1 FK7003 Lecture 6 ● Isospin ● SU(2) and SU(3) ● Parity

2 FK7003 Reminder about isospin (1) ● We’re dealing with the strong force. ● The theory of the strong force works extremely well (can’t be proven wrong) for interactions at high energies (>> 1 GeV).  Forthcoming lectures ● At low energies we can’t do much.  We can’t calculate all hadron masses from first principles.  We can’t calculate all reaction rates from first principles. ● We use symmetry (isospin) as an experimentally established fact to guide us and help us ”feel our way” wrt strong force observables

3 FK7003 Reminder (2) – conservation of isospin

4 FK7003 Reminder (3): invariance to a rotation in isospin space

5 FK7003 Quarks and isospin

6 FK7003 Isospin of antiquarks (not for lecture or exam)

7 FK7003 Isospin with quarks - continued    I3I3 I3I3 Not used by nature

8 FK7003 Question ● Write down a particle decay which does not conserve isospin.

9 FK7003 Isospin and group theory

10 FK7003 Conservation of isospin ● Conserved for strong processes. ● Violated for weak and electromagnetic processes. ● Can think about as: photon, W,Z, and the leptons have zero isospin:

11 FK7003 Why does isospin work ?

12 FK7003 ● Strange, charm and bottom quarks also form hadrons. ● Large mass differences between the quarks. ● What kind of symmetry can we obtain here. Quark Q (e) Mass (GeV) BSCBT u- up2/ /30000 d- down-1/ /30000 s- strange-1/30.151/3000 c- charm2/31.21/30100 b- bottom-1/34.21/3000 t-top2/31711/30001  4 GeV  1 GeV 0.1 GeV  2 MeV The other quarks

13 FK7003 From SU(2) to SU(3)    I3I3 I3I3 ½-½ +1 Meson nonet (spin 0)

14 FK7003 Identifying the states SU(3) is an approximate symmetry. Particles within multiplet have large mass differences. Due to quark mass differences! Strong force is not invariant to SU(3) flavour transformations. Useful to catalogue the states and their quark composition. (6.20) (6.14) (6.21)

15 FK7003 SU(3) Flavour – mesons of spin 1 (vector) (6.22)

16 FK7003 Question 1. What is the strangeness of the   meson ? 2. Give evidence that the   meson is more likely to consist of ss than uu.

17 FK7003 Higher mass meson multiplets Spectroscopic notation – explored further in lectures on bound states.

18 FK7003 Baryons Spin ½ Spin 3/2 Historically, these arrangements of hadrons was termed ” the eight-fold way ” by Murray Gell-Mann after the octet arrangement above. This work allowed the understanding of hadron masses and properties in terms of quarks and was the first evidence for quarks. Like all good theories it gave a prediction which experimentalists could verify.

19 FK7003 Baryon decuplet – something missing? 1964 One particle was missing to make up the baryon decuplet. ?

20 FK7003 Discovery of the  

21 FK7003 Summary of isospin, SU(2) and SU(3) ● Isospin is a good symmetry of the strong force  Hadron masses, reaction/decay rates respect isospin symmetry  The strong force is invariant to SU(2) isospin transformations.  This is due to the small u,d mass difference ● The other quarks are much heavier than u,d and show large mass differences.  SU(3) flavour symmetry is useful for enumerating and ordering the different hadrons and understanding their quark composition.  The strong force is not invariant to SU(3) flavour transformations since the quark masses are so different.

22 FK7003 Parity ● The laws of physics are invariant to, eg a shifted co-ordinate system ( x’ x+a ) or rotated co-ordinate system. ● What happens if we make a parity transformation: invert the co-ordinate system ( x,y,z) (-x,-y,-z) ? ● Parity is a discrete symmetry offering two possible states

23 FK7003 ● Invert the spatial co-ordinate system  Parity transformation (P)  Change handedness of co-ordinate system (eg right to left) ● By 1956 parity invariance had been shown for the strong and electromagnetic forces. ● A test for the weak force was needed.. Parity

24 FK7003 Parity A reflection in the x-z plane followed by a rotation about the y-axis is equivalent to a parity transformation. To test parity invariance: study a reaction and ask if the mirror reflection of that process has the same probability of occuring (no need to consider further rotation since rotation invariance is implied by angular momentum conservation).

25 FK7003 Parity violation – Wu’s experiment Study the   decay of Co-60 At a low temperature 0.01K, the spins can be polarised parallel to an external magnetic field. The electrons are dominantly emitted in the direction opposite to the spin In the ”mirror” image, the electron is dominantly emitted in the opposite parallel to the spin. Parity is violated in weak decays ! A symmetry which is violated means that some quantity is not being conserved

26 FK7003 Helicity A particle possesses helicity – Arbitary z -axis for spin angular momentum – select direction of motion Helicity is not a useful quantity for most particles since it isn’t a Lorentz invariant Can be defined for luminal particles eg a massless neutrino (6.23)

27 FK7003 Muon measured and found to be right-handed  Neutrino oscillations imply that they have a tiny mass ( <2 eV). Maybe its better to say that most neutrinos are left-handed and most anti-neutrinos are right-handed. Certainly, it’s a good approximation since left-handed neutrino and right-handed antineutrino are just about impossible to observe in laboratory experiments. s

28 FK7003 What parity did to the neutrinos in Wu’s experiment Parity transformation means moving from a right-handed to a left-handed co-ordinate system Wu’s experiment is  - decay A ”mirror reflection” of the right-handed anti- neutrino is a left-handed anti-neutrino. We don’t observe the ”reflected” process. ss Change handedness

29 FK7003 Parity ● Parity is a symmetry respected by the electromagnetic and strong forces ● Parity is violated by the weak force.

30 FK7003 Summary ● Isospin and flavour symmetries ● Parity – space inversion ● Weak interactions are not invariant to parity