# I Violation of lepton universality theories

1. Sep 6, 2017

### kodama

in the event violation of lepton universality is measured and established at 5-sigma level

what are some theories that extend the standard model that would explain violation of lepton universality, while consistent in other SM measurements?

how would violation of lepton universality impact popular extensions of SM such as MSSM?

Last edited: Sep 6, 2017
2. Sep 7, 2017

### ohwilleke

This is a very challenging task.

There are modest experimental hints at lepton universality violations in a few kinds of B meson decays (for example https://arxiv.org/abs/1406.6482 and https://arxiv.org/abs/1506.08614 and https://arxiv.org/abs/1612.05014 and https://cds.cern.ch/record/1706212/files/LHCb-TALK-2014-108.pdf and http://www.symmetrymagazine.org/article/june-2014/lhcb-glimpses-possible-sign-of-new-physics and multiple papers cited in https://motls.blogspot.com/2013/07/lhcb-3-or-4-sigma-excess-of-b-mesons.html?m=1). See also the papers linked directly or indirectly in this Quantum Diaries Survivor blog post (maintained by an LHC physicist in the field): http://www.science20.com/a_quantum_...iggs_decays_fit_in_with_lhcb_anomalies-152219.

But, there are lots of other tests of lepton universality which strongly constrain any process that violates lepton universality. For example:

* Violations are not seen in certain other kinds of B meson decays. https://arxiv.org/abs/1612.00529
* Violations are not seen in tau lepton decays. https://arxiv.org/abs/1509.02043
* Violations are not seen in pion decays. https://arxiv.org/abs/1506.05845
* Violations are not seen in Z boson decays. https://arxiv.org/abs/1408.5774

One proposal to explain this is a particular kind of two-Higgs Doublet model. https://arxiv.org/pdf/1501.00993.pdf Other possibilities are discussed by Lubos at The Reference Frame. https://motls.blogspot.com/2015/01/a-model-that-agrees-with-tau-mu-higgs.html#more

But, it isn't clear (to me anyway, without exhaustive analysis of all of the linked papers) that these data points can be squared with the proposed two-Higgs doublet solution or any other theory currently being considered.

Basically, you need a theory that would cause the weak decays of b quarks in some, but not all, B mesons to violate lepton universality, even though lepton universality is not violated anywhere else at observable levels.

It isn't unthinkable that one could come up with such a theory, however.

For example, even though the CP violating phase of the CKM matrix, in principle, affects the weak decays of almost every hadron to some extent, in practice this effect is suppressed so strongly in the vast majority of cases that it is only observable in a tiny minority of hadrons where the suppression is the weakest, and is much more subtle in some kinds of hadron decays than others.

It could be that the lepton universality violations are simply too small in any case observed so far other than B meson decays (the heaviest particles that routinely decay to charged leptons since top quarks overwhelmingly decay hadronically other than the Z boson and Higgs bosons which have symmetries that could prevent violations and W bosons whose behavior is the subject of the question of whether lepton universality is observed) to be seen by detectors that have current levels of observational precision and accuracy.

The fact that lepton universality violations are mediated through W boson decays (since lepton universality mostly involved fermion flavor physics mediated by W bosons), also casts doubt on B mesons being special. One of the deep organizing principles of the Standard Model is that its fundamental particles are interchangeable parts whose behavior is not a product of their histories. A theory that would cause W boson decays from B mesons to act differently than W boson decays from other particles, challenges this very deep and fundamental principle and calls for extraordinary proof.

But, if (an an illustrative proof of concept, not as an actual proposal about reality), lepton universality violations were powerfully suppressed at an energy scale below 4 GeV (slightly below the b quark's mass), for example, for some reason, the only place you would expect to see it is in B meson decays, if symmetry effects could explain why they are not seen in neutral Z boson decays or in the B meson decays where this is not observed. So it could be that B meson decays are capturing a universal property of W boson flavor physics that are just too subtle to observe at lower energy scales.

Honestly, my money is with the lepton universality violations observed to date turning out to be experimental flukes or measurement errors or theory errors, especially after their non-detection in some B meson decays at the LHCb referenced above. But, new BSM physics would be amazing as well.

Last edited: Sep 7, 2017
3. Sep 10, 2017

### kodama

if there is violation of lepton universality wouldn't this imply there are degrees of freedom that distinguish an electron from a muon and tau, beyond simply their mass

4. Sep 11, 2017

### ohwilleke

That is one resolution, although as I sketched in #2, I don't think it is the exclusive means by which it has to be resolved.

5. Sep 11, 2017

### kodama

would a violation of lepton universality also imply quarks in different generations also have an additional degree of freedom

6. Sep 11, 2017

### ohwilleke

Imply is too strong. It would suggest a plausible, theoretically well motivated possibility. But, obviously, not all properties of leptons are shared by quarks. In the same way, the fact that quarks have color charge does not imply that leptons have color charge. But, unlike the charged leptons, quarks aren't universal in the first place.

Perhaps the better question would be whether the lack of quark universality has the same source as a lack of lepton universality.

7. Sep 11, 2017

### kodama

neutrinos are uncharged leptons. does violation of lepton universality in charged leptons imply in uncharged leptons?