Baryon number violation

Let us elaborate some of these conditions. First, the baryon nonconservation. Needless to say, grand unified theories (GUT) predicts proton decay, along with more general baryon number violating processes. This is... 

On the other hand, no sign of baryon number violation has been observed to date in any elementary particle physics experiment. In the Standard Model, one cannot find any process that would involve the transformation of a proton into mesons or leptons. However, in the early 1970s, t Hooft (1976) showed that in the presence of specific configurations of electro-weak vector fields, fermions (leptons and quarks) can be created or annihilated, but the difference of the baryon number and of lepton number B—L) should stay constant (quarks and antiquarks actually carry 1/3 unit of baryon charge, while the lepton charge of the known species is 1). Today the chance for such transitions to occur is negligible (the probability is estimated to about 10 ). However, they must have occurred frequently when the temperature was of the order of 100 GeV (about 10 K). 

In a first-order phase transition, the low-temperature (massive) phase would appear via thermal nucleation, which is a truly far-from-equilibrium process. Inside the bubbles of the new phase the baryon number-violating processes are stopped. So the question is this What is the net baryon concentration frozen ... 

M.P. Mattis. The riddle of high-energy baryon number violation... 

The conditions required for a non-symmetric Universe were first put forward by Sakharov [16] they include non-conservation of the baryon number, C and CP symmetry violation, and the existence of a period of thermal non-equilibrium during the evolution however, the present limits on the proton lifetime (1033 years) are inconsistent with the first condition, and the small degree of CP symmetry violation displayed by kaons is not compatible with the second condition. 

Despite all these impressive progress, we are still too far from the ultimate theory of everything. I listed some obvious avenues for future research in particle physics and cosmology. If I am allowed to say my personal prejudice, I would say that the flavor problem is beyond our reach for years to come, but our understanding of the law of force may further be advanced by a new discovery of violation of empirical conservation laws. The Majorana nature of neutrino masses and proton decay are just manifestation of violation of lepton and baryon numbers, and in my view there is no fundamental obstacle against these being discovered in future, however remote it might be. 

The necessary condition for baryogenesis is well documented since Sakharov, although explicit realization for any of these conditions is rather delicate. They are (1) baryon number nonconservation, (2) CP violation, (3) departure from equilibrium. The 3rd condition for the need of the arrow of time is due to presence of the inverse process, which should be possible if there is sufficient time for that to happen. 

Three main contenders for baryogenesis are GUT genesis, leptogenesis, and SUSY scenarios. The GUT scenario is still alive, for instance in models based on SO(IO) with B - L violation. The best candidate for B-genesis is the colored triplet of Higgs boson Xh, which has 2 types of channels with different baryon numbers, q l and q q. 

Next, I would like to discuss intricacy of CP violation. In gauge theories one may compute the fundamental CP asymmetry, namely the difference of baryon numbers between particle and antiparticle decays using perturbation theory. It is thus given by an interference term of, for instance, the tree and the one-loop contributions. A convenient tool of computing the interference term is the Landau-Cutkovsky rule [19]. The result is like... 

Lepton Family number (LF), Lepton number (L), or Baryon number (B) violating modes... 

An introduction is given to the many and varied attempts to deal with the non-perturbative or confinement region of QCD, especially to the lattice approach and to the sum rule method, and to the exciting new ideas about baryon and lepton number violations. Necessarily the treatment of these is rather brief and not very comprehensive. We seek to convey the basic ideas and methods. 

In keeping with the current interest in tests of conservation laws, we collect together a Table of experimental limits on all weak and electromagnetic decays, mass differences, and moments, and on a few reactions, whose observation would violate conservation laws. The Table is given only in the full Review of Particle Physics not in the Particle Physics Booklet. For the benefit of Booklet readers, we include the best limits from the Table in the following text. Limits in this text are for CL=90% unless otherwise specified. The Table is in two parts Discrete Space-Time Symmetries, i.e., C, P, T, CP, and CPT and Number Conservation Laws, i.e., lepton, baryon, hadronic flavor, and charge conservation. The references for these data can be found in the the Particle Listings in the Review. A discussion of these tests follows. 

---