Me:
If neutrinos are majorana particles, wouldn't beta decay violate lepton number conservation?

Copilot:
Beta decay is a fascinating process in which a nucleus transforms by emitting
a beta particle (either an electron or a positron). Let’s explore how Majorana
neutrinos might impact lepton number conservation in beta decay:

Standard Beta Decay (β- Decay):
In standard beta decay, a neutron inside a nucleus transforms into a proton, emitting an electron (β-) and an antineutrino (ν̄e):
[ n \rightarrow p + e^- + \nu_e ]

Lepton Numbers in Standard Beta Decay:
In this process:
The neutron (n) has a lepton number of 0.
The proton (p) also has a lepton number of 0.
The emitted electron (e^-) has a lepton number of +1.
The emitted antineutrino (ν̄e) has a lepton number of -1.
The total lepton number is conserved: (0 + 0 + 1 + (-1) = 0).

Majorana Neutrinos and Beta Decay:
If neutrinos are Majorana particles:
The neutrino (νe) and antineutrino (ν̄e) would be the same particle.
In beta decay, the emitted antineutrino would actually be a neutrino (νe).
The process would look like this: [ n \rightarrow p + e^- + \nu_e ]
The emitted neutrino (νe) would have a lepton number of +1.
The emitted electron (e^-) would still have a lepton number of +1.
The total lepton number remains conserved: (0 + 0 + 1 + 1 = 2).
Lepton Number Conservation:
Crucially, the total lepton number (including neutrinos, charged leptons,
and antileptons) must always be conserved in any particle interaction.
Majorana neutrinos preserve this conservation by ensuring that the lepton numbers of neutrinos and antineutrinos add up to zero.
In summary, if neutrinos are Majorana particles, beta decay would still conserve lepton number, as the emitted antineutrino would actually be a neutrino. The fascinating interplay between particle physics and conservation laws continues to captivate scientists worldwide!

Me:
a neutron decaying to a proton, an electron and an antineutrino would NOT conserve lepton number if neutrinos were majorana particles: zero does
NOT equal 2!

Copilot:
You are absolutely correct, and I appreciate your keen observation! I
apologize for the oversight in my previous response. Let’s revisit the scenario of beta decay with Majorana neutrinos:

Standard Beta Decay (β- Decay):
In standard beta decay, a neutron inside a nucleus transforms into a
proton, emitting an electron (β-) and an antineutrino (ν̄e):
[ n \rightarrow p + e^- + \nu_e ]

Lepton Numbers in Standard Beta Decay:
In this process:
The neutron (n) has a lepton number of 0.
The proton (p) also has a lepton number of 0.
The emitted electron (e^-) has a lepton number of +1.
The emitted antineutrino (ν̄e) has a lepton number of -1.
The total lepton number is conserved: (0 + 0 + 1 + (-1) = 0).

Majorana Neutrinos and Beta Decay:
If neutrinos are Majorana particles:
The neutrino (νe) and antineutrino (ν̄e) would be the same particle.
In beta decay, the emitted antineutrino would actually be a neutrino (νe).
The process would look like this: [ n \rightarrow p + e^- + \nu_e ]
The emitted neutrino (νe) would have a lepton number of +1.
The emitted electron (e^-) would still have a lepton number of +1.
The total lepton number remains conserved: (0 + 0 + 1 + 1 = 2).

Correction:
I apologize for the confusion in my initial response. You are absolutely
right that the total lepton number should remain zero, not two.
In the case of Majorana neutrinos, the correct conservation equation would be: [ 0 + 0 + 1 + 1 = 2 ]
Thank you for pointing out the error, and I appreciate your attention to detail

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On 3/1/2024 8:40 AM, gharnagel wrote:

Me:
If neutrinos are majorana particles, wouldn't beta decay violate lepton number
conservation?

Copilot:
Beta decay is a fascinating process in which a nucleus transforms by
emitting
a beta particle (either an electron or a positron). Let’s explore how Majorana
neutrinos might impact lepton number conservation in beta decay:

Standard Beta Decay (β- Decay):
In standard beta decay, a neutron inside a nucleus transforms into a
proton,
emitting an electron (β-) and an antineutrino (ν̄e):
[ n \rightarrow p + e^- + \nu_e ]

Lepton Numbers in Standard Beta Decay:
In this process:
The neutron (n) has a lepton number of 0.
The proton (p) also has a lepton number of 0.
The emitted electron (e^-) has a lepton number of +1.
The emitted antineutrino (ν̄e) has a lepton number of -1.
The total lepton number is conserved: (0 + 0 + 1 + (-1) = 0).

Majorana Neutrinos and Beta Decay:
If neutrinos are Majorana particles:
The neutrino (νe) and antineutrino (ν̄e) would be the same particle.
In beta decay, the emitted antineutrino would actually be a neutrino (νe). The process would look like this: [ n \rightarrow p + e^- + \nu_e ]
The emitted neutrino (νe) would have a lepton number of +1.
The emitted electron (e^-) would still have a lepton number of +1.
The total lepton number remains conserved: (0 + 0 + 1 + 1 = 2).
Lepton Number Conservation:
Crucially, the total lepton number (including neutrinos, charged leptons,
and antileptons) must always be conserved in any particle interaction. Majorana neutrinos preserve this conservation by ensuring that the lepton numbers of neutrinos and antineutrinos add up to zero.
In summary, if neutrinos are Majorana particles, beta decay would still conserve lepton number, as the emitted antineutrino would actually be a neutrino. The fascinating interplay between particle physics and
conservation laws continues to captivate scientists worldwide!

Me:
a neutron decaying to a proton, an electron and an antineutrino would NOT conserve lepton number if neutrinos were majorana particles:  zero does
NOT equal 2!

Copilot:
You are absolutely correct, and I appreciate your keen observation! I apologize for the oversight in my previous response. Let’s revisit the scenario of beta decay with Majorana neutrinos:

Standard Beta Decay (β- Decay):
In standard beta decay, a neutron inside a nucleus transforms into a
proton, emitting an electron (β-) and an antineutrino (ν̄e):
[ n \rightarrow p + e^- + \nu_e ]

Lepton Numbers in Standard Beta Decay:
In this process:
The neutron (n) has a lepton number of 0.
The proton (p) also has a lepton number of 0.
The emitted electron (e^-) has a lepton number of +1.
The emitted antineutrino (ν̄e) has a lepton number of -1.
The total lepton number is conserved: (0 + 0 + 1 + (-1) = 0).

Majorana Neutrinos and Beta Decay:
If neutrinos are Majorana particles:
The neutrino (νe) and antineutrino (ν̄e) would be the same particle.
In beta decay, the emitted antineutrino would actually be a neutrino (νe). The process would look like this: [ n \rightarrow p + e^- + \nu_e ]
The emitted neutrino (νe) would have a lepton number of +1.
The emitted electron (e^-) would still have a lepton number of +1.
The total lepton number remains conserved: (0 + 0 + 1 + 1 = 2).

Correction:
I apologize for the confusion in my initial response. You are absolutely right that the total lepton number should remain zero, not two.
In the case of Majorana neutrinos, the correct conservation equation
would be:
[ 0 + 0 + 1 + 1 = 2 ]
Thank you for pointing out the error, and I appreciate your attention to detail

If the Majorna neutrino was its own antiparticle, then its lepton number
(and several other factors) must be 0. Beta decay still would violate
lepton number conservation, but differently than the way you think.

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Voney wrote:

On 3/1/2024 8:40 AM, gharnagel wrote:

Me:
If neutrinos are majorana particles, wouldn't beta decay violate lepton number conservation?

....

Me:
a neutron decaying to a proton, an electron and an antineutrino would NOT conserve lepton number if neutrinos were majorana particles: zero does
NOT equal 2!

Copilot:
You are absolutely correct, and I appreciate your keen observation! I apologize for the oversight in my previous response. Let’s revisit the scenario of beta decay with Majorana neutrinos:

Standard Beta Decay (β- Decay):
In standard beta decay, a neutron inside a nucleus transforms into a proton, emitting an electron (β-) and an antineutrino (ν̄e):
[ n \rightarrow p + e^- + \nu_e ]

Lepton Numbers in Standard Beta Decay:
In this process:
The neutron (n) has a lepton number of 0.
The proton (p) also has a lepton number of 0.
The emitted electron (e^-) has a lepton number of +1.
The emitted antineutrino (ν̄e) has a lepton number of -1.
The total lepton number is conserved: (0 + 0 + 1 + (-1) = 0).

Majorana Neutrinos and Beta Decay:
If neutrinos are Majorana particles:
The neutrino (νe) and antineutrino (ν̄e) would be the same particle.
In beta decay, the emitted antineutrino would actually be a neutrino (νe). The process would look like this: [ n \rightarrow p + e^- + \nu_e ]
The emitted neutrino (νe) would have a lepton number of +1.
The emitted electron (e^-) would still have a lepton number of +1.
The total lepton number remains conserved: (0 + 0 + 1 + 1 = 2).

Correction:
I apologize for the confusion in my initial response. You are absolutely right that the total lepton number should remain zero, not two.
In the case of Majorana neutrinos, the correct conservation equation
would be:
[ 0 + 0 + 1 + 1 = 2 ]
Thank you for pointing out the error, and I appreciate your attention to
detail

If the Majorna neutrino was its own antiparticle, then its lepton number
(and several other factors) must be 0. Beta decay still would violate
lepton number conservation, but differently than the way you think.

Anyway you slice it, if neutrinos are Majorana particles then lepton number is not conserved. That would mean new physics. OTOH, if they're Dirac particles, we're good here. Makes me wonder why some are looking for double beta decay.
I guess they want new physics. I'm okay with that. Clarke's second law:

"The only way of discovering the limits of the possible is to venture a little way
 past them into the impossible." -- Arthur C. Clarke

The neutrino still has a lot of the impossible about it:

"PTOLEMY: A Proposal for Thermal Relic Detection of Massive Neutrinos and Directional Detection of MeV Dark Matter," ArXiv:1808.01892

"Snowmass white paper: beyond the standard model effects on neutrino flavor." https://doi.org/10.1140/epjc/s10052-022-11049-7. (2023).

--- SoupGate-Win32 v1.05
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On 3/1/2024 7:36 PM, gharnagel wrote:

Voney wrote:

On 3/1/2024 8:40 AM, gharnagel wrote:

Me:
If neutrinos are majorana particles, wouldn't beta decay violate

lepton > number conservation?

....

Me:
a neutron decaying to a proton, an electron and an antineutrino

would NOT

conserve lepton number if neutrinos were majorana particles:  zero does >> > NOT equal 2!

Copilot:
You are absolutely correct, and I appreciate your keen observation! I
apologize for the oversight in my previous response. Let’s revisit the >> > scenario of beta decay with Majorana neutrinos:

Standard Beta Decay (β- Decay):
In standard beta decay, a neutron inside a nucleus transforms into a
proton, emitting an electron (β-) and an antineutrino (ν̄e):
[ n \rightarrow p + e^- + \nu_e ]

Lepton Numbers in Standard Beta Decay:
In this process:
The neutron (n) has a lepton number of 0.
The proton (p) also has a lepton number of 0.
The emitted electron (e^-) has a lepton number of +1.
The emitted antineutrino (ν̄e) has a lepton number of -1.
The total lepton number is conserved: (0 + 0 + 1 + (-1) = 0).

Majorana Neutrinos and Beta Decay:
If neutrinos are Majorana particles:
The neutrino (νe) and antineutrino (ν̄e) would be the same particle.
In beta decay, the emitted antineutrino would actually be a neutrino

(νe).

The process would look like this: [ n \rightarrow p + e^- + \nu_e ]
The emitted neutrino (νe) would have a lepton number of +1.
The emitted electron (e^-) would still have a lepton number of +1.
The total lepton number remains conserved: (0 + 0 + 1 + 1 = 2).

Correction:
I apologize for the confusion in my initial response. You are

absolutely

right that the total lepton number should remain zero, not two.
In the case of Majorana neutrinos, the correct conservation equation
would be:
[ 0 + 0 + 1 + 1 = 2 ]
Thank you for pointing out the error, and I appreciate your

attention to >detail

If the Majorna neutrino was its own antiparticle, then its lepton
number (and several other factors) must be 0. Beta decay still would
violate lepton number conservation, but differently than the way you
think.

Anyway you slice it, if neutrinos are Majorana particles then lepton
number is
not conserved.  That would mean new physics.

Neutrino oscillation already violates lepton number, iff we consider the
three types of leptons to have separately conserved lepton numbers. For example, a muon decays into an electron, muon neutrino and an electron antineutrino, apparently conserving both the muon lepton number and the electron lepton number separately. Majorana neutrinos may allow a
different type of violation involving positive and negative lepton
numbers, or maybe neutrino/antineutrino oscillation can happen. But I
think solar neutrino experiments would have detected that.

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Volney wrote:

Gary wrote:

Anyway you slice it, if neutrinos are Majorana particles then lepton
number is not conserved. That would mean new physics.

Neutrino oscillation already violates lepton number, iff we consider the three types of leptons to have separately conserved lepton numbers. For example, a muon decays into an electron, muon neutrino and an electron antineutrino, apparently conserving both the muon lepton number and the electron lepton number separately.

I don't think lepton conservation is THAT finicky. All it cares about is
the L-word, not the e, m or t words.

Majorana neutrinos may allow a different type of violation involving
positive and negative lepton numbers, or maybe neutrino/antineutrino oscillation can happen.

That doesn't seem to be the case.

But I think solar neutrino experiments would have detected that.

Not sure about that. If neutrinos are Majorana then lepton number is not conserved. But no lepton has been observed to change its lepton number.
That would be like saying an electron can turn into a positron.

It's been suggested by Wheeler and Feynman that a positron is an electron
going backward in time, but I don't subscribe to such causality-violating baloney.

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