Why is Baryon and Lepton Number Conservation Important in Theoretical Physics?

[BiGyElLoWhAt]

So this doesn't so much explain baryonic asymmetry, as say that it isn't a thing.
https://en.wikipedia.org/wiki/Rishon_model
This leads to the question, how do we determine what is antimatter and what isn't? The electron is antimatter in this theory ##e^- = \bar{T}\bar{T}\bar{T}##

One big problem I see with this is annihilation, but then it would be matter + matter and antimatter + antimatter annihilation, which would make more sense, to me anyway, since opposites attract in nature. Then matter - antimatter nuclei would be stable and what we observe.

Any thoughts?

 

[HallsofIvy]

You seem to be making a distinction between "matter" and "matter plus matter" as well as between "anti-matter" and "anti-matter plus anti-matter". Exactly what do you mean by that?

 

[BiGyElLoWhAt]

That part was only for annihilation. Conventionally, we have matter + antimatter annihilation, but in rishon theory, we would have matter + matter annihilation. It's all a matter of labels. It would still be the particle formerly known as the electron and the particle formerly known as the positron annihilating each other, but the electron would be antimatter and the positron would be matter (not antimatter).

 

[mathman]

Your example is confusing. You are switching the labels for positron and electron, but the annihilation is still matter-antimatter. Where does matter-matter annihilation come in?

 

[BiGyElLoWhAt]

Oh wow. You're right, I don't know what I was thinking with that. So perhaps annihilation isn't a problem in rishon theory, after all. So back to the original question, what qualities make antimatter "anti".

 

[ohwilleke]

Ultimately, it is arbitrary. We started out with just plain old matter - protons, neutrons and electrons. Anti-matter got so named with regard to these because it was the rare exception, while matter was predominant and so the convention was to treat it as such (antisomething is longer so you want to have to use it less often). Neutrinos are given their neutrino v. antineutrino designation in a manner that causes physical interactions to preserve lepton number. Quark matter v. antimatter classification was generalized from protons and neutrons.

I can't think of any reason that physics would be different (except for adjusting the value of the CP violating phases of the CKM matrix and PMNS matrix based upon the convention used) if electrons were antimatter and positrons were classified as matter and the matter-antimatter classification of neutrinos were flipped. You need consistent definitions for all leptons and you separately need consistent definitions for all quarks, but you don't need the quark definition to be consistent with the lepton definition for the physics to work. You do need to establish a consistent definition for all fermions together as a unit, however, in Beyond The Standard Model theories that conserve B-L number rather than separately conserving baryon number and lepton number (or any other quantity that is a function of both B and L).

For example, if up-like quarks with positive charge a defined to be matter, down-like quarks with negative charges also have to be matter. You can't do physics that work otherwise. But, the equations wouldn't break if you called up-like quarks with negative charge matter and called down-like quarks with positive charge matter. We could just as well call one kind of particle "East" particles and the antimatter counterparts "West" particles without loss of accuracy. (Similarly, the convention of calling the electric charge of an electron negative, and the electric charge of a proton positive is entirely arbitrary.)

Arguably, having the quark matter-antimatter definition and the lepton matter-antimatter definition could matter in the Standard Model for sphaleron interactions which conserve B-L but not B or L separately. But, since those interactions have never been experimentally observed, we can't know for sure that we have correctly defined matter and antimatter classifications while doing so on an essentially arbitrary basis.

 

[BiGyElLoWhAt]

I get pretty much all of that and that's kind of what I thought. One question Ibdo have is about the up and downlike quark classification making the physics not work. Are you talking in terms of bound states or what, specifically? So this actually does bring annihilation back into the question, then. (I knew there was something about it that wasn't quite right) So in bound states, only certain kinds of matter and antimatter would annihilate. An atom would be a stable bound state of matter antimatter. Is this what you're talking about? If not would you please elaborate a little further on the subject?

 

[Drakkith]

One question Ibdo have is about the up and downlike quark classification making the physics not work. Are you talking in terms of bound states or what, specifically?

He means that if we defined the down quark to be anti-matter and the up quark to be matter, the whole matter-antimatter thing wouldn't make any sense because both up and down quarks must be classified on the same side. A down quark and an anti-down quark are equal in mass but opposite in quantum numbers, but an up and a down quark do not have the same mass nor do they have the same or opposite quantum numbers. It's these various quantum numbers (which describe various properties of particles) that determine what type of particle something is and what its anti-particle is.

Think of it like this. If everyone in the world were to swap the word 'left' for the word 'right', it wouldn't cause any harm. Left and right are just conventional descriptions we've given to things. However, if you switch your use of left and right for everything but your arms, it simply doesn't make sense. Your left arm and your left leg must be on the same side of your body. Trying to classify up and down quarks on opposite sides of the matter-antimatter spectrum would be like trying to say your left arm and your right leg are on the same side of your body. It just doesn't work that way.

An atom would be a stable bound state of matter antimatter.

It would not. There is no anti-matter in an atom.

 

[BiGyElLoWhAt]

I think I see what you're saying. I'll need to look more closely to see exactly what happens in certain processes to convince myself it wouldn't work.
In rishon theory, with electrons being antimatter and protons being matter, an atom would, indeed, be bound matter-antimatter

 

[newjerseyrunner]

There are antimatter atoms and there are matter atoms, they can't contain both. It's anti because it's charge is backwards, asking why is like asking why is anti-clockwise anti-clockwise. It's just opposite of clockwise. "antithesis" means opposite.

electrons are not antimatter, they are matter. They have a small mass, and an electric charge of -1.
positrons are antimatter. They have the same mass as the electron, but an electric charge of 1.
Since they have opposite charges, they can not replace each other in an atom. They also have other characteristics that make it impossible to replace a proton with one.

There are matter / antimatter particles: positronium for example is an electron and a positron orbiting each other.

 

[BiGyElLoWhAt]

This thread is in regards to rishon theory. Electrons are antimatter in rishon theory.

 

[no-ir]

You need consistent definitions for all leptons and you separately need consistent definitions for all quarks, but you don't need the quark definition to be consistent with the lepton definition for the physics to work. You do need to establish a consistent definition for all fermions together as a unit, however, in Beyond The Standard Model theories that conserve B-L number rather than separately conserving baryon number and lepton number (or any other quantity that is a function of both B and L).

(...)

Arguably, having the quark matter-antimatter definition and the lepton matter-antimatter definition could matter in the Standard Model for sphaleron interactions which conserve B-L but not B or L separately. But, since those interactions have never been experimentally observed, we can't know for sure that we have correctly defined matter and antimatter classifications while doing so on an essentially arbitrary basis.

Hm, I would think that the quark matter-antimatter and the lepton matter-antimatter definitions are completely indepentent. If they were switched around we would just be talking about B+L conservation instead of B-L conservation, wouldn't we? Or am I missing something (I don't know a lot about models that conserve only B-L but not B or L separately, except superficially)?

 

[BiGyElLoWhAt]

Well one process that I know of that theoretically only conserves B-L is proton decay. I'm pretty sure that is within the confines of SM, as well. I could be wrong about the last part.

 

[ohwilleke]

Well one process that I know of that theoretically only conserves B-L is proton decay. I'm pretty sure that is within the confines of SM, as well. I could be wrong about the last part.

You are wrong. Proton decay does not occur in the SM. Neither does neutrinoless double beta decay. Neither do flavor changing neutral currents (i.e. changes in quark type that don't involve W bosons).

Also, since there seems to be confusion about the subject, not every interaction of matter and antimatter produces annihilation. You need a particular kind of fundamental particle and its exact antimatter counterpart to produce annihilation. For example, an up quark with red color charge and an antiup quark with blue color charge, can't annihilate because that would violate conservation of color charge. Likewise, a positron and a proton isolated from all other matter couldn't annihilate.

And, just to be clear, although I think you know this, rishon theory is a beyond the Standard Model preon theory. Preon theory is a very tempting and plausible approach to model building that gave rise, for example, to the quarks and gluons of the Standard Model and I'm not some anti-preon zealot (I've made contributions to several of the relevant Wikipedia articles while investigating it and still think that at some energy scale preons exist). But, preon theories are experimentally excluded up to higher energy scales than almost any other kind of beyond the Standard Model theory (in part this is because precise measurements of the dipole moment of particles like electrons would not have their experimentally measured values if they were composed of preons bound at less than an extremely high energy scale). This isn't to say that the possibility that the Standard Model fundamental particles are really made of something more fundamental is ruled out entirely. But, if there are more fundamental particles than the Standard Model fundamental particles, the energy scale at which this can be discerned must be very, very high (e.g., it almost certainly wouldn't be possible to see at a 100 TeV linear collider).

 

[BiGyElLoWhAt]

...both up and down quarks must be classified on the same side. A down quark and an anti-down quark are equal in mass but opposite in quantum numbers, but an up and a down quark do not have the same mass nor do they have the same or opposite quantum numbers. It's these various quantum numbers (which describe various properties of particles) that determine what type of particle something is and what its anti-particle is...

I've thought about this, and I just can't see where you're coming from.

No quantum numbers would change, except for baryon number and lepton number, which would mean that we would need either B-L conservation or B+L conservation, which is something that people are already doing.

The properties of the down quark would now be the properties of the anti-down quark, and the properties of the anti-down quark are now the properties of the down quark. The decay process is the same, except in ##u \to d+\nu_e+\bar{e}## it would change to ##u \to \bar{d}+\nu_e+e^+## (the electron is antimatter, positron is matter, so you're just swapping which particle carries which quantum number)
i.e. ##1=-1+1+1## in rishon vs. ##1=1+1-1## in the standard model. I'm not going to claim to have gone through all the decay processes, as I obviously haven't, but this seems consistent.

Edit*
Worth noting:
"https://www.physicsforums.com/wiki/Baryon_number (B) and https://www.physicsforums.com/wiki/Lepton_number (L) are not conserved, but the quantity https://www.physicsforums.com/wiki/B%E2%88%92L is conserved. A baryon number violating process (such as https://www.physicsforums.com/wiki/Proton_decay ) in the model would be
u + u → d + e+
/|\ /|\ /|\ /|\
TTV + TTV → TVV + TTT"
https://en.wikipedia.org/wiki/Rishon_model

Ok, well it won't let me add in the necessary spacing, but you get the idea.

 

[ohwilleke]

I've thought about this, and I just can't see where you're coming from.

No quantum numbers would change, except for baryon number and lepton number, which would mean that we would need either B-L conservation or B+L conservation, which is something that people are already doing.

It follows from the empirically known fact that all hadrons (e.g. mesons like the pion and baryons like the proton and neutron) must be color charge neutral. Thus, mesons must have a quark of a given color charge and a corresponding anti-quark of the same color charge, while a baryon must have three quarks (one color charge red, one color charge blue and one color charge green) or three antiquarks (one color charge antired, one color charge antiblue, and one color charge antigreen). If you change the matter-antimatter classification, the system for determining color neutrality which implies confinement, which is one of the fundamental principles of QCD, wouldn't work properly. Among other things, you would also get, contrary to empirical evidence, hadrons with non-integer electric charges.

 

[BiGyElLoWhAt]

I can't seem to remedy the color charge situation, but the non integer electric charge wouldn't happen. All we're doing is changing labels, the physics (and thus the consequences of the physics) remains unchanged.

 

[ohwilleke]

Worth noting:
"https://www.physicsforums.com/wiki/Baryon_number (B) and https://www.physicsforums.com/wiki/Lepton_number (L) are not conserved, but the quantity https://www.physicsforums.com/wiki/B%E2%88%92L is conserved. A baryon number violating process (such as https://www.physicsforums.com/wiki/Proton_decay ) in the model would be
u + u → d + e+
/|\ /|\ /|\ /|\
TTV + TTV → TVV + TTT"
https://en.wikipedia.org/wiki/Rishon_model

Just to be extra clear. B and L are conserved separately in real life.

No violations of it have been observed, ever, when faced with some of the most precise and strict experimental boundaries known to man, and violations are theoretically prohibited in the SM in all circumstances except hypothetical sphaleron interactions which have never ever been observed. There is not one instance of observed proton decay. Neutrinoless double beta decay has not been observed. There is no evidence supporting the existence of Majorana neutrinos. Flavor changing neutral current have never been observed. This so called "accidental symmetry" simply is not violated in nature.

One of the main ways that GUT models have been ruled out empirically is their frequent prediction of B or L violation which is not observed in nature.

If you want a good guide for BSM theories that match real life, start by rejecting those that violate B or L number conservation or both, even in the B-L sense. People who assume B or L violation or both in their theories (depressingly a very large share of all proposed theories) have drunk the kool-aid or are outcome driven because they want to explain the baryon assymmetry of the universe that may have no explanation.