Monday, February 04, 2008

Unparticles and p-adic physics

The notion of unparticle introduced by the particle physics Nobelist Howard T. Georgi (see this) is the meme of the last year in particle physics. Unparticles differ from ordinary particles in that they have continuum of mass values. Unparticles result in a conformally invariant quantum field theory theory unless one assumes that the fundamental free fields carry only massless excitations. Conformal invariance is understood here as conformal symmetries of the 4-D Minkowski space. Note that the theories possessing conformal symmetry in the stringy sense predict infinite towers of particles with discrete masses and only the lowest lowest excitations are massless.

For unparticles the measurement of momentum does not fix the energy nor does the measurement of energy fix the magnitude of 3-momentum. An objection against the notion of unparticle is that continuous mass spectrum for free particle means that the Fourier expansion of the field is arbitrary in 4-D sense and the field behaves non-deterministically.

The particles of TGD Universe have certain resemblance to unparticles.

  1. In TGD framework scaling invariance is replaced by its discretized variant so that the mass scale as a continuous variable is replaced by a discrete variable whose values are proportional to the powers of square roots of primes.

  2. Massless fermions suffer massivation by p-adic thermodynamics for the scaling generator of the generalization of stringy superconformal algebra - something completely new - whereas gauge bosons gain their mass dominantly via their coupling to Higgs, which in the simplest scenario does not contribute to the fermion massless at all.

  3. The p-adic mass scale of the particle represents a genuinely new degree of freedom, which becomes pseudo-continuous at the limit of very large mass scales so that something analogous to the unparticle like behavior might emerge.

  4. There is a connection with the non-determinism since the failure of the strict determinism is the basic characteristic of TGD Universe and p-adic thermodynamics describes the implications of the light-like randomness of partonic 3-surfaces representing particles/particle orbits. In the case of CP2 type extremals serving as a model for elementary particles it corresponds to the light-like randomness of M4 projection of the extremal appearing above p-adic length scale.

Not all primes are equally favored.
  1. Ordinary particles correspond to p-adic primes near integer powers of 2. Mersenne primes and their complex cousins Gaussian Mersennes are especially favored as are also primes near prime powers of 2. The interpretation is that the counterpart of Darwinian selection has picked up the favored p-adic primes from the pseudo-continuum during the cosmic evolution. Also the particles with unfavored p-adic mass scale could be created with some small but non-vanishing probability in particle reactions, and would be analogous to the creation of unparticles. p-Adic unparticles are however expected to decay rapidly to normal particles and could be seen as on mass-shell analogs of virtual particles.

  2. The prediction is that both quarks, leptons, Higgs and massive gauge bosons can appear with several favored p-adic mass scales. In the case of neutrinos there is a direct evidence for several p-adic mass scales. TGD based model for hadron massess predicts that even in the case of low lying hadrons quarks can possess several favoured mass scales. Experimentally quark masses have been localized only in certain ranges. The observed bumpiness of top mass distribution might have explanation in terms of several mass scales for U type quarks. The most probable values of Higgs mass deduced from leptonic and hadronic measurements of Weinberg angle seem to differ by a factor of 8 and a possible explanation is that Higgs can appear at two different p-adic mass scales.

For more details see the chapters in the first part of the book p-Adic Length Scale Hypothesis and Dark Matter Hierarchy.

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