Z bosons from radioactive elements?

[Yevgenia]

So I heard a little rumor that Beta decays in certain isotopes release an electron at "ultrarelativistic" speeds. I also heard a rumor that Z bosons can be created temporarily by a positron annihilating an electron when the two collide.

My question is, can one place two highly radioactive metals into a single pile, and expect to get at least some Z bosons from this oppositely-charged radioactivity? If yes, how much can we expect to get?


A plausible method of achieving this is to bring enriched 234m-Protactinium into proximity with a heavy isotope of Samarium (143 or such). Samarium (Sm) is used in medicine, and Protactinium (Pa) can be isolated from uranium enrichment processes.

Obviously, a whole library of various isotopes could be mixed and matched here, but in particular we need two isotopes, one producing Beta minus, and the other Beta plus, such that the speeds of the emitted radiative particles are very high. I have no idea which two are best to couple together, because of various factors. One, it is difficult to find the energy emission spectrum of isotopes. And even if it were easy, this doesn't tell me whether these short-lived isotopes can be collected into large amounts or only exist in a lab.

 

[jtbell]

The rest-mass energy of the Z is about 91 GeV = 91000 MeV. If you can find a \beta^{-} emitter and a \beta^{+} emitter with decay energies that add to give 91000 MeV, I will be very surprised. Beta decay energies are generally only a few MeV. I don't know what the maximum is, but I'd be surprised if it's larger than 10 MeV.

 

[Yevgenia]

but I'd be surprised if it's larger than 10 MeV.

Thank you for responding. I was under the impression that particle/antiparticle collisions are a complete annihilation of both particles including their rest masses.

e⁺ + e^- --> Z⁰ + ??

The electrons emitted by this kind of radiation are themselves the products of the decay of a heavy boson. Other than the requisite neutrino that this decay emits, the bulk of this energy goes into the electron and positron already. These initial particles are going to have heavier relativistic masses in this case. (In other words, you just can't throw in the momentum and be done.) Do you know the exact calculation?

One can keep in mind what made these to begin with, namely add up the energy from:

electron is the result of the decay of a massive W^-, with some small portion going to an electron antineutrino.

positron is the result of the decay of a massive W⁺, with some small portion going to an electron neutrino.

Even if a mere 57% of the energy goes to the electron, and 57% to the positron, all of this energy will come to bear on their collision, since complete annihilation will happen. In essence, 45.7 GeV in one and 45.7 GeV in the other, for a grand total of 91.5 GeV. And yet I thought the extra neutrino in the result carried way a "negligable" amount of energy, not say 43% of it. Correct me if I'm wrong here.

I heard a rumor that the collision above was being done with the SLC at SLAC, and that this started around 1991, but I cannot find a paper describing the energies used.

 

[humanino]

Beta decay turns a neutron into a proton (or vice-vera for beta+). No nuclei will gain 90 times the mass of a nucleon by doing so, thus cannot produce a real Z. Besides, beta decay proceeds via virtual W exchange (the discovery of weak neutral current was a big deal).

So clearly no : beta decay does not produce Zs.

However, tuning the center-of-mass energy of electron-positron annihilation to the Z mass will indeed produce a whole bunch of them.

from CERN courier

 

[humanino]

e⁺ + e^- --> Z⁰ + ??

? = nothing

See plot 1.1 page 15 of Measurements @ Z-pole

Note that pretty much anything that proceeds through the Z also may proceed through the photon (and vice-versa) albeit with usually much different strength for the two channels, depending on available energy.

 

[humanino]

Do you know the exact calculation?

I have a hard time understanding the question. It seems you only ask for relativistic kinematics (energy momentum conservation). I do not mean to throw references randomly, but a good free one to know is
PDG review, kinematics section

 

[Yevgenia]

I have a ...

humanino, thank you for your responses. I have a few additional questions in regards to what you said above.

I am very fuzzy on this conceptual distinction you are making between a so-called "virtual exchange of a W" versus a "real Z". I understand these particles have masses near 100 GeV. All the available Feynman diagrams for Beta decay show the emission of a W, which then later decays into a neutrino and an electron. (or their oppositely-charged counterparts). Is it the case that these diagrams are misleading, and are mere conceptual tools for the laymen? You tell me.

So in order for me to square these diagrams with what you are saying, I would assume that the GeV contained in the mass of a W is never real, but it is better described as a nucleon exchanging a virtual W with the vacuum, and then the vacuum spontaneously creates a real electron and a real neutrino. The virtually-exchanging nucleon switches from neutron to proton, or vice-versa. If answering this is too complicated for this thread, feel free to link me to something to read off-site.

 

[kaksmet]

humanino, thank you for your responses. I have a few additional questions in regards to what you said above.

I am very fuzzy on this conceptual distinction you are making between a so-called "virtual exchange of a W" versus a "real Z". I understand these particles have masses near 100 GeV. All the available Feynman diagrams for Beta decay show the emission of a W, which then later decays into a neutrino and an electron. (or their oppositely-charged counterparts). Is it the case that these diagrams are misleading, and are mere conceptual tools for the laymen? You tell me.

So in order for me to square these diagrams with what you are saying, I would assume that the GeV contained in the mass of a W is never real, but it is better described as a nucleon exchanging a virtual W with the vacuum, and then the vacuum spontaneously creates a real electron and a real neutrino. The virtually-exchanging nucleon switches from neutron to proton, or vice-versa. If answering this is too complicated for this thread, feel free to link me to something to read off-site.

I believe you can indeed take the diagrams pretty serious, at least as long as you realize that it is only an approximation. The W in the beta decay is called virtual because it cannot survive, the energy needed to create a W is much large than then energy released in the beta decay. However, you can see this as a manifistation of the uncertainty principle.. thus, the W can excist but only for a short period of time. If it then decays into a neutrino and an electron, which have a combined mass that is less than the energy in the beta decay, these to particles can be, so called, real. i.e. their excistance is not time limited.

If you have two beta decays, producing an electron and a positron, these could in principle combine to form a z. However, since their energy would not be enough for the z mass, the z would have to quickly decay (same reason as for the W).

But, the cross section to produce a Z in e+ e- at such low energies is vanishingly small!

Hope I could clarify things a little.

Also, doing a calculation of the e+e- to z to X, where X are the decay products of the Z boson, requires a little bit of work.

Perhaps you could take a look in Peskin and Schroeders, Introduction to Quantum Field Theory. They do a detailed calculation of mu+ mu- going via photon to e+ e-. Doing the case with a Z boson would then be very similar, but you need to add one projection operator (1-gamma) factor in the vertices and also a change the propagator to 1/(q^2+m^2). Since the mass of the z is so large, this process will have a very small cross section.

 

[arivero]

Related to W in nuclei, I had some intriguing plots. here in this thread:

https://www.physicsforums.com/showthread.php?t=227263

About Z, look again at the two dimensional histogram (actually, a contour plot) of
https://www.physicsforums.com/attachment.php?attachmentid=13427&d=1207614889
the attachment. The Z line is painted parallel to the W line, a bit hidden because it seems less relevant. Still, the nuclei with a mass slighy greater than the mass of Z seem to be more stable than usual, or at least no so many beta rays are known, for them.

 

[Yevgenia]

Related to W in nuclei, I had some intriguing plots. here...

Dear arivero.
Thanks for all the help. In the far future I'd like to eventually be able to ask the question about whether we could construct a material that increases SNU. Or if not an increase in SNU, a scattering spectrum of solar neutrinos would be just as good. If scattering is possible, we could then catalog the neutrino-scattering capability of various metals in the same way IOR is cataloged for visible light. (electromagnetic properties determine IOR, so therefore "bosonic" properties should determine neutrino scattering). The long-term technologies are obvious, for example, a genuine neutrino telescope, with ability to focus the beams from deep space rather than sitting passively.

I read your other threads and I wanted to ask, do you happen to know Mr. Lubos Motl? I contacted him briefly regarding some equations from string field theory. He was very helpful and cordial.