Baryon number

The baryon number is a strictly conserved additive quantum number of a system. It is defined as:

\[B = \dfrac{1}{3}\left(n_\text{q} – n_\overline{\text{q}}\right)\]

where \(n_\text{q}\) is the number of quarks, and \(n_\overline{\text{q}}\) is the number of antiquarks. The Standard Model provides that it is possible to violate the conservation law of the baryonic number due to the chiral anomaly.

The baryonic number of a system can be defined as 1/3 of the difference between the number of quarks and the number of antiquarks in the system, since, according to the laws of strong interaction, there can be no pure color charge (or red or blue or green), i.e. the total color charge of a particle must be zero (‘white’) (see Quark confinement). This can be achieved by putting together a quark of one color with an antiquark of the corresponding anti-color, resulting in a meson with baryonic number 0 (zero), or by associating three quarks in a baryon with baryonic number +1, or by putting together three antiquarks in an anti-baryon with baryonic number -1. Another possibility is the exotic pentaquark which consists of 4 quarks and 1 antiquark.

The quarks are always present in triplets, if you consider the antiquark as a negative quark, and you can divide the number by 3. Historically, the baryonic number was assumed before the discovery of quarks. Currently it would be more appropriate to speak of conservation of the quark number.

Particles without quarks and antiquarks have baryonic number 0 (zero). These particles include leptons, photons, and W and Z bosons.

The baryonic number is almost always preserved in all interactions predicted by the Standard Model. The loophole is the chiral anomaly. However, instantons are not all that common. Conservation means that the sum of the baryonic number of all particles ‘in the making’ is equal to the sum of the baryonic numbers of all particles resulting from the reaction.

Conservation of baryon number

Nature has specific rules for particle interactions and decays, and these rules have been summarized in terms of conservation laws. One of the most important of these is the conservation of baryon number. Each of the baryons is assigned a baryon number \(B=1\). This can be considered to be equivalent to assigning each quark a baryon number of 1/3. This implies that the mesons, with one quark and one antiquark, have a baryon number \(B=0\). No known decay process or interaction in nature changes the net baryon number.

The neutron and all heavier baryons decay directly to protons or eventually form protons, the proton being the least massive baryon. This implies that the proton has nowhere to go without violating the conservation of baryon number, so if the conservation of baryon number holds exactly, the proton is completely stable against decay. One prediction of the grand unification of forces is that the proton would have the possibility of decay, so that possibility is being investigated experimentally.

Conservation of baryon number prohibits a decay of the type:

\[p+n\rightarrow p+\mu^+ +\mu^-\]

\[B=1+1\neq 1+0+0\]

but with sufficient energy permits pair production in the reaction:

\[p+n\rightarrow p+n+p+\overline{p}\]

\[B=1+1= 1+1+1-1\]

The fact that the decay:

\[\pi^-\rightarrow \mu^-+\overline{\nu}_{\mu}\]

is observed implied that there is no corresponding principle of conservation of meson number. The pion is a meson composed of a quark and an antiquark, and on the right side of the equation, there are only leptons. Equivalently, you could assign a baryon number of 0 to the meson.

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