the conservation of strangeness.

Page 13: [Secs 16.1   Dunlap]

Conservation of Strangeness

0 n K

0 0 -1 +1

Consider the reaction that produces K mesons

Strangeness S is conserved if we assign the 0 a strangeness quantum no of –1, and the K+ a strangeness quantum no of +1.

The 0 and K are left to decay on its own - not by the strangeness conserving strong interaction – but by the WEAK interaction

S=

weak0 - p

1 0 0

weakK

1 0 0

S=S=

Page 14: [Secs 16.1   Dunlap]

Conservation of Strangeness

0 0

0

0

p K

K

p

Page 15: [Secs 16.1   Dunlap]

A synopsis of conservation lawsConservation of BASIC SYMMETRY- Quant. no Interaction violated in

Energy TRANSLATIONS in TIME none

Momentum TRANSLATIONS in SPACE none

Ang. momentum DIRECTIONS in space J none

Parity REFLECTIONS in space (or P) *Weak interaction

Charge conjugation parity Particle - Antiparticle C *Weak interaction

Charge Charge in EM gauge Q none

Lepton number (electron) Charge in Weak charge Lenone

Lepton number (muon) Change in Weak charge Lnone

Lepton number (tauon) Change in Weak charge Lnone

Baryon number Quark number invarience B none

Isospin ud quark interchange I for non leptonic)+ *EM

Strangeness u (d)s quark interchange S *Weak interaction (S=1)

Charm qc quark interchange c *Weak interaction (c=1)

Bottomness qb quark interchange b *Weak interaction (b=1)

Topness qt quark interchange T *Weak interaction (T=1)