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Saturday, March 4, 2017 3:35

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CP violation and matter antimatter asymmetry involving it represent white regions in the map provided by recent day physics. Standard model does not predict CP violation necessarily accompanied by the violation of time reflection symmetry T by CPT symmetry assumed to be exact. The violation of T must be distinguished from the emergence of time arrow implies by the randomness associated with state function reduction.

CP violation was originally observed for mesons via the mixing of neutral kaon and antikaon having quark content nsbar and nbars. The lifetimes of kaon and antikaon are different and they transform to each other. CP violation has been also observed for neutral mesons of type nbbar. Now it has been observed also for baryons Λ_{b} with quark composition u-d-b and its antiparticle (see this). Standard model gives the Feynman graphs describing the mixing in standard model in terms of CKM matrix (see this).

The CKM mixing matrix associated with weak interactions codes for the CP violation. More precisely, the small imaginary part for the determinant of CKM matrix defines the invariant coding for the CP violation. The standard model description of CP violation involves box diagrams in which the coupling to heavy quarks takes place. b quark gives rise to anomalously large CP violation effect also for mesons and this is not quite understood. Possible new heavy fermions in the loops could explain the anomaly.

Quite generally, the origin of CP violation has remained a mystery as also CKM mixing. In TGD framework CKM mixing has topological explanation in terms of genus of partonic 2-surface assignable to quark (sphere, torus or sphere with two handles). Topological mixings of U and D type quarks are different and the difference is not same for quarks and antiquarks. But this explains only CKM mixing, not CP violation.

Classical electric field – not necessary electromagnetic – prevailing inside hadrons could cause CP violation. So called instantons are basic prediction of gauge field theories and could cause strong CP violation since self-dual gauge field is involved with electric and magnetic fields having same strength and direction. That this strong CP violation is not observed is a problem of QCD. There are however proposals that instantons in vacuum could explain the CP violation of hadron physics (see this).

What says TGD? I have considered this here and in the earlier blog posting (see this).

- M
^{4}and CP_{2}are unique in allowing twistor space with Kähler structure (in generalized sense for M^{4}). If the twistor space T(M^{4})= M^{4}× S^{2}having bundle projections to both M^{4}and to the conventional twistor space CP_{3}, or rather its non-compact version) allows Kähler structure then also M^{4}allow the generalized Kähler structure and the analog symplectic structure.

This boils down to the existence of self-dual and covariantly constant U(1) gauge field J(M^{4}) for which electric and magnetic fields E and B are equal and constant and have the same direction. This field is not dynamical like gauge fields but would characterize the geometry of M^{4}. J(M^{4}) implies violation Lorentz invariance. TGD however leads to a moduli space for causal diamonds (CDs) effectively labelled by different choices of direction for these self-dual Maxwell fields. The common direction of E and B could correspond to that for spin quantization axis. J(M^{4}) has nothing to do with instanton field.

It should be noticed that also the quantum group inspired attempts to build quantum field theories for which space-time geometry is non-commutative introduce the analog of Kähler form in M^{4}, and are indeed plagued by the breaking of Lorentz invariance. Here there is no moduli space saving the situation (see this) .

Can one understand the emergence of CP violation in TGD framework?

- Zero energy state is pair of two positive and negative energy parts. Let us assume that positive energy part is fixed – one can call corresponding boundary of CD passive. This state corresponds to the outcome of state function reduction fixing the direction of quantization axes and producing eigenstates of measured observables, for instance spin. Single system at passive boundary is by definition unentangled with the other systems. It can consists of entangled subsystems hadrons are basic example of systems having entanglement in spin degrees of freedom of quarks: only the total spin of hadron is precisely defined.

The states at the active boundary of CD evolve by repeated unitary steps by the action of the analog of S-matrix and are not anymore eigenstates of single particle observables but entangled. There is a sequence of trivial state function reductions at passive boundary inducing sequence of unitary time evolutions to the state at the active boundary of CD and shifting it. This gives rise to self as a generalized Zeno effect.

Classically the time evolution of hadron corresponds to a superposition of space-time surfaces inside CD. The passive ends of the space-time surface or rather, the quantum superposition of them – is fixed. At the active end one has a superposition of 3-surfaces defining classical correlates for quantum states at the active end: this superposition changes in each unitary step during repeated measurements not affecting the passive end. Also time flows, which means that the distance between the tips of CD defining clock-time increases as the active boundary of CD shifts farther away.

If the topological mixings are different for U and D type quarks, one obtains CKM mixing. How could the classical time evolution for quarks and for antiquarks as their CP transforms differ? To answer the question one must look how J(M

- J(M
^{4})=(J_{0z}, J_{xy}= ε J_{0z}), ε=+/- 1, characterizes hadronic space-time sheet (all space-time sheets in fact). Since J(M^{4}) is tensor, P changes only the sign of J_{0z}giving J(M^{4})→ (-J_{0z}, J_{xy}). Since C changes the signs of charges and therefore the signs of fields created by them, one expects J(M^{4})→ -J(M4) under C. CP would give J(M^{4})→ (J_{0z}, -J_{xy}) transforming selfdual J(M^{4}) to anti-selfdual J(M^{4}). The sector of WCW changes. - If CPT leaves J(M
^{4}) invariant, one must have J(M^{4}) → (J_{0z}, -J_{xy}) under T rather than J(M^{4})→ (-J_{0z}, J_{xy}). The anti-unitary character of T could correspond for additional change of sign under T. Otherwise CPT should act as J(M^{4})→ -J(M^{4}) and only (CPT)^{2}would correspond to unity. - Same considerations apply to J(CP
_{2}) but the difference would be that induced J(M^{4}) for space-time surfaces,

which are small deformations of M^{4}covariantly constant in good approximation. Also for string world sheets corresponding to small cosmological constant J(M^{4})× J(M^{4})-2≈ 0 holds true in good approximation and induced J(M^{4}) at string world sheet is in good approximation covariantly constant. If the string world sheet is just M^{2}characterizing J(M^{4}) the condition is exact and was has Kähler electric field induced by J(M^{4}) but no corresponding magnetic field. This would make the CP breaking effect large.

Particles and their CP transforms belong to different sectors of WCW with self dual and anti-self dual J(M^{4}). Therefore classical time evolutions induce different CKM mixings for quarks and antiquarks reflecting itself in the small imaginary part of the determinant of CKM matrix. That the WCW sectors for matter and antimatter are different means that they live in different classical worlds! This should relate to matter-antimatter asymmetry: matter and antimatter could live in separate worlds. For instance, antimatter could be dark with different value of h_{eff}/h=n.

See the articles About twistor lift of TGD and Questions related to the twistor lift of TGD.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Source: http://matpitka.blogspot.com/2017/03/what-causes-cp-violation.html