Baryon number

In a closed system, the baryon number remains constant. If a proton can decay, this conservation law is no longer valid. In particle physics there are also other conservation laws, e.g., the conservation of parity, the conservation of color, and others. 

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A small degree of matter-antimatter asymmetry, with a baryon number B (ratio of net number of baryons Nb — N-g in a co-moving volume to the entropy S) in the range 10-11 to 10-8. 

Figure 10. (a) Bag constant B versus baryon number density, (b) EOS including both... 

Here n corresponds to the total quark number density, while ns and ns describe color asymmetries. Note that n/3 also describes the conserved baryon number. The charges are related to four chemical potentials, fi, /13, /tg, and rq, and the chemical potentials of all particles in the system can be expressed through these four chemical potentials. This implies /3-equilibrium,... 

Table 2. Composition of electrically and color neutral mixed phases, corresponding quark number chemical potentials and average baryon number densities pB = n/3 in unities of nuclear matter saturation density po = 0.17/fm3. The various components are defined in Tab. 1.

Figure 5. Axial-vector mean-field (VA) as a function of baryon number density Pb(po = 0.16fm 3). Solid (dashed) lines denote VA in the presence (absence) of CSC.

Here we will discuss two scenarios for the proto-neutron star cooling which we denote by A and B, where A stands for cooling of a star configuration with SC whereas B is a scenario without SC. The initial states for both scenarios are chosen to have the same mass Mi(A) = A(l>) for a given initial temperature of T = 60 MeV. The final states at T = 0, however, have different masses Mf(A) / Mf(B) while the total baryon number is conserved in the cooling evolution. The resulting mass differences are AM (A) = 0.06 M , A M(B) = 0.09 M and AM (A) = 0.05 Me, A M(B) = 0.07 M for the Gaussian and Lorentzian models, respectively. 

Figure 5. Hot (T = 40 MeV) versus cold (T = 0) quark star configurations for the Gaussian model(Left graphic)and Lorentzian(Right graphic) case A with diquark condensation (dashed versus full lines) and case B without diquark condensation (dash-dash-dotted versus dash-dotted lines). When a quark star with initial mass Mi cools down from T = 40 MeV to T = 0 at fixed baryon number Nb the mass defect AM occurs.

Figure 1. Chemical potentials of the three phases of matter (H, Q, and Q ), as defined by Eq. (2) as a function of the total pressure (left panel) and energy density of the H- and Q-phase as a function of the baryon number density (right panel). The hadronic phase is described with the GM3 model whereas for the Q and Q phases is employed the MIT-like bag model with ms = 150 MeV, B = 152.45 MeV/fm3 and as = 0. The vertical lines arrows on the right panel indicate the beginning and the end of the mixed hadron-quark phase defined according to the Gibbs criterion for phase equilibrium. On the left panel P0 denotes the static transition point.

A reference configuration with total baryon number Ni> = 1.51 Nq (where Nq is the total baryon number of the sun) is chosen and the case with (configurations A and B in Fig. 13) and without antineutrinos (/ in Fig. 13) are compared. A mass defect can be calculated between the configurations with trapped antineutrinos and without it at a constant total baryon number and the result is shown in Fig. 14). The mass defect could be interpreted as an energy release if the configurations A, B with antineutrinos are initial states and the configuration / without them is the final state of a protoneutron star evolution. 

Figure 13. Quark star configurations for different antineutrino chemical potentials r = 0, 100, 150 MeV. The total mass M in solar masses (MsUn = M in the text) is shown as a function of the radius R (left panel) and of the central number density nq in units of the nuclear saturation density no (right panel). Asterisks denote two different sets of configurations (A,B,f) and (A ,B ,f ) with a fixed total baryon number of the set.

The Total Leplon Number Remains Constant. Leptons consist of the neutrinos, electrons, muons, and their antipanieles Here again, rhe basic principles applied are analogous to those for baryon number particles count 1 antipanieles count - I and baryons and mesons 0. 

A brief review of the complexities to which the quark theory is addressed is in order. Particles which can interact via the strong nuclear force arc called hadrons. Hadrons can be divided into two main classes—the mesous (with baryon number zero) and the baryons (with nonzero baryon number). Within each of the classes there are small subclasses. The subclass of baryons which has been known ihe longest consists of those particles with spin j and even parity. The members of this class are the proton, the neutron, the A0 hyperon, the three hyperons and the two 3 hyperons. There are no baryons with spin 4 and even parity (or, to the usual notation, Jp = i+). The next family of baryons has ten members, each with Jp = l+. The mesons can be grouped into similar families. One of the first successes of the quark model was to explain just why there should be eight baryons with Jp = 1, ten with 1, etc., and why the various members of these families have the particular quantum numbers observed. 

Like the leptons, there is a number conservation law for baryons. To each baryon, such as the neutron or proton, we assign a baryon number B = +1 while we assign B = — 1 to each antibaryon, such as the antiproton. Our rule is that the total baryon number must be conserved in any process. Consider the reaction... 

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. 

Abstract The theory of baryon asymmetry generation is reviewed, paying attention to leptogenesis scenarios, which do not require baryon number nonconservation in perturbation theory, and may link the problem to neutrino physics. 

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. 

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... 

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... 

T. Yanagida, in Proceedings of the Workshop on the Unified Theory and the Baryon Number in the Universe, Tsukuba, Ibaraki, Japan, edited by A. Sawada and A.Sugamoto (KEK Report No.KEK-79-18,1979) M. GellMann, P. Ramond, and R. Slansky, in Supergravity, edited by D.Z. Freedman and P.Van Niewenhuizen (North-Holland, Amsterdam, 1979). 

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