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 ACP - in both channels separately but due to various limitations it is better to measure the difference of these asymmetries called Δ ACP.
The analysis gives Δ ACP=-.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 M89 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.