Why are leptons antibaryons in gut?

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Discussion Overview

The discussion revolves around the conservation of baryon and lepton numbers in Grand Unified Theories (GUTs), specifically focusing on why the B-L (baryon minus lepton number) is preserved while B+L (baryon plus lepton number) is not. Participants explore the implications of these conservation laws, the role of weak interactions, and the conventions used in defining these quantities.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question why GUTs preserve B-L instead of B+L, suggesting that the choice may be based on convention rather than a fundamental reason.
  • There is a discussion about whether weak interactions treat baryons and leptons similarly, particularly regarding helicity requirements.
  • One participant proposes that the U(1) for B-L must be traceless and that this requirement influences the conservation laws in GUTs.
  • Another participant emphasizes that the conservation of B-L over B+L could be a matter of sign convention, noting that the definitions of lepton numbers could be reversed.
  • Concerns are raised about whether the discussion implies CP violation, suggesting a deeper connection between these conservation laws and symmetry violations.
  • Some participants assert that B+L is violated in the standard model while B-L is considered an accidental symmetry, indicating a distinction in their conservation status.
  • There is a suggestion that examining the Lagrangian in an SU(5) model could provide clarity on the issues being discussed.

Areas of Agreement / Disagreement

Participants express differing views on the reasons behind the preservation of B-L versus B+L, with no consensus reached on the underlying processes or conventions. The discussion remains unresolved regarding the substantive reasons for these conservation laws.

Contextual Notes

Participants acknowledge that the discussion involves assumptions about the definitions of baryon and lepton numbers, as well as the implications of these definitions on the conservation laws in GUTs. There is also mention of non-perturbative effects in the standard model that may influence these conservation laws.

snorkack
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Why does gut preserve B-L, not B+L?

Also, does weak interaction see both baryons and leptons as particles? Is the helicity required for weak interaction the same (left) for both baryons and leptons and the opposite (right) for both antibaryons and antileptons?
 
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In SU(4) lepton-colour unification it is pretty clear. The U(1) for "B L" must be a diagonal of this matrix group, and it must be traceless, and it must have the same charge for the three colours. So it is 1/3 for quarks, -1 for Lepton, or opposite. Now, if the full group keeps this assignment, then B-L survives. But you could engineer that the SU(4) leptocolour components are really no lepton and quarks, but leptons and antiquarks. Or that the full "B L" mixes with some othe U(1). So it is not a strong requisite.
 
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snorkack said:
Why does gut preserve B-L, not B+L?

If (and only if) both B+L and B-L are conserved, B and L are conserved separately.

If you ask why the conserved quantity has a minus sign and not a plus sign, the answer is "convention". By convention, the e- has L=1 and the e+ has L=-1. We could have defined it the other way, and then B+L would be conserved.
 
Vanadium 50 said:
If (and only if) both B+L and B-L are conserved, B and L are conserved separately.
Yes. As they are outside GUT.
So, if B separately is not conserved, why should there be conservation of B-L, but not conservation of B+L without conserving B-L, or not conserving either B+L or B-L?
Vanadium 50 said:
If you ask why the conserved quantity has a minus sign and not a plus sign, the answer is "convention". By convention, the e- has L=1 and the e+ has L=-1. We could have defined it the other way, and then B+L would be conserved.
But that´s a matter of sign definition. I am asking substantive reason for the underlying process. Why does GUT allow baryon decay to antileptons while forbidding baryon decay to leptons?
 
Doesn't the last concern of yours imply CP violation instead?
It's totally different to sign convention.
 
snorkack said:
Yes. As they are outside GUT.
So, if B separately is not conserved, why should there be conservation of B-L, but not conservation of B+L without conserving B-L, or not conserving either B+L or B-L?

B+L is violated on a non-perturbative level in the standard model, while B-L is an accidental symmetry. That it is B-L rather than B+L that is conserved is of course only a sign convention of what leptonic and baryonic charges we assign to the fields.
 
I will repeat the point: The U(1) generator must be traceless. So it has more sense a convention which calls it "B-L" than the contrary.
 
I think writing the fields' Lagrangian, in an SU(5) model for example, and look at the vertices can help you clarify your problem.
 

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