# Trying to understand FCNCs

1. ### Chain

35
Hi, I'm trying to understand the process in the Feynman diagram below:

[/IMG]

Specifically I'm wondering if the virtual quark has to emit a photon / Z boson and if so why? Also I don't understand how the photon / Z boson decays to a di-lepton pair since surely this violates spin conservation given that the photon / Z boson has spin 1 and the di-lepton pair will have opposite spins cancelling each other out.

I'd much appreciate any help :)

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2. ### Hepth

530
You can have an external lepton flip spin states, so that they add to what the decaying particle is (spin 0 or 1), in order to conserve angular momentum. But this will give you an extra factor of lepton mass. Its called "Helicity Suppression".

As for "has to emit a photon / Z boson", what else would it emit to get the in state to the out state? Actually I think you could also draw a box diagram:

Code (Text):

b--o--c--o--s
|     |
W     W
|     |
e--o-nu--o--e
as well as the one where the gamma/Z comes off of the W in the loop, though these contribute less I believe.

3. ### Chain

35
Ah okay I'll look into that. When you say "what else would it emit to get the in state to the out state?" do you mean what else would it emit to have a di-lepton pair in the final state? Because what I'm asking is does there have have to be a photon or di-lepton pair in the final state or is a decay like Lambda_b -> pK possible without emiting a photon?

Thank you for the response!

4. ### Hepth

530
##\Lambda_b \rightarrow p K^{-}## is possible alone, and has been measured :

http://pdg.lbl.gov/2013/listings/rpp2013-list-lambdab-zero.pdf

Scroll down to ##\Gamma_{20}##

5. ### Chain

35
Ah >__< okay thank you for the help :)

6. ### Hepth

530
But also remember without the muon pair the leading diagram to the decal L->pK is NOT a FCNC with a loop. It would be the W emission diagram, where
Code (Text):

u-----u
d-----d
b--w--u

w---> (s ubar)

This will be proportional to Gf Vub Vus, where the FCNC one is a sum over the up-types in the loop, so Vub Vus , Vcb Vcs, Vtb Vts, times the loop factors, and an extra alpha_EM.

7. ### Chain

35
That's interesting, according to the pdg its branching fraction is still of the same order as the FCNC decay modes which occur at the one-loop level. Surely if it occurs at the tree level it should have a higher branching fraction?

8. ### ChrisVer

2,403
massive particles can be both in RH and LH states (because their LH and RH components are coupled through higg's vev)... only the neutrinos which are considered massless the antiparticle and particle exist in one or the other (the coupling to the higgs vev is very weak)...
Am I wrong?

9. ### ofirg

114
Not nessecarily. The tree level mode $\Lambda_{b}->p^{+}k^{-}\mu^{+}\mu^{-}$ is supressed by the small CKM element $V_{bu}$ Where the FCNC is a b->s transition which is only moderatley supressed due to the large top yukawa.

Moreover, this FCNC decay doesn't have helicity supression. Helicity supression happens when a scalar decays to light fermions through a vector coupling, like the decay $B_{s}->\mu^{+}\mu^{-}$

530
11. ### zxz12

2
which symmetries produce FCNC in GUTs? and in general, how it possible, if all GUTs up to E6 describe only one generation (family) of particles