_{μ}-L

_{τ}symmetry. In a more recent posting Lubos mentions another paper explaining the anomaly in terms of a frightingly complex E

_{6}gauge model inspired by heterotic strings.

TGD suggests however an amazingly simple explanation of the τ-μ anomaly in terms of neutrino mixing.

As a matter fact, after writing the first hasty summary of the childishly simple idea discussed below but still managing to make mistakes;-), I became skeptic: perhaps I have misunderstood what is meant by anomaly. Perhaps the production of τ-μ pairs is not the anomaly after all. Perhaps the anomaly is the deviation from the prediction based on the model below. It however seems that my hasty interpretation was correct. This brings in my mind a dirty joke about string theorists told only at late hours when superstring theorists have already gone to bed. How many super string theorists it takes to change the light bulb? Two. The first one holds the light bulb and the second one rotates the multiverse.

**Model for the h→ μ-τ _{c} anomaly in terms of neutrino mixing**

To my humble opinion both models mentioned by Lubos are highly artificial and bring in a lot of new parameters since new particles are introduced. Also a direct Yukawa coupling of Higgs to τ-μ pair is assumed. This would however break the universality since lepton numbers for charged lepton generations would not be conserved. This does not look attractive and one can ask whether the allowance of transformation of neutrinos to each other by mixing known to occur could be enough to explain the findings assuming that there are no primary flavor changing currents and without introducing any new particles or new parameters. In the hadronic sector the mixing for quarks D type quarks indeed explains this kind of decays producing charged quark pair of say type cu_{c}. In TGD framework, where CKM mixing reduces to topological mixing of topologies of partonic 2-surfaces, this option is especially attractive.

- In standard model neutrinos are massless and have no direct coupling to Higgs. Neutrinos are however known to have non-vanishing masses and neutrino mixing analogous to CKM mixing is also known to occur. Neutrino mixing is enough to induce the anomalous decays and the rate is predicted completely in terms of neutrino mixing parameters and known standard physics parameters so that for a professional it should be easy to made the little computer calculations to kill the model;-).

- In absence of flavor changing currents only WL
_{i}ν_{j}vertices can produce the anomaly. The h→ μ-τ_{c}or its charge conjugate would proceed by several diagrams but the lowest order diagram comes from the decay of Higgs to W pair. If Higgs vacuum expectation value is non-vanishing as in standard model then Higgs could decay to a virtual W^{+}W^{-}pair decaying to τμ pair by neutrino exchange. Decay to Z pair does not produce the desired final state in accordance with the absence of flavor changing neutral currents in standard model. Triangle diagram would describe the decay. Any lepton pair is possible as final state. Neutrino mixing would occur in either W vertex. The rates for the decays to different lepton pairs differ due to different mass values of leptons which are however rather small using Higgs mass as as scale. Therefore decays to all lepton pairs are expected.

- In higher order Higgs could decay lepton pair to lepton pair decaying by neutrino exchange to W pair in turn decaying by neutrino exchange to lepton pair. As as special case one obtains diagrams Higgs decays τ pair with final state preferentially ν
_{τ}exchange to W^{+}W^{-}pair decaying by τ neutrino exchange to μ-τ_{c}pair. The CKM mixing parameter for neutrino mixing would in either the upper vertices of the box. Note that Z^{0}pair as intermediate state does not contribute since neutral flavor changing currents are absent.

** What about the anomalies related to B meson decays?**

The model that Lubos refers to tries to explain also the anomalies related to semileptonic decays of neutral B meson. Neutrino mixing is certainly not a natural candidate if one wants to explain the 2.5 sigma anomalies reported for the decays of B meson to K meson plus muon pair. Lubos has a nice posting about surprisingly many anomalies related to the leptonic and pion and kaon decays of neutral B meson. Tommaso Dorigo tells about 4-sigma evidence for new physics in rare G boson decays. There is also an anomaly related to the decay of neutral B meson to muon pair reported by Jester. In the latter case the the decay can proceed via W or Higgs pair as intermediate state. The coupling h→ bs_{c} resulting through CKM mixing for quarks by the same mechanism as in the case of leptons must have been taken into account since it is standard model process.

TGD predicts M_{89} hadron physics as a p-adically scaled up variant of ordinary M_{107} hadron physics with hadron mass scale scaled up by factor 512 which corresponds to LHC energies. Could it be that the loops involve also quarks of M_{89} hadron physics. A quantitative modelling would require precise formulation for the phase transition changing the p-adic prime characterizing quarks and gluons.

One can however ask whether one might understand these anomalies qualitatively in a simple manner in TGD framework. Since both leptons and quarks are involved, the anomaly must related to W-quark couplings. If M_{89} physics is there, there must be radiatively generated couplings representing the decay of W to a pair of ordinary M_{107} quark and M_{89} quark. A quark of M_{89} hadron physics appearing as a quark exchange between W^{+} and W^{-} in box diagram would affect the rates of B meson to kaon and pion. This would affect also the semileptonic decays since the the photon or Z decaying to a lepton pair could be emitted from M_{89} quark.

** But doesn't Higgs vacuum expectation vanish in TGD?**

While polishing this posting I discovered an objection against TGD approach that I have not noticed earlier. This objection allows to clarify TGD based view about particles so that I discuss it here.

- In standard model the decay of Higgs decays to gauge bosons is described quite well by the lowest order diagrams and the decay amplitude is proportional to Higgs vacuum expectation. In TGD p-adic mass calculations describe fermion massivation and Higgs vacuum expectation vanishes at the fundamental level but must make sense at the QFT limit of TGD involving the replacement of many-sheeted space-time with single slightly curved region of Minkowski space defining GRT space-time. Various gauge fields are sums of induced gauge fields at the sheets.

- Note that the decays of Higgs to W pairs with a rate predicted in good approximation by the lowest order diagrams involving Higgs vacuum expectation have been observed. Hence Higgs vacuum expectation must appear as a calculable parameter in the TGD approach based on generalized Feynman diagrams. In this approach the vertices of Feynman diagrams are replaced with 3-D vertices describing splitting of 3-D surface, in particular that of partonic 2-surfaces associated with it and carrying elementary particle quantum numbers by strong form of holography. The condition that em charge is well-defined requires that the modes of the induced spinor fields are localized at string world sheets at which induced W fields vanish. Also induced Z fields should vanish above weak scale at string world sheets. Thus the description of the decays reduces at microscopic level to string model with strings moving in space-time and having their boundaries at wormhole contacts and having interpretation as world lines of fundamental point-like fermions.

- Elementary particles are constructed as pairs of wormhole contacts with throats carrying effective Kähler magnetic charge. Monopole flux runs along first space-time sheet, flows to another space-time sheet along contact and returns back along second space-time sheet and through the first wormhole contact so that closed magnetic flux tube is obtains. Both sheets carry string world sheets and their ends at the light-like orbits of wormhole throats are carriers of fermion number.

- This description gives non-vanishing amplitudes for the decays of Higgs to gauge boson pairs and fermion pairs. Also the couplings of gauge bosons to fermions can be calculated from this description so that both the gauge coupling strengths and Weinberg angle are predicted. The non-vanishing value of the coupling of Higgs to gauge boson defines the Higgs vacuum expectation which can be used in gauge theory limit. The breaking of weak gauge symmetry reflects the fact that weak gauge group acts as holonomies of CP
_{2}and is not a genuine symmetry of the action. Since weak gauge bosons correspond classical to gauge potentials, the natural conjecture is that the couplings are consistent with gauge symmetry.

- Massivation of particles follows from the fact that physical particles are composites of massless fundamental fermions whose light-like momenta are in general non-parallel. It seems however possible to regarded particles as massless in 8-D sense. At classical level this is realized rather elegantly: Minkowskian and Euclidian regions give both a contribution to four-momentum and the contribution from the lines of generalized Feynman diagrams is imaginary due to the Euclidian signature of the induced metric. This gives rise to complex momenta and twistor approach suggests that these momenta are light-like allow real mass squared to be non-vanishing. Also the massivation of light particles could be described in this manner.

This description would conform with M

^{8}-H duality at momentum space level: at imbedding space level one would have color representations and at space-time level representations of SO(4) associated with mass squared=constant sphere in Euclidian three space: this would correspond to the SU(2)_{L}×SU(2)_{R}dynamical symmetry group of low energy hadronic physics.

See the chapter New Particle Physics Predicted by TGD: Part I or the article Some comments about τμ anomaly of Higgs decays and anomalies of B meson decays.

## 6 comments:

Matti, you have clearly failed to understand all the details. For example, the new paper from today is building on a completely different anomaly than the paper that had used three anomalies including "higgs to mu tau".

Your suggestions that these models are unnatural because they produce "new parameters" is completely irrational. The discovery of any new particle beyond the currently established low-energy effective field theory always introduces new parameters to the low-energy effective field theory. This doesn't imply that no new physics may exist, does it? If it did, this wrong argument could have been made at any point in the evolution of physics and "deduce" that nothing new would ever be discovered.

In reality, the models may be totally natural, having more complicated low-energy effective field theories is an inseparable consequence of going to higher energies, and there's nothing wrong about these matters or new parameters.

Naturalness really means the absence of parameters whose values have to be unnatural - typically much smaller than what is possible. Adding new particles only decreases the naturalness informally and by a small amount, anyway.

Sorry for slow response. I did not have opportunity to answer earlier.

I considered only the mu-tau anomaly. From your earlier posting I got the impression that the decay as such is regarded as anomalous rather than

the deviation from the simple model described above. I might of course have mis-understood something.

The new physics of course can and does exist and I have been used my professional life to understand what it is basing my approach to TGD.

I believe in Occam's razor. When one has anomaly it is better to start from experimental facts instead of starting brane world constructions;-). We know that neutrinos have mass and they mix: this is

something, which we definitely know beyond standard model.

Therefore the minimal scenario involves only standard model couplings and particles plus neutrino mixing parameters and masses so that one can generalise existing calculations for quarks. In fact, also other reasonable scenarios should make this prediction as a lowest order prediction. It should be easy to check whether this

simple explanation allows to understand the anomaly or whether something more is required.

The proposed model of course does not try to say anything about other possible anomalies. TGD suggests possible mechanism here but I do not have the needed knowhow to do calculations and I am also too old and lazy;-).

Can Kähler magnetic charge (among standard particles plus neutrino mixing) lead to CPT violation?

I do not know any mechanism of CPT violation (apart from that following from small violation of P and T by the fact causal diamond is basic object of zero energy ontology. These violations are however extremely small. Neutrino mixing could give to rise to CP violation just like CKM mixing of quarks.

Thank you very much, found relevant links:

CPT Violation In The Top Quark Mass ?

Quantitative picture about CPT breaking

Yes I remember now that there was some talk about possibility of CPT violation visible: there were some indications that top and anti-top have different masses. I remember that the claimed mass difference was really large. I indeed looked whether one could understand it in TGD framework.

Next I must bravely predict my geometric past. Probably I considered the possibility of having an inherent breaking of CPT obtained by providing besides CP_2 also causal diamond CD with Kahler form, which would correspond to monopole associated with the light-like boundary of CD. This would induce breaking of Lorentz invariance at the level of CD. I concluded later that this is not a good idea and I have long time ago thrown it away but still feel shame for it;-).

I think that TGD prediction for CPT breaking caused by CD geometry would be extremely small: order of magnitude could be of order 1/p, p-adic prime characterising the particle and size of CD. For electron it would be order of 10^(-38).

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