# Question about the Z Boson

1. ### NoddingDog

2
I have read that the Z boson cannot change the flavour of a particle. So my assumption is that an interaction such as:

usanti -> udanti + Z

Is not possible, is this correct?

2. ### ChrisVer

2,403
yes, that's impossible in the Standard Model....at least in tree level interaction...
The Z boson can couple only to a left or right (with different coupling strength to each) configuration of quark+antiquark...

Last edited: Jun 10, 2014

### Staff: Mentor

That's an important point.

Those interactions are possible, but rare. See Flavor-changing neutral current.

4. ### Bill_K

4,157
So rare that they have never been seen, right? One recent reference quotes a branching ratio of at most 10-12, and concludes that "any evidence of an FCNC process will indicate the existence of new physics."

5. ### ChrisVer

2,403
I think in theory they are not rare/suppressed... we had to make them rare by imposing GIM mechanism (and also by that predicting a new particle-charm quark- by that time).
Why would FCNC indicate the existence of new physics? In general the Standard Model has some limits, if we found FCNC outside the SM limits, then it should have contributions from some other theory (like Supersymmetry). At least that's what I understood out of dealing with the Kaon mixing which I referred to another post.

6. ### Hepth

530
##Br[B_s \to \mu^{+} \mu^{-}]= 3.2 \frac{+ 1.5}{- 1.2} \times 10^{-9}##

Is this measurement not a direct indication of Standard Model FCNC's? I'm not sure how they can claim this requires new physics as the SM prediction is basically right on top of that central measurement. I guess you could argue this result might be in agreement with zero as its a 90% CL and they want more than 3-4 sigma for a true "measurement"? Or perhaps they are just talking about their specific decay.

4,157
8. ### ofirg

114
Any flavor changing process in the SM takes place through W's since it is the only plarticle which has coupling to different flavors. Therefore, in any flavor changing diagram the "flavor changing" itself happens via a W coupling.

I believe that FCNC (flavour changing neutral current) is a term used for any process in which the initial and final state have the same charge but different flavor.

Many processes of this sort have been measured( $B_s \to \mu^{+} \mu^{-}$,$K_0 \to \mu^{+} \mu^{-}$,$b \to s+\gamma$) and found to be in agreement with the SM.

For FCNC processes which involve a virtual Z $B_s \to \mu^{+} \mu^{-}$ is a good example, as can be seen in one the diagrams in Bill_K's reference

Another example is $K^+ \to \pi^+\nu\nu$ in which the Z produces a neutrino pair (neutrino final states remove the photon option and leave you with only a Z)

This has not been established yet as the current measurement reads (1.7 ±1.1 ) x $10^{-10}$ (see http://pdg.lbl.gov/2013/listings/rpp2013-list-K-plus-minus.pdf)

9. ### Hepth

530
It does include the box diagram, but it also has Z channels due to a top/W loop effect, all of these contribute to the C9eff/C10/C7 vertices (in the normal OPE). (which the C10 and C7 vanish due to conservation of the vector current for Bs-> mumu)

Again, this is why we say there are no FCNC's at tree level, but they do exist at one-loop, and have been measured. In my vocabulary "current" isn't restricted to tree-level currents, but time-ordered products too. Maybe this is just because I've done some effective field theory, not sure.

10. ### ChrisVer

2,403
Again that's only true at the tree level... In loop diagrams you can have flavor changing NEUTRAL (Z-boson) currents... But they are highly suppressed because in general loop corrections containing the Ws or Zs bosons contribute very small changes (they are suppressed by the masses of those bosons) and because you have GIM mechanism....Of course you can have flavor changing Z bosons by going from the mass eigenstates to the flavor eigenstates of the quark, but the corresponding matrices (which appear also as the vertices coupling constants) give very small contributions (the last I think is what GIM is about)

11. ### Hepth

530
But for bottom-strange FCNC's the GIM mech is not a problem because the tops in the loops are MUCH heavier than the charms and ups, so there really isnt much cancellation (like there would be if it was strange + down). In the Bs->mumu decay there is suppression from EW loops ##\propto G_F##, suppression from angular momentum conservation (spin-0 state to two spin halfs, introduces a factor of ##\propto 2 m_{\mu}##. Suppression from CKM ##V_{tb} V_{ts}^{*} \propto \lambda^2 ##, AND it occurs only at 1 loop.

And yet it is now an observed decay.

We have come to a point where we have to not overstate the smallness of a decay due to supposed suppression or higher-order loop contributions, even in a popular forum such as this. Our measurements are becoming ever more precise, and I wouldn't want a student walking away from this discussion thinking that when they hear "loop-diagram" they think instantly "small and unimportant".

12. ### ChrisVer

2,403
In my post I told about tree level vs loops, and in general loops are somewhat suppressed when compared to tree diagrams- this doesn't mean they are negligible though.. I didn't mean to say that loop diagrams should be forgotten , sorry if that's what you got...what diagram you take in consideration depends on your measurement precision...

13. ### ofirg

114
But these loop diagrams will always involve vertices with a W boson. You just need two vertices with the W boson to change the flavor without changing the charge. In that sense thay also happen through a W boson.

If you calculate processes in the SM with the renormalizable lagrangian, then I think you can say that all flavor changing vertices in your diagram will involve a W boson

I agree that in an effective field theory approach where effects of loop diagrams can be absorbed to higher dimensionsal operators, these operators will give you direct coupling between a photon/Z to different flavors

### Staff: Mentor

While on the subject of rare decays it should be remembered that we are searching for some decays, such as μ → eγ, which are extremely rare in the standard model. So rare that the current bounds are still orders and orders of magnitude off. Even if nobody is expecting to get to the SM level, seeing something would be a clear indication for beyond SM physics.