### Anomalous direct CP breaking in D-Dbar system?

Jester has a nice posting about the evidence for CP breaking in D-Dbar system found by LHCb collaboration. I warmly recommend the posting of Jester for any-one interested in details of the experiment.

** The finding of LHCb**

The basic object of study is the asymmetry for the decay rates of D and Dbar mesons to π^{+}π^{-} and K^{+}K^{-}. One could measure the difference of D and Dbar decay rates divided by their sum to get pure number -call it A_{CP} - in both channels separately but due to various limitations it is better to measure the difference of these asymmetries called Δ A_{CP}.

The analysis gives Δ A_{CP}=-.82+/- .21 (stat).+/- .11 (sys) per cent. The prediction of standard model is of order .01 per cent. 3.5 sigmas inspire questions about new physics due to the new heavy particles possibly appearing in the loops giving rise to the direct CP asymmetry and involving CP breaking phase of CKM matrix in an essential manner. TGD represents new particle of many kinds (squarks of M_{89} hadron physics and their spartners for instance) but I will not try to say anything but consider to deeper aspects of direct CP breaking.

** Arrow of time at single particle level as a deeper reason for direct CP breaking**

We have a bad habit to get accustomed with miracles so that they do not look miracles anymore. People busily calculating loop diagrams for CP breaking containing new exotic heavy particles tend to forget the main point. Direct CP breaking - observed aeons ago for K-Kbar system - demonstrates arrow of time at single particle level and as such represents new physics. A possible deviation from standard model predictions in D-Dbar system represents just minor technical details.

Direct CP breaking means arrow of thermodynamics at single particle level: Dbar → D rate and D--→ Dbar rate are not same. The fact is that in standard physics we do not have a slightest idea about how this could happen. CKM matrix is only a parametrization.

What TGD can add is to explain what this mysterious arrow of time at single particle level could mean at the level of first principles. Zero energy ontology is the first principle now and distinguishes between standard physics and TGD.

- In zero energy ontology quantum states are zero energy states (positive/negative energy part of state initial/final state in ordinary positive energy ontology). Time like entanglement coefficients define what I call M-matrix. Different M-matrices are orthogonal to each other and rows of a unitary U matrix.
- M-matrix is "square root" of density matrix expressible as a hermitian square root of density matrix and unitary S-matrix. TGD is a square root of thermodynamics in well-defined sense. Thermodynamics and irreversibility enter the game at *single particle level* rather at the level of ensemble. This is new. Arrow of time means that with respect to positive energy states M-matrix involves only
*prepared states*with well defined particle numbers etc. but*not*with respect to negative energy states (final states). - Irreversibility means that the rate for the transformation of D → Dbar is different from that for Dbar → D (for instance). This is just what direct CP breaking is at the level of principle.

** What can one say about CKM matrix at the level of first principles? **

It is a long way from the irreversibility at single particle level to the calculation of CKM matrix from the first principles, which is the real goal at deeper level. Probably for more than decade ago I worked a model for CKM matrix reducing CKM mixing to topological mixing of quarks (see this).

- Number theoretical vision suggests that the elements of CKM matrix are rational or at least algebraic numbers in some simple extension of rationals.
- Physically CKM mixing redues to different mixing of the topologies of quark wormhole throats carrying U and D type quarks. This is of course something totally new.
- p-Adic mass calculations in turn allow to calculate p-adic mass squared for mixed quark as average of known p-adic mass squared values of non-mixed quarks. Number theoretical constraints are extremely tight since the averages divided by p-adic mass scale squared must be integers.
- The principle is simple: entropies associated with mixing matrices U and D are maximized subject to these constraints. When I introduced the model I of course had no idea that this analog of second law could correspond to genuine thermodynamics (or its square root) at single quark level. The idea was that since the orbits of partonic 2-surfaces (wormhole throats) are random light-like surfaces, thermodynamics and the analog of second law could make sense. One can reproduce the observed CKM matrix but this is not a real calculation from the first principles.

Concerning the direct CP violation at the level of hadrons, the standard diagrammatic approach using CKM matrix as input probably makes sense and it is easy to imagine candidates for new heavy particles modifying standard model predictions but it is better to leave this for specialists.

## 8 Comments:

Matti,

Are we having similar if not exact thoughts or in this climate of new physics are ideas sprouting like violets?

Where do the Kaons fit into the TGD idea of particles? I recall a declassified Lawrence lab report in 64 that raised parity issues.

My posts of today and yesterday were still a further stretch but in them I offer first principles perhaps a little deeper as philosophy than the physics.

But these principles I too relate to the structure and adaptability of our brains, neurobiology - as crude as that science stands today.

And why this issue may escape the specialists.

ThePeSla

arXiv:0711.0950v1

Proposal for CP-violating 'chiral magnetic effect' that would 'demonstrate topological nature of QCD vacuum'.

CP violation from anisotropy:

doi: 10.1209/0295-5075/95/21003

Which may be a fact of life, since the fine structure anomaly is anisotropic. One up for old Jyotish astrology which never assumed isotropy. Back when the stars could wander.

Back on the fringe,

O. Costa de Beauguard, Journal of Scientific Exploration 16.4: 651-4

has CPT theorem supporting Dirac-telegraph for paranormal experirence. Doubtless relentlessly degraded by the CP entropy....

Kaons in TGD framework are quark-antiquark bound states just as in QCD. CKM matrix provides the description of direct CP violation just as in standard model.

What new TGD can provide is a first principle approach to CKM matrix whose complex phases allow to parameterize direct CP violation in kaon-antikaon system. In standard model CKM matrix is just a matrix of numbers without any deeper understanding.

This new view comes from several sources: reduction of family replication of fermions to topology via genus-generation correspondence and mixing of the topologies of wormhole throats characterized by U and D matrices defining together CKM matrix, p-adic mass calculations and p-adic length scale hypothesis, and most importantly zero energy ontology implying thermodynamics and arrow of time even at quark level. Arrow of time characterizes zero energy states in TGD. In standard ontology it characterizes the dynamics of positive energy states.

As I emphasized in the posting irreversibility at single particle level manifesting itself as different decay rates for K and Kbar is what is the really new and revolutionary new physics. D-Dbar anomaly relates to details but can be a signal for new heavy fermions.

To Orwin:

Thanks for references. I hope that I could find time to read them.

In passing it is interesting to mention that in TGD framework C has purely geometric meaning just as P and T. C corresponds to complex conjugation in CP_2 degrees of freedom and seems to have nothing to do with the breaking of CP invariance at the level of CKM matrix and mixing of wormhole throat topologies for quarks and leptons.

One can imagine a geometric breaking of CP invariance as something analogous to the chiral selection in living matter selecting second chirality of molecules, say molecules of type L. I have indeed done this. What this C-breaking would mean that partonic 2-surface and its C conjugate (mirror images in CP_2 degrees of freedom) would not be physically equivalent and C-chirality selection would prefer either image.

One can wonder whether the high electromagnetic charges of atomic nuclei might involve inherent geometric C-breaking. C breaking would in turn imply CP breaking relating perhaps closely to matter antimatter asymmetry.

Frankly, your entropy-maximization argument seems very strong to me. Russian 'nuclear chemistry' includes mesons as factor in pH, and where chemistry goes, so must entropy. Your orthogonal matrices seem to give pure spatial degrees of freedom. Could this serve differentiation of space-time flavours in relation to Chaisson's specific power measure (E/ms), or similar?

Chaisson, E. (2001). Cosmic Evolution: The Rise of Complexity in Nature. Cambridge, MA: Harvard University Press.

Chaisson, E. (2006). Epic of Evolution: Seven Ages of the Cosmos. New York: Columbia University Press.

high electromagnetic chargesOr eddy-currents, as follows: classical V - 2K = 0 has double kinetic energy for zero ontology, which is there in orbital case, since nucleus also orbits the common centre of force (Newton's anomaly)! The continual agitation must percolate through nuclear matrix, which could induce AdS/CFT conditions:

arXiv:0905.1727v1

Of course that's an Old Quantum analysis: they were out by a factor of 2 in the spins, which surfaced in the Lande g factor. But radioactive agitation could cause horrid goo in nuclear melt-downs. Also gravitational shock, as at Fukushima.

If Japan's management of Fukishima is anything to go by, then there is something in the Yukawa potential more useful than Feynman's 'equivalent' diagrams. Viz. solitons only stable in 2D. And you are right again: the Boric acid they used orthogonalizes thermal degrees of freedom. Also borax for vibrational df, the trick I learned from Stradivarius.

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