# Baryon Number Non-Conservation

#### 2Xtreme21

Hi all, long time lurker, first time poster. While this is technically a homework question, there is no math related to it and is more of an "understanding concepts" type question.

What kinds of things would happen if the baryon number is not conserved in an interaction?

I know it would make it so protons could decay, and it would also allow baryons (specifically, the quarks associated with them) to be changed into leptons. However, would the same apply in reverse? (Leptons changing to quarks)? And in the reaction itself, would lepton number be non-conserved as well? And if I'm wrong in any of these assumptions, please let me know!

(Gah sorry, I had both forums open in a tab and posted in the wrong one.)

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#### Meir Achuz

Homework Helper
Gold Member
Hi all, long time lurker, first time poster. While this is technically a homework question, there is no math related to it and is more of an "understanding concepts" type question.

What kinds of things would happen if the baryon number is not conserved in an interaction?

I know it would make it so protons could decay, and it would also allow baryons (specifically, the quarks associated with them) to be changed into leptons. However, would the same apply in reverse? (Leptons changing to quarks)? And in the reaction itself, would lepton number be non-conserved as well? And if I'm wrong in any of these assumptions, please let me know!

(Gah sorry, I had both forums open in a tab and posted in the wrong one.)
If quarks could change into leptons, then leptons could also change into quarks, but lepton number could still be conserved.
For instance, p-->positron + neutrino.
It is also possible that baryon number be violated in a reaction like
P+P--> 2 pi+, although that is not the case usually considered in baryon number violating theories.

#### marlon

What kinds of things would happen if the baryon number is not conserved in an interaction?
Well, these kinds of questions always seem quite strange to me. I mean, IMO, you should have asked about why baryon number is conserved. If you know this, you understand the physics behind this principle and you understand why baryons "behave the way they do". In that case, you could have answered your original question yourself because if that conservation law was NOT respected, anyhting could happen that violates the physical formalism describing baryonic interactions. By knowing what could happen if baryon conservation is NOT conserved, you cannot understand the correct phenomena from that answer.

So, go study the correct physics first and then you will find yourself able to answer to such questions yourself AND you will understand what TRUELY goes on.

marlon

#### Meir Achuz

Homework Helper
Gold Member
Well, these kinds of questions always seem quite strange to me. I mean, IMO, you should have asked about why baryon number is conserved. If you know this, you understand the physics behind this principle and you understand why baryons "behave the way they do". In that case, you could have answered your original question yourself because if that conservation law was NOT respected, anyhting could happen that violates the physical formalism describing baryonic interactions. By knowing what could happen if baryon conservation is NOT conserved, you cannot understand the correct phenomena from that answer.

So, go study the correct physics first and then you will find yourself able to answer to such questions yourself AND you will understand what TRUELY goes on.

marlon
Why do physicists spend so much money looking for proton decay?

#### marlon

Why do physicists spend so much money looking for proton decay?
Exactly for what i have said.

marlon

#### George Jones

Staff Emeritus
Gold Member
Well, these kinds of questions always seem quite strange to me. I mean, IMO, you should have asked about why baryon number is conserved. If you know this, you understand the physics behind this principle and you understand why baryons "behave the way they do". In that case, you could have answered your original question yourself because if that conservation law was NOT respected, anyhting could happen that violates the physical formalism describing baryonic interactions. By knowing what could happen if baryon conservation is NOT conserved, you cannot understand the correct phenomena from that answer.

So, go study the correct physics first and then you will find yourself able to answer to such questions yourself AND you will understand what TRUELY goes on.

marlon
As I understand things, the the Langrangian for the Standard Model has separate global U(1) symmetries that correspond to baryon number, and to number conservation for each generation of leptons, i.e., a global U(1)^4 symmetry. This means that these numbers are conserved to any order in perturbation theory.

However, this U(1)^4 is reduced to U(1) symmetry for B - L by certain topological (instanton) configuration configurations of the SU(2) field. Because SU(2) is a spontaneously broken symmetry, baryon number nonconservation is highly suppressed. At the high energies after the big bang, SU(2) is a good symmetry, and baryon number non-conservation is possible within the standard model. See page 475 of Ticciati, page 454 of Weinberg vol. II, or page 434 of the first edition of Ryder.

In some GUTs, the Lagrangian only has a global U(1) symmetry for B - L,
so, even at this level, there is baryon non-conservation.

#### marlon

As I understand things, the the Langrangian for the Standard Model has separate global U(1) symmetries that correspond to baryon number, and to number conservation for each generation of leptons, i.e., a global U(1)^4 symmetry. This means that these numbers are conserved to any order in perturbation theory.

However, this U(1)^4 is reduced to U(1) symmetry for B - L by certain topological (instanton) configuration configurations of the SU(2) field. Because SU(2) is a spontaneously broken symmetry, baryon number nonconservation is highly suppressed. At the high energies after the big bang, SU(2) is a good symmetry, and baryon number non-conservation is possible within the standard model. See page 475 of Ticciati, page 454 of Weinberg vol. II, or page 434 of the first edition of Ryder.
I fully agree with what you say here. Besides, i was not arguing that baryon non conservation does NOT exist. Just to be clear

marlon

#### Haelfix

Correct, Baryon number is an accidental U(1) perturbative symmetry of the standard model. It is broken by nonrenormalizable higher dimension terms (that tend to be suppressed by progressive powers of a high mass scale M as dim > 4). Its clear that proton decay cannot occur in the standard model with these constraints (at least to some huge number << 10^-32). Alternatively you can see this with a T'Hooft elevator topologically. Guts and other models that break baryon or lepton number (but say conserve B+L or B-L) can change this to observable rates just within the limits of constraints, and make things interesting.

#### humanino

However, this U(1)^4 is reduced to U(1) symmetry for B - L by certain topological (instanton) configuration configurations of the SU(2) field. Because SU(2) is a spontaneously broken symmetry, baryon number nonconservation is highly suppressed.
I'm sorry but this is a bit confused. Instantons are supposed to be classical solutions of the gluon field, which lives in SU(3). There are of course instances of solitons in SU(2) (which is the simplest non-abelian Lie group), but those are not directly relevant to QCD.

On the other hand, QCD instantons are very handy because they indeed provide a mechanism for the dynamical breaking of chiral symmetry (see for instance Instantons at work). Be careful when you use "spontaneous", it usually refers to situations where the breaking occurs when you have to choose a vacuum for the theory, just as in the electroweak sector. In the case of chiral symmetry, the SU(2) breaking is a little more subttle (and seems more interesting to me...)

"Baryon Number Non-Conservation"

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