Transcript Flavour symmetry -- 50 years after SU(3)

FLAVOURS
50 Years After SU(3) Discovery
Djordje Šijački
Word “flavour” is used in Particle Physics in two contents:
- for SU(2), SU(3), SU(4), SU(5) and SU(6) symmetries of
hadrons
- for generations of quarks and leptons w.r.t. SU(2) of weak
interactions
Generally, these two notions are considered unrelated.
Flavour is actually the least understood sector of the Standard
Model of Particle Physics. Not much of progress is made since
its introduction (Werner Heisenberg, 1932).
In this talk I consider the flavour question and offer (perhaps) some
new interpretations.
Flavours in the Hadron world - SU(2).
Isospin was introduced by Werner Heisenberg in 1932 to explain
symmetries of the then newly discovered neutron.
The name isospin was introduced by Eugen Wigner in 1937.
Isospin is mathematically described by the SU(2) group (analogously to
spin).
The strength of the strong interaction between any pair of nucleons
is the same, independent of whether they are interacting as protons
or as neutrons.
Isospin is similar to, but should not be confused with weak isospin.
Briefly, weak isospin is the gauge symmetry of the weak interaction
which connects quark and lepton doublets of left-handed particles in
all generations; for example, up and down quarks, top and bottom
quarks, electrons and electron neutrinos. By contrast (strong) isospin
connects only up and down quarks, acts on both chiralities (left and
right) and is a global (not a gauge) symmetry.
Flavours in the Hadron world - SU(3)
SU(3) symmetry was introduced in 1961 by Murray Gell-Mann
and Yuval Ne'eman to accommodate for hypercharge
(strangeness) in addition to isospin.
U(2) = SU(2)xU(1) --> SU(3)
Y = B + S = 2(Q - I_{3})
SU(3) ==> color SU(3) discovery!
Flavours in the Hadron world - SU(4)
SU(4) was predicted by Sheldon Glashow and James Bjorken in
1964 (Glashow Iliopoulos Maiani mechanism).
SU(3), SU(4), SU(5)
Flavours in weak interactions – three generations of quarks and leptons
Gauge symmetries: SU(2) of weak isospin and U(1) of weak hypercharge
Three generations of left
SU(2) dublets and right
SU(2) singlets.
Some Standard Model puzzles.
Three generations of flavours w.r.t. weak SU(2)xU(1).
Baryon number - not related to gauge symmetry.
Lepton number – not related to gauge symmetry.
Triangle anomaly cancelation (total quark + lepton charge vanishes).
Quark mixing: Cabibbo–Kobayashi–Maskawa matrix.
Neutrino mixing: Pontecorvo–Maki–Nakagawa–Sakata matrix.
Mass generation vs. Spacetime symmetries (Dilatation symmetry).
Baryon, B, and Lepton, L, quantum numbers are consequences of
QCD and Electro-Weak interactions.
Electric charge Q is the charge of U(1) local symmetry.
Apparently, B and L are charges of global symmetry. Nothing to do
with SU(3) color and/or U(2) electro-weak.
Do we need them at all?
Electric charge Q is the charge of U(1) local symmetry.
Puzzle: Q is given in terms of global symmetry charges: B, L, I,
S, C ... (generalized Gell-Mann Nishijima formula).
Q and SU(6) of flavour.
Q and “hypothetical” SU(6) of leptons.
N.B. L_{no} = - L
Flavor SU(6) of quarks and leptons (left + right)
Complete gauge symmetry
(left + right)
?