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) ?