I have heard the statement that the Higgs coupling is flavor conserving. What does it mean? What kind of coupling would be flavor non-conserving?
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Higgs couplings of the Standard Model are flavor conserving because the separate "flavor numbers" such as $L_\mu$ – the number of muons minus the number of antimuons plus the number of muon neutrinos minus the number of muon antineutrinos – are conserved in each interaction.
It means that the corresponding interaction (one that is able to produce the Higgs from no Higgs, or destroy it) vertex either creates a muon-antimuon pair, or annihilates it, or destroys a muon and creates another muon, or destroys an antimuon and creates another antimuon.
This holds for the 3 flavor lepton numbers as well as the 3 generational flavor quark numbers. Note that due to the electric charge conservation, the cubic vertices that conserve the 3 lepton and 3 quark flavor numbers automatically conserve the 6+6 of them, too (the Higgs is neutral).
Interestingly, CMS has detected a 2.5 sigma excess of Higgs bosons that seemingly decay to $$ h \to \mu^\pm \tau^\mp $$ This is an example of a process that would violate the flavor numbers. A muon is created with an anti-tau, or vice versa. Note that this process is compatible with the charge (and energy, momentum etc.) conservation laws, the truly important ones. But it changes $L_\mu$ and $L_\tau $ by $\pm 1$ and $\mp 1$, respectively.
About $1.0\%\pm 0.5\%$ of the Higgs decays seem to be of this flavor-violating kind. It's a significant percentage but the error margin is still compactible with the number being zero. New experiments at the LHC will either confirm this flavor-violating decay or show that the excess was just a fluctuation (due to "luck").
answered Jun 24, 2015 at 8:12
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$\begingroup$ @ Luboš Motl- Is there any standard model interaction that is flavor non-conserving? $\endgroup$– SRSCommented Jun 24, 2015 at 8:27
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$\begingroup$ No. Well, the Majorana neutrino masses are typically flavor-violating - they cause flavor-changing oscillations - but those mass terms are usually not considered "parts of the Standard Model" because they must arise from some beyond-the-Standard-Model dynamics as effective terms (they are not gauge-invariant etc. classically). One may talk about the CKM matrix, too - it also changes flavor. But mass terms aren't really "interaction terms", anyway, because they are quadratic. $\endgroup$ Commented Jun 24, 2015 at 9:00
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1$\begingroup$ The charged current component of the weak interaction (i.e. W bosons) changes quark flavour. $\endgroup$– dukwonCommented Jun 24, 2015 at 9:01
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$\begingroup$ cms-physics.web.cern.ch/cms-physics/public/HIG-14-005-pas.pdf See this CMS paper. $\endgroup$– OmryCommented Jun 24, 2015 at 9:45