Question -- Can Muons decay into Quarks ??

[Widdekind]

Can Muons ever decay into Quarks, along the lines of:

 

Muon ---> Muon_Neutrino + ( W- ---> down + anti-up )

 

??

[swansont]

The muon mass is 105 MeV. The lightest meson mass is the pion, at 140 MeV. (Quarks don't appear by themselves, so that's not an option.) Pions decay into muons.

 

 

 

So the answer is no.

[Severian]

Muons decay via [math]\mu^- \to e^- \bar \nu_e \nu_\mu[/math] almost 100% of the time.

 

The decay you point out is not impossible though, since all the vertices are allowed. It is just disallowed kinematically, so the muon would have to be virtual.

[Widdekind]

Thanks for the information. Do I understand correctly, then, that only highly relativistic Muons could, conceivably, decay into quarks ([math]\mu \rightarrow \nu_{\mu} + d\bar{u}[/math]) ?

 

The Muon Neutrino preserves Lepton Number, whilst the quark/anti-quark pair produce no new net Baryon (Quark) Number ?

[Severian]

Thanks for the information. Do I understand correctly, then, that only highly relativistic Muons could, conceivably, decay into quarks ([math]\mu \rightarrow \nu_{\mu} + d\bar{u}[/math]) ?

 

The Muon Neutrino preserves Lepton Number, whilst the quark/anti-quark pair produce no new net Baryon (Quark) Number ?

 

No. When I said it needs to be very virtual, I mean that it has to have an energy which does not respect [math]E^2=p^2c^2 + m^2c^4[/math]. Whether or not a muon is highly relativistic is only a matter of reference frame, so irrelevant to the decay choice (though it will of course effect the lifetime, via time dilation).

[swansont]

IOW, there will always be a frame where it is at rest and cannot decay. KE matters for collisions (induced reactions), but not for decay.

[Widdekind]

Thanks for all the considerable clarifications.

 

 

Muons decay via [math]\mu^- \to \nu_\mu e^- \bar \nu_e [/math] almost 100% of the time...

 

According to Wikipedia, Neutrino mass means Muons can, occasionally decay via [math]\mu^- \to \nu_e e^- \bar \nu_\mu[/math]. Now, in some sense, this is a "cyclic permutation", of the Lepton Family Number, where we've "moved" the "2^nd generation-ness", from the Muon Neutrino, to the Electron Anti-Neutrino.

 

Since there are three (3) decay products on the RHS, one could conceive of effecting the final such "cyclic permutation", and invent the hypothetical happenstance of [math]\mu^- \to \nu_e \mu^- \bar \nu_e[/math].

 

QUESTION ONE: Can such a "pseudo-decay" actually occur ?? (Some sort of "Neutrino-ish Bremsstrahlung Breaking", were one willing to tolerate the title.)

 

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QUESTION TWO: If, as from aforecited information, you can violate [math]L_e[/math] & [math]L_\mu[/math] both by two:

 

 

then why not violate both by only one (?):

 

[math]\mu^- \to \nu_e e^- \bar \nu_e[/math]

 

[math]L_e: 0 \to 1[/math]

 

[math]L_\mu: 1 \to 0[/math]

 

 

 

QUESTION THREE: Is it correct to claim, that this decay is disallowed, according to "Kinematics" (?):

 

[math]\mu^- \to \nu_\mu \mu^- \bar \nu_\mu[/math]

 

[math]L_e: 0 \to 0[/math]

 

[math]L_\mu: 1 \to 1[/math]

Edited May 24, 2010 by Widdekind

[swansont]

According to Wikipedia, Neutrino mass means Muons can, occasionally decay via [math]\mu^- \to \nu_e e^- \bar \nu_\mu[/math]. Now, in some sense, this is a "cyclic permutation", of the Lepton Family Number, where we've "moved" the "2^nd generation-ness", from the Muon Neutrino, to the Electron Anti-Neutrino.

 

Since there are three (3) decay products on the RHS, one could conceive of effecting the final such "cyclic permutation", and invent the hypothetical happenstance of [math]\mu^- \to \nu_e \mu^- \bar \nu_e[/math].

 

Which violates conservation of energy. The other decays do not.

[Severian]

To answer Widdekind's Questions,

 

Question 1: As swansont points out, this is not kinematically allowed, since the masses in the final state are more than the mass of the initial state.

 

Question 2: This decay is more interesting because it depends on how you define your states. In the strictest sense, i.e. that in which the Standard Model is usually defined, no, it can't happen because neither vertex in your diagram is present in the theory.

 

However, the mass eigenstate is not the same as the flavour eigenstate for neutrinos, which causes neutrino oscillations. We define the electron neutrino to be the one which you get if an electron absorbs or emits a W boson. However, that electron neutrino can then oscillate into a muon neutrino giving the decay you conjectured.

 

Question 3: Again, not allowed by kinematics.

[Widdekind]

Thanks again again for the further considerable clarifications.

 

Question 2: This decay is more interesting because it depends on how you define your states. In the strictest sense, i.e. that in which the Standard Model is usually defined, no, it can't happen because neither vertex in your diagram is present in the theory.

 

However, the mass eigenstate is not the same as the flavour eigenstate for neutrinos, which causes neutrino oscillations. We define the electron neutrino to be the one which you get if an electron absorbs or emits a W boson. However, that electron neutrino can then oscillate into a muon neutrino giving the decay you conjectured.

 

I understand, then, that a precisely parallel definition defines the Muon neutrino ? Furthermore, therefore, the decay process I pulled from Wikipedia, to wit [math]\mu^- \to \nu_e e^- \bar \nu_\mu[/math], necessarily involves a "double oscillation(s)", affecting both the Neutrino and the Anti-Neutrino ??

 

From what you said, I seem to sense, that it's trivial to "time reverse" these particular processes, or "pieces parts" of the same, such as [math]\mu^- \nu_\mu \to e^- \nu_e[/math]. What I would want to know, is if it's necessarily impossible, or perhaps possible, to "collisionally excite" 1^st Generation leptons into 2^nd Generation leptons, along the lines of [math]e^- \nu_e \to \mu^- \nu_\mu[/math] ??

[Severian]

I understand, then, that a precisely parallel definition defines the Muon neutrino ? Furthermore, therefore, the decay process I pulled from Wikipedia, to wit [math]\mu^- \to \nu_e e^- \bar \nu_\mu[/math], necessarily involves a "double oscillation(s)", affecting both the Neutrino and the Anti-Neutrino ??

 

Yes, to both questions. Though I do have one caveat. Remember that we have never proven that there is any difference at all between a neutrino and an antineutrino. If there turns out to be no difference (the neutrino would then be a Majorana neutrino) then you should really remove the bars from your antineutrino states. Then the process you mention could come from the standard [math]\mu^- \rightarrow \nu_\mu W^-[/math] with [math]W^- \rightarrow e^- \nu_e[/math].

 

(Majorana neutrinos can of course result in lepton number violation, and are indeed one possible mechanism of generating a lepton asymmetry in the early universe. This is a topic that has seen a lot of research papers in the last few years.)

 

From what you said, I seem to sense, that it's trivial to "time reverse" these particular processes, or "pieces parts" of the same, such as [math]\mu^- \nu_\mu \to e^- \nu_e[/math]. What I would want to know, is if it's necessarily impossible, or perhaps possible, to "collisionally excite" 1^st Generation leptons into 2^nd Generation leptons, along the lines of [math]e^- \nu_e \to \mu^- \nu_\mu[/math] ??

 

Again yes. The cross-section for a neutrino scattering off an electron is very low, but is in fact the way that neutrinos are detected in many neutrino experiments. The decay to the muon and its neutrino is only possible if the kinetic energy of the neutrino and electron in the initial state can make up the difference in the mass energy. But if it does, then this process can happen. (If neutrinos are not their own antiparticle, it would need to be [math]\bar \nu_e[/math] and [math]\bar \nu_\mu[/math] in your process though.)

Edited May 25, 2010 by Severian

[Widdekind]

What about Down-quark decay ?

 

Please ponder Hawking Radiation, arising around Black Holes. It is a process, of:

 

1. Pair Creation
   
2. Partial Interaction -- one particle of pair captured
   
3. Escape -- other particle of pair escapes
   

Now, physicist Frank Close states:

 

Starting with the Neutrino, and removing one unit of electrical charge, gives the Electron... Neutrinos can pick up charge, when they hit nuclei, and turn into Electrons... The simplest explanation is to suppose, that electrical charge is some sort of 'external agent', a property of space perhaps, that is attached to matter in discrete amounts.

 

Frank Close. The New Cosmic Onion, pp. 170,175,111.

Adopting this picture, of Neutrinos as "charge scoops", capable of carrying off "charge packets" from nuclei (to wit, "mugging" Down-quarks), is there, then, any reason why the decay of Down-quarks cannot be explained, as the effective equivalent (at least) of some sort of similar, HR-like process (??):

 

[math]d \to d(\nu_e \bar{\nu_e})[/math]

(Pair Creation)

[math] \to (d \nu_e) \bar{\nu_e} \to (u e^{-}) \bar{\nu_e}[/math]

("Mugging")

[math]\to u + e^{-} + \bar{\nu_e}[/math]

(Escape, "snatch-n-grab")

 

In this picture, a Down-quark (~10^-18m) flitting about inside of a Neutron (~10^-15m) is constantly "harassed" by "near miss" Quantum Fluctuations, until, after roughly 11 minutes, one of the "grasping pick-pocket" pairs manages to emerge within one quark's width (~10^-18m, range of Weak Force) of the "intended target" (Wave Functions literally overlapping), with the Anti-Neutrino making its escape, as its Neutrino "partner in crime" manages to "mug" the Down-quark of {-1} charge, converting the Down into an Up.

 

This picture presents the emergence, of an Electron & Anti-Neutrino, from the vicinity of the Down-quark (which leaves behind an Up-quark in its stead), not so much as an emission (from withinside the Down-quark itself), but rather as an interaction between the Down and its (immediate, even internal) environment.

 

EDIT: Quarks & Neutrinos are stunningly small (~10^-18m). Electrons, emitted by Beta Decay, typically have energies of order their rest mass, and, so, have wavelengths of order their Compton Wavelength (~10^-12). This might mean, that as the "pick-pocket" Neutrino (~10^-18m) "mugs" the Down-quark (~10^-18m) which it appeared "on top of", it "inflates", like a leech, swelling some million times in size (~10^-12), before drinking its fill of "blood" (charge).

Edited June 6, 2010 by Widdekind

[swansont]

Is The New Cosmic Onion a peer-reviwed journal, or a mainstream textbook?

 

Induced reactions are not decays.

[Widdekind]

The book "provides a clear & readable introduction to the fascinating world of particle physics" [back cover]. After further reading (pg. 108), I seemingly strayed after Fermi's "first theory of Beta Decay" from 1933 AD, which treated nucleons as "structureless building blocks of matter", and that "the change of charge, in the decay of the neutron into a proton, is caused by the emission of an electron & antineutrino at a point".

 

But, "in 1938 AD, Oscar Klein suggested that a Spin 1 particle ('W Boson") mediated the decay, this boson playing a role in Weak Interactions like that of the Photon in the Electromagnetic case". This was maybe motivated from the fact that "the electron & antineutrino each have Spin 1/2, and so their combination can have Spin total 0 or 1. The Photon, by contrast, has Spin 1. By analogy with Electromagnetism, Fermi had (correctly) supposed that only the Spin 1 combination emerged in the Weak Decay".

 

Since the decay of down-quarks must be mediated by (big) bosons, my previous picture, of pair creation plus "snatch & grab", goes against the Standard Model, and so is probably an inappropriate picture.

 

Still, the size scales seem striking:

 

Down

-quark [~

10

^-18

m

]

W

^-

-boson [~

10

^-18

m

]

Up

-quark [~

10

^-18

m

]

 

nucleons

[~

10

^-15

m

]

(x 10

³

)

 

Electron (~1 MeV)

[~

10

^-12

m

]

(x 10

⁶

)

Anti-Neutrino (~1 MeV)

[~

10

^-12

m

]

(x 10

⁶

)

 

atoms

[~

10

^-10

m

]

 

Thus, the W^-, barely barreling beyond one quark's width away from the Down, decays, its debris "inflating" furiously, swiftly swelling in size maybe a million times -- in the process, "puffing up" past the size scale of the (new) neutron, and nearing similar sizes of atoms, before "warping away" at significant speed. It sort-of seems, as if the Down "burps" out a W^-, which rapidly proceeds to "pop open", a little like a Jack-in-the-Box, "springing" the then produced pair of particles.

 

 

Question about Spin flips in Down decays (??)

 

From the same said cited source (pg. 95):

 

The effect of colour combined with the Pauli Exclusion Principle is that any two quarks having the same flavour (two up, two down, two strange) in the lowest energy state must spin parallel -- precisely the opposite of what happens in atoms & nuclei... If two flavours are identical, and the third differs (e.g., [math]\Delta^{++}[/math] (uud) or p (uud)), then the identical pair must spin parallel, but the third is not constrained it can spin parallel (hence, total spin 3/2, as in the [math]\Delta[/math]) or antiparallel (hence, total spin 1/2, as in the proton).

 

So, starting with the neutron ([math]d \uparrow u \downarrow d \uparrow[/math]), the proton apparently appears as ([math]d \uparrow u \downarrow u \downarrow[/math]), the Down quark seemingly "spin flipping" from the emission of the W^- (??) ([math]d \uparrow \; \; \; \to \; \; \; u \downarrow \; \; + \; \; W^{-} \uparrow[/math]), with the W^- soon "splitting asunder" into a produced pair of particles ([math]W^{-} \uparrow \; \; \; \to \; \; \; e^{-} \uparrow \; \; + \; \; \bar{\nu_e} \uparrow [/math]).

 

 

 

(It's almost as if the [math]d \uparrow[/math] was "really" an [math]u \downarrow[/math] "all along", but "burdened" with a "counter-rotating" [math]W^{-} \uparrow[/math], which was subsequently "sprung", although this particular picture probably could not accomodate the Down's mechanical angular momentum (1/2) along with its magnetic moment (-1/3)*.)

*

Perhaps you could conceive, of a

Down

, as an

Up

"burdened" with extra (charged, -1) mass. This could account for the

Down

's larger mass. But, to stay spin 1/2, the

Down

's rotation rate would slightly slow, from the rate it would "choose on its own", were it an

Up

. Thus, the "loaded on" charge-mass packet "{-1}" would slowly start to "unscrew", a little like a backwards-threaded lawn-mower blade, as the "buried"

Up

quark started to "spin ahead" of its burden (a little like Earth's core rotates more rapidly than the crust). After, on average, 11 minutes, the "loaded mass-charge packet" {-1} would unscrew, and spin off, as a

W

^-

(?!?!).

Edited June 8, 2010 by Widdekind