fractional charge of quarks

Feeble Wonk

Please help me understand. It seems to me that the fractional charge of a quark suggests that this is actually the smallest (most fundamental) unit of charge, and that an electron has a combined unit charge.

Dickfore

As far as I know, in the standard model, there is no rule that imposes the electric charge of a particle to be an integer multiple of a fundamental charge. Furthermore, I think it is a mere coincidence that the charge of a proton is the same magnitude, but opposite sign of the charge of the electron. By "coincidence", I mean a fact of Nature, that is not explainable within the currently accepted framework of what is known as the Standard Model.

Bill_K

Consistency of the Standard Model (anomaly cancellation) requires that the sum of the charges of the particles in each generation must add to zero. Each of the three quark colors must be counted separately. Thus, neutrino + electron + up quark + down quark = 0 + (-1) + 3(2/3) + 3(-1/3) = 0.
A second similar constraint: (0)² - (-1)² + 3(2/3)² - 3(-1/3)² = 0.

Feeble Wonk

But, if we accept that the electromagnetic charge is quantized, shouldn't there be a minimum fundamental unit?

Bill_K

I've just pointed out that the charges of all of the particles in the Standard Model are required to bear a simple relationship to each other. Doesn't that answer the question?

Feeble Wonk

Well yes, in the sense that it explains the symmetry and the requirement to cancel the anomalies. I suppose what I'm really asking, though, is how there can be a fraction of the charge unit. Please have patience with my ignorance, but my previous understanding was that the fundamental quantum of action with respect to the electromagnetic field was a photon. but this seems to be fractionalized in the quark.

Feeble Wonk

I think my error is basic... I shouldn't equate the charge of "1" as indicating anything with respect to a photon. it simply is a reference to the charge exhibited by the electron.

Feeble Wonk

So... The designation of "1" as a charge for the electron is simply a matter of convention, as the established reference charge unit. Right? We could just as easily call the 1/3 charge of a quark "1", and the charge of an electron "3". A long as the units balance, that's all that matters.

Owled

At first, we thought protons were elementary particles, so they gave them an elementary charge of +1, which is 1,6x10^-19 Coulombs. When we discovered that they were in fact composite particles, the electric charge of the elementary particles making up the protons and neutrons then had to be a fraction of the calculated elementary charge.

So the elementary charge isn't so elementary anymore.

NathanM

So it's more a case of convenience vs reassignment of values eh!

alemsalem

don't grand unified theories predict quantized electric charge?

lpetrich

Going further, the unbroken Standard Model does not feature electric charge. Instead, electric charge emerges from the breaking of electroweak symmetry. Every unbroken-SM multiplet has three gauge-symmetry quantum numbers:

• The QCD multiplicity (strictly speaking: 2 quantum numbers)
• The weak isospin I
• The weak hypercharge Y

WIS behaves like 3D angular momentum, thus the name. Multiplet members have WIS-component value I₃ values -I, -I+1, -I+2, ..., I-1, I.

WHC behaves like electric charge - it's the average electric charge of a multiplet.

The members' electric charges are
Q = I₃ + Y
or
Q = -I + Y, -I + 1 + Y, -I + 2 + Y, ..., I - 1 + Y, I + Y

Standard-Model particles: (WIS, WHC) -> Q's
L = left-handed, R = right-handed

• L quark: (1/2, 1/6) -> -1/3, 2/3
• R down quark: (0, -1/3) -> -1/3
• R up quark: (0, 2/3) -> 2/3
• L lepton: (1/2, -1/2) -> -1, 0
• R electron: (0, -1) -> -1
• R neutrino: (0, 0) -> 0
• QCD particle: gluon: (0, 0) -> 0
• WIS particle: W: (1, 0) -> -1, 0, 1
• WHC particle: B: (0, 0) -> 0
• down Higgs particle: (1/2, -1/2) -> -1, 0
• up Higgs particle (1/2, 1/2) -> 0, 1 (SM: conjugate of down Higgs, MSSM: separate particle)

Antiparticles: same I, reverse-sign Y, L <-> R

However, that puts the problem back a step, and the weak hypercharges have even more fractional values. But there's a solution. From QCD multiplets' quantum numbers can be deduced "triality", a quantity that adds modulo 3. Gluons and colorless particles have triality 0, quarks triality 1, and antiquarks triality 2. Hadrons have triality 0. From the SM particles, one can deduce this expression for the weak hypercharge:

Y = - (triality)/3 + I + (integer)

For the electric charge, that gives us

Q = - (triality)/3 + (integer)

That Y expression is a consequence of some GUT's, like Georgi-Glashow, Pati-Salam, and their supersets.