# Beta Minus Decay

1. Nov 23, 2014

### Jimmy87

Hi, I'm just trying to get my head around beta decay and would appreciate it if someone could correct me if I'm wrong.

Beta minus decay involves the transformation of a neutron into a proton, electron and electron antineutrino. This is all mediated by the weak nuclear force and involves W and Z bosons. In the case of beta minus decay it involves a W- boson which is released when the neutron turns into a proton. The W- boson then rapidly decays into an electron and an antielectron neutrino. The mass of the products is less than the mass of the reactants which is explained by binding energy where the products (electrons and antineutrinos) have high kinetic energy which compensates for the missing mass. I just had a couple of questions:

As I understand it, the neutron undergoes a quark flavor change which is why it transforms into a proton. What causes the flavor change? Is it the W- boson?

Also, could someone clarify what is meant by a virtual particle? As I understand it, the term is somewhat arbitrary and refers to a particle that is very short lived, e.g. W- boson. Is the W- boson in beta minus decay a virtual particle? How do scientists prove virtual particles exist?

2. Nov 23, 2014

### Staff: Mentor

"Cause" is a problematic word in physics. The flavor change corresponds to the emission of a (virtual) W, yes.

The proton does not have enough energy to produce a real W (with a mass of about ~90 times the proton mass). The produced object in the decay has some properties of a W, but it is not a real particle.
There are real W bosons, for example in the decays of top quarks (they have much more mass than a W).
How do you define "existence"? The models with virtual particles give very good predictions for the observable processes (like beta decays).

3. Nov 23, 2014

### Staff: Mentor

A reasonable good description of a virtual particle - "A particle which can exist only within the constraints of the uncertainty principle is called a "virtual particle", and the time in the expression above represents the maximum lifetime of the virtual exchange particle."
Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/forces/exchg.html

and - http://teachers.web.cern.ch/teachers/archiv/HST2005/bubble_chambers/BCwebsite/articles/06.pdf
and - http://www.scientificamerican.com/article/are-virtual-particles-rea/

In beta decay, a neutron (udd) decays into a proton (uud), so d-quark transforms to a u-quark.
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/beta.html#c2

Last edited: Nov 23, 2014
4. Nov 23, 2014

### Jimmy87

Thanks for the information. If the W- boson is not real where is it (and other virtual particles) needed? What I mean is, what is it that the W- explains in the beta minus decay that it couldn't if we did not include it in the model? Also could anyone explain what people mean when they say an antineutrino is going backwards in time?

5. Nov 23, 2014

### Staff: Mentor

In our description of the decay.
The beta decay.
Not completely true, there is a model without W, but that does not work any more once we go to higher energies.

6. Nov 23, 2014

### ChrisVer

Before including the W bosons as mediators, we had the 4-point Fermi Interaction to describe processes such as beta decay and so on...So...
If there was no W bosons in the interaction, then it would have to be described by the Fermi 4-point interaction. That theory is problematic because it is non-renormalizable...

7. Nov 24, 2014

### Jimmy87

Thanks for the info. So if W- bosons in beta decay are virtual then, by definition, they are not observable but are required to explain the features of beta decay - I get that now. But how do scientists detect REAL W bosons? What sort of interaction involves a real W boson that can be detected?

8. Nov 24, 2014

### ChrisVer

You can't detect real W bosons because they decay fast into leptons...
Mainly the channels you are looking into is the W boson to give lepton + missing energy (corresponding to the fleeing neutrino)... What you actually measure is then the lepton.

How do we determine that the W boson was real? the "reality" versus "virtuality" is translated into "on-shell" or "off-shell" W bosons. The on-shell condition means that the W boson obeys the $E^2 = p_W^2 +M_W^2$ relation, something that the off-shell doesn't (they appear to have arbitrary masses)...
That is done by looking at the momentum spectrum of the observed leptons... if the W boson was real, the spectrum shows a peak at some lepton momentum at $p_e^{max}=M_W/2$ (if the W boson is at rest). The rest $M/2$ energy is shared with the neutrino and so gets lost/unobserved.

Last edited: Nov 24, 2014
9. Nov 24, 2014

### Staff: Mentor

And the missing energy.
The decays to two quarks are easy to find as well, as you get a nice peak for the reconstructed invariant mass.

10. Nov 24, 2014

### ChrisVer

Well, the missing energy is determined by the measurement of the lepton [and momentum conservation] :D So I was half but essentially complete.

How do they distinguish the W decay in the quark case from the QCD background? From the hadron energies?

11. Nov 24, 2014

### Staff: Mentor

With additional requirements for the event, like asking for a second W.
DELPHI 2008, the mass peaks are on page 29 (26 with their own numbering).
OPAL 2005, pages 18/17 and 19/18 and 26/25

I didn't see a mass measurement with quarks from the Tevatron or the LHC, so they don't see it clear enough apparently.