Baryon number ($B$)

Baryon number assigns $B=1/3$ to each quark, $B=-1/3$ to each antiquark and zero to leptons. A proton has baryon number one.

The difference between baryon number and lepton number. Standard electroweak sphalerons violate $B+L$ while conserving $B-L$. Consequently an early baryon asymmetry with zero $B-L$ need not survive equilibration; a surviving nonzero $B-L$ can be redistributed between baryons and leptons. Additional lepton-number-violating interactions can change this conclusion.

Baryon plus lepton number is the sum of baryon number and lepton number. It is an accidental classical symmetry of the renormalizable Standard Model but has an $SU(2{)}_L$ chiral anomaly, so electroweak instantons and sphalerons violate it.

Proton decay is a hypothetical transition of a proton into lighter particles that violates its ordinary baryon-number assignment. A possible searched-for channel is $p\to e^{+}+{\pi }^0$, followed by the neutral pion's decay into two photons. The existence and rate of any channel depend on interactions beyond the ordinary perturbative Standard Model processes.

A large water Cherenkov detector can search for the charged lepton and electromagnetic showers, reconstructing a candidate invariant mass and total momentum. Atmospheric-neutrino interactions can imitate parts of the signature, so background modeling and event selection are essential. Bound protons additionally involve nuclear motion and final-state interactions. Searches report channel-dependent limits using exposure and efficiency rather than assuming that every hypothetical baryon-violating operator gives the same lifetime.^[ref]

A proton-decay operator is a local effective interaction that violates baryon number. Standard Model gauge invariance first permits such operators at dimension six, including $QQQL$ and $u^c{u}^c{d}^c{e}^c$.