3 Corrected some minor errors introduced in the previous edit

Quarks have electric charges proportional to one third of the elementary electric charge, but both mesons and baryons have integer electric charge.

Is there some deep explanation from a more fundamental and generalizable conservation law that any state that forms an $$SU(3)$$ singlet must have an integer electric charge? Are there any common beyond-the-standard-models (BSM) where this does not hold?

I can show this for systems with just quarks & gluons, since quarks carry -1 colorelectric charge quanta (1/3 of elementary charge) mod 3, antiquarks carry 1 colorelectric charge quanta mod 3, and gluons carry 0 colorelectric charge quanta mod 3 (same as a quark + antiquark pair), which implies that for any $$SU(3)$$ representation $$D(p,q)$$ composed of these, we must have that the electric charge mod 3 is equal to $$(p-q)$$ mod 3. So an integer Baryon number implies an integer electric charge (in terms of elementary charges). The same derivation also works for the U(1) weak hypercharge.

But this derivation just uses the explicit list of fundamental particles with color chargeparticle in the standard model with tables of their electric & color charges, and doesn't necessarily put it into any wider context. Is this just a coincidence in the standard model? Or is it a property of some GUTs as well? It feels like a really crazy coincidence that the SU(3) and the U(1)xSU(2) sectors are related to each other in this way.

Quarks have electric charges proportional to one third of the elementary electric charge, but both mesons and baryons have integer electric charge.

Is there some deep explanation from a more fundamental and generalizable conservation law that any state that forms an $$SU(3)$$ singlet must have an integer electric charge? Are there any common beyond-the-standard-models (BSM) where this does not hold?

I can show this for systems with just quarks & gluons, since quarks carry -1 color charge quanta mod 3, antiquarks carry 1 color charge quanta mod 3, and gluons carry 0 color charge mod 3, which implies that for any $$SU(3)$$ representation $$D(p,q)$$ composed of these we must have that the electric charge mod 3 is equal to $$(p-q)$$ mod 3. So an integer Baryon number implies an integer electric charge (in terms of elementary charges).

But this derivation just uses the explicit list of fundamental particles with color charge in the standard model and doesn't necessarily put it into any wider context. Is this just a coincidence in the standard model? Or is it a property of some GUTs as well?

Quarks have electric charges proportional to one third of the elementary electric charge, but both mesons and baryons have integer electric charge.

Is there some deep explanation from a more fundamental and generalizable conservation law that any state that forms an $$SU(3)$$ singlet must have an integer electric charge? Are there any common beyond-the-standard-models (BSM) where this does not hold?

I can show this for systems with just quarks & gluons, since quarks carry -1 electric charge quanta (1/3 of elementary charge) mod 3, antiquarks carry 1 electric charge quanta mod 3, and gluons carry 0 electric charge quanta mod 3 (same as a quark + antiquark pair), which implies that for any $$SU(3)$$ representation $$D(p,q)$$ composed of these, we must have that the electric charge mod 3 is equal to $$(p-q)$$ mod 3. So an integer Baryon number implies an integer electric charge (in terms of elementary charges). The same derivation also works for the U(1) weak hypercharge.

But this derivation just uses the explicit list of fundamental particle in the standard model with tables of their electric & color charges, and doesn't necessarily put it into any wider context. Is this just a coincidence in the standard model? Or is it a property of some GUTs as well? It feels like a really crazy coincidence that the SU(3) and the U(1)xSU(2) sectors are related to each other in this way.

2 added 57 characters in body; edited tags

Quarks have electric charges proportional to one third of the elementary electric charge, but both mesons and baryons have integer electric charge.

Is there some deep explanation from a more fundamental and generalizable conservation law that any state that forms an SU(3)$$SU(3)$$ singlet must have an integer electric charge? Are there any common BSM modelsbeyond-the-standard-models (BSM) where this does not hold?

I can show this for systems with just quarks & gluons, since quarks carry -1 color charge quanta mod 3, antiquarks carry 1 color charge quanta mod 3, and gluons carry 0 color charge mod 3, which implies that for any SU(3)$$SU(3)$$ representation D(p,q)$$D(p,q)$$ composed of these we must have that the electric charge mod 3 is equal to (p-q)$$(p-q)$$ mod 3. So an integer Baryon number implies an integer electric charge (in terms of elementary charges).

But this derivation just uses the explicit list of fundamental particles with color charge in the standard model and doesn't necessarily put it into any wider context. Is this just a coincidence in the standard model? Or is it a property of some GUTs as well?

Quarks have electric charges proportional to one third of the elementary charge, but both mesons and baryons have integer electric charge.

Is there some deep explanation from a more fundamental and generalizable conservation law that any state that forms an SU(3) singlet must have an integer electric charge? Are there any common BSM models where this does not hold?

I can show this for systems with just quarks & gluons, since quarks carry -1 charge quanta mod 3, antiquarks carry 1 charge quanta mod 3, and gluons carry 0 charge mod 3, which implies that for any SU(3) representation D(p,q) composed of these we must have that the electric charge mod 3 is equal to (p-q) mod 3. So an integer Baryon number implies an integer electric charge (in terms of elementary charges).

But this derivation just uses the explicit list of fundamental particles with color charge in the standard model and doesn't necessarily put it into any wider context. Is this just a coincidence in the standard model? Or is it a property of some GUTs as well?

Quarks have electric charges proportional to one third of the elementary electric charge, but both mesons and baryons have integer electric charge.

Is there some deep explanation from a more fundamental and generalizable conservation law that any state that forms an $$SU(3)$$ singlet must have an integer electric charge? Are there any common beyond-the-standard-models (BSM) where this does not hold?

I can show this for systems with just quarks & gluons, since quarks carry -1 color charge quanta mod 3, antiquarks carry 1 color charge quanta mod 3, and gluons carry 0 color charge mod 3, which implies that for any $$SU(3)$$ representation $$D(p,q)$$ composed of these we must have that the electric charge mod 3 is equal to $$(p-q)$$ mod 3. So an integer Baryon number implies an integer electric charge (in terms of elementary charges).

But this derivation just uses the explicit list of fundamental particles with color charge in the standard model and doesn't necessarily put it into any wider context. Is this just a coincidence in the standard model? Or is it a property of some GUTs as well?

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# Color confinement and integer electric charge?

Quarks have electric charges proportional to one third of the elementary charge, but both mesons and baryons have integer electric charge.

Is there some deep explanation from a more fundamental and generalizable conservation law that any state that forms an SU(3) singlet must have an integer electric charge? Are there any common BSM models where this does not hold?

I can show this for systems with just quarks & gluons, since quarks carry -1 charge quanta mod 3, antiquarks carry 1 charge quanta mod 3, and gluons carry 0 charge mod 3, which implies that for any SU(3) representation D(p,q) composed of these we must have that the electric charge mod 3 is equal to (p-q) mod 3. So an integer Baryon number implies an integer electric charge (in terms of elementary charges).

But this derivation just uses the explicit list of fundamental particles with color charge in the standard model and doesn't necessarily put it into any wider context. Is this just a coincidence in the standard model? Or is it a property of some GUTs as well?