We have what I presume are two talks on the theory of flavour (the second one is another TBA talk).

Talk addresses three current anomalies of some interest: h → μτ, b → s and b → c.

For h → μτ, if real needs large off-diagonal Yukawa: 0.003. By itself, this is okay; does not conflict with

For b → s decays, loop-level and suppressed in SM so room for relatively large NP contributions. 2.6 sigma discrepancy for lepton universality from LHCb; small, but very cleam signal. 3.5 sigma discrepancy in differential branching rate for B to φμμ (confirming earlier result). 3.7 sigma in discrepancy in differential branching rate for B to Kμμ.

Global fit in terms of effective operators. All discrepancies seem to lie in muon operators. Can get a good fit with just one dimension-6 operator, with an effective suppression of just 35 TeV. Can consider using other operators, but don't get anything better. Best operators involve vector currents.

Finally, b → c anomalies show up in B to D(τ/μ)ν decays. Again, discrepancy in muon sector and about 3.9 deviation from SM.

Returning to h → μτ, "standard" explanation used nHDM. Obvious question: can we relate this in some way to the PMNS matrix? Models based on A4 or S4 symmetries require 3HDM, but predict a too-large branching ratio h → eτ. (Not excluded, but tension.)

So instead use an

Returning to b → s anomaly, seek to explain with a flavour non-universal

Both models here are very similar, so can easily be put together. Have 3HDM. Can now predict the τ to 3μ rate, since know

Unfortunately, can not also explain b → c anomaly in this way.

Explain this anomaly using a charged Higgs. Can get this to work with again a single effective operator, coupling to left-handed quarks. Can work in type-2 2HDM; but also consider nearly-type-X 2HDM (type III), which can also explain muon magnetic moment. Like all type-III models, this is (in my opinion) a less elegant model than the previous one. Uses light scalar to explain muon moment, with a flipped sign coupling for the τ so as to also not go the wrong way for the (small) leptonic τ decay anomalies. However, this model can not explain the h → μτ; it will always give large τ → μγ.

What if anomalies occur in ee final states? Well, obviously it no longer works as written.

What about leptoquarks? They can be done, supporters claim all anomalies can be explained.

A study within the SM. How can the SM be tested without solving QCD? Problem: cancellation of IR loop divergences and soft emission. No free gluons, so soft emission corresponds to modification of hadronic wavefunctions. Need to use factorisation to justify this, but that needs to be proved. Proved to all orders in strong coupling, but only to a certain order in powers of the hard momentum scale. For B decays this scale is the b quark mass.

I really wish this talk was already online.

Flavour physics has only been tested at 10% level.

**11:20 am:***Hints for new phyiscs in flavour observables*, Julian HeeckTalk addresses three current anomalies of some interest: h → μτ, b → s and b → c.

For h → μτ, if real needs large off-diagonal Yukawa: 0.003. By itself, this is okay; does not conflict with

*e.g.*τ → μγ. Of course, problems may exist in specific models.For b → s decays, loop-level and suppressed in SM so room for relatively large NP contributions. 2.6 sigma discrepancy for lepton universality from LHCb; small, but very cleam signal. 3.5 sigma discrepancy in differential branching rate for B to φμμ (confirming earlier result). 3.7 sigma in discrepancy in differential branching rate for B to Kμμ.

Global fit in terms of effective operators. All discrepancies seem to lie in muon operators. Can get a good fit with just one dimension-6 operator, with an effective suppression of just 35 TeV. Can consider using other operators, but don't get anything better. Best operators involve vector currents.

Finally, b → c anomalies show up in B to D(τ/μ)ν decays. Again, discrepancy in muon sector and about 3.9 deviation from SM.

Returning to h → μτ, "standard" explanation used nHDM. Obvious question: can we relate this in some way to the PMNS matrix? Models based on A4 or S4 symmetries require 3HDM, but predict a too-large branching ratio h → eτ. (Not excluded, but tension.)

So instead use an

*abelian*flavour symmetry, specifically L_{μ}−L_{τ}. Anomaly-free, could explain muon magnetic moment and offers a decent 0th-order fit to the PMNS. Break symmetry using second Higgs at weak scale. Symmetry constrains second doublet to*only*couple to μτ. Also require it has small VEV. Model thus looks like type-I 2HDM outside of the μτ sector. New*Z'*leads to τ to 3μ, which bounds the mass and coupling; TeV scale for order-1 couplings.Returning to b → s anomaly, seek to explain with a flavour non-universal

*Z'*. In particular, same one as above except must couple it to quarks somehow. Try using an additional scalar doublet (can also use new vector-like quarks). Extend L_{μ}−L_{τ}with quark generation charges. In particular, give first two generations same charge to ensure safety from those flavour problems. Off-diagonal Yukawas involving top quark generated by new scalar, charged under new gauge group. In this case, couplings heavily constrained by CKM matrix. Similarly, off-diagonal elements for*Z'*couplings are given in terms of CKM elements, and largest one is precisely the*bs*term. Only get sizeable corrections to desired operator, and prefers*Z'*at 3 TeV. Constraints from Bs mixing are mild. Coupling of*Z'*to first generation quarks means produced at LHC. Current bounds are about 2.5 TeV, so this can be tested very quickly in run 2.Both models here are very similar, so can easily be put together. Have 3HDM. Can now predict the τ to 3μ rate, since know

*Z'*mass. Does remain one free parameter, tan β, so not clear if can ever completely exclude it this way. New gauge symmetry anomaly free.Unfortunately, can not also explain b → c anomaly in this way.

Explain this anomaly using a charged Higgs. Can get this to work with again a single effective operator, coupling to left-handed quarks. Can work in type-2 2HDM; but also consider nearly-type-X 2HDM (type III), which can also explain muon magnetic moment. Like all type-III models, this is (in my opinion) a less elegant model than the previous one. Uses light scalar to explain muon moment, with a flipped sign coupling for the τ so as to also not go the wrong way for the (small) leptonic τ decay anomalies. However, this model can not explain the h → μτ; it will always give large τ → μγ.

__Question__What if anomalies occur in ee final states? Well, obviously it no longer works as written.

What about leptoquarks? They can be done, supporters claim all anomalies can be explained.

**12:00 pm:***Theoretical study of hadronic D/B meson decays*, Cai-Dian LuA study within the SM. How can the SM be tested without solving QCD? Problem: cancellation of IR loop divergences and soft emission. No free gluons, so soft emission corresponds to modification of hadronic wavefunctions. Need to use factorisation to justify this, but that needs to be proved. Proved to all orders in strong coupling, but only to a certain order in powers of the hard momentum scale. For B decays this scale is the b quark mass.

I really wish this talk was already online.

Flavour physics has only been tested at 10% level.

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